a wide range of mechanical gears used in gear boxes of this machine ... a â locking plate of the high-speed head; b â circular cut spiral bevel gear; câ bracket of ...
Krol O., Sokolov V.
3D MODELING OF MACHINE TOOLS FOR DESIGNERS Monograph
Prof. Marin Drinov Publishing House of Bulgarian Academy of Sciences Sofia 2018
Reviewers: Permyakov Oleksandr, Doctor of Sc., National Technical University “Kharkiv Polytechnic Institute”, Ukraine Nemtinov Vladimir, Doctor of Sc., Tambov State Technical University, Russia Tsankov Petko, PhD, Technical University of Sofia, Bulgaria Kovalevskyy Sergiy, Doctor of Sc., Donbass State Engineering Academy, Ukraine
Oleg Krol, Volodymyr Sokolov 3D MODELING OF MACHINE TOOLS FOR DESIGNERS: monograph / Krol O., Sokolov V. – Sofia: Prof. Marin Drinov Academic Publishing House of Bulgarian Academy of Sciences, 2018. – 140 p.: Table. 7. Fig. 127. Bibliogr. 57 names. English language. DOI: https://doi.org/10.7546/3d_momtfd.2018 The monograph deals with the problems of constructing and exploring threedimensional models of projected metal-cutting machines. The toolkit of solid models creation for the equipment of milling-boring-boring type in the environment of integrated CAD KOMPAS-3D is resulted. Features and effective methods of constructing components of machine and tool systems, drives of main motion and rotary tables, tool storage and tool positioners are considered. The effectiveness of using in the design process methods and means of structures parameterization and photorealistic representation in the Artisan Rendering module is shown. Great attention is paid to 3D modeling of the carrier system and the most complex housing parts of the machines. A study of spindle nodes by the finite element method was carried out using the APM FEM module on the basis of their 3D models. New design solutions are proposed relating to the tooth belt transmissions of the chevron profile and the zero-gap worm gears in the form of 3D models. For specialists in the field of three-dimensional modeling and research of machine tools, scientists, lecturers, graduate students and students. © Krol O., Sokolov V., 2018
ISBN 978-954-322-950-5
Prof. Marin Drinov Academic Publishing House of Bulgarian Academy of Sciences Acad. Georgi Bonchev Str., Bl. 6, 1113 Sofia, Bulgaria www.baspress.com
INTRODUCTION The methods and procedures of 3D Modeling and the transition of design-engineers to the 3D Design strategy are becoming increasingly widespread. What are the advantages of 3D Modeling? 1. In the process of intellectual activity, it is easier for a designer to operate with volume objects. 2. Three-dimensional models are the most informative - from the point of view for product constructs, which carry the complete information. In the process of three-dimensional modeling, it is possible to change the viewing angle, analyze the internal structure of the part, research the surface, and for the virtual assemblies and disassemblies of aggregates are performed. 3. In the designing of metal-cutting machines, the final goal is considered to be three-dimensional products, on the basis of which working drawings of their components can be obtained. 4. The analyze of operating conditions: the displacement mode, the type and location of applied loads for the projected object are becomes possible. 5. The mathematical description of 3D Models is effectively converted into a control program code for CNC machines and 3D printers. The development of new information technologies transforms the nature of the activity of a modern design engineer. In the past there 3
was a, when the main tools of the designer were a pencil and a culmination. The correctness of "manual" technology for performing design calculations, drawings and documentation was determined by the thoroughness of the graphic image, the qualification of the designer, etc. One of the main drawbacks was the impossibility of efficient editing for drawings and the operational improvement of construction. The quality of the produced design documentation and the time of project implementation made this process not competitive. Modern information technologies radically changed the principles of
design,
significantly
intensified
the
process
of
product
development, increasing its accuracy and reliability many times. In graphic editors there are functions of re-use of a pre-designed product, promptly create standard and unified elements, to speed up the production of drawings and other documentation as quickly as possible. A great impetus to the progress of the entire design process is the appearance of a mechanism for parameterizing the graphic image. The revolution in industrial design was the introduction of threedimensional graphics in the toolkit of drawing. Project institutes implementing various CAD systems and calculation complex sharply shortened the deadlines for completion of the working project, in contrast to those organizations that did not use CAD and could prepare only one draft project. Associative communication, installed in the CAD between the product model, its drawings, as well as specifications, implements 4
automatic display of design document changes when making changes to the 3D Model. This significantly increases the productivity of the designer. Further improvement of CAD gradually transforms them into product life cycle management systems and engineering data, and also flexibly manage these data in various conditions of functioning for industrial enterprises. Among the systems of the middle class, the system of threedimensional solid-state modeling KOMPAS-3D is distinguished. It includes an embedded calculation module ARM FEM, which implements the finite element method in the research of machine design by criteria of strength, stiffness and vibration steadiness. CAD KOMPAS today is a multifunctional 3D-CAD system with its own mathematical core. The benefits of this system include support for both foreign and domestic standards for the implementation of drawings and documents preparation. In addition, own inventions in the field of three-dimensional modeling, a convenient drawing and graphics editor, a large number of libraries and applications can make the design process fast and efficient. Another direction of development for design computer systems is engineering calculations. This class of programs began to intensively develop in parallel with the appearance of 3D in the design. Threedimensional representation of stresses from the existing loads, threedimensional temperature distribution, strength, kinematic and dynamic analysis and much more have become the arsenal of an engineer using such systems. A large number of design tasks that were previously 5
difficult to implement or which required highly qualified specialists are currently being effectively solving through such programs. The subject of research for this monograph is methods and procedures for computer modeling of metal-cutting machines and systems of drilling-milling-boring class designs. The aim of such studies is to improve the design product preparation in the machine-tool industry by using advanced facilities and computer-aided design systems. In the process of such studies, the construction and investigation of solid models are realized: - CNC machine tools and machining centers; - a wide range of mechanical gears used in gear boxes of this machine tools class; - tooling, including tool storage, tool positioners, auxiliary and cutting instruments; - various and complex housing-type parts of carrier system. At
the
Machinery
Engineering
and
Applied
Mechanics
Department Volodymyr Dahl East Ukrainian National University in 2012 ... 2018 years works on 3D-modeling of metal-cutting machine tools and instruments were carried out. The students of the department became winners of the International Contest "Future Asses of Computational 3D-modeling", conducted by the ASCON-group of companies. With the competitive projects you can find in the Project Gallery for 2012 ... 2017 years.
6
The authors express gratitude to the students of the department Burlakov E.I., Osipov V.I., Sukhorutchenko I.A., Zhuravlev V.V., Khmelnitsky A.V., Litvinenko S.S. and Fironov D.V. for a high level of professional skill in creating 3D models of machine systems with the maximum use of the KOMPAS-3D system capabilities.
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1. 3D MODELING OF MACHINE TOOLS FOR DRILLING-MILLING-BORING TYPE
1.1. 3D modeling of the machine center of model SF68VF4
Four-coordinate drilling-milling-boring machine model SF68VF4 has found wide application in the tooling, experimental and low-volume production. It is equipped with horizontal and vertical spindles, which provides machining of parts from all sides, as well as coaxial boring of holes without work mounting. Additional accessories in the form of a small angular- and shaper spindle heads allow processing in hard-to-reach places, as well as rectangular and shaped grooves. The presence of a supporting cross rail in the design of the machine provides for productive processing by disk and shaped cutters. Students of the Machinery Engineering and Applied Mechanics Department Khmelnitsky A.V. and Osipov VI have developed a 3D model of the machine SF68VF4 [1, 2] which is presented in the gallery of the Competition “The Future Aces 3D Computer Simulation”, held by the ASCON group of companies in 2013 and 2015 years. The 3D model consists of 2,640 models of parts and assemblies and is shown in Fig. 1.1. The spindle head of the machine (Figure 1.2) consists of: housing сrude iron сasting; spindle block with automatic clamping mechanism, 8
camshaft, which transmits rotation to horizontal or vertical spindle with the help of automatic device shifting driver gear; a two-speed gearbox driven by a hydraulic-operated shift mechanism; feed drive; coolant supply device to the cutting area; electrical and optoelectrical sensors that control the position of the spindle head and its mechanisms, as well as a number of other parts and components that ensure the normal functioning of the spindle head from the CNC device. The cross-section of the horizontal spindle head in 3D is shown in Fig. 1.3.
Fig. 1.1. 3D model of machine center model SF68VF4
9
Fig. 1.2. 3D model of spindle head
Fig. 1.3. 3D model of transverse section for SF68VF4 spindle head
In the process of creating the SF68VF4 machine project, various solid models of the machine parts were made (Fig. 1.4).
10
a
b
c
d
Fig. 1.4. 3D models of machine parts SF68VF4: a – locking plate of the high-speed head; b – circular cut spiral bevel gear; c– bracket of the screw and nut transmission; d – gear shaft bevel
Rotation of the spindle (Figure 1.5) is performed as follows: from the electric motor through the poly-V-belt to a two-speed gearbox, from the output shaft of which the motion is transmitted to the coupling of the vertical spindle head or shaper spindle heads. Another option is to transfer on the driven gear of a horizontal spindle with at rotational speed of 20 ... 4000 min-1.
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Fig. 1.5. Kinematics of the spindle head in 3D
The photorealistic image of the horizontal spindle head creates a certain technical aesthetics and affects the competitiveness of the construct (Figure 1.6).
Fig. 1.6. Photorealistic image of the horizontal spindle head
The spindle is mounted on two supports on duplexed angular contact ball bearings with preload under the "tandem-O" scheme (Figure 1.7). The front support uses bearings of light-weight series 12
2-446113 GOST 832-78 with contact angle α = 26 0. The outer rings of these bearings mounting face to face with opposite ends. The type of connection "tandem" is characterized by the ability to withstand large axial unidirectional loads. The magnitude of the radial load and the radial rigidity depend on the preload value. When mounti ng such a connection, it is strictly necessary to check the coincidence of the contact angles α. Two duplexed angular contact ball bearings of the light-weight series 2-446112 by GOST 832-78 are mounted on the tail support.
Fig. 1.7. Spindle with supports in 3D
For a more efficient procedure of the analysis for manufacturability, animation of the spindle nodes for the machine model SF68VF4 is performed (Figure 1.8)
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Fig. 1.8. Spindle nodes animation
In the general case, this construction scheme (Figure 1.3) should be considered as a statically indeterminate beam on four bearings (bearingsupport), which in common have linear and angular compliance. To reduce ratio of labour to output, it is sufficient to correctly replace the duplexed bearings with one support, proceeding to a two-bearing design scheme [3–6]. The 3D model of the horizontal headstock spindle is shown in Fig. 1.9
Fig. 1.9. 3D model horizontal headstock spindle
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In the general case, this construction scheme (Figure 1.3) should be considered as a statically indeterminate beam on four bearings (bearing– support), which in common have linear and angular compliance. To reduce ratio of labour to output, it is sufficient to correctly replace the duplexed bearings with one support, proceeding to a two-bearing design scheme [3–6]. The 3D model of the horizontal headstock spindle is shown in Fig. 1.9 For efficient modeling and calculation of the stress-strain state taking into account the angular compliance of the supports, we use the module of the complex analysis of three-dimensional construct APM Structure3D [7], which is integrated into CAD KOMPAS-3D as an FEM ARM module [8]. In the modeling process in the environment APM Structure3D, a "wireframe" model of the spindle with arbor construct is created (Figure 1.10). The boundaries of the rod elements of this wireframe are determined by the nodes at those points where the load is applied or the bending stiffness of the cross-section changes. Each rod has specific dimensions and is connected by means of nodes with the rest of the construct rods.
Fig. 1.10. Wireframe model of horizontal spindle
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To calculate this design, is necessary additionally specified: - cross-sections to each of the rods; - supports for the created construct, determining its position in space; - external loads which acting on the construct; - material parameters of construct elements. The peculiarity of the support assignment is the possibility of combining in one support: rigid and elastic restraining, each of which are completely different objects. They will function together in the event that they operate in different directions of the coordinate system in the node. For the projected design, displacements along the direction of the forces Py (z-axis), Fr (elastic restraining) and rotation around the z-axis are allowed. In the work holding mode, by including the indicator to the displacements fields in the axis direction, must set the displacement restrictions in the x and y axes direction, as well as rotations around the same axes. Calculation in the APM Structure3D environment allows to estimate the complete picture of the stress-strain state for the shaft in any of its sections, including load estimation, power factors, etc. They presented in the menu item "Results". In Fig. 1.11 the displacement field is characteristically for a typical boring operation performed on a multioperation machine SF68VF4 are represented.
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Fig. 1.11. Displacements diagram of the spindle unit
Maximum displacements in the console part of the node with allowance for angular displacements are ymax = -0,0285 mm; θmax = 0,000768 rad. The analysis of the obtained results allows choosing the best design solutions, working with different loads and their combinations. At the same time, it becomes possible to design constructs that are similar in to full strength by the criterion of rigidity.
1.1.1. Vertical spindle head The presence of a vertical spindle and a rigid horizontal table makes it possible to fully use the working site when machining large parts with a size of 1000 × 500 × 500 mm.
17
The vertical head is attached to the spindle head with four screws and is centered with two conical pins and sleeves. The maximum stroke of the pinole is 90 mm. The clamping of the pinole is carried out on four sides, using clamping sectors by rotating the handle. For power modes of operation, the locking of the pinole with a toothed pin retainer is applied within the rack pitch – 4,166 mm. Due to the presence of the T-shaped groove in the adapter plate, the head rotates 900 in both directions. The head is mounting in the desired position by a pin. For accurate of the head mounting in a vertical position, a control arbor and pointer indicator is used. This arbor inserted and clamped in the internal taper of the spindle. The clamping and unclamping of the tool is carried out by a hydroficated mechanism fixed to the rear section of the spindle. The tool is clamped in the working spindle by a spring disc pack. Consequently, the clamping is carried out mechanically, and the tool remains fixed even in the event of hydraulic failure. Unclamping occurs when pressure is applied to the cylinder chamber with a non-rotating spindle. During the time of unclamping, the spindle bearings are unloaded from the force required to compress the spring disc pack, which ensures the accuracy and durability of the bearings. The 3D model of the vertical spindle head is shown in Figure 1.12, a; b. The vertical spindle is mounted in a sleeve having movement in the housing receiving rotation through a pair of bevel gear and a cam clutch.
18
a
b
Fig. 1.12. 3D model of vertical spindle head: a– general view; b – section
The vertical spindle is mounted on two supports (Figure 1.13): - lower support - duplexed angular contact ball bearings 2-446112 GOST 832-75 of an especially light series of diameters 1, mounting according to the "tandem" scheme with preload PN = 390 N. They provide fixation of the spindle and housing in the radial and axial direction; - upper support - single angular contact ball bearing 2-446111 GOST 831-75 mounting with preload PN = 370 N.
Fig. 1.13. Vertical spindle with supports
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1.1.2. Angular spindle head The 3D model of the angular spindle head (Fig. 14, a, b) in CAD KOMPAS-3D has been created to analyze the operability of the design, to select the optimal design variant and to study it using the finite element method.
а
b
Fig. 1.14. The angular head of the machine model SF68VF4: a – general view; b – section
The angular head of the SF68VF4 machine allows to expand the technological capabilities of milling-drilling-boring machines. The angular head is used for the processing recess surface and grooves located in hard-to-reach areas of workpiece plane. It implements highperformance processing at spindle speeds up to 4000 min-1 with the possibility of a spindle rotation angle of 3600 in the horizontal plane. The movement from the vertical spindle to the angular head spindle is transmitted via a bevel gear. The most characteristic operation performed with the help of angular head is the milling of planes, grooves and recess
20
surface by an end mill cutter. This type of head is equipped with a kit of end mills with a diameter in the range 3 ... 25 mm. The spindle of the angular head is mounted on two supports (Figure 1.15): – front – bearing 3182108 – radial double row roller with short cylindrical rollers with a tapered hole and shoulders on the inner ring. The direction of perceived loads is radial. Allow the adjustment of the radial clearance. The bearing corresponds the standard GOST 7634-75. – rear: – bearing 246205 –duplexed angular contact ball bearings, outer rings of which mounting face to face with wide ends, contact angle α = 26º. The direction of perceived loads is radial and axial in both sides. The bearing fixates the shaft and housing in both axial directions and provides a stiffer angular fixation of the shaft than the corresponding bearing 346205. The bearing corresponding the standard GOST 832-78.
Fig. 1.15. Angular head spindles with supports
21
Complex engineering analysis of the spindle stress-strain state for the SF68VF4 machine (Figure 1.16, a) with the help of the APM FEM module is carried out [8]. This module equipped with the finite element mesh generator included in the CAE library, which implements engineering solutions by the finite element method (FEM). In the design process, fastening is carried out in the front and rear supports and the applied loads are set (Figure 1.16, b); the coinciding faces are determined (for the FE-analysis of the assembly); the generation of the mesh is realized (Figure 1.16, c) using the MT Frontal method (with multi-core processor); calculation and viewing of results in the form of stress and displacements maps is performed. In the process of FEM analysis, it is possible to evaluate and analyze the decomposition for different values of the viewing depth (Figure 1.16, d).
а
b
с
d
Fig. 1.16. Procedures for the finite element method: a –3D model of the spindle: b – supports and loads acting on the spindle; c –finite element mesh; d– depth of view
22
Within the environment of the APM FEM module, all of the above actions were implemented and obtained: – fields of equivalent stresses according to Misses (fourth theory of strength), presented in Figure 1.17; – displacement fields (Figure 1.18) on the set of spindle cross sections; – safety factor against yielding (Figure 1.19). Below the calculation protocol in the APP FEM is given (Figure 1.20).
Fig. 1.17. Strain state of the spindle
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Fig. 1.18. Total linear displacement
Fig. 1.19. Safety factor against yielding Information about loads Name
Selected object
Load parameters
Specific force along length Specific force along length 1
Edges: 1
Specific force along length Specific force along length 2
Edges: 1
Loading vector X=870; Y=2516; Z=0 Value 2662,171 N/mm Loading vector X=755; Y=2265; Z=0 Value 2387,520 N/mm
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Information about clampings Name Clamping Clamping 1 Clamping Clamping 2
Selected object Face: 1 Face: 1
X [mm]
Y [mm]
Z [mm]
Not allowed Not allowed
Not allowed Not allowed
Not allowed Not allowed
Rot. X
Rot. Y
Rot. Z
-
-
-
-
-
-
Fig. 1.20. Calculating protocol of the machine SF68VF4 spindle
1.2. 3D modeling of the vertical multioperational machine model SVM1F4 As a simulation object, a specialized multioperational machine with CNC of the second-dimension type for a milling-drilling-boring group based on the model SVM1F4 is considered. The machine can process 25
vertical, horizontal and inclined planes, shaped surfaces, holes, grooves with various technological methods. In the design of the CNC machine, there are specific components such as a hydraulic unit for precise positioning of the spindle and a special spindle head that implements the main shaping motion. The drive of the main movement uses an adjustable drive based on a DC motor and a thyristor voltage converter. For automated manipulation of workpieces and cutting tools of various sizes and shapes, this machine uses an additional modular equipment and, in particular, a turntable, which allows the realization of a large number of different technological operations without the need to remounting the workpieces. The machine is equipped with a dosed automatic lubrication system by "Tribon" type for plain slideway, crew-and-nut transmissions well as rolling bearings of the spindle group. The 3D model of the machine [9, 10] in CAD KOMPAS-3D was created to analyze the operability of the design and to select the optimal version of the project for a specialized multioperational CNC machine model SVM1F4, which equipped with an automatic tool changers construction and a rotary table (Figure 1.21). Solid models of the details for various machine nodes are shown in Figure 1.22.
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Fig. 1.21. 3D model SVM1F4 machine
a
b
c
d
Fig. 1.22. 3D models of the details for SVM1F4 machine: a – the flange of the hydraulic unit; b – the cover of the hydraulic unit; c – piston; d – spindle head tube
27
The kinematic chains realizing the execution of technological operations are shown in Figure 1.23. Providing a certain level of accuracy and vibration resistance of machines is associated with the analysis and determination of their rigidity and compliance. Evaluation of the rational balance of machine compliance is an actual task and can be as a criterion of optimization in determining the static rigidity of basic parts and the design as a whole. Thus, the deformations of the movable spindle head of milling and multioperational machines can be up to 70% of the total.
Fig. 1.23. Kinematic chains of SVM1F4 machine
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1.2.1. Spindle head 3D model of this forming assembly to evaluate the rigidity of the spindle head for machine SVM1F4 are developed (Figure 1.24) [9]. The design of the spindle head is shown in the section (Figure 1.24, a), and its rendering in the Artisan Rendering module in Figure 1.24, b. The precision double row tapered roller bearing in the lower support of the spindle is mounted. This support perceives radial and bilateral axial loads and is characterized by an allowable radial load of 1,7 times higher than that of the corresponding single-row bearing. In addition, it provides increased rigidity of the support.
a
b
Fig. 1.24. The spindle head of the SVM1F4machine: a – section of the spindle head; b – rendering in the Artisan Rendering module
The single-row tapered roller bearing is mounted in the upper support, which allows separate mounting of the rings and its design provides a preloading of spring type (Fig. 3). In the process of 29
constructing complex 3D assemblies, 3D models of parts and components included in the spindle head are performed. Complex engineering analysis of the stress-strain state of the machine spindle is carried out with the help of the APM FEM module [7, 8] which equipped a finite element mesh generator included in the CAE library, which implements engineering solutions using FEM. In the design process, fastening in the upper and lower supports and the applied loads are carried out. The coinciding faces are determined (for the CEanalysis of the assembly); the grid is generated by the MT Frontal method; calculation and viewing of results in the form of stress map and displacements map is performed. Within the APM FEM environment, all of the above actions are implemented and obtained: - fields of equivalent stresses according to Misses (fourth theory of strength), presented in Fig. 1.25, a; - the displacement field (Figure 1.25, b) on the set of spindle cross sections.
a
30
b Fig. 1.25. The results of calculating the stress-strain state of the spindle: a – stress fields; b – displacement fields
1.2.2. Rotary table In the conditions of production more increasing number of dimension type and a constant change in the configuration of machined parts, it is promising to design and manufacture a ruler for rotary tables equipped with hydromechanical drives [11]. The rotary controlled table is made in the form of an independent unit, mounted on the machine table in two positions with a vertical and horizontal axis, depending on the location of the surface to be treated. In CAD KOMPAS, the 3D model of a rotary table consisting of more than 300 parts (Figure 1.26) was built [12].
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Fig. 1.26. The rotary controlled table
The table consists of a housing in which there is a worm pair that transmits the motion from the high torque engine to the executive node – the faceplate (Fig. 1.27, a). Rotary table controlled carried out by means of the CNC apparatus through the circular inductosyn PUI-18A. Rotation of the circular faceplate by a given angle is controlled by an optical sensor mounted on the vertical axis of the turntable. Fastening of parts to the rotary table is made along the T-shaped grooves. The change in the working speed of the rotary table faceplate is made smoothly in the range from 0,1 to 3,5 min-1; the accelerated movement is 6,5 min-1. In the case of a rotary table with a horizontal axis, a tailstock is used to support the cantilevered part.
32
To increase the accuracy of the worm wheel base (Figure 1.27, b), it is not sufficient to use only one cone fit surface in the rotary table drive. It is also necessary to provide for fit on the face surface.
a
b
Fig. 1.27. Rotary table: a; b – cross-section
To ensure the synchronization of the worm and the wheel, it is necessary the construct of a without clearance worm gear is realized [13, 14]. Zeroing of lateral clearances in worm gearing is possible by shifting the worm in a direction parallel to the axis of the worm wheel (Figure 1.28).
33
Fig. 1.28. Transmission scheme with zeroing of side clearances
At the same time, both sides of the worm thread will be in contact simultaneously with the surfaces of two adjacent teeth of the worm wheel. We consider the thus obtained gapless worm gear in two aspects – geometric and force. To determine the magnitude of the worm displacement – u, the calculation scheme is used (Figure 1.29).
Fig. 1.29. To determine the worm displacement
34
For clarity, the engagement elements – the relationship between the radii ra1 and r02 ra1 , ( 0,2 m – radial clearance), are given not in the proportions that take place in actual transmissions (the values u and
1 would be practically indistinguishable). Known are: ra1 0,5 m (q 2) – the radius of the vertices of the worm turns; r02 ra1 m [0,5 (q 2) 0,2] – the radius of the circle arc delineating the tops of the teeth of the wheel in the axial section;
b2 1,5 ra1 0,75 m (q 2) –wwidth of the worm wheel rim; ( m and q is the modulus and coefficient of the worm diameter). It follows from
O2OA that b /2 arcsin 2 . r02
It follows from
O1BA that
r 2 (b / 2) 2 2 1 arccos 02 ra1
;
11 / 2 1 .
It's obvious that:
0 / 2 11 1 ; It follows from
21 / 2 2 .
O2O1O that
(0 21 ) 1 2 / 2
35
As a result, from the angle
O2O1O , where the two sides – ra1 and r02
also
between them, are known, there is the required displacement
of the worm u :
u ra21 r022 2 ra1 r02 cos
(1.1)
Calculations on the dependence (1.1) for worm gears with different engagement parameters have shown that
u / d1 0,02...0,03 , that is, to form a no-gap engagement, it is sufficient to provide for the possibility of displacing the worm parallel to the wheel axis by an amount
u equal to 2 ... 3% of its pitch diameter d1 . Naturally, the worm must be in a displaced position under the action of external loads. With a certain direction of the circumferential force on the worm, the worm will tend to return to the unshifted position (dotted image in Figure 1.28). This will result in clearance in the mesh, which will violate the accuracy of rotation synchronization for the worm and the wheel. Counteract this displacement can compression springs, mounting in the sliding supports of the worm shaft. The forces of the springs FП are calculated from the equilibrium condition of the system of forces shown in Figure. 1.30.
36
Fig. 1.30. To calculate the force of springs compression: 1 – worm; 2 – wheel worm; 3 and 4 – bearings in the sliding supports of the worm shaft, which are springs-load 5;
T1 and T2 – the torques on the worm
shafts and the wheels; G – the weight of the worm shaft assembly
3D-representation of the rotary table construct with sliding supports gives the developed solid model (Figure 1.31)
Fig. 1.31. Sliding supports of the rotary table worm
37
By the condition of forces equilibrium: 2 FП G Ft1 , whence FП ( Ft1 G) / 2 , H.
After the transformations, we get
FП T2 where d 2
tg ( ) G ,H d2 2
(1.2)
m z 2 – the diameter of the wheel worm, m;
arctg ( z1 / q) –pitch angle of the worm thread lifting, degree;
–reduced friction angle in engagement, degree. In deriving the relation (1.2), an approximate version of the calculation of the efficiency of the worm pair was used [15, 16]:
tg / tg ( ) . With a specified version of the efficiency calculation, the force of the springs FП is determined as follows:
FП T2
tg G d 2 2
(1.3)
tg f пр S tg ( ) 2 z2
Here [17]: where f пр B C VS –the reduced coefficient of friction during rolling of the teeth along the threads, Band C- according to [17];
38
Overlapping coefficient of worm gear
S in the middle of the wheel
end plane; (x– is the worm displacement coefficient)
S [0,17 z2 0,34 ( x 1)]2 (0,16 z2 ) 2 0,058 z2 1,01 (1 x) Calculations show that the specified version (1.3) differs from the approximate variant (1.2) by no more than 5 ... 6%. For the machine SVM1F4, where the table rotation is carried out by a worm gear with the following parameters:
aW 98 мм; m 3,15 мм; q 12,5; z1 / z2 1 / 50; x 0; b2 34 мм, the displacement and the required spring force take the values:
u 0,824 mm, which is 2,1% from d1 = 39,375 mm; Fп ≈156 H. Broadened design calculation of the worm gear (WG) is implemented in the module APM Trans for designing rotational mechanical transmission [18, 19]. Given the external load, the material of the worm and the wheel, the type of heat treatment, we determine the basic geometric parameters of the transmission, the forces acting in it, the parameters for monitoring the position of the side surfaces, as well as the tolerances and fit in engagement (Figure 1.32).
39
a
b
c
d
Fig. 1.32. Results of calculation WG in the module APM Trans: a– forces in engagement; b – control parameters; c – geometric parameters; d – tolerances in gearing
A finite element mesh (Fig. 1.34, a), with a 11515 number of finite elements and a number of nodes for rod elements of more than 3000 is constructed in APM FEM [7]. In the APM FEM system, each final rod element includes two nodes that have 6 degrees of freedom. The interaction of finite elements with each other is realized through their nodes, with account taken of which a stiffness matrix is formed. The solution of this matrix is reduced to solving a system of algebraic equations. The joint solution of the system of equations is the displacement values (Figure. 1.33, b) and the stress values (Figure 1.33, c). The calculation of the rod elements is carried out with allowance for all stress concentrators. This allows more accurate determination of the effective stresses values.
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a
b
c
Fig. 1.33. Results of stress-strain analysis worm gear state: a – finite element mesh; b – stress fields; c – displacement fields
Obtained 3D models of the machine center and its main nodes are presented at the international contest "Future Aces of Computational 3Dmodeling", conducted by ASCON group of companies (October 2014). The presented project became the silver medallist of this contest. Received three patents for utility models: – No. 95715 UKRPATENT "Worm gear without clearance "; – No. 99664 UKRPATENT "Rotary table of metal cutting machine" – The application for the invention is submitted and 2015 04681 UKRPATENT "Rotary table".
1.3. 3D modeling of a milling-drilling machine with six-spindle head of model SF16MF3
As the object of modeling, a specialized vertical milling-drilling machine of the second standard model SF16MF3 is considered. This 41
machine is used in small-scale and batch production and is designed for multi-operation processing of products of a complex profile for steels, cast iron, light and non-ferrous metals. The machine can process vertical, horizontal and inclined planes, shaped surfaces, holes, grooves with various technological methods: milling, drilling, hole enlarging and reaming. In the integrated CAD KOMPAS student of the Machinery Engineering and Applied Mechanics Department Zhuravlev V.V. has been constructed the 3D model of the machine (Figure 1.34) which consisting near 800 solid models of parts and 73 assembly units of various nodes and aggregates for the machine assembly [20, 21].
Fig. 1.34. 3D model machine SF16MF3
42
The developed project in the 3D model of the machine form became the winner in the XII International Competition of Future Aces Computer 3D Simulation-2014, conducted by the ASCON group of companies. The main kinematic chains are shown in Fig. 1.35.
Fig. 1.35. Kinematic of machine SF16MF3 in 3D
3D models of individual parts that are included in assemblies of various nodes are shown in Figure 1.36. 43
a
b
c
d
Fig. 1.36. Details of the machine SF16MF3: a – spindle sleeve; b – housing of the oil pump; c – support; d – rod of the rotation mechanism
1.3.1. Six-spindle turret The machine is equipped with a tool changers construction, which is performed by turning the six-spindle turret into the desired position by the program. The choice of the tool is carried out with the help of special cams, and the rotation of the head is realized by gearing with the use of a hydraulic motor. The six-spindle turret is an alternative to a fairly expensive Tool storage with its own drive. This is true in the case of processing a certain nomenclature of housing products. When the machine is working, the movable part of the turret is fixed with a disc pack springs with a constant force of 20580 N. 44
In the six-spindle turret, which is a cast-iron housing, in the radial bores of which six spindle nodes are fixed (Figure 1.37). In Figure 1.38 its cross sections are presented.
Fig. 1.37. 3D model of the spindle head
In the process of creating this model, the latest functional capabilities of CAD KOMPAS and specialized applications are used. In the development of such complex parts as a bed housing with a gear box and a six-spindle turret housing, specialized CAD libraries applications have found, which greatly improved the process of geometric modelling. Using the Artisan Rendering photorealistic image module built into KOMPAS creates the appropriate design and representation of the machine construct. 45
Fig. 1.38. The spindle head Sections
The machine bed is the base unit on which its components and mechanisms are mounted. Rigid bed construction is achieved due to the developed base and a large number of ribs. In the upper part of the bed housing the speed box with a corresponding mechanism for speeds switching and the mechanism of turret rotation are mounted (Figure 1.39, a, b)
46
a
b
Fig. 1.39. The mechanism of head rotation: a – 3D-assembly; b – section
1.3.2. Spindle node The shaping spindle unit represents a two-bearing structure [21, 22]. In the process of research, a solid model of the spindle head assembly was constructed (Figure. 1.40, a, b). The high-precision double-row angular contact tapered roller bearing is mounted in the front support of the spindle, which perceives radial and double-sided axial loads and is characterized by an allowable radial load of 1.7 times higher than that of the corresponding single-row bearing. In addition, it provides increased rigidity of the support. In the rear support, duplexed angular contact ball bearings are mounted, which radial combined and bilateral axial load received. This load allows these bearing in floating supports without fixing the outer rings in the axial direction to be used. Therefore, they can be effectively used in nodes with large axial forces at relatively high
47
rotational speeds. The spindle node is rendered in the Artisan Rendering system integrated into KOMPAS-3D (Figure 1.41)
Fig. 1.41. Spindle node rendering
When mounting the rear support, the X-shaped connection of the angular contact ball bearings ("face" sides) with using preloading in the form of spacer rings of different widths is selected. Adjusting the rings can reduce the excessive heating of the supports. In this case, it is necessary to increase the spacer width between the inner bearing rings (replace it) or reduce the spacer sleeve width between the outer rings by the size of the grinding. In the practice of machine-tool construction, the size of the re-grinding depends on the bearing diameter hole. For internal diameter in the range from 70 to 100 mm– the size of the grinding is about 6 μm.
48
Adaptability to manufacture of the spindle unit design is illustrated in Figure 1.42.
Fig. 1.42. Spindle unit separation
1.3.3. Modelling the spindle in the APM Structure 3D environment
One of the effective means for solving labour-consuming design tasks for the creation of optimal engineering structures is the APM Structure 3D module [7]. This module intends for analyse the elastically deformed state of arbitrary three-dimensional engineering constructions, which consist of rod, plate, shell and volume elements in their arbitrary combination. The calculation is performed by the numerical method – the finite element method (FEM) and allows to calculate the stresses and strains at any structure point, taking into account the intrinsic weight of each elements and considering the stress concentrators. The definition of unknown force factors in each of the nodes and internal force factors within each finite element provides information for calculating spline, threaded and other connections. 49
Consider the problem of modelling the vertical spindle drive the main movement of the milling machine model SF16MF3. During the modelling process, a "wire" model of the structure is created in the APM Structure 3D environment (Figure 1.43), in which each rod is represented as a line that is centered on the weight of the future intersection. Each rod has specific dimensions and is connected by means of nodes with other rods of the spindle structure, solid-state and framework model of which is shown in Figure 1.44, a; b.
Fig. 1.43. Spindle wire model
a
b
Fig. 1.44. Spindle models in the APM Structure 3D: a – solid-state; b – wireframe
To calculate this design, it’s necessary additionally specify: - the cross sections to each of the rods (Figure 1.45);
50
- supports for the created structure, which determine its position in space; - external loads, that affect the design (including the intrinsic weight of its elements); - parameters of the structural elements material.
Fig. 1.45. Cross sections of spindle
Calculation in the APM Structure 3D allows to estimate the complete picture of the shaft stress-strain state in any of its crosssections, including load estimation, force factors, etc., presented in Table. 1.1 – Table 1.6.
Table 1.1 Loads in nodes: (Load 0) N
Type
Node Number
Projections on: x
y
Modulus
0
сила , Н
0
-6442.00
0.00
Z -5187.00
1
сила , Н
3
-2355.00
0.00
-2616.00
51
8270.69 3519.87
Table 1.2 Displacements in nodes: (Load 0) N
Lineardisplacements [mm]
Angulardisplacements [degree]
x
y
z
x
Y
z
0
-0.0707
6.56e-038
-0.0576
0.0251
-0.0454
-0.0297
1
-0.0504
6.56e-038
-0.0412
0.0135
-0.00234
-0.0182
2
-0.0226
2.54e-037
-0.0219
-0.000167
0.00946
-0.00135
3
-0.0254
3.1e-021
-0.0293
-0.00428
0.0191
0.00236
Table 1.3 Rod index 0 (Rod 0) Node
Moment [N·m]
Force [N] Fx (axial)
Fy
Fz
Mx(torsion)
My
Mz
0
-0.00
5187.00
6442.00
347.00
0.00
-29.00
1
-0.00
5187.00
6442.00
347.00
-289.89
-262.41
Table 1.4 Rod index 1 (Rod 1) Node
Moment [N·m]
Force [N] Mx
Fx (axial)
Fy
Fz
1
0.00
1485.91
1894.83
2
0.00
1485.91
1894.83
My
Mz
138.92
-121.73
-102.34
138.92
-390.79
-313.34
(torsion)
52
Table 1.5 Rod index 2 (Rod 2) Node
Moment [N·m]
Force [N]] Mx
Fx (axial)
Fy
Fz
2
-0.00
-2616.00
-2355.00
3
-0.00
-2616.00
-2355.00
My
Mz
347.00
-346.18
-384.55
347.00
0.00
-0.00
(torsion)
Total mass of the structure –7.89 kg; The maximum displacement is 0.09 mm (Rod 0) (Load 0).
N
Table 1.6 Stress in the rod (max.) [MPa] (Load 0) Designation Nodes Equivalentstress
0
Rod 0
0,1
124.0
1
Rod 1
1,2
24.7
2
Rod 2
2,3
12.2
The maximum stress is 123.6 MPa (Rod 0) (Load 0)
The toolkit of the APM Structure 3D module allows performing a complex calculation of the SF16MF3 machine spindle. In Fig. 1.46 the depicted bending moment diagrams (Figure 1.46, a) and transverse forces (Figure 1.46, b). The elastic-deformed state in an arbitrary section of the spindle makes it possible to determine by the finite element method (FEM). With the help of this method, stress fields and displacement fields of the spindle are buil (Figure 1.47, a, b, c) The analysis of the obtained results allows choosing the best constructive solutions, working with different loads and their combinations. In this case, it becomes possible to design structures that 53
are closest to equally strong in terms of strength, rigidity, and vibration resistance.
a
b
Fig.1.46. Strength calculation results: a – bending moment diagrams; b – diagrams of transverse forces
a
b
c
Fig. 1.47. Output characteristics of the spindle: a – fields of equivalent stresses; b– fields of principal stresses; c – displacement fields
Complex calculation of double-row angular contact tapered roller bearing 3182116 GOST 7634-75) is implemented in the module APM 54
Bear [23]. This module implements a new approach to the calculation of bearings, which takes into account the essentially statistical nature of the processes, caused by the presence of an error in the shape of the surfaces in real contact between the rolling elements and the raceways. The amplitude of these errors is comparable with the magnitude of the contact displacements, which, in this case, makes classical methods of solving the contact problem unsuitable. APM Bear calculates a selective realization of bearing contact displacements, consisting of 100 elements. Using this implementation, you can determine the mean values of displacements and stiffness, their variances, maximum, minimum and most frequent values, the shape of dispersion fields, and so on (Figure 1.48). Average durability Maximum contact stress Heat release Dynamic load-carrying Radial beats Lateral runout Frictional moment Power loss a 10
20
hours MPa
59628 127831 31.478 0.216 0.989 16.564
J/h N μm μm N·m W b
Гис тограмма рад иальных бие ний Амплитуда и инте рвалы 31.6385 30 40 50 60 70
Поле бие ний (ос е вые - рад иальные ) Боковые бие ния, мкм
80
36.4385 , мкм 90 100 %
-20
Частота, %
15 20
Радиальные биения, мкм
20 25
Частота, %
25
10 15 5 10
-15
-10
-5
0
5
10
15
28
28
32
32
36
36
40
40
0 5 0
-20
0
10
20
30
40
50
60
70
80
90
100
-15
-10
-5
0
5
10
15
%
c d Fig. 1.48. The results of calculating the front support of the spindle: a – calculated parameters; b – distribution of normal forces; c – histogram of radial beats; r – beat field (axial-radial)
55
24
24
Радиальные биения, мкм
26.8385 0
2511 1285
As a result of complex calculations, the values of the calculated parameters for the spindle front support on the most loaded roller double row bearing 3182116 GOST 7634-75 (Figure 1.49, a),the distribution of the normal forces for one of the variants (iteration number 3) of the virtual position of the bearing center (Figure 1.49, b), the histogram of radial beats (Figure 1.49, c), and the field of combined axial and radial beats (Figure 1.49, d). According to calculations, the movements in the front support (at a fixed rigidity j = 98000 N/mm) approach the permissible values. At the same time, the presence of parts providing axial fixation (spacer bushings, rings) increases the stiffness of the spindle device, which makes it possible to consider the designed version of construction, is satisfied the rigidity criterion.
1.4. 3D modeling of the spindle unit for machining center model MTs200
The prevailing finishing operations at high cutting speeds predetermine a set of calculation procedures, the main ones of which are the procedures for evaluating the stiffness and vibration resistance of the forming units in various computer-aided design environments. In this paper, the complex procedure for estimating the spindle node stiffness of milling, drilling and boring type machining center (MC) by model MTs 200 in CAD KOMPAS and APM WinMachine is proposed [24, 25]. 56
To analyse the design of the spindle device by the criterion of rigidity and its complex calculation it is necessary to build solid models using CAD KOMPAS- 3D. We will use the principle of "bottom-up", that is, we first build 3D models’ components (housing, flange, half-coupling, nut, etc.) with their subsequent integration into the assembly construction of the unit. To create an assembly design of a spindle device consisting of 149 parts (26 original, 31 standardized), solid models have been developed (Figure 1.49). Large amounts of information: tabular and text data, parametric models and drawings make it expedient to use well-organized databases. The APM Base toolkit [26, 27] is very effective, which provides a unified information environment for CAD. Such a module provides wide opportunities to modify the provided databases or create custom databases.
a
b
57
c
d
Fig. 1.49. 3D models of spindle unit parts: a – housing; b – flange; c – tooth wheel; spline net
Based on the developed solid models of individual components, 3D model of the spindle device assembly design was created (Figure 1.50), The realism of models was achieved thanks to the Photo360 module [28, 29]. In this module, there is the possibility of imposing textures like the real ones; either the existing library of structures is used or its own one is created. In Fig. 1.51 shows the section of the spindle assembly. To assess the adaptability of the structure assembly, it is efficient to use CAD animation tools. Applying the animation project as a step-bystep strategy consisting of a sequence of combinations of steps (each of which represents the action of one or more components of the mechanism in space in accordance with the law of motion), an animation is constructed for assembling the spindle device MTs 200 (Fig.1.52).
58
Fig. 1.50. Solid 3D models of spindle unit MTs 200
Fig. 1.51. Cross-section of spindle unit MTs 200
59
Fig. 1.52. Animation of spindle unit assembly for MTs 200 Beginning with the 9th version of KOMPAS, a mechanism is used to calculate and display translucent objects in two variants - mesh or realistic [30, 31]. In this case, when using mesh transparency, the display of overlapped objects will always be correct. When editing a component (part or assembly) in the context of an assembly, there are several options for displaying the transparency of the component. These settings affect only those components that are not currently being edited. In Fig. 1.53 represents the design of the spindle assembly in a mesh translucent form. The main limiting factor determining the efficiency of the spindle unit is its rigidity [32, 33]. To assess its characteristics, the shaft and axis design module of the APM Shaft was used [1, 18, 34]. This module operates with a special set of primitives, which include the basic elements of the spindle design (Figure 1.54).
60
Fig. 1.53. Mesh translucent spindle structure
Fig. 1.54. Schematic of spindle unit: a – constructive scheme; b – the design scheme; c – cutting forces
61
As a result of the stress-strain state calculations by the Mor method. The movements of the spindle unit under the influence of cutting forces and force, which can occur in the gear clutch in the case of misalignment of the shafts were estimated. The most difficult case was calculated, when the cutting force and the force acting in the cam clutch act in one direction. In Fig. 1.55 shows the plots of the spindle movements.
Fig. 1.55. Spindle movements in vertical and horizontal planes
The total deflection lies behind the formula:
√
√
With an allowable deflection of 0.04 mm, it can be argued that the necessary rigidity is ensured. The reduced elastic spindle line corresponds to the design scheme with rigid supports. Accounting for the compliance 62
of the supports [35] somewhat changes the picture of the stress-strain state, the characteristics of which are presented in Table 1.7.
Table 1.7 Summary table of spindle stiffness characteristics
According to calculations, the movements in the front support on the triplexed angular contact ball bearings (at a fixed rigidity j = 98000 N/mm [34]) slightly exceed the allowable ones. At the same time, the presence of parts providing axial fixation (spacer bushings, rings) increases the stiffness of the spindle device, which makes it possible to consider the considered construction variant satisfying the rigidity criterion.
63
2. 3D MODELING OF MECHANICAL TRANSMISSIONS
2.1. Belt drives
The drives of the main movement of CNC machine tools and machining centers use drives with a DC motor and a thyristor voltage converter. Drives of this design need two-zone control. So, for the DC2P-series motor, the range of adjustment for the spindle speed is only 1:4. Often, according to technological requirements, this range needs to be increased, which is done by introducing an additional box of speeds and belt transmission. There are a number of advantages that are characteristic of different types of belt gears. First of all, it is low noise, smoothness and compensation of overloads in the start-up mode (V-belt (Figure 2.1, a) and poly-V-belts (Figure 2.1, b) transmission). 3D-models are constructed in the integrated CAD KOMPAS-3D [36, 37]. An increasing number of metal-cutting machines are oriented to gear belt drives, which are characterized by the possibility of maintaining the transmission ratio when changing the external load and a sufficiently high efficiency. Toothed belts have the greatest number of design variations compared to flat, round and V-belts. They have a number of advantages, providing a smoother transmission operation, eliminating the possibility 64
of slippage relative to the pulley; while they do not create such a high load on the shafts and bearings from the tension of the belt drive and provide the highest coefficient of efficiency. In Fig. 2.2 shows a 3D model of the belt drive in the drive of the main movement of the multi-operation machine model SF68 [38]. There are a number of ideas related to the improvement of the belt gear transmission [39, 40]. Patents for utility models are received: 1. Transmission to the toothed belt No. 99663 of 10.06.2015; 2. Transmission to the toothed belt № 100880 from 10.08.2015. The drawback of the traditional gear belt drive is the deformation of the belt teeth when they enter into engagement, the presence of flanges at the ends of the pulleys and the increased influence of the accuracy of the tooth profile on the load distribution over the height of the teeth. The reduction in the level of deformation in the transmission by a toothed belt is achieved by using belts (Fig. 2.3, a, b) and pulleys (Fig. 2.3, c) with the teeth of the trapezoidal profile in the normal section (Fig. 2.3, d), and in the longitudinal direction they are made in form of chevrons. The sheaves of the pulleys are divided by an annular groove into two half-chevrons with a slope α. At the same time, the width of the toothed belt b is determined by the criterion of traction of the belt. The presence of an annular groove makes it possible to avoid contact of the pulley teeth with the working sections of the belt teeth, where their left hemi chevron intersect with the right hemi chevron– a radius curve
r 0,2 m,
(m – the engagement module, mm). The proportions
65
between the parameters of the belt teeth profiles and the pulleys are the same.
а
b
Fig. 2.1. Belt transmission: a – V-belt; b – poly-V-belts
Fig. 2.2. Toothed belt drive
66
Using a gear with this arrangement of teeth on the belt and pulleys will prevent the belt from slipping from the pulleys, which will eliminate the flanges from the pulley design and, in the end, reduce friction losses and increase the transfer capacity of the transmission by a toothed belt.
а
b
c
d
Fig. 2.3. Toothed belt drive with chevron profile: a, b – serrated chevron belt; c – sheave of chevron gear; d – cross-section of teeth in normal section
67
The increase of the serviceability of the tooth drive belt with increased loads is ensured by the use of belts on the inner surface of which (see 2.4, a, b) and pulleys, on the outer surface of which (Fig.2.4, c) there are teeth formed in the form of arches with an angle of inclination at the ends pulleys: ( / 6)...( / 4) [3].
а
b
c
Fig. 2.4. Transmission toothed belt with arched teeth: a, b – belt with arched teeth; c – pulley with arched teeth
A diverse park of metal cutting equipment is rigged with various types and designs of belt drives. This leads to an increase in the complexity of the designing process for workable construction. One way to increase the productivity of design procedures is through the use of parameterization tools and solid modeling. The generated parametric transmission models will allow to rationalize the design process in a 2D editor and modeling in the 3D editor of the APM WinMachine [31]. For the construction of parametric models, the 2D graphical editor APM Graph is used, which is included as a module in the APM 68
WinMacine CAD [34]. This module implements its own software for creating a drawing and graphic parametric editor. For a wide range of belt pulleys, computational forms are developed that are used in the variable APM Graph windows [41]. The graphical pulley contour obtained on the basis of the parametric model can serve as a basis for the subsequent creation of a V-belt pulley drawing in the APM Graph module (Figure 2.5), as well as 3D models in the APM Studio module [18]. A similar procedure is also carried out for a poly-V-belt transmission.
44
19
7
12.5
a
b
c
Fig. 2.5. V-belt drive pulley: a – fragment of the parametric model; b – fragment of the drawing; c – fragment of the 3D model
69
а
b
c
Fig. 2.6. Poly-V-belt pulley: a – fragment of the parametric model; b – fragment of the drawing; c – fragment of the 3D model
2.1.1. Design of gear transmission in the KOMPAS system To build the pulley, you must use the Build Model command with the following selection in the KOMPAS-SHAFT 2D icon window New Model and one of the drawing types (for example, In Section (Figure 2.7).
Fig. 2.7. Selecting the pulley drawing type
70
In the main KOMPAS-SHAFT 2D window, the type of steps for the part, the elements of the mechanical gears, the additional elements of the steps are selected (Figure 2.8). To generate a 3D model, use a command with the appropriate name. With its help, the 3D pulley model is generated. (Figure 2.9). With the help of additional commands, sections and views are generated on the left and right. Integrative properties of CAD KOMPAS are provided by the team Mechanical properties of the materials of the projected parts, the selection of which is loaded with the material selection module. Working with this module is possible in the form of selecting the material of the part from the proposed database, or in the form of manually adding new material to the database. The material can be taken from the guide "Pilot: Materials and Assortments" Constructing the model of a gear tooth pulley. We construct the pulley with the following parameters: modulus m = 7 mm; number of teeth z = 26; width of rim of the pulley b = 32 mm. In dialog window the built outer contour with use pictogram Elements of Mechanical Transmission the type of transmission: Pulley of gear tooth belt is selected. In this window the option Demension for automatic put down dimension on drawing can selected. In dialog window Calculation of gear tooth belt transmission (Figure 2.11) the design calculation transmission is realized. Input initial data in window Design calculation is carry out.
71
Fig. 2.8. The main window of the KOMPAS-SHAFT 2D dialog
Fig. 2.9. Window for generating 3D models
72
Fig. 2.10. "Gear Belt Pulley" Dialog Box
Fig. 2.11. Gear Belt Calculation Window In the data entry window (Fig. 2.12), the pulley module is defined, which is the main design value when determining the tooth sizes, when selecting the cutting tool and setting up the machines. The values of the normal modules for gearing with a toothed belt are determined by the industry standard OST 38-05114-76 and selected from the drop-down context menu. After the input of the initial data, the calculation is 73
performed (Figure 2.12) and the recording of the received design data in a separate document.
Fig. 2.12. The initial data input window
The KOMPAS-SHAFT 2D system allows the implementation of multivariate gear calculations. For a specific variant (Figure 2.13), corresponding to the above initial data, the calculation is performed and the external and internal contours are constructed in the Selection window of the construction object (Figure 2.14). In the drawing field, a pulley with a toothed ring width of 32 mm and a diameter of the teeth external circles – 180,566 mm will be drawn. To display the tooth profile of the pulley, the option Additional Step Elements → Tooth Profile is used. The drawing of the profile will create a profile of the teeth, and a corresponding entry about the operation will appear in the dialog box (Figure 2.15).
74
The 3D model of the pulleys is constructed on the basis of the constructed flat model KOMPAS-SHAFT 2D. The finished threedimensional model is placed in the new KOMPAS-3D document. An example of the drawing is shown in Fig. 2.16.
Fig. 2.13. Transfer option selection window
Fig. 2.14. Object Selection Window
75
Fig. 2.15. Tooth profile dialog box
Fig. 2.16. Pulley of a gear belt drive
76
2.2. Gears The history of the KOMPAS-Shaft application is more than 20 years old. In 1991, the first modules were developed for the calculation of mechanical transmissions (the basis of the GEARS system for MS-DOS was created). The KOMPAS-3D V14 system application KOMPAS-Shaft 2D and KOMPAS-Shaft 3D came under new names –- "Shafts and mechanical transmissions 2D" and "Shafts and mechanical transmissions 3D" [42, 43] The KOMPAS-3D version with index 15 introduces a number of major changes [44]: 1. Replenishment of the normative base of the library with foreign standards. So, when choosing the module of mechanical transmissions in the calculation of gear and worm gears, you can choose not only "gost" source circuits and modules (large, small, circuits for high-strain gears), but also foreign pitches and metric (AGMA 201.02, ASAB6b, DIN 397252, ISO 53: 1998, JIS B 1701-1973). Also, it became possible to enter non-standard module values. For gears with non-standard or foreign module and the original circuit, it became possible to select a nonstandard pinion-shaped gear. The list of such pinion-shaped gear is formed independently. When you add a new pinion-shaped gear, it automatically performs its simplified geometric calculation. In the process of work, the list of pinion-shaped gear can be replenished and corrected. 2. Design of slots. The functional design of the slots is supplemented with the mode of constructing non-standard splines according to the 77
prototype or without it. As a prototype, splines can be chosen whose parameters correspond to the domestic standards or the standards of foreign countries (DIN 5482-1973, SAE J499A-1975, DIN 5471-1974, DIN 5472-1980). If necessary, almost any parameter of non-standard splines can be changed. 3. Worms of types ZT1, ZT2, ZN3, ZK4 are added to the calculation of the worm gear. 4. Calculation and construction of a screw involute gear transmission with subsequent visualization of the work of the gearing and the use of a "still frame". 5. Key slot of the expanded type and sizes. 6. Bearings and cuffs are built using a reference book or a library of standard products. 7. All databases are translated to a more modern and convenient database Absolute DataBase. In the new version of the library, it became possible to establish parametric dependencies between the various stages of the projected model. In the application of Shafts and mechanical transmissions of 3D, a new technique for optimizing the gearing of the cylindrical gearing by external gearing has been reflected. Automated calculation of displacement coefficients allows to design a transmission with optimal properties by the following criteria: – contact strength; – bending strength; –- equal strength of teeth; 78
– wear resistance and seizing resistance; – wear resistance and seizing resistance; – smooth operation. This design mode extends to a rack and pinion gear, an orthogonal transmission (a cylindrical involute worm / cylindrical helical gear). In this type of gears, instead of a worm wheel, a conventional helical cylindrical wheel is used, which greatly simplifies the manufacturing process. The range of the transmission under consideration includes a James planetary gearing, which found application in the summing links of the kinematic circuits of metal-cutting machines. In the application Shafts and 3D mechanical transmissions, the models of gears used in multi-operation machines of milling and drilling-boring groups are developed. In the specialized vertical milling-drilling machine of the second standard model SF16MF3, which is designed for multi-operation processing of complex profile products for steels, cast iron, light and nonferrous metals, a stepped speed box is used (Figure 2.17).
Fig. 2.17. Tooth gearbox transmissions
79
In the machine SF16MF3 blocks of tooth wheels are used, the 3D models of which are shown in Fig. 2.18 [20, 21]. Cylindrical gear wheels are widely used in the design of a special cantilever-milling machine with numerical control based on the model SVM1F4. In the Appendix "Shafts and mechanical transmissions" a number of models of gear wheels and shaft-gears have been developed (Figure 2.19) The wide-universal CNC machine model SF68VF4 uses bevel gears of various designs with a straight and circular tooth (Figure 2.20).
а
b
Fig. 2.18. Blocks of gear wheels: a – at the first stage of the gearbox; b – in the second stage
а
b
80
c
d
Fig. 2.19. Cylindrical gears: a – with axial fixation; b – mobile; c – shaft-gear wheel; d – sleeve-gear wheel
а
b
c
d
Fig. 2.20. Bevel gears: a – with slots; b – with key; c – bushing-pinion; d – a shaft-gear wheel
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Modern CAD systems are able to simulate the elements of some types of gears with a sufficiently high accuracy of working surfaces visualization (cylindrical gears, worms, pulleys, etc.). When simulating bevel gears with a circular tooth, the visualization is far from complete – the system does not generate teeth (or rather, toothing pitch between them), so these models are very conventional. To obtain a full 3D model of a conical gear wheel with a circular tooth, it is necessary to apply other modeling methods, one of which is presented below in the example of CAD KOMPAS-3D. Profiling of the tooth is done by cutting the cavity, as is the case when cutting teeth on a gear cutting machine by removing the material. Practically, the cutting is carried out by the end sections that are constructed and located in the appropriate positions using the command "Cut the element by sections". The following features of the circular teeth must be taken into account: 1. Along the cavity of the tooth, the geometric similarity of the profiles is not preserved (the section constantly changes in shape and size). 2. The trajectory of the location of the sections is a helical surface, therefore the sections occupy complex spatial positions. The solution of this problem can be conditionally divided into the following stages: 1. Determination of the spatial position of the end sections (the planes on which they are built);
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2. Calculation of additional geometrical parameters of the gear wheel, on the basis of which the end sections are built; 3. Construction of sections; 4. Cutting itself. For geometrical constructions, as well as calculating the parameters of an equivalent cylindrical wheel, the following data, determined with the standard geometrical calculation of the conical wheel, should be known: z – number of the conical wheel teeth; δ – angle of the reference cone for the conical wheel; mn – normal module; βn – pitch angle of the median tooth line for the conical wheel; R – mean cone distance; ha; hf – height of the reference head and the tooth feet, respectively; θa; θf – the angle of the reference head and the tooth feet of the conical wheel, respectively; d0 – diameter of the gear head; αn – the normal angle of the profile on the reference circle of the conical wheel with circular teeth. The position of each section is determined by the cone distance Rx having its own value, accepted for each section. To obtain a surface of the cavity without sharp transitions between the cross sections, five sections are sufficient. In this case, the outermost sections must be located at some distance from the ends of the ring of the conic gear wheel (2 to 5 mm), and the average cross-section for convenience of calculations is located at 83
the length of the average cone distance R, then the parameters in this section are equal to the average calculated for the conical wheel. The position of the planes on which the cross-section sketches are located is determined by the points of intersection of the cylindrical surface (formed by the "Extrusion surface" command), imitating the tool and having a corresponding diameter (d0) and position in space (taking into account βn and the direction of the spiral) and the reference cone surface of the conical wheel. The sketch of a cylindrical surface (circle) is built on a plane tangential to the reference cone of the conical wheel. The circle is located in such a way that at the point located on the average cone distance R (usually the middle of the ring gear) between the tangent to the circle at this point and forming the cone passing through this point, an angle βn was formed (Figure 2.21).
Fig. 2.21. Position of sketch for sections planes
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Also, for each cross-section, at the distances Rx, conic surfaces are formed, which are additional cones whose generatrix is perpendicular to the generator of the reference cone. The planes on which sketches of sections will be constructed are tangent to additional cones and pass through the points of intersection of a cylindrical surface, a reference cone and additional cones. In the future, these same points are the base points for the construction of sections sketches. For the construction of the end section, it is necessary to conditionally replace the conical gear wheel by an equivalent cylindrical gear. The parameters of the initial contour of the equivalent cylindrical wheel are corresponding to the end parameters of the bevel gear. The parameters of the equivalent cylindrical wheel, which are required for constructing the cross-sections of the cavity, are determined from known analytical dependences [45]. These parameters of an equivalent cylindrical wheel are calculated for each section. On the basis of the data obtained, involutes are formed, forming the lateral surface of the tooth in the section (Fig. 2.22). The thickness of the tooth (for simplification of calculations) is not calculated, but is adopted in a graphic construction, starting from the angular pitch of an equivalent cylindrical wheel. As practice has shown, it is necessary to further expand the cavity by an amount approximately equal to the upper tolerance for the thickness of the tooth for a given conical wheel.
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Fig. 2.22. Building an evolvent of the tooth's lateral surface
After the construction of all sections, the "Cut element by sections" command is applied. As a result, a cavity is formed on the wheel (Figure 2.23). Then, using the command "Array on a concentric grid", the number of cavities is reduced to the number z. This method allows to obtain 3D models of bevel gears with a circular tooth with a sufficiently high degree of similarity with real wheels. The described method of profiling the cavity has some simplifications and errors in geometry, but they can be neglected, since they are small enough and practically do not affect the visual perception of the 3D model (Figure 2.24).
Fig. 2.23. Sketches of sections
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Fig. 2.24. Engagement of bevel gears with a circular tooth
2.3. Worm gears In the design of the feeds boxes and rotary tables, worm gearings (whose 3D models are shown in Fig. 2.25) are used. They are performed without a gap, the problem of which is the complexity of manufacturing turns with varying axial angles and thicknesses on the right and left sides. Consequently, the need for the manufacture of a special cutter whose reference diameter is greater than the reference diameter of the worm. Complexity also represents non-orthogonal installation of a special cutter when cutting the teeth of the worm wheel.
а
b
Fig. 2.25. Worm transmission: a – worm; b – wheel worm
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The proposed patent [14] and the paper [12] set the task of providing a gapless gearing in a worm gear using standard worms, mills and existing manufacturing techniques. The task is achieved due to the fact that the worm 1 under its own weight
G
is displaced vertically
downwards, keeping the horizontal axis of rotation, until its tip tooth come into contact with the cavity of the worm teeth for wheel 2 located in the horizontal plane (Figure 2.26). As a result, the gaps in the engagement are reset.
Fig. 2.26. Scheme of a gapless worm gear
To carry out the vertical displacement of the worm shaft, its bearings are in sliding supports 4, which allow the shaft of the worm to self-align in the vertical direction while maintaining the horizontal axis of rotation. The supports 4 are able to move in the housing 3 in a vertical direction due to the projections A of the triangular profile on the supports 1 and grooves B of the same profile in the housing 2 fixedly fixed to the mechanism housing (Figure 2.27).
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Fig. 2.27. Sliding support
Circular force of the worm, directed downwards, contributes to the preservation of the gapless engagement for the worm with the worm wheel. When reversing, when the force is directed downward, Fig. 2.26. The lifting of the worm upwards and, accordingly, the formation of gaps in engagement is impeded by the compression force of the springs 4 mounted in the housing 3 on the sliding supports in which the bearings of the worm shaft are fixed. The 3D model of a gapless worm gear with sliding supports is shown in Fig. 2.28 [12].
Fig. 2.28. Gapless worm gear in sliding supports
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3. 3D MODELING TOOL SYSTEMS
3.1. Tool storage with a tool positioners A tool system is understood as a set of devices and means that provide the process of surface treatment by cutting [46, 47]. Management of the process of tool provision is carried out by means of Tool Changers Construction (TCC) Changing the tool manually on multipurpose machines determines the significant downtime of these expensive machines. Automatic tool change is carried out for 5…10 s against 25…40 s when changing manually. Since the frequency of tool changes is approximately 20…25 times per hour, the use of the TCC on these machines significantly improves the processing capacity by increasing the degree of machine automation, and also eliminates possible errors when changing the tool. In general, the TCC devices of multipurpose machines consist of the following components: tool storage, which are tool stores (blocks of cutting and auxiliary tools for tool spindles); tool manipulators are intended to change tools in the machine spindle; intermediate transport manipulators are intended to transfer the tool from the storage to the tool manipulators or to intermediate positions – the tool stores in the position of its change.
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The basic requirements for tool storage are as follows: reasonably capacity; high accuracy of the tool positioning in the working part of the machine; ease and convenience of loading storage and good access to them; the minimum time taken to change the tool; high reliability; the smallest number of coordinates when the tool is changed. The equipment for changing tools in the spindle of the machine with the manipulator can be semi-automatic and automatic. Semi-automatic devices consist the tool storage and a manipulator for automatic tool mounting into the machine spindle and back. In automatic devices, the manipulator automatically picks up the tool from the tool storage or transport manipulator and places the tool in the machine spindle. Storages of TCC devices with a manipulator are divided into disk, drum and chain. Disk storage are used with horizontal, vertical and inclined axes of rotation. In storages with a vertical axis of rotation, the tools can be mounted vertically, horizontally or at an angle (crowned). The following requirements are imposed on tool storage of multioperation machines: 1) the capacity of the storage must be such that the set of tools loaded in it is sufficient to process a typical part; 2) it must have a simple construction, be compact enough; 3) the storage must be located outside the machine working area, do not interfere with the working movements of the machine, the mounting and removal of workpieces, setting up the machine; 4) easy, convenient and safe access of the adjuster and the operator to the tool storage must be provided; 91
5) all preparatory actions for changing tools must be performed on the machine in parallel with the cutting of the part, which reduces the time spent on changing the tool; 6) the operation of changing tools should not cause vibrations of the machine itself. The choice of the type of storage is determined by the purpose, type and layout of the multioperation machine. The analysis of the entire variety of medium-sized housing parts, which it is advisable to process on multioperation machines, shows that about 18% of the details require the use of no more than 10 tools, 50% - up to 20; 17% - up to 30, 10% - 40 and 5% - up to 50 or more tools. Therefore, they often use storages with a capacity of up to 30 instruments, mainly disk storages. In a specialized multioperation CNC machine based on the model SVM1F4, the TCC device with a disk magazine mounted on the machine column and a two-grip manipulator are used (Figure 3.1). The tool is changed in the fixed position of the spindle head. Student Litvinenko S.S. of the Machinery and Applied Mechanics department of Volodymyr Dahl East Ukrainian National University the TCC device was developed, including 1330 3D models of parts and assemblies. The project is presented in the gallery of the XIII International Contest "Future Asses of Computer 3D Modeling", organized by the ASCON Group of Companies in 2015.
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Fig. 3.1. Design of the automatic tool changers construction
The tool store is designed for keeping and delivery to the tool position, tool holders with a cutting tool. Regardless of the type of storage and method of tool change, all cutting tools and other auxiliary tools and devices are mounted in the hole of the machine spindle or in the storage socket using standardized mandrels where the tools are fixed and, if required, are adjusted to the specified machining size either outside the machine, or automatically from the machine's CNC system. In Fig. 3.2 represents the design of a disk tool storage for 14 tool holders, and Fig. 3.3 its section, giving an idea of the parts and assembly design of the storage.
а
b Fig. 3.2. Disk Tool Storage: a – with tools and fastener; b – assembly
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Fig. 3.3. Cross-section of the tool storage
Fig. 3.4. Manipulator–tool positioners
The tool change in this disk tool storage is performed by a two-grip rotary manipulator (Figure 3.4). In the tool change position, the manipulator rotates by 900, grasping the tool in the storage and the tool in 94
the machine spindle, then moves forward, taking the tools out of the socket and spindle. The manipulator rotates 1800, changing tools in places, then moves backwards, mounted tools in the socket of storage and spindle. After that, the manipulator rotates 900 to its original position. This design of the manipulator provides a simple cycle of operation. Lack of design – a small number of tools mounted in the storage, because with a small distance between the tools when turning the manipulator will graze the adjacent tool. Separate assemblies of tool positioner functional units are shown in Fig. 3.5.
а
b
c
d
Fig. 3.5. Assemblies of auto operator's units: a – brachium; b – grand axle-box; c – piston; d – pump-rod
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3.2. Tooling Tooling is a specific set of devices, with the help of which fastening and mounting of workpieces processed on machines, assembling of various structures, and also transportation of workpieces and finished products is carried out. In this monograph, the procedure for constructing 3D models of tooling [21] in the KOMPAS-3D system is implemented: for milling (Figure 3.6, a), for reaming (Figure 3.6, b), drilling (Figure 3.6, c), thread cutting (Figure 3.6, d) and others.
а
b
c
d
Fig. 3.6. Tooling: a – milling mandrel; b – mandrel with a ream; c – drilling mandrel; d – threading tool
In the KOMPAS-3D system, a solid model of a boring mandrel with micro-adjustment of the cutter for finishing boring (TU 2-035-774-80), also shown in Fig. 3.7.
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а b Fig. 3.7. Boring mandrel: a – assembly; b – section The main component of the boring mandrel is a microbore – cutter – carbide tip of angular boring with micrometric adjustment with mechanical fastening of tip on OST 2I29-1-81. The solid model of the microbore is shown in Fig. 3.8.
а
b
Fig. 3.8. Microbore: a – assembly; b – section
а
б
Fig. 3.9. Rendering: a – boring mandrel; b – microbar
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The assembly movement direction of the boring bar is shown in Fig. 3.10. When building assemblies of tool blocks (Figure 3.11), 3D models of original parts are used. For the milling tool block, they are shown in Fig. 3.12.
Fig. 3.10. Aassembly movement direction of the boring bar
а
b
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c
d
Fig. 3.11. 3D models of the milling tool block: a – tool block for face milling; b – holder; c – transition sleeve; d – key
The components of the drilling tool block are shown in Figure 3.12. The composition of the instrument block component parts for gear cutting is shown in Figure 3.13.
а
b
c
Fig. 3.12. 3D models of the drilling tool set: a – tool block for drilling; b – holder; c – sleeve transition
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а
b
c
d
Fig. 3.13. 3D models of component toolbox for thread cutting: a – tool block for thread cutting; b – bushing; c – converter; d – nut
The CAD KOMPAS-3D software creates a photorealistic image of the tool block for the drilling operation example (Figure 3.14) and milling (Figure 3.15). In the module Artisan Rendering there are possibilities of a combination of materials and lighting, texture and relief. At the same time, textures contain reflections and transparency of such elements as a mirror or glass.
Fig. 3.14. Rendering of the tool block for drilling
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Fig. 3.15. Rendering an instrument block for milling
A high-speed tool head is also used as a replacement tooling arbor, which is designed for high-performance processing of non-ferrous metals and their alloys with end mills, drills and other tools with a minimum diameter of 5 mm. A 3D model [2] of the high-speed head was developed (Figure 3.16), the cross section of which is shown in Fig. 3.17.
Fig. 3.16. High-speed drilling head
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Fig. 3.17. Cross section of high-speed drilling head The clamping of the high-speed head in the spindle of the machine is carried out as well as the tool. The pin of the head lock is inserted into the hole of the bracket attached to the end of the sleeve to exclude the rotation of the high-speed nozzle in the end hole of the spindle. In this case, the speed of the leash is increased 2,5 times from the initial one on the spindle. In the above-mentioned tooling of multi-operation machines, mandrels with a conical shank with a conicity of 7:24, excluding selfbraking, are used. This makes it possible to base the mandrel in the spindle with high accuracy and to easily extract it with the help of a tool positioners. In the spindle, the mandrel is usually held by traction and a spring disk pack or fixed with a screw. The pull rod has a gripping device on its end that provides grip with the shank screwed into the mandrel. The following basic requirements are imposed on the auxiliary tool for CNC machines of a drilling-milling-boring group: high accuracy; minimum installation error; high rigidity in all directions of component cutting forces application; vibration resistance; quick change; reliability; 102
easy and quick tool adjustment to the required size outside the machine; universality; simplicity of design and manufacturability; minimum nomenclature of auxiliary tools.
3.3. Cutting tool In the multi-operation machines of the drilling-milling-boring group, cutting tools of various types have found application. The drill, as an axial tool in its working part, includes cutting and calibrating components, on which two screw grooves are formed, creating two teeth that provide the cutting process. The most common are spiral drills with a cylindrical and conical shank end. To reduce friction during the work of the drill along the entire length of the slideway part, there is an understatement on the back, forming a ribbon with a width of 0,2 ... 2 mm on the cutting edge. The helical part of the rear surface is a deploying helical surface, which makes it possible to obtain a more rational distribution of the values of the rear corners. This also helps reduce axial loads by increasing the rear corners on the transverse cutting edge. In CAD KOMPAS-3D, taking into account the above design features, a solid model of a spiral drill with a cylindrical and taper shank was developed (Figure 3.18).
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а
b
Fig. 3.18. Spiral drills: a – with a cylindrical shank; b – with a conical shank
When drilling large diameter holes, holes are formed in succession by two drills of different diameters, the ratio of which must be such that the diameter of the first drill is greater than the length of the transverse edge of the second drill. Under this condition, the transverse edge of the second drill does not participate in the cutting, which significantly reduces the force required for the feeding, and, what is very important, reduces the drift away from the axis of the hole being machined. The design of the drill for reaming in 3D is shown in Fig. 3.19, a. For the treatment of center holes in accordance with GOST 14034-74 of different configuration and dimensions, centering drills are combined. They have an angular profile of grooves (angle 900 ... 1100) and they do not have a ribbon on both the drill bit and the countersink part of the drill. In this case, the back of the cutting part is full-form relieving along the Archimedean spiral (Figure 3.19, b).
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а
b
Fig. 3.19. Drills: a – for reaming; b – for centering
For the finish machining of holes 6 ... 10 accuracy grades, the reamers with the working part in the form of chip grooves (straight or screw), dividing the teeth of the reamers are used. The shape of the teeth in the cross-section perpendicular to the axis of the reamer is characterized by a rectilinear front surface, and the ribbon is executed along the cylinder (Figure 3.20).
Fig. 3.20. Solid model of a cylindrical reamer
For the treatment of planes often used end mills, which belong to the group 1800 by Classification of Products (CP), subgroup 1890 – cutters for CNC machines, type 1895 – end carbide cutters with mechanical fastening of polyhedral and round cutter plates. The main feature of mills equipped with throw-away carbide insert is a fixed arrangement of cutting elements relative to the milling cutter housing. The geometric parameters of the milling cutters are thus constant and are determined by the design of the milling cutter. In Figure 3.21. the 3D model of the Arbor-type end milling cutter with throw-away carbide inserts is shown. 105
When processing slots and ledges, surfaces in hard-to-reach places, end cutters (subgroup CP 1820, type 1821) are used, which are made of end-cylindrical with the location of the cutting edges both at the end and on the cylinder. In general-purpose end mills, the directions of the helical grooves and the direction of rotation do not coincide and the shape of the end teeth is distinguished by a transitional section in the form of a chamfer (Figure 3.22).
Fig. 3.21. Arbor-type end milling cutter with throw-away carbide inserts
Fig. 3.22. End milling cutter
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The multi-operation machine model SF68VF4 has a modification with a trunk and a package of disc milling cutters, which expand the technological capabilities of the machine for gear cutting. Disk gearcutting modular cutters belong to special tools. By construct and design methods are similar to shaped mills with teeth, relieving in the radial direction, with straight or milled on the sides of the flute grooves. Since the disk gear milling cutter has a zero front angle and when cutting a cylindrical spur gear, it works by copying, the profiling of its cutting edges is reduced to determining the shape of the teeth grooves for the workpiece. According to GOST 10996-64, the tooth profile of the cutter consists of an involute, non-involute sections and a straight line. For a large range of disc milling cutters with unified functional elements: involute profile of cutting blades; transitional surfaces approximated by arcs; the relieving back surface described by the Archimedean spiral. It is expedient to use the instrumentation of parametrization [21, 22]. The algorithm for constructing the parametric model and the syntax of the CAD APM WinMachine is presented in [37]. When profiling tools that work by the copying method, along with the involute part, it is necessary to research the profile of the inoperative and non-involute part of the cutter, which in turn depends on the teeth number of the cut wheel z1, as well as the number of the twin wheel teeth z2. A method is known for finding the point K on the involute section of the tooth profile, which is the boundary of the profile tooth active part that actually participating in the gear [48]. The position of the point K is given by the radius Rk. With further rotation, the wheels come out of mutual contact. 107
With a large number of teeth, the base circle radius of wheel rb will be less than the radius tooth of the cavity Rf (Figure 3.23) and the profile of the wheel tooth AB (from the addendum circle, to cavity circle) is involute. In Figure 3.23 shows techniques for constructing the involute and transition profile using the parameterization technique. The parameterized relieving back tooth of the milling cutter is shown in Figure 3.24.
а
b
Fig. 3.23. Groove profile of the toothed wheel: a – involute profile with a transition curve; b – tooth groove contour
а
b
Fig. 3.24. Back tooth relieving: a – single relieving; b – double relieving
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Based on the profiles obtained in the "Sketch" mode, solid models of disk milling cutters are built in the APM Studio module (Figure 3.25).
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b
Fig. 3.25. Solid models of a disk mill: a – construction; b – cutting scheme
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4. 3D MODELING OF HOUSING TYPE PARTS
4.1. Basic parts of milling machines The spatial arrangement of the machine's forming units is provided by the machine carrier system, as a set of basic units [49–51]. These include, in the first place, housing parts: columns, housing of spindle headstock and others. The base parts should be characterized by high accuracy and rigidity, as well as increased damping properties (the ability to extinguish vibration in the working area of the machine). Housing parts are under the action of combined loads (bending with torsion) and are made hollow with a closed profile. In the design of milling machines, vertical machine bed (spine of the machine) is most often used. The form of the bed approaches a box with internal walls and partitions (ribs), which are necessary to increase the rigidity and the formation of individual cavities and compartments. The ribs of a special configuration, for example diagonal, provide an even greater increase in rigidity. Spine of the machine experiencing complex spatial loads has a profile approaching the square. From the point of view of the influence on the deformation in torsion, it is advisable to change the cross sections in such a way that, as the column is removed from the base, the cross-sectional shape approaches a square cross section. Such a profile is typical for the base 110
part of the "column" of the machine of the wide-universal multioperation machine with CNC model SF68VF4. On the cast-iron base of the machine is fixed a column on which all the main parts of the machine are mounted. The spindle head (Z-axis) moves along the horizontal slideways of the column, to which the vertical head or additional devices and accessory are attached [52, 53]. On the vertical slideways of the column, the carriage (Y-axis) moves, and along its horizontal slideways the main vertical table (Xaxis), to which, depending on the configuration, a rigid corner table or rotary table is mounted for processing workpieces on them [54]. 3D model of the column was created in CAD KOMPAS [1, 2] (Figure 4.1). Figure 4.2 shows the cross section of the machine column.
Fig. 4.1. Solid model of the column for the machine SF68VF4
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Fig. 4.2. Cross-section of the column In the vertical milling cantilever machine tools with CNC models SVM1F4 and SF16MF3, the "Bed with gearbox" is used as the main base part. Machine components and hydraulic drive are mounted on this bed [54, 55]. On the housing of the bed there are vertical slideways along which the cantilever moves, and in the upper part of the housing is mounted a speed box. Increased stiffness of the base part is achieved by the presence of a large number of diagonal-type stiffeners. To prevent warping of the walls, the distance between the ribs should not be more than 400 mm. For most machines, the moment of forces acting on the rack at the base is greater than above, so the racks are often carried out expanding downwards, at least in one plane. In the KOMPAS system, 3D models of the basic component "Bed with a speed box" were developed [9, 10, 20], which are presented in Figure 4.3 and Figure 4.4. The cross-sections of these parts are shown in Figure 4.5. Modeling these basic parts is quite a complicated process – the drawings of each are presented on 5 sheets of A1 format. The maximum unification is expedient. A fragment of the housing drawing of the bed with a speed box based on the associativity principle is shown in Figure 4.6. For this purpose, the KOMPAS system has the command "Create a 112
new drawing from the model", which provides creation of a drawing with an associative view of the current three-dimensional model.
Fig. 4.3. 3D model of the bed housing with the speed box of the machine SVM1F4
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Fig. 4.4. 3D model of the bed housing with the speed box for the machine SV16MF3
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a
b
Fig. 4.5. Cross sections of housings: a – the machine CBM1F4; b – machine SF16MF3
4.2. Basic parts of transmissions Elements of machines carrier system include various constructions of boxes (gear boxes, spindle headstocks, etc.). Most of these designs have the form of a parallelepiped. The greatest influence on the box rigidity is the increase in the stiffness of the wall directly at the place where the load is applied. Rigidity can be significantly increased due to bosses and special ribs, reinforcing the bosses. In the KOMPAS system, a 3D model of the housing for the horizontal spindle head of the machine model SF68VF4 [1, 2, 5] is developed, which is shown in Figure 4.7. The cross-section of this part is shown in Figure 4.8. 115
Fig. 4.6. Fragment of the machine housing drawing for the SF16MF3
Fig. 4.7. The horizontal spindle head housing for the machine SF68VF4
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Fig. 4.8. Cross-section of the machine speed box SF68VF4
The spindle head consists of: cast iron housing, spindle block with the mechanism of tool automatic clamping, the camshaft, which transmits the rotation to the horizontal or vertical spindle by means of an automatic gear shifting gear. The design of the headstock is equipped with a two-speed gearbox controlled by a hydraulic-operated gearshift mechanism; a device for supplying coolant to the cutting zone and electrical and optoelectrical sensors that control the position of the spindle head and its mechanisms. The wide-universal machine is equipped with various modular equipment, including a vertical and angular spindle heads. The vertical head is attached to the spindle headstock with four screws and is centered with two conical pins and bushings. The vertical spindle is mounted in a sleeve having movement in the housing receiving rotation through a conical pair and a cam clutch. Due to the presence of a T-shaped groove in the adapter plate, the head rotates 90 ° in both directions. Setting the head to the desired 117
position is carried out with a pin. To precisely position the head in a vertical position, use a control mandrel, inserted and clamped in the cone hole of the spindle and the pointer indicator. A 3D model of the vertical spindle head housing [7] is developed, which is shown in Figure 4.9.
a
b
Fig. 4.9. Housing of vertical spindle head: a – construction; b – section
The corner head is included in the scope for delivery of the designed machine SF68VF4 and allows to expand the technological capabilities for milling and drilling-boring machines. The angular head is intended for processing in hard-to-reach areas of workpieces for planes, ledges and grooves. It provides high-performance processing at spindle speeds up to 4000 min-1 with the possibility of a spindle rotation angle at 3600 in the horizontal plane. 118
The design of the angular head in 3D is shown in Figure 4.10. Spindle headstocks, along with the shape of the parallelepiped, have a cylindrical shape. To such constructions it is possible to carry the housing of the horizontal spinel headstock for the machine MTs200. Vertically movable headless without cantilever spindle headstock is mounted on a portal rack, carrying out a cross movement along the X and Y axes. A 3D model of the spinel head of the machine МЦ200 with a horizontal spindle arrangement [24, 25], presented in Figure 4.11. In the design of the machine SVM1F4 is provided, as a stand-alone module, a rotary controlled table. It is mounted in two positions with a vertical and horizontal axis, depending on the location of the treated surface. It consists of a housing in which there is a worm pair that transmits the motion from the high torque engine to the executive unit – the faceplate.
a
b
Fig. 4.10. Angled spindle head: a – construction; b – cross-section
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а
b
Fig. 4.11. Spindle headstock of the machine МTs200: a – construction; b – section
Along with the forms of a parallelepiped and a cylinder for vertical spindle headstocks, more complex shapes can also be characteristic. These include the spindle head of the machine model SVM1F4. The base part of head is the housing, which is an irregular shaped cast iron. Inside the housing is mounted a spindle group with a tool clamping mechanism, an intermediate shaft and a pinion shaft. In the KOMPAS-3D system, a solid model of the spindle head housing [9, 10] is developed, shown in Figure 4.12. The complexity of this housing can also be illustrated by its drawing obtained in KOMPAS on the basis of the associativity principle (Figure 4.13).
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а
b
Fig. 4.12. The spindle head of the machine SVM1F4: a – construction; b – cross-section
Fig. 4.13 Drawing of the spindle head housing
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On the upper base of the housing is mounted a hydraulic unit, intended to unclamping movement the tool and orient the spindle for changing tools [56, 57]. In Figure 4.14 shows a solid model of the hydroblock housing [9].
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Fig. 4.14. Hydraulic block housing of the spindle head: a – construction; b – cross-section
In CAD KOMPAS-3D the model of the rotary table housing is developed (Figure 4.15)
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b
Fig. 4.15. Rotary table housing: a – construction; b – cross-section
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4.3. Basic details of six-spindle turret head Among the basic details is a rather complex six-spindle turret head of a specialized vertical milling and drilling machine with CNC model SF16MF3. This is a cast-iron housing, in the radial bores of which six spindle nodes are fixed (Figure 1.4.4 and Figure 1.4.5), and six rigid stops are fixed on its ends. In the grooves of the head are mounted cams, which serve to select the tool. In the central bore, the gear of the head rotation is mounted. In the process of research for the specialized machine SF16MF3, the turret housing solid model was constructed [20, 21], shown in Figure 4.16.
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b
Fig. 4.16. Six-spindle turret head: a – construction; b – section The turret is rotated by means of a pinion, which, in turn, receives a clockwise rotation from the hydraulic motor (Figure 1.4.6). The basic 123
housing part of the turret rotation mechanism in 3D was created in the KOMPAS system [20, 21] and is shown in Fig. 4.17.
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b
Fig. 4.17. Turret rotation housing: a – construction; b – section
Form-forming spindle node represents a two-support structure. In the process of research, a solid model of the spindle head assembly was constructed. The high-precision angular contact double-row tapered roller bearing is mounted in the front support of the spindle, which perceives radial and double-sided axial loads and is characterized by an allowable radial load of 1,7 times higher than that of the corresponding single-row bearing. In addition, the angular contact double-row roller bearing provides increased rigidity of the support. In the rear support, duplexed angular contact ball bearings are mounted that take radial combined and bilateral axial loads, which in turn allows them to be used in floating supports without fixing the outer rings in the axial direction. Therefore, they can
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be effectively used in nodes with large axial forces at relatively high rotational speeds. The 3D model of the spindle assembly basic part – the sleeve, shown in Figure 4.18.
а
b
Fig. 4.18. Spindle node housing of the machine SF16MF3: a – construction; b – cross-section
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CONCLUSIONS 1. In this monograph as a basic computer-aided design system, a well-known, dynamically developing KOMPAS system is selected, reinforced with the FEM module for the purposes of complex research of the stress-strain state of multi-operation machine designs and the Artisan Rendering module for creating photorealistic images. 2. A complex study of the structures for specialized drilling-millingboring machines of the second and third standard sizes of models SF68VF4, SVM1F4, SF16MF3 and MTs200PF4 using geometric modeling in CAD KOMPAS and engineering analysis of the projected object using the APM FEM module was carried out. 3. 3D models of the above-mentioned metal-cutting machines and their forming units in the KOMPAS-3D system have been built, which give a real idea of the design and are the basis for design calculations and the research efficiency of the machine. 4. Solid models of the main parts of spindle devices are built in the CAD KOMPAS-3D environment with extensive use of KOMPAS application libraries and parameterization tools. 5. On the basis of 3D models of spindle nodes components and assemblies are implemented using procedures for imposing realistic textures and rendering in the Artisan Rendering module integrated into CAD KOMPAS. 126
6. Simulation of the assembly process using animation tools was performed. It ensures the efficiency of the analysis procedure for manufacturability. 7. Design and calculation schemes of spindle nodes as beams on two hinged supports are created. The stress-strain state is calculated and the spindle movements are determined in the case of both fixed and elastic supports. The working capacity of the constructions under consideration was confirmed by the rigidity criterion. 8. The use efficiency of the complex analysis module APM Shaft for shaft modeling in the mode of spindle nodes multivariate design is shown. 9. 3D model of the rotary table for the machine model SVM1F4 was developed and a fundamentally new solution for the introduction of a zero-gap worm gear, providing increased accuracy in the process of longterm operation, was proposed. Such a rotary table with a vertical and horizontal rotation axes can be a unified unit and can be used in a wide range of milling machines. The proposed idea of a zero-gap worm gear is confirmed by the proposed patents. 10. A comprehensive analysis of the stress-strain state of spindle milling machines in the APM STRUCTURE-3D module by the finite element method is performed. Fields of equivalent stresses and displacements are constructed in different sections of the projected object, which makes it possible to perform express analysis of the structure by the criteria of strength and rigidity.
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11. The toolkit for parametric modeling of the APM WinMachine integrated CAD was used and parametric forms were constructed to ensure the productivity of the designer during the creation of 3D models and the execution drawings of the machine parts and assembly units. 12. The results obtained in this paper allow the construction of parametric models, drawings and 3D models of belt gears for various design implementations in the multivariate design mode. With the help of the application "Shafts and mechanical transmissions", the design of gear belts is performed. For gear belt transmission, new patent solutions are proposed related to the chevron profile of the tooth, for which threedimensional transmission images are constructed. 13. The analysis of the design features of bevel gears with a circular tooth is given. This shows how to effectively replace the bevel gear with an equivalent cylindrical gear using known analytical dependencies. 14. Three-dimensional models of machine tool basic details are developed. Such complex models (the housing of the bed with the speed box of the machine SVM1F4 are depicted on 5 sheets of A1 format) make it possible to implement complex assemblies and ensure the creation of models for machine tool designs as a whole. 15. To investigate the workability of the automatic tool changers construction, a set of solid models of its main components – a 14-position disk tool store, a tool positioners and a whole set of 3D models for tooling milling machines – is proposed. 16. A wide range of the features described above, provided by the integrated CAD KOMPAS-3D, the FEM and Artisan Rendering modules 128
built into the system and a large set of application libraries, allows to significantly improve the design quality of metal cutting machines and shorten the preparation period for design documentation.
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CONTENT
INTRODUCTION ................................................................................... 3 1. 3D MODELING OF MACHINE TOOLS FOR DRILLING-MILLING-BORING TYPE .............................................. 8 1.1. 3D modeling of the machine center of model SF68VF4 ................ 8 1.1.1. Vertical spindle head ........................................................... 17 1.1.2. Angular spindle head ........................................................... 20 1.2. 3D modeling of the vertical multioperational machine model SVM1F4 ................................................................................... 25 1.2.1. Spindle head ........................................................................ 29 1.2.2. Rotary table ......................................................................... 31 1.3. 3D modeling of a milling-drilling machine with six-spindle head of model SF16MF3 .................................................. 41 1.3.1. Six-spindle turret ................................................................. 44 1.3.2. Spindle node ........................................................................ 47 1.3.3. Modelling the spindle in the APM Structure 3D environment ............................................................................. 49 1.4. 3D modeling of the spindle unit for machining center model MTs200 ......................................................................... 56 2. 3D MODELING OF MECHANICAL TRANSMISSIONS ........... 64 2.1. Belt drives .................................................................................... 64 2.1.1. Design of gear transmission in the KOMPAS system ......... 70
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2.2. Gears ........................................................................................... 77 2.3. Worm gears ................................................................................. 87 3. 3D MODELING TOOL SYSTEMS ................................................ 90 3.1. Tool storage with a tool positioners ........................................... 90 3.2. Tooling ........................................................................................ 96 3.3. Cutting tool ............................................................................... 103 4. 3D MODELING OF HOUSING TYPE PARTS .......................... 110 4.1. Basic parts of milling machines ................................................ 110 4.2. Basic parts of transmissions ..................................................... 115 4.3. Basic details of six-spindle turret head ..................................... 123 CONCLUSIONS ................................................................................. 126 REFERENCES .................................................................................... 130
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