Lubrication of thrust cone bearings

Elastohydrodynamics '96 / D. Dowson et al. (Editors) 1997 Elsevier Science B.V.

287

Lubrication of thrust cone bearings L M Rudd", H P Evan:, a

b

R W Snidleb and D W Parkin;

DERA, Pyestock, Hants, GU14 OLS, UK

University of Wales, Cardiff, CF2 lXF, UK

'Cranfield University, Bedford, MK43 OAL, UK SYNOPSIS

This paper describes investigations into various aspects of the lubrication dynamics of thrust cone bearings. When single helical gears are used to transmit power between parallel shafts there is an axial component of force between the two gears. The common way of reacting this force is by the use of separate thrust bearings mounted on the shafts of the gears. An alternative arrangement involves the use of thrust cones which are conical rims mounted on the edges of the gears close to the teeth. The results of full EHL analyses, validated by film thickness experiments using the interference method, have revealed a very load-sensitive film thinning effect at the edges of such contacts. With a rational comparison to rolling element bearing design and based on the work reported here, it is suggested that edge relief in the form of a circular arc is applied to one of the cone tracks (a 'crowned' cone) to avoid this effect and provide a self aligning elongated elliptical point contact. As a result of the work, validated lubrication design guides for both straight and crowned thrust cones have been produced and descriptions of these will follow in papers to be published elsewhere. NOTATION

Elastic moduli of the bearing surfaces + (1-v,3/Ez 2/E'=(1-vl2)/El Film thickness Central film thickness Minimum film thickness pressure Relative radius of curvature Entraining velocity Load per unit length (line contacts) Pressure - viscosity coefficient Thrust cone angle Dynamic viscosity at ambient pressure Poisson's ratios of the bearing surfaces 1. INTRODUCTION

The work described has been part of a wider ranging study involving collaboration between the Defence Evaluation and Research Agency @ERA), the University of Wales College of Cardiff (VWC), Cranfield University (CU), Leicester University (LU) and Imperial College, London (ICL). In essence the main objective of the work reported here

was to provide validated lubrication design guidance to effect the full economic potential of thrust cone bearings. In particular information relating to localised film thinning and how best to avoid it was obtained. 2. DESCRIPTION OF THRUST CONES

In essence, thrust cone bearings consist of annular rings concentric with the gear axes that form a flange outside the pinion gear addendum circle, with a similar feature on the wheel gear, but inside the wheel dedendum circle, as shown schematically in Figure 1. Apart from the economic and noise benefits afforded by the use of single helical gears, thrust cones have the advantage of compactness and the axial space needed for high power intensity drives can be significantly reduced. Also, as the contact can occur close to the pitch line of the gears further design advantages are possible with reduced bending of the gears and frictional losses. These bearing surfaces may be referred to as rims, rings, cones or tracks and form a nominally rigid 'overlap' thus reacting the out of mesh forces and preventing relative axial movement of the gears. If the track on

288 Wheel axis

/v

Wheel track

Figure 1. Schematic of basic thrust cone geometry showing the overlap area. The left-hand **-.diagram shows the transverse section of the wheel and

Pinion track

CD. The right-hand diagram shows a projection of the thrust cones edge into the common tangent plane at the line of contact.

the wheel and the flange on the pinion were made perpendicular to the gear axes, then contact would occur over the whole of the overlap area. Although, resulting in a low theoretical contact stress, the generation of an oil film at the contact would be ineffective as the converging clearance necessary for hydrodynamic oil film formation would not exist. Consequently h e surfaces are inclined at a small angle to the end face of the gears, called the thrust cone angle, such that a nominal conical geometry results. This allows the formation of a hydrodynamic oil film in the presence of an oil and appropriate angular velocity. Typically, the tracks are no more than 3Omm wide with a cone angle of between one half and two degrees. Thrust cones are by no means a recent invention and although their origin is not clear, it is apparent they have been used with success for some considerable time. In fact some aspects of their lubrication dynamics have already been reported by Langer [l] and Simon [2]. In general their work was appropriate to lightly loaded thrust cones operating

Pinion track

at high speeds where the effects investigated in the work reported here are insignificant. Although Simon forewarned of misalignment producing a point contact at the edges of a thrust cone overlap, no general quantitative design guidance was offered. 3. PRELIMINARY LUBRICATION APPRAISAL

Considering the geometry of these bearings, at first sight, and on the basis of a simple analysis, low contact pressures, thick oil films and good tribological performance are implied. To explain this, in concept a thrust cone with a straight radial profile (or ‘straight’ cone) may be taken as a line contact. The small change in relative radius of curvature (R) across the track width is neglected, which is a reasonable omission for small cone angles. Referring to Figure 2, the radii of curvature of rollers of identical radii to the cone tracks at midpoint, R, and 5,are:-

289 to the cone track radii. In the limit as p tends to zero the surfaces become plane and R tends to infinity as expected. As the contact stress in a line contact is inversely proportional to (R')"2, low contact pressures can be achieved with smaller angle cone tracks. Allied to this, the formula for calculating the minimum oil film thickness in a line contact is given by Dowson and Higginson [3] as:-

'mi"

-

1.63(0r)O.~ ( q , ~ ) ~(E')0.03 .~ (R')o.43

(w')o. 13

(4)

0.43

Here hminis proportional to (R') and therefore for small cone angles substantial oil films are expected.

Figure 2. Schematic showing the development of radii of curvature of rollers of identical radii to the cone tracks at mid-point.

R, =- RP

sin p

R --

RW

*-sin~

Table 1. Conditions and parameters considered.

Then for a thrust cone configuration it can be shown that R is given by:R' =

Relevant data for the design conditions initially investigated are given in Table 1. The minimum oil film thickness at the mean centre line of the cone track was calculated with equation 4 and estimated . the short width of the contact some at 1 6 ~ Given thinning of this centre line value was also anticipated due to side leakage. (In the work that follows and described in section 5 , a reduction of more than 20% was computed). In comparison to the nominal surface roughness of the ground steel cone tracks of 0.4 pm Ra, complete surface separation could be expected. However, it was realised that the actual minimum film thickness could occur at the edges of the contact due to a combination of side leakage and elastic deflection across the cone tracks, implying a possible load dependency not usually anticipated from a cursory analysis using the chosen design formula. Therefore some form of edge relief is appropriate for what may be considered a special case of a short roller.

Rw R, (R, + RP) sin p

(3)

Thus for thrust cone contacts, where the angle p is close to zero, R' is surprisingly large when compared

Maximum normal load on contact Mid-track entraining velocity Cone angle Nominal cone track width Young's Moduli of both cones Relative Radius of Curvature Operating temperature Lubricant - I S 0 VG 68 mineral oil

106kN 24.2ds 1" 20mm 2OOGPa 11.6m 70°C

290 4. QUALITATIVE COMPARISON WITH ROLLING ELEMENT BEARING DESIGN

Before proceeding with a description of the EHL analyses and validation experiments, it is worth making a simple comparison to standard rolling element profile design to rationalise a priori the suggestion of crowning highly loaded thrust cone bearing tracks. For roller bearings, a so called ‘duboff radius is used to provide relief at the roller ends k 1 9 . 1 3 mm-!

I

l

l

contacts of small aspect ratio (straight thrust cones), a radical end or edge relief is required. As effective tribodesign practice of rollers having large contact aspect ratio dictates the form of end relief shown in Figure 3, then for thrust cones a centrally located circular arc across one of the cone tracks seems appropriate. With this in mind, on completion of isothermal EHL analyses relevant to the thrust cone design outlined here, further modelling work was centred on developing a methodology for selection of a crowning radius. 5. RESULTS OF THE STRAIGHT CONES EHL ANALYSES

I

R=7500mml \

I

Figure 3. A typical roller profile design.

(after Hartnett [4])

which improves film forming ability, tolerance to misalignment and reduction in contact stress, all resulting in improved fatigue life. Typically these radii are applied on the end quarters of rollers and may be over a thousand times the roller radius to achieve the correct effect. Figure 3 is extracted from work by Hartnett [4] who developed the design methodology for economic application of this type of end relief in the production process. However, a useful comparison can be made with the contact aspect ratio (roller width/contact length) of Hartnett’s roller contact and the thrust cone contact defined here. For Hartnett’s roller, made of steel and loaded to 20 kN against a steel shaft of 50mm diameter this ratio is approximately 70. In comparison, for the thrust cone set it is 0.4. Therefore it may be implied that for nominal line

A description of the model used in the analysis of the straight cone case considered is given elsewhere by Barragan de Ling et a1 [ 5 ] . Therefore only a brief review of the results is presented. Several analyses were completed at part-load conditions up to the full load also accounting for the fact that the gearing considered was connected to a final drive where the thrust load was proportional to the square of the speed. Although a full thermal EHL analysis was not completed an estimation of temperature rise in the inlet region was made and accounted for in the analysis.

Figures 4 and 5 show pressure and film thickness plots along the nominal cone track overlap centre line (or longitudinal direction) for 25% and full load conditions. As expected for such a contact the value of minimum film thickness was not particularly sensitive to this change in load. However, shown in Figures 6,7 and 8 are similar plots in the radial direction across the cone track (or transverse direction). As originally anticipated these demonstrate the marked effect of load on film thinning at the edges of the contact with a reduction in minimum film thickness there from 6 pn at 25 % load to 0.3 p at full load conditions. Compared to the surface roughness this implies the strong possibility of running in mixed lubrication conditions with the prospect of attendant wear and failure mechanisms associated with this lubrication regime.

-40

80 -

-30

- 20

- 10

20 -

-50

-40

-30

-20

-10

-

0

0

10

,,J

, I

I

-2.5 0.0 2.5

I

I

I

0

I

7.5 "10.0 12.5 15.0 17.5

5.0

mm

Figure 4. The longitudinal film thickness (h) and pressure distribution (p) at 25% load.

Figure 6. The transverse film thickness (h) and pressure distribution (p) at 25% load.

150-

-40

P

125-

- 30 - 20

h

50-

-10

-50 -40 -30 -20 -10

0

-

10

20

30

-2.5 0.0 2.5

I

0

I

7.5 10.0 12.5 15.0 Y -

5.0

mm

mm

Figure 5. The longitudinal film thickness (h) and pressure distribution (p) at full load.

Figure 7. The transverse film thickness (h) and pressure distribution (p) at 80% load.

6. INTRODUCTION OF EDGE RELIEF BY CROWNING

200-

Given confirmationof the load driven film thinning effect with the straight cone profile, further analytical work concentrated on developing the existing model to analyse a crowned cone track profile. This results in a slightly asymmetric elongated elliptical point contact for which some lubrication design formulae may be considered

i/z g!

e~

150-

- 40

P

P

-30

u) u)

8

25 Y C

loo-

-20

h

-E

-10 ii

I

I

I

I

I

0

Figure 8. The transverse film thickness (h) and pressure distribution (p) at full load.

292 crowned thrust cones. This has led to a design rationale for selection of crown radius accounting for the starvation effect caused by transverse misalignment of cone tracks and this will be described in papers that are in preparation.

"

1

1

I

1

1

I

I

1

I

-2.5 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 Y rnrn

-

Figure 9. The transverse film thickness at 25%, 80% and full load with a 1 m crown radius.

the influence of reduced pressure generation area associated with the proximity of the cone track overlap edges. In associated work concentrating on more general cases and reported by Barragan de Ling [8], at certain conditions this effect was found to be very influential on the film forming ability of

...

.

encoder

With the original model modified to account for the lubrication dynamics of crowned cones, analyses were made for the same conditions used in the straight cone work with various crown radii. Figure 9 shows a film thickness plot in the transverse direction for a crown radius of lm. Although the centre line film thickness value (or central film) reduced to approximately 5pm because of this geometry modification, the minimum films were located inside the cone track edges and had increased to between 3pm and 2pm for the 25% and full load condition respectively. 7. EXPERIMENTAL WORK

In support of the modeling work a special test facility was developed and used to provide

Figure 10. Schematic of the test facility spindles and drive layout.

293

the oil film thickness, the corresponding fringe colours in air were divided by the refractive index of the oil. This latter value was dependent on pressure and the nominal Hertz pressure was used in the case of the central film thickness. The minimum film thickness was expected from numerical work to occur at substantially lower pressures, and no pressure correction was made for the minimum oil film thickness measurements. In this way relations of minimum and central oil film thickness with speed were obtained for both straight and crowned cone track profiles. Figure 11. Close up of the wheel and

pinion overlap.

experimental oil film thickness data to validate the numerical work. This facility is more completely described by Parkins and Rudd [9].Although the facility is unique by virtue of configuration and scale, the essence of the method used to measure film thickness is not. The light interference technique was first used to measure oil film thickness by Kirk [lo] and has been developed since that time by a number of workers. A schematic of the test facility layout is shown in Figure 10 while Figure 11 shows a close up of the contact overlap made between the steel wheel specimen and glass pinion specimen. When viewing the contact with either a standard metallurgical microscope for crowned cones or a wide field macro system, for the straight cone experiments, light interference patterns were observed. A wide field macro system was used for the straight cone simply because the contact area was much larger. In both cases a white light source was used with a Kodak Wratten No. 12 filter resulting in a duochromatic system of vivid red and green light fringes. The inference of film thickness information from such fringe patterns required careful calibration of the interference fringes. This was completed in a similar manner to that described by Foord et d [ll]. The calibrations established the separation of two surfaces (in air) corresponding to each fringe colour up to a maximum of approximately 1.4 pn. The calibration was carried out both in-situ using the contact between the thrust cone elements and separately with a specially designed calibration rig so that good agreement was confirmed. To obtain

Experiments were performed at a constant load and oil supply temperature, with the pinion and wheel gearing set for pure rolling at the track over-lap centre line to avoid damage to the reflective coatings on the glass pinion. An experiment consisted of varying the speed gradually and recording the light interference fringe detail on video for subsequent evaluation of the oil film thickness data. Figure 12 shows a typical frame from the video recording of a nominally straight cone experiment which has been reconstructed as a black and white image for the p~nposeof producing this paper. The ‘fringes’ illustrate the main features of contact between nominally straight cone tracks. The film thickness within the contact region was greatest in the region of the cenm of the track and is essentially flat in the direction of lubricant entrainment. There was a ‘nip’ to the rear of the contact which is characteristic of the oil films found in elastohydrodynamic line contacts. The contacts differed significantly from standard line contact behaviour with a significant degree of thinning of the oil film towards the edges of the contact as determined by the associated modelling, as Figure 13 shows. In the ‘fringe’ pattern shown in Figure 12, the minimum film thickness can be seen formed inboard of the edge of the track. The apparent degree of thinning was of the same order as that expected from the theoretical treatment. However, the difference in location was due to a slight rounding of the nominally straight steel track. This slight error of form was apparent at the end of the polishing process necessary to obtain the appropriate degree of reflectivity and fineness of surface finish.

294

--

Contour Key

1

Figure 12. A reconstructed black and white image of a

Figure 13. Theoretical oil film

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ' 18 19 20 21 22 23

'

0.48 0.50 0.55 0.60 0.65 0.70 0.80 1 .oo 1.20 1.40 1.60 1 .80 2.20 2.60 3.00 3.40 3.80 4.60 5.40 6.20 7.00 7.80 8.60

video frame for a straight cone experiment. Entraining velocity 0.375d s , load 4OON. * h,,, - 3rd green fringe at a thickness of 0.63p,0.63 p by model. + h,, 2nd green fringe at a thickness of 0.47p,0.46 pn by model. Refractive index approximately 1.48.

thickness contour plot for the conditions shown in Figure 12.

When measured this slight rounding at the wheel edges equated to a nominal crowning radius of approximately 3 metres. This was taken into account in the modelling and it did not affect the results sufficiently to warrant a further expensive, and probably impossible, finishing operation.

Figure 14 shows a typical frame from the video recording of a crowned cone experiment which again has been reconstructed as a black and white image. The 'fringes' illustrate the main features of an EHL contact with crowned cone tracks. Again, the film thickness within the contact region was greatest at the centre of the track. I t was essentially flat i n the of lubricant direction entrainment and the characteristic 'nip' was seen to the rear of the contact. The nip developed into minimum film thickness lobes towards the edges of the nominal Hertz contact area. The film shape and thickness was found to agree well with the full EHL analysis and sufficient data was acquired to directly validate the relevant numerical models.

--

Figures 15 and 16 show logarithmic plots of oil film thickness with speed for a Figure 14. A reconstructed black and white image of a video frame from a crowned cone experiment. Entraining velocity 0.5 d s . load 660N. crown radius 3oOmm.

295 crowned cone experiment. The linearity is reassuringly good and it can be seen that theory and experiment agree within the 95% confidence limits derived from the experimental data. 8. DISCUSSION 0 Computeddata % confidence

0 Experimental data

limits

0.1

1

Meanspeed m/s

Figure 15. Measured and computed central film

thickness for a crown cone experiment

0.1 ! 0.01

0.1

I

Mean speed m/s

1

- I

Figure 16. Measured and computed minimum film thickness for a crown cone experiment 4 A

Straight surfaces

10

0

25

0

Minimum nm thrkness

A

Mnirmm nm thickness

0 centralfilm thickness

Crowned surfaces

50

75

100 Load kN

-

v

Central nim thickness

125

150

Figure 17. Comparison of the variation of film thickness with load for straight and

crowned thrust cone tracks.

175

It has been shown that thrust cone bearings with straight cone tracks have a nominal line contact and may be compared to a rolling element bearing. To this end when compared with best tribo-design practice for such bearings, as the transverse width of the thrust contacts may not be significantly larger than the nominal Hertzian contact dimension a radical degree of edge relief is implied. In the case of highly loaded slow speed thrust cones it has been shown that the lubrication of such configurations can suffer significantly from the effects of side leakage, and load-driven edge film thinning. To avoid such problems, it is suggested that edge relief in the form of a circular arc is applied to one of the cone tracks to effectively crown one of the surfaces to promote better minimum oil film thinning resistance with respect to load, as justified by the data shown in Figure 17. Although such a modification is an ‘on cost’, even for more lightly loaded higher speed thrust cones where such effects may be less evident, it has a further advantage in that it leads to an intrinsically self aligning contact which can be made more tolerant to misalignment. It will be realised from the comparisons made that crowning also has the effect of increasing contact pressure. However, given the film forming advantage and the fact that for such high conformity bearings contact pressures are generally much lower than those in the associated gear contacts, concern about fatigue resistance is unlikely to dictate any restriction on the use of crowning. 9. CONCLUSIONS

1.

Under certain loading conditions straight thrust cones can suffer from severe oil film thinning at the contact edges.

2.

To counter the edge film thinning effect, profiling one of the cone tracks with a circular arc and effectively edge relieving a nominal line contact by ‘crowning’, leads to more loadstable minimum oil films.

296 10. ACKNOWLEDGEMENTS

The authors gratefully acknowledge the support made available by MOD. We also thank Paul Maillardct and Forbes Morgan of MOD; Norman IIopkinson and Chris Bartlett of DRA; Fkc Frisk of Ealing Optics for supply of the excellent quality glass discs and Harry Shearman of Micro Instruments for the supply of the two special optical systems. REFERENCES

Langer, I{., Hydrodynamische axialkraftubertrgungbei wellen schjnellaufendergetriebe, Konstruktion, 1982, 34,473478. Simon, V., Thennal elastohydrodynamic lubrication of rider rings, Trans ASME, J. Trib., 1984,106,492-498. Dowson, D. and Higginson, G. R. ElastohydrodynamicLubrication, 1977 (Pergamon, Oxford) Hartnett, M. J., The analysis of contact stress in rolling element bearings, JLT, Vol 101.105 - 109, 1979. Barragan de Ling, FdM., Evans, H.P. and Snidle, R.W., Thrust Cone Lubrication: elastohydrodynamicanalysis of conical rims, Proc. I.Mech.E, JET, Vol210,85-96,1995.

Chittenden R.J., Dowson, D., Dunn, J.F., and Taylor, C.M. A theoretical analysis of the isothermal lubrication of concentrated contacts, Pt 1 & 2, Proc.Roy. SOC.,Ser.A, 397,245, (Ptl), 271, (Pt2), 1985. Barragan de Ling, FdM., Lubrication of thrust cones. PhD thesis, University of Wales, 1993. Barragan de Ling, FdM., Evans, H.P. and Snidle,R.W., Thrust Cone Lubrication: elastohydrodynamic analysis of crowned rims, Proc. I.Mech.E, JET, Vol210,97-105,1995. Parkins, D. W. and Rudd, L. M., Thrust Cone Lubrication: a test facility and preliminary measured data, Proc. I.Mech.E, JET, Vol210, 107-112, 1995. [ 101 Kirk, M. T., Hydrodynamic Lubrication of

Perspex, Nature, 1944, 1962,965.

[l 13 Foord, C. A., Wedeven, L. D. Westlake, F. J and Cameron, A,Optical Elastohydrodynamics. Proc. I. Mech. E, Vol 184, Ptl and Pt2, 1969-70. (c) British Crown Copyright 1996DERA Published with the permission of the controller of Her Brittanic Majesty's Stationery Office