Buletinul Ştiinţific al Universităţii „POLITEHNICA” din Timişoara Seria HIDROTEHNICA TRANSACTIONS on HYDROTECHNICS Tom 58(72), Fascicola suplimentară, 2013
CAD Modeling of Helical Cylindrical Surfaces with Applications for Helical Drills Nicuşor BAROIU1
Silviu BERBINSCHI1
2. GEOMETIC DEFINITION CYLINDRICAL HELICAL LINE
OF
THE
The helical line or the helix – is the curve from point A on a meridian of a Σ rotation surface,
D XII 11' 10'
XI X
9'
IX
8'
VIII
7'
3'
4'
5'
2'
ω
VII 6'
VI
p
12'
V IV III
p/2
Different solutions and applications were imagined and developed in order to develop profiling the cylinder-frontal tools, the cylindrical ones, etc. and other tools edging the revolving surfaces. There are different methods defining the helical surfaces of drills: analytical methods [5], [8] – the surfaces are defined through specific mathematical laws which permit determining the tangent curves for the winding surfaces, 2D graphical methods [7], [2] – cylindrical helical surfaces and of constant pitch are modelled in a solid way, in Auto LISP – AutoCAD for profiling the cylinder-frontal tools, 3D graphical methods [4], [9] – winding the helical canals is made from a virtual CAD representation of the tool shape, thus inferring the point coordinates on characteristic sections of the helical flute or methods based on reverse engineering [10], [3]. In order to develop the conception and design of some products, different 2D and 3D graphic representations systems appeared in a virtual environment. These software applications are also used for modelling the CAD helical surfaces of drills, some of them being dedicated Anca Tools, SV & Toolbox etc. or generalized – Pro/ENGINEER, NX Simens [12], Catia [11] etc. The advantage of these design applications is that the virtual drill is modelled in a 3D environment, this can be optimized from a geometric and constructive parameters or design point of view before being physically realised.
p
1. INTRODUCTION
meridian rotating around the surface axis ∆, so that the distance on a meridian point (or according to the case, its orthogonal projection on ∆ axis) is proportional to the revolving angle of the meridian between its axis [1]. The parameters defining the helical line are: the shape and the size of the rotating surface, the axial pitch or the meridian pitch, the winding direction. According to the meridian shape and its position to the rotation axis ∆, the helical drill is associated to a cylindrical helix having a constant pitch, p. The cylindrical line is traced 2D geometrically from the cylinder representation having a diameter D in plan [V] and [H], considering the axis ∆ ⊥ [H] – fig. 1.
p/12
Abstract: The present paper deals with a CAD application correlated with CATIA and NX Siemens software packets for defining the cylindrical helical surfaces through particularities of modeling some helical drills having different geometry, particularly the drill with straight lined cutting edge and the helical drill with three curved cutting edges. Keywords: CAD, CATIA, NX Siemens, helical surface, drill, curved cutting edges.
II
1'
I
0'
πD/2 10 9 8 11
πD
7
0=12
6
1
5 2 3 4
a) b) Fig. 1 Constant-pitch helix winding on the right (a), through helix winding on the line (b)
Both the base circle and the known helix pitch p, in the same number of equal parts (for example, 12); through the circle’s division points (1, 2,…, 12) going parallel to the cylinder generators, and through the pitch division points parallels are taken to the cylinder base; the intersection points (1', 2',…, 12') of the parallels drawn to the generator, and respectively the base, belong to the helix. Obviously, if we consider point A situated in the initial position in point (0, 0'), at its movement on the generator with a distance p/12, the generator rotating with an angle 3600/12, reaching 1 position. Figure 1a presents the cylinder helix winding on the right and figure 1b – cylinder
”Dunărea de Jos” University of Galaţi, Department of Manufacturing Engineering1, Machine Elements and Graphics Department2, 47 Domneasca st., 800008, Galaţi, Romania,
[email protected],
[email protected]
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developed where the helix winding to the right was drawn. This is a rectangle diagonal having the dimensions π .D .p. The helix angle, ω, is defined by the relation: tgω =
π ⋅D
Making the helical channel of the drill Due to the straight shape of the cutting edge, the helical surface of the flute will be generated by moving the cutting edge on a cylinder helical main curve, having a constant pitch, the parameters to be taken into account being r 0 – radius of drill core, κ working angle and helix lifting (p.θ), according to angle θ turning. The movement of the generating line is made by a helical line, the generating straight line does not coincide to the curve tangent, and open (the generating straight line does not intersect the helix main axis), the helix pitch (p) being determined from relation (1). The command used to draw the helical curve is . The curve will multiply, Helix symmetrically to the first one in order to make the second pitch. Determining the drill channel profile is performed on a perpendicular plane perpendicular on the helix axis, this meaning sectioning the helical surface with plane z = 0 – fig. 4. Obtaining the helical flute from the Fig. 4 Helix command parameters cylinder solid is realized with the command Swept with controls the shape of the flute along the two helixes considered guidance elements – fig. 5.
(1)
p
3. MODELLING A STANDARD DRILL Modelling the standard helical drill is done by using a complete integrated soft – NX CAD/CAM/CAE, produced by SIEMENS company. Variant NX7.5 benefits from an easy to use interface which allows using some advanced functions through modularizing and personalizing. The main geometric parameters of a drill with straight lined cutting edge (standard) are defined in table 1 and figure 2. Table 1 Geometric parameters of the standard drill
D Df R r f
Drill diameter Margin height Radius of helical flute Radius of helical flute Margin width
L
ω
Flute length Helix angle
2κ
Point angle
γ
Lip relief angle
ψ
Chisel edge angle
Fig. 2 Geometric parameters of the standard helical drill Fig. 5 Generating the helical flute – Swept command
Making the drill Geometric modelling of a helical drill with a diameter D = 20 mm, begins with a detail drawing of from Model . the main body, using Sketch After building the main circle and applying the drawing constraints, Sketcher is closed, and the drawing can be used to create the cylinder solid . though the modelling operation, type Extrude The length L of the flute is separated at a distance settled through calculation (140 mm) from the total length of the drill, settled standard at 215 mm, with the help of two separation plane, one perpendicular on the drill axis and the other with a 300 slope with the same angle used for the helix – fig. 3.
While defining the chisel edge of the drill, the diameter of the drill core d 0 is taken into account, with is chosen according to the exterior diameter of the drill D, in the case under discussion, for D = 18÷25 mm, d 0 = (0,125÷0,25) .D. At the same time, the chisel edge angle is chosen ψ = 550. In order to make the locating surface, the longitudinal section of the drill will be projected; the two straight cutting edges have a usual point angle 2κ = 1180 – figure 6.
Fig. 6 Flank modelling
The major flank of the main cutting edge is generated in a helical movement on a Z axis and a
Fig. 3 Separation plane between the drill end and the cutting edge
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helical parameter (p a ), with Helix command, according to Suhov sharpening procedure. The minor flank (tooth back) is executed with the purpose of easing the transport and evacuating the chips. This modelling is realised based on the helical elements guidance leading to eliminating extra material equal to the margin height – Df – fig. 7.
curve starting point, the helix winding axis (the helix radius will result as distance between these two parameters), ditch, curve height (ratio between the helix height and pitch representing the number of curls), orientation direction (hour or trigonometric), start angle – measured from the selected point where the curve starts and the helix bending angle, respectively its orientation inside or outside. The helical curve is used as a guidance element for the plane profile to be generated through Sweep command - fig. 10.
Fig. 7 Modelling the back of the tooth Fig. 10 Helix and Sweep commands
The shaft with a Morse cone, allowing drills to fix the machine axis is obtained by turning its longitudinal section around the drill axis – fig. 8.
Making the helical flute of the drill The curved shape of the cutting edges will influence the way the drill flute is formed. Thus, part I-II is defined as the profile of the top surface in transversal plane, respectively parts II – III and III – IV as elements comprising the flute profile of chips, graphically modulated by two circular curves – fig. 11.
Fig. 8 Modelling the shaft of the drill
4. MODELLING A THREE CURVED CUTTINGEDGES DRILL Modelling the three curved cutting-edges in a Catia graphical medium starts from the same principles as in the case of standard drill. The differentiating elements consist of replacing the chisel edge of the standard drill with the three pyramidal cutting edges of the curved drill, as well as modifying some geometrical parameters apparition of the working angle, decreasing from the tool’s point - κ v = 600, at the tool periphery κp =
Fig. 9 κ p and κ v angles
Fig. 11 Helical flute shape
For the three flutes of the helical drill, the helix is multiplied, respectively the circular curves defining the shape of the flute by using the Circular Pattern command. The transversal section of the drill results from combining the elements of the flute and the exterior diameter of the drill in a single line – fig. 12.
5÷120, instead of unitary working angle κ - for the straight drill – fig. 9.
Fig. 12 Transversal section of the drill
Producing the drill body In order to model the helical drill with curved cutting edges, of D = 20 mm diameter, the starting point is a cylinder of length L = 130 mm. The function allowing the production of the helical curve in space is Helix. It has the following parameters: the
In practice, disk-tools are used to profile the compound helical surfaces. These are defined on a complex generator made by an assembly of simple, plane curves spatially disposed (compound profile). The shape of the characteristic compound curve
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drill with straight lined cutting edge (b) in NX CAD Siemens and Catia software.
corresponding to the geometric elements of the compound generator of the drill channel is obtained by using the Projection command. Generating the 3D model of the primary peripheral surface of the tool is obtained by using the Revolve command and the model of the axial section of the tool – with Intersection command – fig. 13.
Fig. 16 Drill’s representation in NX CAD Siemens software
Fig. 17 Drill’s representation in Catia software
5. CONCLUSIONS
Fig. 13 Generating the helical flute with the disk-tool
In modelling the theoretic curved cutting edge the starting point is assuring the optimal angles (tool normal clearance, tool normal rake, peripheral working angle, the point angle) – see fig. 9. Thus, the laying surface is obtained by intersecting the body drill with the defined surface on the curved theoretical cutting-edge – fig. 14.
Modelling the marks in the present paper is realised in a simple manner, emphasizing the capacity of NX CAD Siemens and Catia software packets of applying the specific commands in order to generate cylinder helical surfaces through developing some products from the helical drills series having two straight cutting edges, respectively three curved cutting edges. It is important to notice the software applications dedicated to modelling some compound surfaces, these defining the first stage in a product life cycle, the modelling one, stages that can be subsequently developed through digital analyses with a finite element (CAE), or simulation CAM. REFERENCES
Fig. 14 Modelling the flank [1] Alexandru, V., ş.a., Geometrie descriptivă – curs şi aplicaţii, Galaţi. 1982. [2] Baicu I., Oancea N., Profilarea sculelor prin modelare solidă, Ed. Tehnica–Info, Chişinău, 2002. [3] N. Baroiu, S. Berbinschi, V. Teodor, The reconstruction of a 3D component through reverse engineering, Buletinul Institutului Politehnic din Iaşi, Tomul LVII (LXI), 2011, pp. 125-132. [4] Berbinschi S., Teodor V., Oancea N., 3D graphical method for profiling tools that generate helical surfaces, The International Journal of Advanced Manufacturing Technology, Vol. 60, 2012, pp. 505–512. [5] Liukshin V. S., Theory of screw surfaces in cutting tool design, Machinostroyenie, Moscow, 1968. [6] Makarov V. M., Model for regulating the shaping precision of helicoid surfaces in the design of machine – tool systems, Russian Engineering Research, 2009. [7] Nankov G., Ivanov V., CAD for profiling of rotational tools for forming of helical surfaces, Proceedings of Internat. Science Conf. AMTECH’97, Gabrovo, Bulgaria, 1997, pp. 39–46. [8] Oancea N., Generarea suprafeţelor prin înfăşurare, The „Dunărea de Jos” Publishing House, Galaţi, Vol. I, II, 2004, ISBN 973–627–106–4. [9] Teodor, V.G., Contribution to elaboration method for profiling tools wich generate by envelloping, Lambert Academic Publishing, 2010, ISBN 978–3–9433–8261–8. [10] Yuwen S., ş.a., Modeling and numerical simulation for the machining of helical surface profiles on cutting tools, International Journal of Advanced Manufacturing Technologies, Vol. 36, 2008, pp. 525 – 534. [11]*** http://www.3ds.com. [12]*** http://www.nxsiemens.com.
Modeling the shaft drill with three cutiing edges shaft is similar to that of the standard drill, by using specific commands: Sketch, Pad, Pocket, Mirror, Groove – fig. 15.
Fig. 15 Modelling the shaft of the drill
In figure 16 and 17, are presented the helical drill with three curved cutting edges (a) and the helical
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