Prod. Eng. Res. Devel. (2011) 5:651–657 DOI 10.1007/s11740-011-0343-9

PRODUCTION PROCESS

Prognosis of the local tool wear in gear finish hobbing Fritz Klocke • Christof Gorgels • Gerd-Thomas Weber Rolf Schalaster

•

Received: 11 April 2011 / Accepted: 26 August 2011 / Published online: 21 September 2011 Ó German Academic Society for Production Engineering (WGP) 2011

Abstract Gear finish hobbing is a method for soft finishing of external cylindrical power transmission gears. The application of this process is required when the process chain of gear production is to be set up completely free of coolant. Since this finishing technology is relatively new, there is some practical experience, but no fundamental knowledge regarding economical process design. One challenge in process design is that unbalanced tool wear typically leads to geometrical deviations of the machined gear profile. The aim of the investigations described in this paper is to develop a wear model which is capable to predict the local tool wear of gear finish hobbing tools. This model is based on analogy cutting trials and geometrical analyses of the chip geometries in gear finish hobbing. The results of the model are validated by flycutting trials with different local loads on the tool. The validation shows that an optimization of the local tool wear development can be achieved by means of the prediction model. Therefore, an optimization of the technological process parameters can be carried out based on this model to reach an efficient process design. Keywords Production process  Gear finish hobbing  Tool wear prediction

F. Klocke  C. Gorgels  G.-T. Weber Laboratory for Machine Tools and Production Engineering (WZL), Steinbachstraße 19, 52074 Aachen, Germany R. Schalaster (&) Klingelnberg GmbH, Peterstraße 45, 42499 Hu¨ckeswagen, Germany e-mail: [email protected]

1 Introduction and challenge To reach the necessary strength and geometrical accuracy, gears in power transmissions generally undergo a case hardening procedure as well as a finishing process. In case of medium accuracy requirements, e.g. for automotive gears, the finishing process can be applied in the soft condition, which is more cost-efficient than hard finishing. Today, machining with a geometrically defined cutting edge is common for soft finishing of gears. This includes gear shaving and the growing market of gear finish hobbing. Compared to gear shaving, finish hobbing offers ecological as well as economical advantages. Hobbing is the only process that enables a coolant free gear finishing operation and—by this—designing a coolant free process chain of gear manufacturing. In rough and finish machining of running gears by hobbing a separate roughing and finishing pass is worthwhile. During roughing a large share of material has to be machined, which leads to high cutting forces and the corresponding deviations. In this operation only relatively low cutting speeds are applied. Concerning the finishing process, restrictions exist regarding surface quality, feed marks and generated cut deviations, since the quality requirements of the part are in a range of only a few microns. Due to the fact that only a small stock is machined, cutting speeds can be increased significantly. Consequently a high speed cutting process with the advantages of lower cutting forces and a superior surface finish is reached. For gear finish hobbing of power transmissions mostly complexly shaped cemented carbide tools are applied. Since it is a relatively new application there is no fundamental scientific knowledge about a technologically and economically optimized process design. One critical point

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of applying this process is the profile accuracy since profile deviations of the machined gear have been identified with increasing tool wear.

2 Objective and approach For the effective application of gear finish hobbing the advantages offered by the technology have to be fully developed. Precise knowledge of the machining process and the technological influences is therefore required. The objective of the investigations described in this paper is to develop a wear model which is able to predict the local tool wear in gear finish hobbing. Based on this model a theoretical process optimization can be accomplished without carrying out machining trials for the concrete process application. The model will be developed for a sample tool system consisting of a cemented carbide cutting material with an aluminum chrome nitride ((Al,Cr)N) coating. Machining a typical gear material 16MnCr5N will be considered. The wear model is planned to be an empiric model based on cutting trials. Nevertheless, the model shall be valid for different process designs and gear geometries. The approach to reach this aim consists of four steps. At first, the undeformed chip geometries occurring in gear finish hobbing are analyzed and geometrically specified. In the second step, similar chip geometries in the same range of length and thickness are created in an appropriate analogy trial. Trials are carried out covering the relevant range of cutting speed of vc = 750 m/min to 2,000 m/min. The chip geometry for each trial is kept constant in order to be able to analyze the tool life as well as the progress of the tool wear caused by creating a defined chip geometry. The third step is to mathematically describe the determined wear progress based on chip geometry parameters and the cutting speed. Finally, in the last step, a model has to be derived that enables the local wear prediction for gear finish hobbing processes. This prediction shall be applicable for all finish hobbing processes in the analyzed range of geometrical parameters and cutting speed. To verify the wear model a wear prediction is carried out for a concrete gear finish hobbing process sample. This prediction as well as the opportunity of a process optimization is verified by fly-cutter hobbing trials.

3 Wear model development To analyze the chip geometries and the local load on the cutting edge in geometrically complex gear cutting processes, geometrical simulations are used [1–5]. The software SPARTA developed by Winter [2] is based on

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penetration calculation and enables to determine undeformed chip geometries in gear hobbing. This software has been applied for the analysis of sample process designs of gear finish hobbing in order to determine the range of the geometrical chip forming characteristics for this process. Since only the flanks of the gear have to be finished with very high geometrical accuracy (deviations in the range of a few microns) the tooth root does not have to be machined in the finishing pass. For the examinations the utilization of a finishing tool geometry with a reduced addendum has been assumed. Hence the wear critical tip of the tool is not engaged and only the flanks of the teeth are cutting. 3.1 Characterization of undeformed chip geometries Considering a wide range of process designs has shown, that the undeformed chip geometries look alike and can be basically characterized by their width, length and thickness (Fig. 1). Since the chip width is not expected to influence the local wear behaviour on a single position of the cutting edge the parameters maximum chip thickness and maximum cutting length are considered in the following to describe the geometry. Differences in the position of the highest point of the undeformed chip geometry along the cutting length resulting from the machining direction are not considered in the following analyses. The examinations have shown, that the maximum undeformed chip thickness in typical gear finish hobbing applications is in the range of hcu,max = 8–25 lm. At the same time, maximum cutting lengths occur between lcu,max = 2 and 8 mm. All undeformed chip geometries have in common that the minimum undeformed chip thickness for every point of the cutting edge is always close to zero. A critical point in the gear finish hobbing process is, that the functional surface is always generated by an area of the cutting edge where the minimum undeformed chip thickness is about zero. Other high speed cutting applications showed, that there is a minimum chip thickness required for chip creation [6]. Below this minimum chip thickness, plastic displacement of material beneath the cutting edge occurs. Caused by this, high temperatures, excessive abrasive wear and an increased surface roughness have been found in different applications [7]. The value of the minimum required chip thickness depends on the radius of the cutting edge [7–9] which therefore has to be as sharp as possible for the machining process. In contrast, coating technology requires a certain edge radius to prevent chipping. A negative effect of very low undeformed chip thicknesses would lead to excessive tool wear also in analogy trials and would therefore be included in the wear model.

Prod. Eng. Res. Devel. (2011) 5:651–657 Climb Cutting

-5 generating position -9 -6

position on cutting edge [mm]

position on cutting edge [mm]

Conventional Cutting vc

hcu,max = 17 µm

-7 -8 -9

4.7 mm -4

0

4

-4 generating position -9 -5 -6 -7

3.4 mm -8

8

hob rotation angle [°]

3.2 Examination of tool wear behaviour by analogy cutting trials In gear finish hobbing operations with a shifted tool different chip geometries are created by the same position of the cutting edge. Consequently it is not possible to deduce from the final tool wear to the wear causation of single chip geometries. Therefore, an analogy process is applied for a fundamental analysis of wear causation in which constant chips are created by a cutting insert. The selected analogy process is a fly-cutter turn-milling process. It has successfully been used as an analogy trial for skive hobbing before [10]. The kinematics and dynamics of this analogy process are similar to gear finish hobbing. This leads to similar undeformed chip geometries that can be adjusted by the cutting parameters. The derivation of the analogy process from gear finish hobbing is displayed in Fig. 2. Instead of a gear flank the outer diameter of a cylinder with a radius rWP that is similar to the curvature radius qt at the pitch circle of the gear is machined. The rotation of the workpiece nWP emulates the generating motion in gear hobbing. The angular position of the cutting insert aAT can be set up similar to the pressure angle of the hob an. The flank stock can be set by the radial infeed a. To reach an undeformed chip geometry with a defined maximum thickness and length, theoretical examinations

Gear Finish Hobbing

vc

hcu,max = 17 µm

-8

Legend hcu [µm]

Fig. 1 Sample undeformed chip geometries in gear finish hobbing simulated by SPARTA

653

-4

0

20 16 12 8 4 0

hob rotation angle [°]

have been carried out as well as geometrical analyses by means of 3D CAD Software. To verify the theoretical examinations, sample chips from the analogy process have been analyzed by scanning electron microscopy and compared to the theoretical undeformed chip geometry determined by means of the CAD Software. Figure 3 shows a very good qualitative correlation between the theoretical and practical result. Due to the compression of the chip during cutting the only value that can be quantitatively compared between the undeformed chip geometry and the chip is the width. The maximum width of the chip of bcu,max = 1.5 mm is identical with the maximum width of the theoretical undeformed chip geometry. The frayed left flank of the chip displayed in the left magnification of the surface refers to the very thin undeformed chip thickness in this area. The periodic structure displayed in the right magnification refers to the surface structure of the workpiece given by the turning operation prior to the trial. To cover the range of undeformed chip geometries in gear finish hobbing, chips have been cut with an undeformed thickness of hcu,max = 10, 20 and 40 lm and a cutting length of lcu,max = 2, 4 and 8 mm. The resulting wear development and appearance have been examined at different cutting speeds in the range of vc = 750–2,000 m/min. The trials have shown that abrasion is always the major influence on the resulting flank wear land. Therefore, a mathematical

Fly-Cutter Turn-Milling αAT ρt

da d db

analogy workpiece

αn

r WP

= ρt

cutting insert

nWP

dWZ hobbing tool

a analogy tool

dAT nAT

Fig. 2 Derivation of the analogy process

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Prod. Eng. Res. Devel. (2011) 5:651–657 Tool cutting material HW K10F coating (Al,Cr)N rake angle γ 0 = 0° clearance angleα0 = 3°

Chips (Start of Tool Life) upper chip side

Cutting Parameters cutting speed vc = 1,500 m/min chip thickn. hcu,max = 20 µm cut. length lcu,max = 4,0 mm

lower chip side

1.5 mm

0.5 mm

0.5 mm

Undeformed Chip Geometry mm

0.1 mm

cut

ing mo tion 4.0 mm

1.5

turned surface 0.1 mm

Fig. 3 Comparison of theoretical undeformed chip geometry and chips of the analogy trial

description of the tool wear depending on tool life and cutting parameters seems to be achievable. 3.3 Setting up the wear model Based on the analogy trials described above a mathematical description of the wear development has been set up. For this purpose an expression for tool life had to be found, that is applicable for the analogy trial as well as for gear hobbing. The total cutting length lcu,total was selected. For the analogy trials it is calculated as the number of cuts times the cutting length of a single cut. For the mathematical description of the total cutting length mathematical functions that describe the trial results with physically plausible boundary conditions have been examined by means of regression analysis. One boundary condition is a declining assimilation of the total cutting length to zero with increasing cutting speed. Another boundary condition is a declining increase of the total cutting length with increasing length of the single cut which serves the theoretical approximation of a continuous cut. The characteristic of the tool life can be modelled with a good correlation by the formula:   lcu;max c2 c3 vc lcu;total;0 ¼ c1  e ð1Þ ½m The index ‘0’ indicates the predicted value of the tool life. The symbols ci indicate constants. The formula regards the cutting speed vc and the maximum cutting length lcu,max as the major influences on the tool life. The effect of the maximum chip thickness is not significant and much lower than the influence of lcu,max. Negative influences on the tool life, such as excessive tool wear, due to cutting very thin chips have not been identified.

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Therefore, a required minimum chip thickness has not been found within the varied range of parameters. Figure 4 shows a graphic display of the tool life model as well as the correlation with the results of the analogy trials. Since there is variation in experimental results, the resulting coefficient of determination R2 = 0.93 shows a good fit of the model. Besides the prediction of tool life, the tool wear at a certain point in time is required for a prediction of the local tool wear along the cutting edge. Therefore, the wear development also had to be modelled. This means modelling the development of the wear indicator maximum flank wear land (VBmax) over the tool life. All measurements of the flank wear width during tool life in the analogy trial were analyzed to reach a suitable mathematical approximation of the wear development. Since the reached tool lives lcu,total are different, the variable lnorm is introduced as a normalized tool life variable with a range between 0 for the beginning of tool life and 1 for the end of tool life. The end of tool life is defined by exceeding the wear criterion of VBmax = 0.15 mm for the analogy trials. Similar to lnorm, a normalized flank wear land VBmax,norm is introduced with VBmax,norm = 1 as the tool life criterion corresponding to a maximum flank wear land of VBmax = 0.15 mm. This means, that there is a boundary condition for all trial results with VBmax,norm(lnorm = 1) = 1. The status of the cutting edge at lnorm = 0 is not clearly defined due to possible imperfections of the new cutting edge. Therefore no boundary condition is defined for this status. The cutting speed was identified as the only significant influence on the flank wear land besides the normalized tool life. A regression analysis for VBmax,norm with a

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Fig. 4 Tool life model based on analogy trials

Graphic Display (Model)

Correlation with Trials 1,200

900

lcu,total [m]

Lcu,total,0 [m]

1.200 900 600

300

8

300

m]

4 0 500

1,000

1,500

2 2,000

ax

600

R2 = 0.93

[m

0

l cu,m

0

300

cubical approach for lnorm and the square root of vc including interactions shows a good correlation of the trial results with the formula: pffiffiffiffiffi pffiffiffiffiffi VBmax;norm;o ¼c1 þ c2  vc þ c3  vc  lnorm þ c4  lnorm þ c5  l2norm þ c6  l3norm

ð2Þ

Again the index ‘0’ indicates the prediction by model and the symbols ci represent constant values. Figure 5 displays the modelled, normalized wear development for different cutting speeds. The correlation of the model results with the cutting trials that show a correlation of R2 = 0.93. The combination of the tool life model and the wear development model can be used for a tool life prediction of a gear finish hobbing tool as long as a geometrical process analysis e.g. by the software SPARTA has been carried out. At first, the possible tool life for every point of the cutting edge has to be determined by the tool life model. The overall tool life of the cutting tool is determined by the point of the cutting edge that reaches the tool life criterion first. The ratio of the overall tool life and the tool life of any point of the cutting edge is the tool life lnorm for the concrete point of the cutting edge at the end of the overall tool life. By this, the normalized tool life can be determined along the cutting edge. The normalized wear distribution at the end of tool life can be calculated by applying the model of the wear development for every point of the cutting edge. This enables predicting the wear distribution of the tool at the end of tool life as well as for any other tool life. Fig. 5 Model of normalized wear development based on analogy trials

1,200

To verify the model fly-cutting trials have been applied. The advantage of this trial compared to machining with a real hob is, that a similar wear distribution can be reached with a much lower number of workpieces. Additionally the single fly-cutting tooth can easily be analyzed e.g. by scanning electron microscopy due to the good accessibility of the cutting edge. The setup of the verification trials is shown in Fig. 6. A roughing hob and the fly-cutter for finishing are clamped in a hobbing machine on the same arbor similar to a so-called tandem hob with two separate areas for roughing and finishing. By this setup, the relative position of both tools is known exactly and not changed during the trial. This is important to machine the same stock of the gear with both flanks of the fly-cutter. During the trial, the workpieces are first rough machined by the hob. Afterwards they are finished by the fly-cutter. The machine kinematics for fly-cutting are designed in order to simulate the cutting process with a real hob machining almost identical chip geometries. The flank stock for gear finish hobbing typically is equidistant along the tooth flank. For a sample process design at a cutting speed of vc = 1,000 m/min the left of Fig. 7 shows the prognosis of the flank wear width by the model and the corresponding wear image of the tool. The magnification of the wear image is chosen different for the direction of the cutting edge and the perpendicular direction in order to examine the wear distribution along the

Normalized Wear Development (Model)

Correlation with Trials 1

0.75 v = 750 m/min c 1,000 m/min 0.5

VBmax,norm

VBmax,norm,0

900

4 Verification of the model

1

1,500 m/min 2,000 m/min

0.25 0

600

lcu,total,0 [m]

vc [m/min]

0

0.25

0.5

lnorm

0.75

1

0.75 0.5 0.25 0

R2 = = 0.93 0.93 0

0.25

0.5

0.75

1

VBmax,norm,0

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656 Fig. 6 Experimental setup for fly-cutting trials in gear finish hobbing

Prod. Eng. Res. Devel. (2011) 5:651–657 Machine: Liebherr LC120 spindle power P = 31 kW spindle speed ns = 10,000 min-1

Experimental Setup z x

Roughing: diameter da0 = 80 mm tooth root clearance

A

fly-cutter

vshift

v

Fly-Cutter Finish Gear Hobbing

roughing hob

vc

machining trial

roughing

Equidistant Finshing Stock TF

trailing flank TF

TF

leading flank LF

trailing flank TF

0.2 mm

0.2 mm

0.2 mm

0.5 1.0 0 prognosis VBnorm,0

cutting edge easily. The wear images show an increasing flank wear land from the tooth tip (lower end) to the tooth root (upper end) which corresponds with the prognoses displayed besides the wear images. This means, that the aim of predicting the wear distribution has been reached by the model based on analogy trials. The remaining question is if the load on the tool—and by this the wear distribution along the cutting edge—can be modified in order to reach a homogeneous wear distribution. Iterative theoretical analyses were carried out to modify the profile of the roughing tool in a way that a uniform wear prognosis is reached. By a symmetric pressure angle modification and a profile crowning of the roughing tool, an equidistant wear prognosis has been reached at least for the trailing flank. The results of a cutting trial carried out with the optimized finishing stock is displayed at the right of Fig. 7. The trailing flank shows a homogenous wear distribution that correlates with the prediction. However, the wear image of the leading flank

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1 mm

1 mm

1 mm

etched

leading flank LF

LF

1.0 0.5 0 prognosis VBnorm,0

0.5 1.0 0 prognosis VBnorm,0

etched

LF

Optimized Finishing Stock

1 mm

Fig. 7 Comparison of wear prediction and experimental tool wear on fly-cutters

0.2 mm

1.0 0.5 0 prognosis VBnorm,0

also shows a general correlation with the prediction but inhomogeneous wear that may be caused by a failure in the tool preparation.

5 Conclusion Today, for finish hobbing of transmission gears mostly coated cemented carbide tools are applied. The local load leads to unbalanced tool wear along the flanks of the tool that causes profile deviations on the gear. Within the investigations described in the present paper a wear model has been built up based on analogy trials in order to predict the local tool wear in gear finish hobbing. The predicted wear distribution of the model has been verified by flycutter hobbing trials. Additionally, an optimization of the finishing stock based on the wear model has been presented that is able to cause a homogeneous tool wear and therefore reduce typical profile errors in gear finish hobbing. The

Prod. Eng. Res. Devel. (2011) 5:651–657

feasibility of local wear prediction without carrying out cutting trials for the concrete application thereby is proven. Since the model is not only capable to predict the wear distribution but also the reached tool life it can also be used for a technological and economical process optimization under given boundary conditions. For a further process optimization also different cutting materials such as cermet and PCBN should be considered.

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