new methods for compensating the machining errors by cad modelling

Annals of the University of Petroşani, Mechanical Engineering, 9 (2007), 169-184 169

NEW METHODS FOR COMPENSATING THE MACHINING ERRORS BY CAD MODELLING OF THE MACHINING SURFACES ON MILLING MACHINES IN COORDINATES CONSTANTIN ISPAS 1, FLOREA DOREL ANANIA 2, CRISTINA MOHORA 3, IOANA IVAN 4 Abstract: In this paper, we propose a solution for improving the machining precision by the diminution of the machine-tool’s errors (geometrical errors, cinematic errors, errors because of static and dynamic loads, errors because of the thermal deformations and of the wear in time of the structure elements). The purpose is the diminution of these errors, but not by modifying the machine-tool, but by modifying the 3D model of the surfaces for the piece to be machined.

Keywords: machine-tool’s errors, 3D model

1. INTRODUCTION Worldwide machine-tools production business value is around 5 %. In 2005 the world production was 51,9 billions of dollars and 99% was accomplished by 31 countries. Drawing up a classification for the machine-tools producers countries from the point of view of the business value, Japan has the first place with a business value of 13,3 billions of dollars, followed by Germany with 9,5 billions of dollars, China with 6 billions of dollars, Italy with 4,5 billions of dollars, Taiwan with 3,3 billions of dollars, USA 3,2 billions of dollars, South Korea 2,8 billions of dollars, Sweden 2,6 billions of dollars, Spain 1,1 billions of dollars etc. It is to be noticed that the first two countries have a business value of over 45% of the global one. Machine-tools production, in 2005, in Romania was about 72,4 millions of 1

Ph.D.prof. eng. at University Polytechnic of Bucharest Ph.D.prof. eng. at University Polytechnic of Bucharest 3 Ph.D.prof. eng. at University Polytechnic of Bucharest 4 Ph.D. assoc.prof.eng. at University Polytechnic of Bucharest 2

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dollars (is on the 23rd place in the world classification), and the consumption value was 213 millions of dollars (the 21st place). The revenue obtained from the machine-tools export, in 2005, was 154,5 millions of dollars – 20th place. This business value mentioned earlier was obtained as a result of exporting retroffited machine-tools. The machine-tool is a working machine for generating working surfaces in specific predefined conditions regarding the productivity, the dimensional precision, the surface quality, the price and the delays. The recent history of the humanity was and still is strongly influenced by the machine-tool, machine which led to change the perception over the reality through developing in about 300 years a technical civilisation (in continuous expansion). The machine-tools represent the basic instruments for the development of all aspects of the daily life of the human society. The usage of machine-tools since 1800 has modified the fabrication process, in a positive way like increasing the productivity and the quality of the products of over 50 times. The integration of different components of computer aided design and computer integrating manufacturing in the fabrication process, as well as the implementation of fabrication flexible lines has led to a productivity of three times bigger then in the last decade. No matter which industrial field is approached (electronics, aerospace, nuclear, munitions, automobiles) it can not be imagine the evolution of today’s technology without the usage of machine-tools which fulfil the exigencies of the specific criteria foe each field. Today’s machine-tools represent a synthesis of different domains of science and of technique , their performances being directly influenced by the knowledge obtained after researches in different domains, like mechanic, mathematic, physic, metallurgic, thermo, electronic, electro-technical, informatics etc. [1] Machine-tools represent an assembly of the best from the technical domains with the purpose of obtaining some complex technical-functional characteristics by joining together mechanical, hydraulic, pneumatic, electric characteristics. Today a modern machine-tool represents an assembly composed from 35% mechanical part (structure elements, carcass, spindles, cinematic chain etc), 30% electronic part (numerical command, sensors, command and control system etc), 30% hydro-pneumatic part, 10% electric part (engines, couples etc) and 15% software. Machine-tools have a social calling, direct or indirect. They influence all the fabrication processes, the quality of the personnel from the point of view of their professional training and last but not least the number of personnel. A single modern machine-tool entails the activity of a number of 25-40 persons, from which, about 35% qualified personnel, 15% engineers, 40% technicians, 10% workers for maintenance, programming, packing activities and machine serving activities. (Mazak document) The human has created the machine-tool and gave it a unique quality of procreation. The machine-tools create machine-tools on a progressive scale. Machine-tools have the role of being the engine of the modern technique and

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deserve the attention of the society through all the aspects that define it: research, conception, industry, economy, politic etc. The machine-tools performances have raised constantly in the last decade, first of all due to the increase of the demands from the industrial domains of “high tech” products like auto, aerospace industry etc. All the components from the industrial domain, starting with basic things and ending with components that have extremely high technical-functional characteristics, have as basis the machining in the production systems, which at their turn have as basis unit the machine-tool. The higher the technical-functional performances of the machine-tools the higher are the performances of the pieces machined on these machine-tools. In this paper, we propose a solution for improving the machining precision by the diminution of the machine-tool’s errors (geometrical errors, cinematic errors, errors because of static and dynamic loads, errors because of the thermal deformations and of the wear in time of the structure elements). The purpose is the diminution of these errors, but not by modifying the machine-tool, but by modifying the 3D model of the surfaces for the piece to be machined. The basic idea is the automatic modification of the surfaces to be machined since the design phase CAD (computer aided design) based on the machine-tool errors measured with external instruments (LASER interferometer for geometric error, Vibroport for the dynamic behaviour study etc). Based on the surfaces modified in this way, the numerical command program will be generated (through CAM modules), program which will be implemented on the working machine-tool. QUALITY

Design quality

Conformation quality

• • •

• • •

Marketing Design Specifications

Technology Manual labour Characteristics

Availability

• • •

Reliability Maintenance Change pieces

Service quality • Promptitude • Competence • Integrity personals

Fig.1. Quality components after J.M.Juran

The conditions for this idea to be functional are a very good knowledge of the machine-tool and of its working environment. 2. MACHINE-TOOLS PRECISION The quality expresses all the essential features and aspects which together

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define the utility level of a product. By the assembly of its technical, functional, psycho-sensorial characteristics and its economical parameters, the product satisfies in a certain way the needs for which it was created, but in the same time the product must respect some restrictions imposed by the general interests of the society, regarding the human and the environment protection and by the achievement of a certain economical efficiency. [2] The quality, under different forms, has always represented and represents still a concern of the human kind. Socrates himself said that “what it is good is useful, and what it is bad is harmful”. A similar interpretation regarding quality was given by Genichi Taguchi (2) in 1983. Is to be remarked the association made between the quality and the economical aspects and implications. The objective of quality has evolved from the simple establishment and sorting of inadequate elements to the complete satisfaction of all demands and expectations of the clients, as well as the objective of the preventing the faults. This fact has changed the concepts, the organisation and the working methods which now are inconceivable without mathematical statistics. The effect of this change is similar to the five Olympics zeros: zero effect, zero breaks, zero delays, zero stocks and zero papers. Trying to cover the multitude of involved aspects, J.M.Juran (7) points out four main components of the quality: design quality, conformation quality, availability and service quality (Figure 1). A machine-tool, a product of a special complexity, has quality if it can provide from a technical point of view the machining precision imposed by the category that belongs. The technical quality of a machine-tool is appreciated by the dimensional, micro-geometric precision of the machined surfaces and by the correctitude of the relative position of the generated surfaces, in certain conditions of productivity. [3] 3. GEOMETRIC PRECISION Geometric precision is evaluated by verifying the relative positions of the structure elements of the machine-tools which are functioning without load and characterises the quality with which are accomplished the plane (rectilinear or circular) generators trajectories of the simple generative movements materialised through the inferior kinematics couples slide and bearing. The machining precision for the pieces machined on machine-tools has a very strong dynamic. The quantification of the precision is made by admissible errors towards a theoretical or ideal value. Precision can be generally defined in two different ways: feature of a product to have the characteristic dimensions in a range as tight as possible around the desired value, or the maximum admissible error, in plus or in minus, when measuring or producing a product. The two definitions point out two aspects for evaluating the quality of a product at fabrication and measurement (verification), but not in exploitation.

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The precision of a product is demanded by the functional role which imposes the admissible limits between which the quality of the product must be placed. The same product considered as precise for a certain purpose, could be declared imprecise for a different one, or much too precise for a third application (not economical). [3] The machining precision of the piece represents a quality indicator which reveals the correspondence level of the real technical conditions for generating the machined surfaces of the piece to the theoretical values of the same conditions (dimensional, shape conditions, surface quality conditions, relative position of the component surfaces conditions) prescribed on the execution drawing of the piece. The geometrical precision of structure elements of the machine-tools

Functional effects • • • • • •

Deformation because of the weight Deformation because of binding forces Stick-slip Thermal effects Vibrations Dynamic errors because of the displacements

Geometrical precision of the machine-tools • The precision of reference surfaces • The rotation precision of the main spindle • The precision of linear /circular displacements • The positioning precision

The machining precision of the piece • • • •

The shape precision The dimensional precision The relative positions of the surfaces Roughness

Fig. 2 Geometrical precision of machine-tools

According to some European standards, the geometric precision is appreciated through rectilinear, plane, parallel, perpendicular, coincidence, rotation characteristics of some reference surfaces (guilding, flange and principal spindle bore etc). In this way, is established the precision of geometrical parameters for the generative trajectories. The geometrical precision of the machine-tools is influenced by the geometrical precision of the structure elements, but also by a series of multifunctional factors presented in Figure 2. 4. DYNAMIC PRECISION The dynamic precision represents the quality of the machine-tool under the stresses action (stress of every kind) to keep its stability at vibrations. The dynamic

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precision represents one of the most important indicators in appreciating the quality of a machine-tool, because its evaluation is made in very similar conditions to those of exploitation. [4] The dynamic system of the machine-tool is a closed system, which appears in the interaction between the elastic system (machine-tool-device-piece-tool) and the processes (cutting, milling, processes in action engines). The interruption of one connection leads to the transformation of the system in an opened one, and the interruption of two connections allows the separation of the elements and the determination of the dependencies between it’s in and out dimensions. The dynamic precision of the machine-tools is determined depending on the vibrations of any nature, which come along with the generation through cutting of a surface. During this generation, because of some internal or external causes of the cutting process, vibratory movements which determine the dynamic precision overlap the generative or auxiliary movements. Among the main dynamic phenomenon which come along with the surface cutting, are to be noticed free vibrations, forced vibrations and auto-vibrations. 5. FREE VIBRATIONS. This type of vibrations characterises the transitory processes, which due to big amortisements in machine-tools joints have a very short duration. Transitory processes are the components of the complex process of the machine-tool. Thus, the dynamical phenomenon which come along with the auxiliary operations (starting the action engines, acceleration and deceleration of the movement of the mobile sub-assemblies, changing the revolution in the adjusting mechanisms etc) of the machining process can influence the whole vibratory process of the machinetool. The transitory processes are provoked by inversing the movements’ way of the assemblies during the machining process. The frequencies of the free vibrations are the elastic system proper frequencies, a dynamic parameter very important for the development of the vibratory process. The stability of the dynamic systems is appreciated based on the solutions for differential equations which describe the transitory process of the system. The study of free vibrations is made with linear homogenous differential equations. [4] 6. FORCED VIBRATIONS. Forced vibrations which depend on the cutting process and their appearance is tied on many factors. Among these the most important are: the variation of machining shim, the periodical variation of the chip’s section (characteristic for milling, rectifying operations), the variation of machining material hardness.

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Vibrations which do not depend on the cutting process. Their appearance is tied to the actions of inertia forces, which appear as a result of rotation movements, not equilibrated mass inside the cinematic chains of the machine-tools, and also of the vibrations transmitted by other machines and installations. 7. AUTO-VIBRATIONS. Auto-vibrations are not amortised vibrations, caused by excitatory factors which do not have periodical variation. After the nature of the excitatory factors, auto-vibrations which appear in the elastic systems of the machine-tool can be auto-vibrations which appear in the cutting process as a result of the interdependency between the cutting force dimension and the relative displacement between the tool and the semi-fabricate. Auto-vibrations appear due to the friction process through the dependency character between the friction force and the slip velocity inside the cinematic couples. The auto-vibrations due to the phase (the difference) between the force and displacement variation appear in the cinematic chains of the machine-tools. The dynamic test of the machine-tools can be made basing on two main types of measurements: [3] • The establishment of the global level of the vibrations at which the machine-tool is subjected to, in normal working conditions and in the specific working environment. • The determination of the characteristics of the vibrations of the elastic structure of the machine-tool or of one component element. The first category of measurements implies, for the majority of cases, the establishment of amplitudes and frequencies of the vibrations which exist on the machine-tool, the dimension of excitatory forces remained undetermined. Parameters’ values of the vibrations will be compared. 8. THEORETICAL CONSIDERATIONS CONCERNING THE ERRORS’ MODELLING OF THE MACHINE-TOOLS The majority of the machine-tools are designed so that they have in their structure rotation and translation joins. Physically speaking it is practical impossible to make cinematic chains and ideal guiding elements (zero errors) for driving different elements of the machine. Usually the cinematic and guiding errors of the machine-tools are taken into account and partially compensated by the command and control system of the machine. In time these errors modify being permanently influenced by the usage level of the machine and by the environment conditions in which the machine is functioning. [3] Always the ideal position of the tool is calculated depending on the geometrical and/or thermal errors. Despite all the real position of the tool will be different from the ideal position, because the positioning precision measurements are

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made on different cinematic chains (feeding chains) and not exactly on the last element (the tool). In Figure 3 the tool’s ideal and real positions are presented. The real position in comparison with the ideal one will be translated after 3 directions and rotated after the three axis because of the linearity and angularity errors cumulated in the measured point. Thus due to geometrical errors and not only (thermal, dynamic etc) the real position of the tool in space will be translated and rotated after each axis of the Cartesian system (Figure 3). The point that represents the centre of the tool will be translated on the X axis with x r (linear errors cumulated on the X axis), on Y axis with y r (linear errors cumulated on the Y axis), on Y axis with z r (linear errors cumulated on the Z axis) and rotated with Ψ (angular errors cumulated by rotating after X Fig. 3. Ideal and real positions of the tool axis), with Φ (angular errors cumulated by rotating after Y axis) and with θ (angular errors cumulated by rotating after Z axis). In reality this position can not be measured by the command system of the machine-tool, so it can not be corrected. For transforming the Cartesian system OXYZ in the Cartesian system O’X’Y’Z’ they have been used the following homogenous transformations:

 rx  Tr = ry  vector for linear errors  rz 

R Rz

R Ry

0 1  = 0 cosψ 0 sinψ

(1)

0  − sinψ  rotation matrix 3x3 on the x axis cosψ 

(2)

 cos ϕ 0 sin ϕ  =  0 1 0  rotation matrix 3x3 on the y axis − sin ϕ 0 cos ϕ 

(3)

cos θ R Rz =  sin θ  0

− sin θ cos θ 0

0 0 rotation matrix 3x3 on the z axis 1

(4)

The transformation vector from the O point to the O’ point is defined by the

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TOO ' = R x ⋅ R y ⋅ R z ⋅ Tr

(5)

relation:

So, the following relation is obtained:

TOO '

TOO '

0 1  = 0 cosψ 0 sin ψ

0   cos ϕ − sin ψ  ⋅  0 cosψ  − sin ϕ

0 sin ϕ  cos θ 1 0  ⋅  sin θ 0 cos ϕ   0

− sin θ cos θ 0

0  rx  0 ⋅ ry  1  rz 

(6)

 (cosψ ⋅ cos ϕ − sin ψ ⋅ cos θ ⋅ sin ϕ ) ⋅ rx + (cos ϕ ⋅ sin ϕ + sin ψ ⋅ cos θ ⋅ cos ϕ ) ⋅ ry + sin ψ ⋅ sin θ ⋅ rz  (sin ψ ⋅ cos ϕ + cosψ ⋅ cos θ ⋅ sin ϕ ) ⋅ r − (sin ψ ⋅ sin ϕ − cosψ ⋅ cos θ ⋅ cos ϕ ) ⋅ r − cosψ ⋅ sin θ ⋅ r  x y z (7) =   sin θ ⋅ sin ϕ ⋅ rx + sin θ ⋅ cos ϕ ⋅ ry + cos θ ⋅ rz    

Thus, the real position of the tool’s centre has the coordinates given by the vector TOO’:

x real = x i + (cosψ ⋅ cos ϕ − sin ψ ⋅ cos θ ⋅ sin ϕ ) ⋅ rx + + (cos ϕ ⋅ sin ϕ + sin ψ ⋅ cos θ ⋅ cos ϕ ) ⋅ r y + sin ψ ⋅ sin θ ⋅ rz

y real = y i + (sin ψ ⋅ cos ϕ + cosψ ⋅ cos θ ⋅ sin ϕ ) ⋅ rx − − (sin ψ ⋅ sin ϕ − cosψ ⋅ cos θ ⋅ cos ϕ ) ⋅ r y − cosψ ⋅ sin θ ⋅ rz z real = z i + sin θ ⋅ sin ϕ ⋅ rx + sin θ ⋅ cos ϕ ⋅ ry + cos θ ⋅ rz

(8)

(9) (10)

Where, x i , y i , and z i are the ideal coordinates of the studied point. The expressions from the 7 relation are actually the expression of the errors on each axis. The expressions for determining the position of the compensated point regarding the ideal position are the following:

x comp = x i − (cosψ ⋅ cos ϕ − sin ψ ⋅ cos θ ⋅ sin ϕ ) ⋅ rx − − (cos ϕ ⋅ sin ϕ + sin ψ ⋅ cos θ ⋅ cos ϕ ) ⋅ ry − sin ψ ⋅ sin θ ⋅ rz ycomp = yi − (sinψ ⋅ cosϕ + cosψ ⋅ cosθ ⋅ sin ϕ ) ⋅ rx + + (sinψ ⋅ sin ϕ − cosψ ⋅ cosθ ⋅ cosϕ ) ⋅ ry + cosψ ⋅ sin θ ⋅ rz

z comp = z i − sin θ ⋅ sin ϕ ⋅ rx − sin θ ⋅ cos ϕ ⋅ ry − cos θ ⋅ rz

(11)

(12) (13)

These relations are implemented in the CAD compensating program of the

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surfaces. Depending on the machine type for which the errors’ compensating method will be applied by modifying the CAD model’s surfaces, the previous written relations (8 … 13) can be modified. The position of the real and compensated points will be calculated depending on the machine’s errors and the ideal points which describe the machine’s working space. The points which define the machine-tool’s working space are in fact the ideal points measured by the command and control system of the machine-tool. Figure 4 presents a modelling in Cartesian coordinates for the working space of a milling machine in coordinates. It is recommended the defining of a threedimensional network of Fig. 4. CAD modelling for the working space points for the mathematical points of the machine-tool modelling of the working space of the machine as follows: • for strokes over 2000 mm, the discretisation pitch of the working space to be of 100 mm. • for strokes under 2000 mm, the digitisation pitch of the working space to be of 50 mm. For each of these points the linear and angular position errors will be measured, obtained depending on the systematic errors of the machine-tool in normal working conditions. The basic idea of the method is that depending on the machine-tool’s errors to modify not the compensation errors matrix within the command and control system, but to modify the 3D model of the working piece surfaces in a CAD (computer aided design) system. This modified model should be used to generate the numerical command program in a CAM (computer aided manufacturing) system. Thus, it is proposed the calculus of the real position of the tool relying on the relations 8 … 13 (from the 8th Chapter – Theoretical considerations concerning the errors modelling of the machine-tools) in different points, the generation of the compensated points and with their aid the surfaces generation in CAD systems. Figure 5 presents a generation model for a real surface in CATIA V5 depending on the measured errors for machining a plane surface. The idea is to make the numerical command program for the milling operation, not on the ideal or real surface, but on the compensated surface (obtained depending on the two surfaces – the ideal and the real one).

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Ideal surface

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Real surface

Fig. 5 CAD modelling for the ideal and real surfaces

Figure 6 presents the real surface and also the compensated one, obtained after the machining of the positioning errors of a milling machine in coordinates. The compensated surface

Real surface

Fig. 6 CAD modelling for the real and compensated surfaces

The machine-tool’s errors will be measured with external devices (LASER interferometer, Vibroport 41) and by specific measurements methods. The idea is to measure the positioning errors (linear and angular) as close as possible to the tool’s centre position, in a points’ network which describes the working space of the machine. The points’ network will be defined depending on the producer’s specifications. In these points the linear and angular errors will be measured for the machine-tool in normal working conditions. As measuring method of the global

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positioning errors the interferometer LASER method is recommended together with dynamic measurements through the frequency spectrum analysis. Proposed solution for 3D modelling of the surfaces (the ideal, the real and the compensated) is that of generating a program in C++ programming language for the errors calculus and the automate generation of the folders which are specific to the design advanced environment CAD-CAM-CAE-CATIA V5. Inside the program are implemented the errors measured according to the designed method, the coordinates of idea, real and compensated points will be modelled and calculated and files CATSCRIPT will be generated for CATIA V5. The CATIA environment has been chosen as it has a wide spread in the industrial field, being used in top industries as the automobiles industry, aeronautic industry, the moulds fabrication industry etc. 9. RESULTS AND CONCLUSIONS Figure 7 presents the rectification operation of a piece inside of a mould. This operation was the first executed on a milling machine after making the correction for the numerical command program, modification made based on the studied method. Inside the program were implemented a part of the values for the errors measured on the machine. As a demonstration have been implemented some values for a restrain working space of 1000 x 1000 mm for the machining of a plane surface (or of a plane curve – Figure 7). In this first step of adjusting the Fig. 7 Example of a machined piece algorithm and development of the program for the automated generation of the ideal, real and compensated surfaces, a particular case has been studied, for the milling of plane surfaces on a milling machine in coordinates. A modular program in the C++ language has been made. All the different steps specific to this errors’ modelling method were modularised inside the program through specific functions. Three types of function are generated: two functions types which are specific for the calculus and the generation of parameters and commands for the external file and one function type for calculating the ideal, real and compensated coordinates which are specific to one point from the working space of the machine, based on the positioning errors measured in that point. Through modularisation of the program a high flexibility is provided for the program. In practices, this means a fast adaptability to precise situations, depending on the machine-tool’s type and on the studied cutting process, and not least also depending on the errors’ types and the methods used to measure them.

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Fig. 8 Laser assembly (according to Renishaw documents)

In the same time the equations that have been used can be changed very easily depending on the calculating method, on the architecture of the machine-tool etc. The program can easily adapt for different types of machine-tools as well as for industrial robots. The main advantage of this method and of the program is that the machining surfaces are regenerating depending on the errors which are specific to a machine-tool and after that the numerical command program is generated. The surfaces’ regeneration is made based on the errors which can not be measured and taken into account by the command and control calculating system of the machine-tool. Another lighter advantage, specific to the program is that the generation of the files is made directly for advanced design environments CAD-CAM, especially CATIA V5. Errors values introduced in the correction program are those systematic errors with high level o repeatability. There have been implemented errors’ values for the linear positioning precision and repeatability, measured with the LASER interferometer. Figure 8 presents the assembly schema for linear measurements for the LASER interferometer Renishaw. Figure 9 presents under a graphic form the measurements made on the z axis of the gantry machine (fig.7) Fav 3300. The obtained values have been used as input data.

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Fig. 9 Positioning precision and repeatability on the Z

Table 1 presents the environment conditions in which the measurements have been made: Table .1 Environment conditions ENVIRONMENT:: Stroke 1 Air temp [oC] 15.035580 Air press [mBar] 95.331260 Air humid [%] 42.813570 Mat temp [oC] 17.105120 Env factor [mBar] 0.31642380 Exp coeff [ppm/0C] 11.700000

Stroke 2 14.006580 95.310720 31.149630 17.099300 0.31642351 11.70000

Table 2 presents the measured values for the stroke on the Z axis. Table .2 Measurements for stroke on Z axis Deviation in µm Position in mm Position in mm 0 0.000 1300 100 11,300 1200 200 8,600 1100 300 3,300 1000 400 4,100 900 500 3,000 800 600 -0.600 700 700 1,800 600 800 2,200 500 900 -0.400 400 1000 0.100 300 1100 -1,700 200 1200 -4,200 100 1300 -2,500 0

Deviation in µm -4,700 -5,800 -1,200 -2,600 -5,500 -2,700 -2,300 -4,700 -2,800 -1,800 -3,200 3,000 4,300 -8,100

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A second set of measurements have been made, from dynamic point of view through experimental study with the equipment Shenk Vibroport 41. There have been made measurements for transfer functions through impact (Fig.10) and for the frequency spectrum of the machine in functiong conditions (Fig.11).

Fig. 10 The results from the measurement of the transfer functions

Fig.11 The results from the measurements of the frequency spectrum

The measurements have been made in several measuring points and in several working conditions (machine off, machine on, main spindle on with different revolution). After analysing the obtained values there have been established the following frequencies (Tabel 3) with a high level of repeatability (almost in all measurements); the amplitudes for these frequencies expressed in micrometers, and their directions have been implemented into the CAD correction program.

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Ispas, C., Anania, F.D., Mohora, C., Ivan, I. Table 3. Displacements vibrations Displacements ( µm ) Frequencies (Hz) Position and direction 2,1237 µ m 20,00 Hz Z 0,2152 µm 33,75 Hz X 1,3785 µm 41,25 Hz Z 1,0719 µ m 57,5 Hz; Z 1,5087 µm 76,75 Hz Z 1,3771 µm 80 Hz X 1,6874 µ m 90 Hz Z

The equipments which have been used for the experimental study belong to the National research centre for the performances of the technological systems – Optimum (http://sun.cfic.pub.ro) within the “Politehnica” University of Bucharest. REFERENCES [1]. Ispas C., Machine outils pour l’usinage a grande vitesse. 1. Contexte, 2.Particularites, 3. Conception 4. Recherches en Roumanie, 4-emes Assies Machines et Usinage Grand Vitesse, 8,9 juin 2006, ENSAM, Aix-en-Provence, www.lsis.org/AssisesMUGV2006 [2]. Micu C., Aparate şi sisteme de măsurare în construcţia de maşini, Editura tehnică, Bucureşti, (1980) [3]. Ispas C., Predincea N., Zapciu M., Mohora C., Boboc D., Masini-Unelte Incercari Şi Receptie -, Editura Tehnica,Bucuresti, (1998 ) [4]. Marinescu I., Ispas C., Boboc D., Handbook of Machine Tool Analysis, United States of America, ISBN 0-8247-0704-4, 002, 2002 [5]. Ispas C., Zapciu M., Mohora C., Anania F.D., Theoretical and experimental studies of the spindle of a high speed turning machine. 6th International Multidisciplinary Conference BAIA-MARE Romania 2005, ISSN-1224-3264, ISBN 973-87237-1-X