Grinding at very Low Speeds

E. Brinksmeier (2), C. Schneider University of Bremen, Germany

Received on January 8,1997

Abstract

In recent years a new method for hard gear finishing that produces a favourable surface texture and possibly allows gear correction was introduced. Material removal by the shave-grinding or gear honing process is the result of a rolling and sliding movement between the geared workpiece surface and the abrasive grits bonded in a resin, vitrified or metal tool matrix, shaped similar to an internal gear wheel. A laboratory set-up based on a grinding process with speeds between 0.3 mls and 3 mls was designed in order to investigate fundamental process behaviour and to compare the knowledge gained with conventional grinding processes. Moreover recommendations for improvement of the shave-grinding process could be derived.

Keywords: Gear finishing, Grinding process, Modelling

Introduction

Gear finishing operations are used to improve the accuracy and/or uniformity of the various gear tooth elements. The functional requirements of gears determine the degree of accuracy required. Greater accuracy is necessary if the gears are required to operate quietly and at high speeds andlor to transmit heavy loads. Methods used to finish gears include rotary gear shaving and roll-finishing that are done in the green or soft state prior to heat treating. Hard skive hobbing, hard shaving, profile grinding, involute- generation grinding, shave-grinding and lapping are other methods applied after hardening. Fiaure 1 shows a shave-grinding process with meshing tool and workpiece.

Fiaure 1 ; Shave-grinding with internal geared tool (source: PFAUTER)

Shave-grinding is a particularly effective method of removing nicks and burrs from the active profiles of the teeth. Combined with i ts ability to improve surface

finish and make minor form corrections the process is rapidly being accepted as an operation through which many gears are processed. It is also free from risk of thermal damage of the subsurface [ 11.

Nomenclature

The nomenclature of this process is not yet standardised and therefore not uniform in literature. Shave-grinding is also called "gear honing" or "power honing". The tool type determines that shave-grinding is an abrasive process that has nothing to do with lapping. The question is whether it should be called honing or grinding. Honing in general is characterised by t w o components of cutting movement where at least one component has an oscillating character 121. Result of the total cutting movement is the typical "honing pattern" of crossing traces of active grains on the workpiece surface. Such a pattern cannot be detected on shave-ground workpieces because the amount of oscillative speed is by much lower than any of the other cutting speed components. The other reason why the mentioned way of gear finishing should be regarded as a grinding process is that the material removal is the result of a periodic contact between active grains and workpiece which is characteristic for grinding [21, 131, 141. As the process kinematics has many similarities wi th gear shaving [ 5 ] the authors and several companies encourage the use of the word "shave- grinding".

Shave-grinding o f gears

Shave-grinding processes are grinding operations with gear shaped tools meshing with the workpiece in the way of a crossed helical gear pair IS]. The mostly internal geared tools consists of abrasive grits of corundum, CBN or diamond and a bakelite, vitrified or metal matrix similar to single or multiple layer grinding wheel specifications. The material removal is a result of the kinematically imposed relative movement (sliding)

Annals of the ClRP Vol. 46/1/1997 223

between abrasive grits of the tool and workpiece. The total sliding speed vg results of the relative motion in direction of the involute vgev through the rolling action between the gears and the relative motion in direction of the helix vgs due to different helix angles of tool and workpiece. The cutting angle a describes the geometrical deviation of the total sliding speed vg from the direction of the helix (speed component vgs). The relative movement is responsible for the typical pattern of scratches on shave-ground workpiece as shown in fiaure 2.

Fiaure 7: Surface texture of a shave-ground gear tooth

Shave-grinding is a highly complex abrasive process which makes fundamental investigations of material removal nearly impossible due to the following reasons:

Relevant process parameters (e.g. sliding speed vg and the circle of curvature of workpiece and tool) are changing periodically depending on the rotation angle.

There are constraints between parameters. Because of meshing between tool and workpiece, an increase of the number of revolutions of the driving tool for example is combined with an equivalent increase in the number of revolutions of the driven workpiece.

Parameters for process evaluation are difficult to measure. Grinding forces on the tool for example change in direction. Moreover due to the contact on both sides of the wedge-shaped tool tooth, the components of forces in direction of tooth thickness in opposite points of the flanks sum up to zero.

Design of an analogous process

As shave-grinding with internal geared tools is a rather young technology, first applied in the 80s, there is a high potential for further improvement of process and tool. To overcome the mentioned disadvantages of the complex shave-grinding a grinding process fanalogous process) wi th as many conformities as possible compared to the "real" shave-grinding process on one hand and with as many conformities as possible compared to already investigated abrasive processes on the other hand was designed. The goal is the optimisation of shave-grinding operations and tools

based on the knowledge of a selected process which is easier to understand.

The conformities of the developed analogous process (illustrated in lfiaure 3) with the real shave-grinding operation concern:

grinding as basic material removal mechanism,

uniform specification of tool and cutting fluid.

Creation of an equivalent speed situation (fiaure 3) represented by speed components in direction of the main circles of curvature (the speed in tangential direction vCt is equivalent to vgev and the speed in axial direction vca is equivalent to v 1. The speed components form the resulting cutting speed vc respectively the sliding speed' vg which include an angle a (cutting angle) to the direction of the big main circle of curvature (axial direction respectively direction of helix).

Range of machining parameters: cutting speed vc =0.3 ... 3 mls, working engagement aea0.05 pm, cutting angle a = -6OO.. .60°, amount of workpiece speed vft and tool speed vs in the same range as the cutting speed vc.

As workpiece material the specially heat treated, through hardening 90 MnCrV 8 was used. It is relative to hardness, microstructure and chemical composition comparable to the case hardened surface of the gear steel 16 MnCr 5 and has the advantage of uniform material properties.

Furthermore the analogous process shows conformities t o conventional grinding processes concerning following items:

kinematic near t o orthogonal process with constant input parameters and a conventional fixed-feed infeed strategy,

process description by the well known machining parameters according to DIN and ISO.

9s

Shave-grinding Analogous process

tooth workpiece grinding wheel

Fiaure 3: Design of an analogous grinding process

Kinematic of analogous process

The chosen process kinematic is defined as axial grinding (external face plunge grinding) with an offset Ay between workpiece and tool axis. The analogous grinding process is near to an orthogonal process since machining parameters such as cutting speed vc are only slightly changing with workpiece co-ordinate zw. For further investigations chip formation progress is assumed to be symmetrically along the workpiece width bw and all parameters are calculated in the

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principle point D. The total offset depends on the distance between pivot of the tool Ms and the principle point D. It is quantified by the offset angle 0.

Vca Fiaure 4: Kinematics of analogous process

The cutting speed results from the relative movement between the peripheral speed of wheel vs and from the workpiece speed vft and as shown in fiaure 4. It can be calculated to:

( 2 )

Equation (2) strongly differs from calculation of cutting speed for conventional grinding processes, where the cutting speed is the arithmetical sum or difference of the speeds and morefover feed speed vft is often neglected.

The experiments were performed with a sense of rotation of the spindles as show in fiaure 4. Positive and negative angles a could be reached. An angle u = 9 0 ° means down grinding. The cutting angle a describes the direction of the cutting speed vc and is the angle between the scratches of active grains on the workpiece and the axial direction of the workpiece. For a = [-90 O... 90°1 it can be calculated to:

v c = Vf t+VS-2 .Vf t .VS.COS0 2 2

vs . c o s o - V f t s ina =

VC (3)

Resulting process forces were measured in direction of the machine axis. The comparable forces F', and F't were calculated w i th the help of the following equations:

(5 )

Dependence o f process parameters on time

Dressing of the wheel leads to a smooth surface with a low number of cutting edges as shown in the top of fiaure 5. The high density of the wheel specification with a very low percentage of pore volume of about 10% is also obvious. A t t = O s forces do not reach the maximum Fnmax immediately, because a part of the

infeed is transformed into machine tool deflection. The initial straight-line slope is rather flat due to the relatively high time constant T (T= 150 ... 200 sl for the analogous process. Measurement of conventional processes have shown that T is 20 ... 30 s for internal grinding and about 1 ... 2 s for external grinding [7]. Due to the low wear resistance wheel topography is changing rapidly 181. As the wheel is at work more and more cutting edges come into contact and process forces decrease towards a steady-state value Fnm which was later used for further investigations. After cutting and spark-out the investigation of the same spot of the wheel topography (bottom of fiaure 51 shows that the resin bond between the corundum grains is partly removed and single grits are torn out of the matrix or are splintered. A self-sharpening state is reached which is independent from the dressing conditions, a behaviour well known from literature (91.

Fiaure 5; Process forces and wheel topography

process: wheel: workpiece:

conditions:

coolant: mineral oil

face grinding with axial offset resin bonded corundum; dsD = 65 mm 9 0 CrMnV 8, 62 HRC; bw = 6 mm; dw = 65f2 mm vc =0.82 rnls; vft = 1.1 rnls; a, = 0.05 pm; a = 55O

Table 1 ; Grinding conditions (corresponding to fig. 5)

A similar behaviour of a normal force reaching a peak value followed by a progressive decrease towards a steady-state value is known from grinding with CBN [lo] and other grit materials. As dulling of grains cannot be detected there is a potential of achieving higher wear resistance of the shave-grinding tool by using a harder bonding.

Influence of cutting speed

The basic grinding force model for conventional processes based on chip thickness [l 11, [121 as shown

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in equation (6) is composed of physical parts which include the speed ratio q =vc/vft, the working engagement a, and the equivalent diameter deq, as well as the empirical additives: cwp, cgw, e l , e2, e3.

e l F', = cwp . cgw. (z) az2 . de3 eq ; (6)

If working engagement and equivalent diameter are assumed to be constant the equation (6) results in:

F' n - - c . v-el c (7)

Using equation (7) for modelling the tendency by empirical determination of the additives c and el has equation (8) as result,

(8) FInm = 1 9.6. ~ c ~ ' ~ ~ which is illustrated as curve in fiaure 6. Cutting speed ranges in the area of vc=0.5 ... 3.5 mls being comparable to the typical range of honing processes. Low cutting speeds vc result in very high specific normal forces Fncc up t o 40 Nlmm for a material rate of Q', =0.055 mm31(mm s). Process forces of shave-grinding can significantly be lowered by employing higher cutting speeds. Wear resistance of the tool will also increase with this method.

0 0.5 1 1.5 2 2.5 3 3.5

v, ids1 Fiaure 6: Process forces and G-ratio dependent on

cutting speed

process: wheel: workpiece:

conditions:

coolant: mineral oil

face grinding with axial offset resin bonded corundum; dsD = 65 mm 9 0 CrMnV 8, 62 HRC; bw = 6 mm; dw = 65+2 mm vft = 1.1 mls; a, =0.05 pm; a = 1 0 O... 70°

Table 2; Grinding conditions (corresponding to fig. 6)

The scattering of the process forces may possibly be result of the changing cutting angle a which influences the effective circle of curvature of the trajectory of the grain at the contact line between tool and workpiece and with this the effective kinematic grinding length I&. As the contact length is regarded as important input parameter for grinding processes [121 further investigations are necessary to clarify the influence of

the cutting angle' u especially concerning the cutting length.

Conclusion

The design of an analogous process for the real shave- grinding process led to an axial grinding operation with an offset between workpiece and tool axes. Cutting speeds vc were very low (0.5 ... 3 mls). The ratio of the amount of cutting speed vc and infeed speed vft covered a range between 0.5 and 3. The working engagement was also very low ae=0.05 pm. Moreover an angle between infeed speed vft and cutting speed vc was introduced. The resulting process behaviour showed many similarities concerning force over time behaviour and dependence of forces on cutting speed with conventional processes. Moreover first experiments with shave-grinding of gears show many promising similarities wi th results of the analogous process. The analogous process was not only used for fundamental investigations but also for testing new wheel specifications. The tested tool materials were classified according to the achieved process forces for a constant material removal rate, the wear behaviour and surface roughness values of the workpiece. The use of the recommended tool specifications for real gear finishing through shave-grinding had comparable results. Thus development of new tool materials by use of the analogous process has decisive advantages.

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