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The Skiving of Ball-Bearing Tracks
The Skiving of Ball-Bearing Tracks B. J. Stone, E. J. Bonikowski, D.J. Chapple, University of Bristol/UK - Submitted by A. E. De Barr, MTIRA (1)
Skiving is s h m to be a very effective method of manufacturing the ourved track of the inner race of b a l l bearings, the most significant advantages over conventional turning being reduced cycle time, lower ener& consumption and less tendency to vibration. The errors in geometry caused by skiving are shown to be insignificant. The requirements of a suitable skiving machine are discussed.
1moDUcT1m The current practice of msrrufacturing the races of ball bearings involves the use of a multi-spindle automstic machine tool, the cycle time being governed by the station involving the slowest operation. This, because of the volume of material to be removed and the large width of cut, is the machining of the bearing track. U s i n g a conventional turning process. this is subject to vibration which leaves a wavy amface which it is difficult to remove completely during the finiEhing processes of grinding and lapping.
I I
F.otatlon
The skiving process is a turning operation in which the direction of tool feed is tangential to the periphery of the Comparisons made between orthogonal workpiece (Figure 1). akiving and centreline turning suggest that there are advantages to be gained from this process’. The more important of these are: (1)
‘_
I
Zound tool
High metal-removal rates, even with mall diameter reduction. The skiving of a ball-bearing track
(2) Reduction or elimination of vibration.
( 3 ) Extended tool life. If these advantages are valid for the skiving of bearing tracks, then a reduction in cycle time with an improvement in surface finish and tool life is possible. However, since turning machines have not been designed with skiving in view, then it is probable that 8additional/different facilities might be required for skiving. The purpose of this paper is to describe an investigation into the skiving of bearing tracks with the object of reducing cycle time and the tendency to vibration. Also. by comparison with the conventional turning process. the requirements of a mitable akiving machine are discussed. PRFllIoUs WORK
There are several p b l i ~ a t i o n s ” ~ ’which ~ describe experimental investigations of skivFng; these omitted the aspect of non-circularity of the finished workpiece whlch w ~ 8 however considered by Duggan et al.4. They fo-ated the basic equations for predicting the finished geometry: rake angle and chipthickness variations through a cut for both the deflected (taking account of cutting forces) and undefleoted cases, and obtained wide rangins cutting data from a limited number of cutting tests. hence d i n g it possible to make predictions of cutting forces t h m m a skiving cut.
-
-
The nature of the skiving process is such that many parameters vary through the cut, e.g. u n d e f o m d chip thickness, rake engle, cutting speed and cutting forces. These are all modified by any deflections that are produced as a result of the cutting forces. When all the relevant cutting data are available, it is then po sible to predict the variation of these However, when the skiving of bearing parameters through a cut!. traaks is analysed it is evident that there are not sufficient cutting-force data to allow such an analysis. The chip orosssection varies to such an extent (see Figures 2a and 2b) that data for r e c t m a r chip cross-sections is not relevant. Without t h i s cutting-force data it is not possible to take account of deflections without measuring the forces during a cut. This was therefore the method adopted for prediction of the final workpiece geometry but for the investigation of other parameters, the undeflected situation was analysed.
I
0 (a)
Fia. Zla)
UnrotateC tool & (b)
jnun
(b)
b t a t e d tool
Variation of undeformed chip thichess through a skiving out
w Tool face subdivided into orthogonal Cutting M E
\
I
The geneapproach was to consider the circular tool as a series of elemental tools (Figure 3) m a n g e d so as to correspond to a continuous circular edge. Identifying any
Annals of the ClRP Vol. 29/1/1980
275
element around the tool e Q e by its angular position r. it was possible to obtain the state of any variable for that element, assuming no deflections, and hence by sumAng over all the elements the result for the whole tool could be established. As an example, Appendix I gives details of the calculations used to predict the undefomed chip-thickness variations shown in Figures 2a and b; it includes the effect of rotating the circular tool. The obvious tool shape vaa circular since the track required was a seeplent of a circle and to give appropriate clesrance angles a conical tool uas used (Figure 4). This could be rotated about a horizontal a r i s to give a desired rake angle (Figure 4s). However, if a large positive reke is required et the completion of the cut then an increased taper on the cone is needed for clearance and the tool is weakened. If a negative rake at completion is acceptable, then an even greater negative rake is present at the start of the cut. Thus a zero rake W l e at completion waa chosen so that the rake engle varies between negative values and zero.
"mi-un
Fig. 5
anele
7ar:ation 05 the w x b u - ; anzle of roo1 rotation iritt CJ? Zepth f o r 1 ranae 0" too! -c?eararce anales
A P P m T m (a)
The choice of machine for the cutting tests w a a limited because machines have not been developed for skiving. The most appropriate w h i n e available waa SF. Adcock-Shipley 25 horizontal m i l l b machine which allowed the m v i n g of the tool in three translational directions, The circular tungstencarbide cutting tool waa fired to an adaptor mounted on a Kistler dynamometer.
Rotation &out horizontal a x i n
r, i-3
0
The layout of the electrical apparatus is shom in Figure 6. The three outpts from the dynamometer which measured components of the cutting force in the X, Y and 2 directions were fed into char@ amplifiers and then into a transient capture unit (XU). From the TCU the signals could be displayed on oscilloscopes or individually &awn on a plotter.
I
(5)
Xotation
vertical axis
bout
Eotation of too! Rotation about the vertical axis (Figure 4b) w a s also investigated 88 this offered the possibility of producing a rsnge of track radii with a single tool. The profile produced by such a rotated tool is elliptical and an approximation to a circular profile has to be accepted. However, since the track would be finished by grinding and lapping, the Small deviation fmm a circular arc would be acceptable. The limitation on rotating the tool is that interference occurs on the clearance face. An analysis of this limitation is given in Appendix I1 and the main results are sumnarised in F i m 5 where orthogonal cutting is represented by an angle of rotation p = 900. Ba a result of these snalyses it became evident that in practice only d l rotations were possible and these did not produce a si&icent rauge of track radii frm one tool. Thus, only orthogonal cutting with a round tool w 8 8 investigated experimentally.
I
A Uqne-Kerr displacement transducer in conjunction with a single toothed wheel. keyed on to the arbor, was used to provide an indication of the variation in rotational speed of the workpiece during a cut. "he output from the probe w a s fed to the TCU and w a s synchronously displeyed with the three force signals. The ssme probe w a a also used during the measurement of the flexibility between tool and workpiece. The tool feed rate w a s measured using a ten-turn linear potentiometer with a pulley attached to its shaft. A weighted cord waa attached to the table and mapped amund the pulley, thus converting the linear motion of the table into rotational motion of the potentiometer shaft. The output of the potentiometer could also be fed to the TCU.
h 3 1 bearfng steel (in the unhardened state) 65 nm diameter, was used for all the tests and the cutting tool was a Sandvik 150
P grade carbide of 12 m diemeter which gave a top clearance
I '
I I1 I
Transient
-I,
I Experinental lajrout
276
a - l e of 7' when c u t t i n g with zero rake angle, i.e. completion of a cut.
at t h e
Tne dynenometer w a s c a l i b r a t e d i n the X. Y and Z directions. I n the Z direction known weights were placed on the top of the dynamometer. For the Y and X directions a cable attached t o the face of the dynamometer w a s mn over a pulley at the edge of the table and had a pan attached to i t s end upon which the weights could be placed.
1.0
The c a l i b r a t i o n range was nade lsrge enough t o incorporate a l l forces expected during a cut. The TCU w a s set t o a long record period and the f i n a l t r a c e of load increments wa8 displayed on t o the p l o t t e r , giving d i r e c t calibration.
1.7
The Yayne-Kerr probe vas a l s o calibrated, using a picrometer screw gauge, v i a the TCU on t o the p l o t t e r . 7
L .
c
Measurement of f l e x i b i l i t y The r e l a t i v e f l e x i b i l i b f between the tool and the workpiece w a s neasured using a hydraulic jack placed between them. As load w a s applied, the displacement w a s measured by a Wayne-Kerr probe mounted on the same base as the tool and s e t above the workpiece. The t r a c e s f o r t h e f o r c e and the displacement were stored i n the TCU and could thus be plotted against one another t o provide a load/displacement p a p h . Each t e s t w a s repeated three times without significant v a r i a t i o n i n r e s u l t . Measurements were taken at f i v e positions along the workpiece. The load range f o r the f l e x i b i l i t y measurements w a s Small but corresponded roughly t o the maximum forces experienced i n the f i n a l revolution of a cut. It i s therefore possible that there is a l i m i t of proportionality at a g r e a t e r load, which would mean inaccuracies when predicting "deflected" variables during a cut. However, because of the small magnitude of the deflections r e l a t i v s fo the geometries considered, further p u r r n i t of exact f l e x i b i l i t y values for higher loads w a s not considered worthwhile. The XZ cross f l e x i b i l i t i e s were very d l and were thus not signlficant. The e f f e c t of the deflections on the finished p r o f i l e wa8 analysed 88 described in Appendix I11 .using the forces measured during the last revolution.
Selection of the workinn meeds and feeds It w a s known that, f o r the s i z e of track t o be machined, i.e. initial di e t e r 65 m, a conventio turning speed would a feed of 20 1110. m i g . In order t o be 380 rev min-?with investigate a l a r g e range of possible speeds and feeds f o r skiving, a small depth of cut of 2 1110. w a s chosen t o avoid s t a l l i n g t h e machine (motor rating appror. 5 kW). As one object w a s t o reduce the cycle t i m e a high feed r a t e ( f e e d u n i t time) b r a s desirable and t o avoid excessive ohip t h i o h e s s (and therefore possible t o o l f a i l u r e ) a high r o t a t i o n a l speed was a l s o required. It was found that the hi&est machine speed could be used (1500 rev min-') and that a feed of 600 um min-' was possible without f r a c t u r e of the t o o l or excessive wear. A t lower feeds there was an increased tendency f o r vibrations t o occur at the end of the cut.
Eowever, i n order t o c u t a typical bearing track i n one pass, the maximum depth of c u t needed t o be approximately 3 m.
At t h e speed and feed quoted above, the machine would have
3.11
4.3
1
rrhl 'X
:axe t r a c e s used t o jds-ify the l i v i d i n g of a cut Into tilo zeuarate >asses
General mocedure during a c u t t i n n t e s t Before and a f t e r each test the dynamometer YBB c a l i b r a t e d and periodically the input leads t o the charge amplifiers were pounded t o prevent the display of any Dc shift which might have occurred.
For skiving, the v e r t i c a l position of the t o o l r e l a t i v e t o the workpiece could be set t o within 0.01 nm of the required the tool i n t o contact position. This was checked by brwith t h e workpiece and measuring the horizontal distance between the centre of the tool face and t h e remote workpiece edge with a vernier c a l l i p e r and a square. The t a b l e w a n then backed off end a c u t taken. The t r a c e s from each c u t were stored i n the W U and subsequently plotted. Occasionally the input from the feed-ratemeasuring potentiometer w a s substituted f o r that of the Y force, t o verify t h a t the variation of feed r a t e tbrough a cut Y(LB insignificant.
For the conventional turning t e s t s the tool w a s positioned under the centre of the workpiece and the v e r t i c a l feed used. This required the use of a stop when the required depth of cut had been taken. However, this resulted i n c h a t t e r occurring on dwell and this c c A d not be eliminated. Thus the t o o l w a s l e f t i n the dwell condition f o r as short a time 88 possible. This resulted i n the f o r c e t r a c e s f o r centreline turning having a rubbing component following the stopping of the feed (Figure 8 ) .
s t a l l e d because, although skiving uses l e s s energy, the time is a l s o reduced and the instantaneous power requirements can be large. The track w a s therefore machined in two passes which would r e s u l t i n the sane finished track provided the forces on the final revolution were unchsnged. To verifij this, two 2 mm msximum depth tracks were cut, one i n a single pass, the other i n two. The f o r c e t r a c e during the last revolution of the single-paas c u t waa compared with that of the second i n t h e two-pass case. Both t r a c e s a r e shown i n Figure 7. It i s c l e a r t h a t the forces over t h e final p a r t of each cut a r e very similar. It was therefore concluded t h a t t h e p r o f i l e formed by machining a 3 mm deep track by a c u t of 2 urn followed by one of 1 mm. would produce s u b s t a n t i a l l y the seme finished profile. Finally, f o r conparison with centreline turning, t w o c r i t e r i a f o r speed s e l e c t i o n were used. The f i r s t was t o keep the r o t a t i o n a l speed the Sane as f o r the skiving and t o s d j u s t the feed t o give approximately the sane time f o r a similar cut. The second waa t o choose This l e d t o a feed of 90 nm min-'. t h e approximate conditions which me used i n t h i n d u s t r i a l production of such a track, namely 380 rev min-' and 20 mu min-1.
'x >ti
' a x e t r a c e for tuzme< track. a t cieptn of 3 mm
277
The f o m e trace for skiving the final 1 m deep cut is shown in Figure 9.
1.c
"5
I
t5
kN
X'
& (final rorce trace skived track cut) at depth for
of 3 nm
The !ICU w a s triggered m a l l y just before tool-workpiece contact as the total time of cut was required for finished profile predictions see Appendix 111. Also, a oheck was made of the variation of speed and feed during a cut. Any uneven spacing of the pulses from the Wayne-Kerr probe indicated a variation in rotational speed; the deviation f m m linearity of the potentiometer output showed up any chenge in the feed rate. BEsuIlps DISCUSSIoly
-
The final geometry of both a skived and turned track was a Talymnd and the results shown in Figure 10. examined us-
The most significant comparison between the two finished geometries is the clear lack of vibration during the skiving cut. There are several possible reasons for this. Firstly, the a k i v h process does not involve a prolonged dwell and therefore chatter from this source would not have time to build up. Secondly, the nature of chatter is such that steady-state cutting conditions allow the vibration to build up. l b s skiving has the advantage of continuously chenging the tool position with respect to the workpiece centre and steady-state coaditions are not achieved. Thirdly, the variation of power consumption during a skiving cut results in some speed variation t h r o w the cut. The workpiece will be tending to speed up as the cut is completed and this @ would result in departure from a steady-state condition. Another advantage of skiving wae found when the energy required to produce a track was evaluated. For tunring at conventional speeds and feeds 23 kJ were used and t h i s ignores the energy consumed during nibbing. For turning at the hi&er speed this waa reduced to 18 kJ. However, s k i v h resulted in the total energy consumed for the 2 mn deep cut and the subsequent 1 mn deep cut being 8.5 kJ. This is likely to be greater than the value that would be obtained for a single 3 W IU deep cut because the small inefficient chip thicknesses which occur at the end of a cut have been duplicated. Such a single cut could not be taken because of the limited power available. The reason for such a large reduction in energy consumed is not readily apparent. The increased chip thickness during the initial stages of the cut would result in more efficient cutting but the negntive rake angles would tend to offset this advantage. This is clearly an area when a proper understanding of the cutting mechanics could .perhaps indicate some effects which would be more generally useful. As a result of using skiving, it would be possible to manufacture a track within 1.5 second if a single cut could be
taken. This compares with the 9 second for the conventional k m i is turning process. The need for a machine designed for S thus apparent. In particular, a method of storing energy such as a flywheel would be beneficial and would not increase the siee of motor required. This would also have the advantage of chatter suppression due to the chMge in speed as the energy stored in the flywheel waa used. Finally, a limited investigstion of wear w a s undertaken. Fifty tracks were skived with a noticeable improvement in surface finlsh between the last and the first. The reduction in tool diameter that this produced could not be measured accurately but w m not greater than 20 Wua.
The work described in this paper has indicated the advantages to be gained from skiving ball bearing tracks. i.e. lower energy consumption, less tendency to vibration and reduced cycle time. However, as machines have not been designed with skiving in view, there is a need for a suitable machine. Particularly, the provision of ahort-duration high-power requirements is required. As the final geometry is governed by the forces during the last revolution of cut the stiffness requirements are not increased since these forces are relatively small.
w 29.86
(b) Turned Track
revolution was approximately 18 pn. It should be noted that this error is well within the tolerance for the material that would be removed during grinding and lapping. The turned track shows the result of the vibration that oc-ed on dwell and also indicates a much greater out-of-round (Figure 10). The latter could be the result of the rubbing that was shown to occur at dwell (Figure 8). This would mean that the workpiece did not spring back fully when the feed was stopped and the transition from cutting to rubbing may account for this out-of-round.
130.00 ~30.00
The work described waa carried out in the Department of Mechanical w e e r i n g , University of Brietol, end the authors would like to thank Professor C. Andrew for his support and encouragement.
3c.00
Thanks are also due to the Department of Mechanical Engineering of Brietol Polytechnic for help with roundness measurements.
29.86
L. FINE, "Metal removal by skiving on turning machines". Machinery & Production &&neering, 11th k h , 1970. '30.00
m, "Off-centre turnin#'. Int. J. k h . Tool Dee., Vol.10, Pergemon Press. 1970. L.
Fig. 10 Final workpiece Reometry
The skived track waa out of round by 18 w. This waa not the result of the inherent non-circularity of workpieces manufactured by skiving4 since t h i s waa calculated to be only 0-7 Vm- However. the maximum error resulting from the variation in deflection caused by the varying force during the last
270
J.M. WMIIl(0v and 1. MATlTIIAS, "Special aspects of tengentid turning with linear feeds". F e r t i w , Vol.5, Febzuary 1914, pp.9-15. DUGGAN, R.J. SMKES and B.J. STOW. "The use of skiving cuts to obtain data on cutting forces and some predictions of workpiece e o m e t r y and force variation Vol.190, 25/76. for skiviq". Proc. I.Mech.E., C.K.
Determination of the chip p o f i l e for a rotated t o o l d u r j q a cut, eval uated assuming no deflections of the system
It is necessary t o find the distance Ft' which must be r traversed before the element on t h e tool, a t angular position r, s t a r t s t o cut, measured from i t s position a t f i r s t contact, a s shown. F i s the feed r a t e (Figure A1.1).
Ft' 0
r
r
n
- h - a s i n r cos
f
p
-
Xl s i n @
r
is defined a s shmm, i.e.
Using t h e equations for p.c.t. derived by Duggan e t a l . u.c.t.
P
-
u.c.t.
,I
\
:rhere
(undefor??ed chip thickness;
[g + ( L - F ( t - I/N))2]h - [R:
+ (L
-
- [RE
R1 2
- Ftj2]'
+ ( L *]')%F
Clip
t 1 1/N
t
profile
< l/N
TOO1
-
t h e chip thlcloless corresponding t o an element of the t o o l a t anguLsr position r on t h e circular tool, can be evaluated.
Thus: u.c.t.
=
bE
(Lr
A
- [R; for t
- t'
P
- F(t
(Lr
- tr' - 1/N)) 2J%
- F ( t - t'))']' r
?ig. AI.3
1/N APEZIDC( I1
and u.c.t. for
= :R
t
- [<
+ (Lr
- F ( t - ti))']'
3etermination of the maximwn angle of rotation without rubbing
- tr' < l/i?
The limits of
r
For any generator of the cone (Figure A I I . 1 ) :
are given when t
- tr'
= 0.
The u.c.t. above is defined radially, so i n order t o produce t h e p r o f i l e as it I s presented t o the t o o l i n the d b e c t i o n of feed it i 5 necessary t o multiply these w l u e s kf the secant o? instantaneous rake angle a t the point r (Figure AI.2). Thus a profile is f o n r d a s shown in Figure AI.3.
..
3.C.t.
required
Approximat ion It0 U.C.t.
;caused by p i n g cos2
Fig. AI.2
k-asiny
-I
Fig. AII.l
279
and a s t'le : coordinate OF t h e intersection of the radial 1 . i ~ r and the horizontal plane a t distance s fron the F axis i s F, = s.t:m; suhstitution yields
The locus of the intersection between the horizontal plane defining the lmrest m i n t s on the t o o l used i n the cut and the cone of which t h e t o o l is a p w t , can be plotted (Figure ,411.3). The tangent t o t h i s curve a t the front face of the t o o l yields t h e instantaneous clearance angle f o r the given depth of cut.
APrnIDTX I11
?rediction of final workpiece GeometFj after a cut with a rotated tool, takiFe account of t o o l feed and r e l a t i v e deflection of srorkpiece and t o o l it i s necessary t o express ~ P Jradius cut in terms of the angle around the vorkpiece from t h e Initial Contact Xadius (IC3 see Figure AII1.1). This can be done by recording the an@-= displacement OC t h e Im from i t s i n i t i a l m s i t i o n and findim d i s p n c e m n t contributed by the t o o l the ad6itlonal notion r e l a t i v e to the displaced centre (Figure A I I I . 9 ) . z
-7iece taticn
-'
=ositi&x of (:.c.u.) 3it
tine t
The limiting position i s a t the front face of the tool where : t o deflecteC ..:or>-
Initial
contact D i f f e r e n t i a t w with respect t o 5 yields
I
Y
.'/
%sition of centre a t tfne t
/
Tig.AIII.? Position of
The angle between the "deflected" ICii and the r a d i a l l i n e through any point on the t o o l i s !J'wfiere
.. *
pe
=
./'
- tan-l
The actual angular position of any radius becose,,i
27Nt +
cut i s
'I'
The radius of any elsment being formed i s : Rom t h i s equation t h e p a @ OP possible cutting positions may be obtained (Figure 5).
The r a d i i forned during t h e final work.Siece revolution before cuttin& ceases m y thus be calculated, provided the t h e frun the cannncemcnt of cut and t h e other geometric p a m e t e r s are Imam.
280
Skiving is s h m to be a very effective method of manufacturing the ourved track of the inner race of b a l l bearings, the most significant advantages over conventional turning being reduced cycle time, lower ener& consumption and less tendency to vibration. The errors in geometry caused by skiving are shown to be insignificant. The requirements of a suitable skiving machine are discussed.
1moDUcT1m The current practice of msrrufacturing the races of ball bearings involves the use of a multi-spindle automstic machine tool, the cycle time being governed by the station involving the slowest operation. This, because of the volume of material to be removed and the large width of cut, is the machining of the bearing track. U s i n g a conventional turning process. this is subject to vibration which leaves a wavy amface which it is difficult to remove completely during the finiEhing processes of grinding and lapping.
I I
F.otatlon
The skiving process is a turning operation in which the direction of tool feed is tangential to the periphery of the Comparisons made between orthogonal workpiece (Figure 1). akiving and centreline turning suggest that there are advantages to be gained from this process’. The more important of these are: (1)
‘_
I
Zound tool
High metal-removal rates, even with mall diameter reduction. The skiving of a ball-bearing track
(2) Reduction or elimination of vibration.
( 3 ) Extended tool life. If these advantages are valid for the skiving of bearing tracks, then a reduction in cycle time with an improvement in surface finish and tool life is possible. However, since turning machines have not been designed with skiving in view, then it is probable that 8additional/different facilities might be required for skiving. The purpose of this paper is to describe an investigation into the skiving of bearing tracks with the object of reducing cycle time and the tendency to vibration. Also. by comparison with the conventional turning process. the requirements of a mitable akiving machine are discussed. PRFllIoUs WORK
There are several p b l i ~ a t i o n s ” ~ ’which ~ describe experimental investigations of skivFng; these omitted the aspect of non-circularity of the finished workpiece whlch w ~ 8 however considered by Duggan et al.4. They fo-ated the basic equations for predicting the finished geometry: rake angle and chipthickness variations through a cut for both the deflected (taking account of cutting forces) and undefleoted cases, and obtained wide rangins cutting data from a limited number of cutting tests. hence d i n g it possible to make predictions of cutting forces t h m m a skiving cut.
-
-
The nature of the skiving process is such that many parameters vary through the cut, e.g. u n d e f o m d chip thickness, rake engle, cutting speed and cutting forces. These are all modified by any deflections that are produced as a result of the cutting forces. When all the relevant cutting data are available, it is then po sible to predict the variation of these However, when the skiving of bearing parameters through a cut!. traaks is analysed it is evident that there are not sufficient cutting-force data to allow such an analysis. The chip orosssection varies to such an extent (see Figures 2a and 2b) that data for r e c t m a r chip cross-sections is not relevant. Without t h i s cutting-force data it is not possible to take account of deflections without measuring the forces during a cut. This was therefore the method adopted for prediction of the final workpiece geometry but for the investigation of other parameters, the undeflected situation was analysed.
I
0 (a)
Fia. Zla)
UnrotateC tool & (b)
jnun
(b)
b t a t e d tool
Variation of undeformed chip thichess through a skiving out
w Tool face subdivided into orthogonal Cutting M E
\
I
The geneapproach was to consider the circular tool as a series of elemental tools (Figure 3) m a n g e d so as to correspond to a continuous circular edge. Identifying any
Annals of the ClRP Vol. 29/1/1980
275
element around the tool e Q e by its angular position r. it was possible to obtain the state of any variable for that element, assuming no deflections, and hence by sumAng over all the elements the result for the whole tool could be established. As an example, Appendix I gives details of the calculations used to predict the undefomed chip-thickness variations shown in Figures 2a and b; it includes the effect of rotating the circular tool. The obvious tool shape vaa circular since the track required was a seeplent of a circle and to give appropriate clesrance angles a conical tool uas used (Figure 4). This could be rotated about a horizontal a r i s to give a desired rake angle (Figure 4s). However, if a large positive reke is required et the completion of the cut then an increased taper on the cone is needed for clearance and the tool is weakened. If a negative rake at completion is acceptable, then an even greater negative rake is present at the start of the cut. Thus a zero rake W l e at completion waa chosen so that the rake engle varies between negative values and zero.
"mi-un
Fig. 5
anele
7ar:ation 05 the w x b u - ; anzle of roo1 rotation iritt CJ? Zepth f o r 1 ranae 0" too! -c?eararce anales
A P P m T m (a)
The choice of machine for the cutting tests w a a limited because machines have not been developed for skiving. The most appropriate w h i n e available waa SF. Adcock-Shipley 25 horizontal m i l l b machine which allowed the m v i n g of the tool in three translational directions, The circular tungstencarbide cutting tool waa fired to an adaptor mounted on a Kistler dynamometer.
Rotation &out horizontal a x i n
r, i-3
0
The layout of the electrical apparatus is shom in Figure 6. The three outpts from the dynamometer which measured components of the cutting force in the X, Y and 2 directions were fed into char@ amplifiers and then into a transient capture unit (XU). From the TCU the signals could be displayed on oscilloscopes or individually &awn on a plotter.
I
(5)
Xotation
vertical axis
bout
Eotation of too! Rotation about the vertical axis (Figure 4b) w a s also investigated 88 this offered the possibility of producing a rsnge of track radii with a single tool. The profile produced by such a rotated tool is elliptical and an approximation to a circular profile has to be accepted. However, since the track would be finished by grinding and lapping, the Small deviation fmm a circular arc would be acceptable. The limitation on rotating the tool is that interference occurs on the clearance face. An analysis of this limitation is given in Appendix I1 and the main results are sumnarised in F i m 5 where orthogonal cutting is represented by an angle of rotation p = 900. Ba a result of these snalyses it became evident that in practice only d l rotations were possible and these did not produce a si&icent rauge of track radii frm one tool. Thus, only orthogonal cutting with a round tool w 8 8 investigated experimentally.
I
A Uqne-Kerr displacement transducer in conjunction with a single toothed wheel. keyed on to the arbor, was used to provide an indication of the variation in rotational speed of the workpiece during a cut. "he output from the probe w a s fed to the TCU and w a s synchronously displeyed with the three force signals. The ssme probe w a a also used during the measurement of the flexibility between tool and workpiece. The tool feed rate w a s measured using a ten-turn linear potentiometer with a pulley attached to its shaft. A weighted cord waa attached to the table and mapped amund the pulley, thus converting the linear motion of the table into rotational motion of the potentiometer shaft. The output of the potentiometer could also be fed to the TCU.
h 3 1 bearfng steel (in the unhardened state) 65 nm diameter, was used for all the tests and the cutting tool was a Sandvik 150
P grade carbide of 12 m diemeter which gave a top clearance
I '
I I1 I
Transient
-I,
I Experinental lajrout
276
a - l e of 7' when c u t t i n g with zero rake angle, i.e. completion of a cut.
at t h e
Tne dynenometer w a s c a l i b r a t e d i n the X. Y and Z directions. I n the Z direction known weights were placed on the top of the dynamometer. For the Y and X directions a cable attached t o the face of the dynamometer w a s mn over a pulley at the edge of the table and had a pan attached to i t s end upon which the weights could be placed.
1.0
The c a l i b r a t i o n range was nade lsrge enough t o incorporate a l l forces expected during a cut. The TCU w a s set t o a long record period and the f i n a l t r a c e of load increments wa8 displayed on t o the p l o t t e r , giving d i r e c t calibration.
1.7
The Yayne-Kerr probe vas a l s o calibrated, using a picrometer screw gauge, v i a the TCU on t o the p l o t t e r . 7
L .
c
Measurement of f l e x i b i l i t y The r e l a t i v e f l e x i b i l i b f between the tool and the workpiece w a s neasured using a hydraulic jack placed between them. As load w a s applied, the displacement w a s measured by a Wayne-Kerr probe mounted on the same base as the tool and s e t above the workpiece. The t r a c e s f o r t h e f o r c e and the displacement were stored i n the TCU and could thus be plotted against one another t o provide a load/displacement p a p h . Each t e s t w a s repeated three times without significant v a r i a t i o n i n r e s u l t . Measurements were taken at f i v e positions along the workpiece. The load range f o r the f l e x i b i l i t y measurements w a s Small but corresponded roughly t o the maximum forces experienced i n the f i n a l revolution of a cut. It i s therefore possible that there is a l i m i t of proportionality at a g r e a t e r load, which would mean inaccuracies when predicting "deflected" variables during a cut. However, because of the small magnitude of the deflections r e l a t i v s fo the geometries considered, further p u r r n i t of exact f l e x i b i l i t y values for higher loads w a s not considered worthwhile. The XZ cross f l e x i b i l i t i e s were very d l and were thus not signlficant. The e f f e c t of the deflections on the finished p r o f i l e wa8 analysed 88 described in Appendix I11 .using the forces measured during the last revolution.
Selection of the workinn meeds and feeds It w a s known that, f o r the s i z e of track t o be machined, i.e. initial di e t e r 65 m, a conventio turning speed would a feed of 20 1110. m i g . In order t o be 380 rev min-?with investigate a l a r g e range of possible speeds and feeds f o r skiving, a small depth of cut of 2 1110. w a s chosen t o avoid s t a l l i n g t h e machine (motor rating appror. 5 kW). As one object w a s t o reduce the cycle t i m e a high feed r a t e ( f e e d u n i t time) b r a s desirable and t o avoid excessive ohip t h i o h e s s (and therefore possible t o o l f a i l u r e ) a high r o t a t i o n a l speed was a l s o required. It was found that the hi&est machine speed could be used (1500 rev min-') and that a feed of 600 um min-' was possible without f r a c t u r e of the t o o l or excessive wear. A t lower feeds there was an increased tendency f o r vibrations t o occur at the end of the cut.
Eowever, i n order t o c u t a typical bearing track i n one pass, the maximum depth of c u t needed t o be approximately 3 m.
At t h e speed and feed quoted above, the machine would have
3.11
4.3
1
rrhl 'X
:axe t r a c e s used t o jds-ify the l i v i d i n g of a cut Into tilo zeuarate >asses
General mocedure during a c u t t i n n t e s t Before and a f t e r each test the dynamometer YBB c a l i b r a t e d and periodically the input leads t o the charge amplifiers were pounded t o prevent the display of any Dc shift which might have occurred.
For skiving, the v e r t i c a l position of the t o o l r e l a t i v e t o the workpiece could be set t o within 0.01 nm of the required the tool i n t o contact position. This was checked by brwith t h e workpiece and measuring the horizontal distance between the centre of the tool face and t h e remote workpiece edge with a vernier c a l l i p e r and a square. The t a b l e w a n then backed off end a c u t taken. The t r a c e s from each c u t were stored i n the W U and subsequently plotted. Occasionally the input from the feed-ratemeasuring potentiometer w a s substituted f o r that of the Y force, t o verify t h a t the variation of feed r a t e tbrough a cut Y(LB insignificant.
For the conventional turning t e s t s the tool w a s positioned under the centre of the workpiece and the v e r t i c a l feed used. This required the use of a stop when the required depth of cut had been taken. However, this resulted i n c h a t t e r occurring on dwell and this c c A d not be eliminated. Thus the t o o l w a s l e f t i n the dwell condition f o r as short a time 88 possible. This resulted i n the f o r c e t r a c e s f o r centreline turning having a rubbing component following the stopping of the feed (Figure 8 ) .
s t a l l e d because, although skiving uses l e s s energy, the time is a l s o reduced and the instantaneous power requirements can be large. The track w a s therefore machined in two passes which would r e s u l t i n the sane finished track provided the forces on the final revolution were unchsnged. To verifij this, two 2 mm msximum depth tracks were cut, one i n a single pass, the other i n two. The f o r c e t r a c e during the last revolution of the single-paas c u t waa compared with that of the second i n t h e two-pass case. Both t r a c e s a r e shown i n Figure 7. It i s c l e a r t h a t the forces over t h e final p a r t of each cut a r e very similar. It was therefore concluded t h a t t h e p r o f i l e formed by machining a 3 mm deep track by a c u t of 2 urn followed by one of 1 mm. would produce s u b s t a n t i a l l y the seme finished profile. Finally, f o r conparison with centreline turning, t w o c r i t e r i a f o r speed s e l e c t i o n were used. The f i r s t was t o keep the r o t a t i o n a l speed the Sane as f o r the skiving and t o s d j u s t the feed t o give approximately the sane time f o r a similar cut. The second waa t o choose This l e d t o a feed of 90 nm min-'. t h e approximate conditions which me used i n t h i n d u s t r i a l production of such a track, namely 380 rev min-' and 20 mu min-1.
'x >ti
' a x e t r a c e for tuzme< track. a t cieptn of 3 mm
277
The f o m e trace for skiving the final 1 m deep cut is shown in Figure 9.
1.c
"5
I
t5
kN
X'
& (final rorce trace skived track cut) at depth for
of 3 nm
The !ICU w a s triggered m a l l y just before tool-workpiece contact as the total time of cut was required for finished profile predictions see Appendix 111. Also, a oheck was made of the variation of speed and feed during a cut. Any uneven spacing of the pulses from the Wayne-Kerr probe indicated a variation in rotational speed; the deviation f m m linearity of the potentiometer output showed up any chenge in the feed rate. BEsuIlps DISCUSSIoly
-
The final geometry of both a skived and turned track was a Talymnd and the results shown in Figure 10. examined us-
The most significant comparison between the two finished geometries is the clear lack of vibration during the skiving cut. There are several possible reasons for this. Firstly, the a k i v h process does not involve a prolonged dwell and therefore chatter from this source would not have time to build up. Secondly, the nature of chatter is such that steady-state cutting conditions allow the vibration to build up. l b s skiving has the advantage of continuously chenging the tool position with respect to the workpiece centre and steady-state coaditions are not achieved. Thirdly, the variation of power consumption during a skiving cut results in some speed variation t h r o w the cut. The workpiece will be tending to speed up as the cut is completed and this @ would result in departure from a steady-state condition. Another advantage of skiving wae found when the energy required to produce a track was evaluated. For tunring at conventional speeds and feeds 23 kJ were used and t h i s ignores the energy consumed during nibbing. For turning at the hi&er speed this waa reduced to 18 kJ. However, s k i v h resulted in the total energy consumed for the 2 mn deep cut and the subsequent 1 mn deep cut being 8.5 kJ. This is likely to be greater than the value that would be obtained for a single 3 W IU deep cut because the small inefficient chip thicknesses which occur at the end of a cut have been duplicated. Such a single cut could not be taken because of the limited power available. The reason for such a large reduction in energy consumed is not readily apparent. The increased chip thickness during the initial stages of the cut would result in more efficient cutting but the negntive rake angles would tend to offset this advantage. This is clearly an area when a proper understanding of the cutting mechanics could .perhaps indicate some effects which would be more generally useful. As a result of using skiving, it would be possible to manufacture a track within 1.5 second if a single cut could be
taken. This compares with the 9 second for the conventional k m i is turning process. The need for a machine designed for S thus apparent. In particular, a method of storing energy such as a flywheel would be beneficial and would not increase the siee of motor required. This would also have the advantage of chatter suppression due to the chMge in speed as the energy stored in the flywheel waa used. Finally, a limited investigstion of wear w a s undertaken. Fifty tracks were skived with a noticeable improvement in surface finlsh between the last and the first. The reduction in tool diameter that this produced could not be measured accurately but w m not greater than 20 Wua.
The work described in this paper has indicated the advantages to be gained from skiving ball bearing tracks. i.e. lower energy consumption, less tendency to vibration and reduced cycle time. However, as machines have not been designed with skiving in view, there is a need for a suitable machine. Particularly, the provision of ahort-duration high-power requirements is required. As the final geometry is governed by the forces during the last revolution of cut the stiffness requirements are not increased since these forces are relatively small.
w 29.86
(b) Turned Track
revolution was approximately 18 pn. It should be noted that this error is well within the tolerance for the material that would be removed during grinding and lapping. The turned track shows the result of the vibration that oc-ed on dwell and also indicates a much greater out-of-round (Figure 10). The latter could be the result of the rubbing that was shown to occur at dwell (Figure 8). This would mean that the workpiece did not spring back fully when the feed was stopped and the transition from cutting to rubbing may account for this out-of-round.
130.00 ~30.00
The work described waa carried out in the Department of Mechanical w e e r i n g , University of Brietol, end the authors would like to thank Professor C. Andrew for his support and encouragement.
3c.00
Thanks are also due to the Department of Mechanical Engineering of Brietol Polytechnic for help with roundness measurements.
29.86
L. FINE, "Metal removal by skiving on turning machines". Machinery & Production &&neering, 11th k h , 1970. '30.00
m, "Off-centre turnin#'. Int. J. k h . Tool Dee., Vol.10, Pergemon Press. 1970. L.
Fig. 10 Final workpiece Reometry
The skived track waa out of round by 18 w. This waa not the result of the inherent non-circularity of workpieces manufactured by skiving4 since t h i s waa calculated to be only 0-7 Vm- However. the maximum error resulting from the variation in deflection caused by the varying force during the last
270
J.M. WMIIl(0v and 1. MATlTIIAS, "Special aspects of tengentid turning with linear feeds". F e r t i w , Vol.5, Febzuary 1914, pp.9-15. DUGGAN, R.J. SMKES and B.J. STOW. "The use of skiving cuts to obtain data on cutting forces and some predictions of workpiece e o m e t r y and force variation Vol.190, 25/76. for skiviq". Proc. I.Mech.E., C.K.
Determination of the chip p o f i l e for a rotated t o o l d u r j q a cut, eval uated assuming no deflections of the system
It is necessary t o find the distance Ft' which must be r traversed before the element on t h e tool, a t angular position r, s t a r t s t o cut, measured from i t s position a t f i r s t contact, a s shown. F i s the feed r a t e (Figure A1.1).
Ft' 0
r
r
n
- h - a s i n r cos
f
p
-
Xl s i n @
r
is defined a s shmm, i.e.
Using t h e equations for p.c.t. derived by Duggan e t a l . u.c.t.
P
-
u.c.t.
,I
\
:rhere
(undefor??ed chip thickness;
[g + ( L - F ( t - I/N))2]h - [R:
+ (L
-
- [RE
R1 2
- Ftj2]'
+ ( L *]')%F
Clip
t 1 1/N
t
profile
< l/N
TOO1
-
t h e chip thlcloless corresponding t o an element of the t o o l a t anguLsr position r on t h e circular tool, can be evaluated.
Thus: u.c.t.
=
bE
(Lr
A
- [R; for t
- t'
P
- F(t
(Lr
- tr' - 1/N)) 2J%
- F ( t - t'))']' r
?ig. AI.3
1/N APEZIDC( I1
and u.c.t. for
= :R
t
- [<
+ (Lr
- F ( t - ti))']'
3etermination of the maximwn angle of rotation without rubbing
- tr' < l/i?
The limits of
r
For any generator of the cone (Figure A I I . 1 ) :
are given when t
- tr'
= 0.
The u.c.t. above is defined radially, so i n order t o produce t h e p r o f i l e as it I s presented t o the t o o l i n the d b e c t i o n of feed it i 5 necessary t o multiply these w l u e s kf the secant o? instantaneous rake angle a t the point r (Figure AI.2). Thus a profile is f o n r d a s shown in Figure AI.3.
..
3.C.t.
required
Approximat ion It0 U.C.t.
;caused by p i n g cos2
Fig. AI.2
k-asiny
-I
Fig. AII.l
279
and a s t'le : coordinate OF t h e intersection of the radial 1 . i ~ r and the horizontal plane a t distance s fron the F axis i s F, = s.t:m; suhstitution yields
The locus of the intersection between the horizontal plane defining the lmrest m i n t s on the t o o l used i n the cut and the cone of which t h e t o o l is a p w t , can be plotted (Figure ,411.3). The tangent t o t h i s curve a t the front face of the t o o l yields t h e instantaneous clearance angle f o r the given depth of cut.
APrnIDTX I11
?rediction of final workpiece GeometFj after a cut with a rotated tool, takiFe account of t o o l feed and r e l a t i v e deflection of srorkpiece and t o o l it i s necessary t o express ~ P Jradius cut in terms of the angle around the vorkpiece from t h e Initial Contact Xadius (IC3 see Figure AII1.1). This can be done by recording the an@-= displacement OC t h e Im from i t s i n i t i a l m s i t i o n and findim d i s p n c e m n t contributed by the t o o l the ad6itlonal notion r e l a t i v e to the displaced centre (Figure A I I I . 9 ) . z
-7iece taticn
-'
=ositi&x of (:.c.u.) 3it
tine t
The limiting position i s a t the front face of the tool where : t o deflecteC ..:or>-
Initial
contact D i f f e r e n t i a t w with respect t o 5 yields
I
Y
.'/
%sition of centre a t tfne t
/
Tig.AIII.? Position of
The angle between the "deflected" ICii and the r a d i a l l i n e through any point on the t o o l i s !J'wfiere
.. *
pe
=
./'
- tan-l
The actual angular position of any radius becose,,i
27Nt +
cut i s
'I'
The radius of any elsment being formed i s : Rom t h i s equation t h e p a @ OP possible cutting positions may be obtained (Figure 5).
The r a d i i forned during t h e final work.Siece revolution before cuttin& ceases m y thus be calculated, provided the t h e frun the cannncemcnt of cut and t h e other geometric p a m e t e r s are Imam.
280