Gear Skiving Process (2)

Journal of Materials Processing Technology 146 (2004) 213–220

A simulation model of gear skiving

A. Antoniadisa,∗, N. Vidakisb, N. Bilalisc

a Department of Natural Resources Engineering, Design & Manufacturing Laboratory,Technological Educational Institute of Crete, Romanou 3, 73133 Chania, Greece

b Department of Mechanical Engineering, Technological Educational Institute of Crete,Stavromenos, 72100 Heraklion, Greece

c Technical University of Crete, CADLAB, Chania, Greece

Received 20 February 2002; received in revised form 8 October 2002; accepted 24 October 2003

Abstract

The key components in demanding transmission chains are doubtlessly premium well designed and properly fabricated gears. Thedesired gear quality is performed, through three manufacturing stages, i.e. the rough cutting, the heat treatment and the finishing process.One of the most adopted methods in gear finishing is a variation of hobbing, the so-called gear skiving or hard hobbing. As every cuttingprocess based on the rolling principle, gear skiving is an exceptional multiparametric and complicated method, which can and must befully optimized. This paper illustrates an involved algorithm that simulates rigorously the skiving process and yields data, such as thedimensions of the non-deformed chips and consequently the cutting force components. This algorithm is supported by a computer codethat offers the aforementioned parameters, with the aid of a user-friendly graphical interface, built modular and object oriented. Bearingin mind that gear skiving is a finishing gear cutting process, the developed software initially performs the simulation of the gear cutting, inorder to determine the cutting boundary conditions. The aim of this research work is to interpret quantitatively cutting phenomena relatedto the course of the cutting force components and is extendable to predict the wear progress of complex and expensive cutting tools. In thisway, the optimization of the cutting process is enabled.© 2003 Elsevier B.V. All rights reserved.

Keywords: Gear skiving; Simulation; Cutting forces; Optimization

1. Introduction

Design engineers, when are working on demanding geardrives, claim for toothed wheels with higher loading ca-pacity, increased wear performance, longer service life andreduced operating noise. These specifications are difficultto be achieved simultaneously, remembering the heat treat-ment distortions and the consequent finishing difficulties.The completion of gears is carried out with various methods,such as traditional grinding, honing, shaving and skiving[1,2]. Each of these methods has advantages and limitations,so that the application of the proper one is strongly casedependent. Gear skiving has gained the recent years consid-erable reputation among gear producers and is nowadays apowerful alternative to traditional grinding. The main rea-sons for this fact is the development of highly evolved and

∗ Corresponding author. Tel.:+30-28210-23070;fax: +30-28210-23072.E-mail address: [email protected] (A. Antoniadis).URL: http://www.ionia.chania.teiher.gr.

automated machine tools, which make the method practicaland economical, whereas it is convenient to achieve theAGMA quality level 10 [3]. Moreover, the induction ofwell-designed cemented carbide tools and the implemen-tation of stock dividing systems in gear hobbing machinetools, make the skiving process attractive and efficient.

The rolling principle kinematics that governs the skiv-ing process sets its simulation a complicated task. How-ever, the affinity between gear skiving and gear hobbingallows the exploitation of the experience gained by exist-ing investigations, related to the last process. Gear hobbingis nowadays completely understood analytically, while datasuch as chip geometry, cutting force components, mechani-cal stresses and wear performance are determined with theaid of highly sophisticated software[4]. In former researchwork, the FRS, FRSDYN and FRSFEM software packageswere developed and are thoroughly presented[5–8]. Thecore of these codes is the geometrical simulation of the cut-ting teeth penetrations into the gear gaps and the determi-nation of the chip dimensions per generating and revolvingpositions. All these codes are built open and modular, so

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214 A. Antoniadis et al. / Journal of Materials Processing Technology 146 (2004) 213–220

Fig. 1. The principle of the cutting process and tool geometry in gear skiving.

that they are extendable to other cutting processes based onthe same cutting principle, i.e. rolling[9,10].

This paper illustrates such an extension for the case ofgear skiving, aprocess that exibits particularities and fea-tures, which make its simulation even more complicated.The main discreteness of skiving is that it is performed inprecut gears, which have been manufactured with variouscutting profiles. It is obvious that a precedent simulation of

Fig. 2. The flow-chart diagram of the developed FRSSKIV code.

the gear rough cut must be carried out. On the other hand,the particular geometry of the teeth profiles of the skivingtool should be treated specially. All these features were im-plemented in the FRSSKIV code, which is presented in thispaper. The program allows the precise determination of thenon-deformed chip dimensions, whereas in a step forward itpredicts the course of the cutting force components, in var-ious coordinate systems. The analytically determined force

A. Antoniadis et al. / Journal of Materials Processing Technology 146 (2004) 213–220 215

components are compared to experimentally derived ones,illustrating a very good agreement.

2. Gear skiving features and simulation strategy

The upper left part ofFig. 1 illustrates a typical gearskiving cutter. The geometry of such cutting tools is verysimilar to hob cutters. The same occurs considering thetool-workpiece system, as it is presented in the upper rightpart of the same figure. The skiving tool is rotating againstto the also rotating precut gear, whereas it is simultaneouslydisplacing along the direction of the axial feed. The spe-cial geometry of the skiving tool cutting teeth is presentedin the bottom left part ofFig. 1. The main differences be-tween skiving and gear hobbing cutting teeth are the nega-tive rake angleγk and the tooth rake offsetδk. The negativerake angle protects the carbide cutter by shocks and instan-taneous overloadings. In the case of hob teeth the rake an-gle equals to zero, whereas the rake plane includes the hobaxis.

As in gear hobbing, owing to its complicated kinemat-ics, the skiving process brings on modeling problems, since

Fig. 3. Analytical determination of the protuberanz and skiving hob profiles.

each gear gap is produced through successive penetrationsof the tool teeth into the workpiece, in the individual gen-erating positions (GP). Considering also the tool rotationduring each hob tooth penetration, a number of revolvingpositions is used to describe the chip cross-sections in thecorresponding generating positions. The bottom right part ofFig. 1 illustrates a confrontation between the cutting toothkinematics of gear hobbing (rake angle= 0◦) and skivingtools (rake angle= −30◦), respectively. The dashed area inthis figure corresponds to the active part of the skiving pro-file. As it is expected the active parts of the skiving toothprofile are onto its flanks.

Fig. 2 illustrates the algorithmic process, which is ap-plied to determine the produced chip geometry and thecutting force components. The required data refer to thetool geometry, the workpiece specifications and the cuttingconditions. These data are identical to the ones of gearhobbing, in addition to the teeth negative rake angleγk andoffsetδk. All these data may be inserted interactively usingthe graphical user interface (GUI) or selected by the im-plemented database. Besides these data, remembering thatskiving is a finishing process, the geometry of a precut geargap is also required. The geometry of such a gap depends


on the geometry of the rough cutting teeth profiles and isalso determined with the aid of the FRSSKIV code.

The principle of the algorithm is based on the mathe-matical description of the tool penetrations into the work-piece. The developed code allows the determination of thenon-deformed chip cross-sections on the development of thecutting edge, as it is illustrated in the bottom part ofFig. 2for a typical manufacturing case. The chip cross-sectionsare presented in successive tool revolving positions for ev-ery generating position, with a desired accuracy. In the mid-dle part of this figure, the chip cross-sections are presentedon the development of the cutting edge. It is obvious andexpected that only the sides of the cutting teeth contributeto the material removal from the precut gear gaps. Thechip geometry, besides its contribution to the descriptionof the wear development on the cutting edge, is also usedto automatically calculate the anticipated cutting forces andtool stresses in every generating position. Such parametersare very significant, in order to establish stress strain andfatigue calculations for the cutting material, especially incases of coated HSS or cemented carbide hobbing tools[11].

Fig. 3illustrates the method that was adopted to determinethe cutting profiles of the rough and finishing cutting teeth,respectively. For the first case, the geometry of the hard cut-ting profiles is designated with the aid of formulation thatmay be found in the corresponding literature[12] (see theupper left part ofFig. 3). There are various profiles that maybe applied and the ensemble of them has been implementedin the FRSSKIV software. Furthermore, the geometry ofthe skiving teeth profile is determined analytically, using astrategy also presented in the same figure. The first step ofthis task is to produce analytically the screw path that corre-sponds to the examined module and to the other geometricaltool features. This screw path is univocally defined and itsformulation corresponds to the normal helix equations. Theskiving tooth profile is then determined by intersecting the

Fig. 4. Determination of undeformed chip cross-sections in gear pre-cutting.

screw path by the shaded plane, which corresponds to therake angleγk and to offset distanceδk.

The rough cut profile simulates the first manufacturingstage of the initially cylindrical workpiece and leaves a thinmaterial volume, 0.2 mm thick in the case of the same figure,to be removed by the skiving profile. The bottom part ofFig. 3 illustrates the precut profile of the tool gap and thefinal one, which is produced by the skiving finishing process.Moreover, the initial and the final profiles of the tool gapare compared in a single diagram, whereas a magnificationof the material to be removed by the skiving process is alsoinserted.

3. Determination of the chip dimensions with theaid of hard cut profiles

The simulation principle of the gear rough cut is identicalto the one that is utilized by the FRS modules in the case ofhobbing, which is almost exclusively performed using pro-files according to the DIN 3792 norm[13]. Various roughcut profiles may be selected from the FRSSKIV database,whereas in the case ofFig. 4, results of normal protuber-anz profile are presented. The cutting process is divided ingenerating positions, which correspond to the successivecutting teeth of the protuberanz tool. The penetration ofeach of these generating positions within a gear is furtherdivided in successive revolving position, whose number isa user-selectable parameter.

The left part ofFig. 4 illustrates the produced chip forthe generating position 0 of the specific cutting case. Thisgenerating position has been divided in 15 revolving posi-tions and the non-deformed chip is presented over the de-velopment of the protuberanz profile. As it is expected, theleading flank, the trailing flank and the head of the roughcut profile together, contribute to the material removable, incontrast to the skiving profile that cuts only at its flanks. The


Fig. 5. Gear hobbing and skiving kinematics and consequent coordinate systems of the chain—tool, machine tool and workpiece.

right part of the same figure, illustrates the arrangement of15 successive revolving positions, which divide the generat-ing position inserted in the left part ofFig. 4, relatively to theworkpiece. From these revolving positions of the examinedcutting tooth, it is evident that only 11 are active (5–15th),i.e. they contribute to the material removal and produce chipcross-sections. This illustration has been produced by out-put data of the FRSSKIV code and exhibit the progressiveformation of one gear gap.

4. Coordinate systems

In order to be able to simulate sufficiently the tool pen-etrations into the workpiece, for both rough cut and finish-ing processes, a complicated sequence of plane intersections

Fig. 6. Discretization of the momentary gear gap of hobbing and calculation of skiving tool rake sections with the produced gear gap.

has to be performed. For this purpose, the tool–machine–workpiece chain is approached by means of specific coordi-nate systems. Any data swapping between these coordinatessystems is carried out with the aid of transformation matri-ces. In former investigations (FRS, FRSDYN and FREFEMmodules) six discrete coordinate systems were determinedand are presented in the left part ofFig. 5. In the casesof protuberanz or other rough cut profiles, where the rakeangle equals to zero, the same coordinate systems can beadopted.

On the other hand, the negative rake angleγk requiresan additional seventh system, in order to be handled. Thiscoordinate system is presented in the right part ofFig. 5andis situated on the skiving rake profile. The graph insertedin the same figure part explains how the seventh coordinatesystem follows the path of the cutting profile.


Fig. 7. Chip cross-sections in gear skiving.

5. Determination of chip formation in gear skiving

The core task, when simulating processes based on therolling principle, is the determination of the tool–workpieceintersections. This is the pure geometrical assignment andnormally the consequent mission is to turn the output datainto chip terms. The purpose of this transformation is topredict cutting parameters, such as the cutting force com-ponents and the tool wear progress, which are magnitudesdirectly correlated to the non-deformed chip dimensions.

The method for this conversion is presented inFig. 6and is based on the gear hobbing simulation introduced inthe FRS code. The momentary gear gap at hobbing, i.e.the one that is produced by one generating position, is de-termined by analyzing the intersection planes of each re-volving position. These discrete intersections compose athree-dimensional mesh, which is the final form of the geargap that is produced by a gear hobbing generating posi-tion. To compose this three-dimensional mesh of a geargap, each of the polylines describing the gap section at thecorresponding cutting levels, is divided to a certain num-ber of nodes. In a step forward the simulation of skivinguses this gear hobbing gap, in order to calculate the toolrake sections with the gear gap, also considering the spe-cial geometry of the skiving tooth profile. This approach istotally reasonable, considering that both skiving and hob-bing tools execute identical kinematics and follow the samepath. The final step is the computational determination ofthe chip cross-sections, which are laid on the aforemen-tioned sections. This precedure is carried out with such asequence, remembering that the rake angle in gear skivingteeth is too high to suppose perpendicular sections to thethree-dimensional gear gaps, as in the case of gear hob-bing. The intersecting reference plane density increases the

numerical accuracy but not infinitely. Normally, 30–50 re-volving positions was found to be the appropriate range forsufficient accuracy.

The aforementioned method is presented inFig. 7for onespecific manufacturing case. This cutting event was found torequire 31 successive positions (−15 to 15 including 0), inorder to be competed. The diagram of the bottom left part ofthis figure illustrates the maximum produced chip thicknessby the leading and the trailing flanks, respectively. The upperleft part of the same figure presents the chip cross-sections ofgenerating position zero, over the development of the skivingprofile. The tool penetration is produced using 15 referenceplanes, according to the previously described algorithm. Onthe other hand, the diagrams inserted in the right part ofFig. 7 illustrate the 15 corresponding reference planes, afterthe end of the cutting proccess. Diagram 15 exhibits the finalformation of the gear gap. With the aid of this algorithm,the chip geometry is precisely determined and the developedprogram is able to determine the cutting force components.

6. Cutting force components determination andcomparison between analytical and experimental results

The formulation of the cutting force components, giventhe dimensions of the non-deformed chips, is well estab-lished and thoroughly described in the corresponding litera-ture. The applied method is similar to the one that has beenpresented in former investigations, in the case of millingand gear hobbing[4–8]. However, the analytical predictionof the cutting force components in gear skiving was notpossible, since the chip formation mechanisms were notspecified up to the present research work. Despite the lackof analytical results related to the skiving cutting force


Fig. 8. Calculated and measured cutting force components at the tooth rake face coordinate system 7.

components, considerable work has been performed mainlyin the field of experimental determination for such data[14,15]. Hereby, the experimentally derived force data arehere compared to the analytical ones, for identical cuttingconditions and tool–workpiece systems.

The cutting force components are calculated automati-cally by the FRSSKIV software, through the integration ofelementary force components that each particular chip crosssection produces. The coefficients of the Kienzle–Victorequations for the specific tool and workpiece materials wereanalytically experimentally determined.Fig. 8illustrates an-alytical and experimental results for a certain cutting case.More specifically, the cutting force componentsFX, FY andFZ are presented for one cutting tooth, versus the rake face

Fig. 9. Calculated and measured cutting force components at the machine tool coordinate system 3.

revolving position. The dashed regions of the analytical re-sults correspond to the same revolving positions of the ex-perimental ones. The analytical cutting force componentsalong theX- andZ-axis are in good agreement with the cor-responding experimental ones, whereas the correspondinganalytical ones along they-direction are considerably lower.This diversion is attributed to chip thickness modificationsfor various revolving positions, which are not able to be in-cluded in the method developed.

Moreover,Fig. 9 illustrates analytical and experimentalcutting force components, which have been transformedto the machine tool coordinate system 3. Such data maybe exploited by skiving machine tools designers, in or-der to optimize their products. The diversion between the


Fig. 10. Cutting force components at individual generating positions, occurring in gear skiving.

analytical force components along they-axis and the corre-sponding experimental ones may be observed, also in thiscase. Finally,Fig. 10presents computational and measuredcutting force components versus the successive generatingpositions. The divergence of the force component alongthe y-axis is still present, but it is remarkable that the ana-lytically determined of the distribution of this axis closelyfollows the corresponding experimentally one.

7. Conclusions

Gear skiving is nowadays an attractive alternative in gearfinishing process. However, the analytical determination ofthe chip formation mechanisms and the consequent defi-nition of the course of the cutting force components werenot available. The research work presented in this paper,extends forward investigations related to the simulationof gear manufacturing and yields the aforementioned dataquantitatively, with the aid of software tools. The highlightsof the present investigations are the possibility to simulatethe rough cut of gears with various cutting profiles, theconsequent analytical determination of the finishing mate-rial removal and the final prediction of the cutting forcescourse. Further work in this field aims to step forwardthe optimization of the skiving process, implemented alsothe wear progress prediction of expensive tools, which arerequired in this gear finishing method.

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Gear Skiving Process (2)