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On prediction and experimental assessment of engine-bearing performance
On prediction and experimental assessment of engine-bearing performance M. Dede and R. Holmes*
Semi-analytical methods of predicting journal loci and dynamic oil film pressures in engine bearings are discussed and methods are described utilizing simplifying features in the solution of the Reynolds equatidn. These are similar to, but more accurate than, the analytic short- or long-bearing solutions and it is shown that the results predicted by computer programs based on these new methods agree well with the results given by more 'exact' methods. Comparisons of journal-centre orbits and of oil film p.ressures with results taken from test rigs and from an operating engine are given. Keywords: engine bearing, journal loci, oil film pressure
The prediction of journal-centre loci and dynamic oil film pressures in engine bearings has been approached in a number of ways which have been extensively reviewed in Ref 1. Broadly speaking, these methods divide into two categories: (1) analytical methods, using certain simplifying assumptions to solve the Reynolds equation, such as the short and long-bearing approximations and, (2) methods involving the storage in a computer of a large number of basic solutions of the Reynolds equation, using as parameters eccentricity ratio, attitude angle and journal velocities. By the use of such methods the journal-centre locus is marched out using a time-marching routine, such as the Runge-Kutta method, or Hammings predictor-corrector method. The advantage of methods in the first category is the simplicity of analysis but their disadvantage is poor accuracy at the usual operating conditions of many engines, often at high eccentricity ratios. For methods in the second category this disadvantage is overcome in that accurate solutions of the Reynolds equation can be used. However, the need for high computer storage capacity can be a major problem and this makes these methods much less attractive. Also in practice, it is not easy to specify the oil temperature or its variation in the clearance space of the bearing and with many engines elastic distortion of the bearing shell 2 ,3 leads to departure from established theoretical models. New models would have to be evolved comprising complicated lubrication analysis involving the simultaneous solution of the lubrication equation, the energy equation and the elasticity equations. These requirements make the use of pre-computed data even more complicated and demanding of computer storage 4 • There is thus a need to develop analytic methods which preserve the simplicity of the earlier analytic methods but which give more accurate results at high eccentricities. Such methods are considered here. *Dept. ofMechanical Engineering, University ofSouthampton ' Highfield, Southampton S09 5NH, UK
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Improved analytical methods of solution A comm0l! way of obtaining a fast yet not too inaccurate solution of a partial differential equation such as the Reynolds equation is to use Galerkin's variational method. We first of all recognise that the well known Ocvirk shortbearing solution, say, is likely to give a meaningful shape to the hydrodynamic pressure distribution in a journalbearing oil film 4 • Hence if a multiplication factor can be deduced to correct the level of oil pressure to a reasonably accurate value then we have achieved considerable improvement in the short-bearing analytic approximation. This multiplication factor would in general have to be allowed to take on different values at different points in 'the journal locus. Consider the Reynolds equation for an aligned journal bearing in standard notation: 1
R2
a ae
2 ap* 3 a p* (h ae)+h ~ 3
= 6/1 {(w- 21/1) ah/ae + 2ah/ at} = 6/1B, say
(1)
where
B=(w-2~) ah + 2ah
ae
at
In the conventional Ocvirk solution the first term on the left-hand side is neglected, leaving the equation integrable in z. Putting p* = 0 at z = ± Z/2 (l being the land length) gives
p* = po* = -
3J.1B z2
h3 2
2z 2 (1 - (-Z-) )
(2)
in which the film thickness h is a function of e. It is now assumed that p* = exPo*, where ex is a multiplying factor to be determined. Thus Eq (1) may be rewritten: 1
ex' R 2
a ae
3
h apo* (--ae)+ h
3
a2 po*
ex . ~ = 6/1B
0301-679X/84/050251-08 $03.00 © 1984 Butterworth & Co (Publishers) Ltd
251
Dede and Holmes - assessment of engine-bearing performance
The error E in the above equation may be written as:
Nomenclatu re A 1TIJ.R(1/c)3.jkm b 6tJ.B/Pch3 , . 3h 2ah B (w-21J;) 30 +at
a 3 h 3 3po* 32 Po* E= - 2 - ( - - )+h 3 a - -61J.B R 30 30 3z 2 and an optimum value of a found by requiring that:
f
1/2 f (J. Epo* dO dz = -1/2 0 1
a
By this means we make the error E orthogonal to p *. This has the effect of minimizing the error in a kind of least squares fashion, provided Po* is a fairly good approximation to the solution in the first place. We could adopt a cruder approach by noting that: 3
2
h 3 po*
= 6IJ.B (the short bearing approximation)
3z 2
h 3 3po*
a
a
Thus R 2
h30p*
I 0 or a = [ - - • - C o ) + 1]
.
6IJ.BR 2
30
-1
30
radial clearance journal diameter journal eccentricity
G
oPc -aeo [h ae ]IPc h
(3)
k
k
k/mw 2
K 1
multiplying factor journal-land length journal mass per land maximum pressure in axial direction long·bearing pressure average pressure in axial direction oil film pressure oil film pressure using Ocvirk short-bearing approximation dynamic load per land
P p*
HaVing found a at a given point on the locus, the pressure distributionp(O, z)can be found, from which the sub· ambient pressure region is usually curtailed before integration to form the oil film forces. If we used a still cruder approximation we could even assume that a were not a function of z, but the results would be expected to be only a little more accurate than the Ocvirk solutions.
3
oil film thickness = c(l + € cosO) stiffness ofparallel spring support
h
Pc p...
Although Po* isa parabolic function of z (Eq (2)), p* = apo* will no longer be a parabolic function of z.
Po*
Pc lmcw 2
z
Alternatively, but in the same vein, we may argue that the long·bearing solution gives an adequate form of circumferential pressure distribution, while retaining a parabolic form in the axial direction 6 • Thus we might postulate by comparison with Eq (2), that: 2z
3
m
(---a7J ) = 61J.B (1 - a)
30
•
c D e
w
journal radius time axial coordinate eccentricity ratio static eccentricity ratio circumferential coordinate oil film limits lubricant viscosity attitude angle rotational speed of journal
2
p* = Pc{O) [1 - ( - ) ] 1 K
whence:
R2
02 p *
8
=-
3z2
[2 Pc (0)
3 h 3 0p...(0) 30 ( ao
12h 3
)- J2 KP...(O) = 6IJ.B
and K found by minimizing the error as before. But using the long-bearing approximation:
Thus, Eq (1) becomes
6 B= ~ ~ ( h p...(0) ) IJ. R 2 00 30 3
1 0 h 30p* 8h 3 R 2 00 (---ae) "/2 Pc ((f) = 6IJ.B
(4)
we can achieve a crude estimate by writing: Now the average pressure p(O) in the axial direction is given by:
p(O)
=j
6IJ.B (K - 1) =
Pc(O) where K = [1 -
and so Eq (4) becomes:
I R2
0
ao
3
h 0p* (----ae)- r12h
3
p (0) =' 6IJ.B
(5)
in which p(O) is constant in the axial direction. As such it can be compared with the long-bearing pressure p...(O), and indeed we may again use the variational approach by writing p(O) = KpOo(O). Eq (5) may thus be written:
252
r12h
3 K·p...(O)
2h3p...(0) 2
1 IJ.B
-1 ]
(6)
This compares with Eq (3) for the variational method applied to the short·bearing pressure Po*(O, z), but Eq (6) has the advantage that p... (O) is not now a function of z and so the utilization of K is that much easier. Furthermore, boundary conditions in 0 can still be accommodated if axial grooves are to be considered. HaVing found K at a given point in the journal·centre locus, we can write:
October 1984 Vol 17 No 5
Dede and Holmes - assessment of engine-bearing performance
c
b
a
d
.Fig 1: (a) The 1800 cc engine load pattern; (b) journal-centre orbit, plain bearing; (c) journal-eentre orbit, bearing with single supply hole, approximated as an axial groove; (d) journal-centre orbit, bearing with a halfcircumferential groove
p(O):Kp~(O)
and integrate to find the oil film forces, again curtailing the negative pressure at some prescribed value. Yet another semi-analytical solution is obtained by assuming that the pressure distribution in the lubricant film is given by:
p*(O, z): fez) . Pe(O) where Pe(O) is the circumferential pressure around the axial centre line. Under these circumstances Eq (1) becomes: G
Ii. )
b +(
2
d2 f f - dz 2
:
(7)
0
where b : 6J.1BIPeh3 and G 2
:
• ~ [h2 ape]
__ 1_
ao
Peh3
ao
At this stage no prior assumption is made about the forms of fez) and Pe(O). If we employ the usual boundary conditionsf: 0 at z: -112 and z: +112 we obtain:
6J.1B
p*(O, z): -
Y
R
cosh(GzIR)
2
( G) [1 - cosh(G1ID) ]
(8)
If in Eq (7) we observe that dfldz ~ 0 and f ~ 1 as liD ~ 00, then we can write: G
2
2
6J.1BR = --p~h3
for liD ~ 1
in which p~(O) is the long-bearing pressure distribution. Hence Eq (8) becomes: cosh (GzlID) p*(O,z):p~[l- cosh(G1ID) ]
(9)
where z : 2zl1 and G 2 : - 6J.1BR 2 Ip~h3. The term in brackets may be looked upon as a modifying factor applied to the long-bearing pressure distribution p~ and accounting for end leakage. p* may be curtailed as required before integration to allow for cavitation and to find the film forces. Eq (9) compares with the pressure distribution obtained from the solution of Eq (5) using Eq (6), namely _
2
2h3p~
P (0): - Pe(O): p~ [1 - - 2 - ] 3 1 J.1B
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-!
(10)
To the authors' knowledge, neither Eq (9) nor (10) has been previously applied in predictive work on engine bearings and so both were investigated. Of the two, Eq (9) looked the more promising, since it utilized less a priori assumptions about the shape of the pressure profile, without sacrificing computing time. The method leading to Eq (3) was not used as Eq (3) is rather more cumbersome, involving as it does both z and O. The accuracy and speed of the method selected were assessed against solutions of the full two-dimensional Reynolds equation, using typical engine-bearing load patterns and oil-inlet geometries. Finally the numerical results for both journal-centre orbits and dynamic oil film pressures were compared with experimental findings from laboratory test rigs and from an operating diesel engine.
Comparisons with experimental journal-centre orbits The load pattern of the intermain bearing of a 1.8 litre 4-cylinder in-line gasoline engine was first considered, having one of several oil-inlet arrangements. The polar-load diagram for this bearing indicated that most of the load was concentrated in the bottom half of the bearing (Fig 1(a)). Journal-centre orbits were computed for the bearing with a full circumferential groove for different values of effective rotating mass. These illustrated that the inertia force due to the effective mass results in quite different orbits for cases where this mass may playa significant role. For example, for the drive-end main bearing of an engine the mass of the flywheel could be important. It was apparent that the larger the mass, the smaller the orbit, that is the smaller the relative effect of the external forces! . Journal-centre orbits were then compared for a plain bearing (Fig l(b)) and for a bearing with a single supply hole (Fig l(c)), both assuming that cavitation commences at -14.7 lbf/in 2 ( -1 bar) and curtailing the negative pressure region at this value. In both cases the orbits were almost indistinguishable from those obtained by using the full two-dimensional solution ofthe Reynolds equation. Fig 1(d) shows the journal-centre orbit for a bearing which is grooved in its upper half. The lower portion of the orbit remains essentially the same as in Figs 1(b), (c), but the upper portion is of greater eccentricity, owing to the reduced load-carrying capacity arising from the presence of the groove.
253
Dede and Holmes - assessment of engine-bearing performance
The load patterns of the big end bearings of the 6VEB engine 1 and of the ASRI 16 VMS engine have also been used in the past for reference purposes. These load patterns have been simulated on a dynamic bearing test-rig at the National Engineering Laboratory, East Kilbride, Scotland 7,8. They are shown in Figs 2(a) and 2(d), respectively. The experimental and numerically-predicted orbit comparisons for a full-circumferentially grooved bearing are shown for each engine in Figs 2(b), (c) and 2(e), (f), respectively and show good agreement, although the film thickness is generally greater in the experimental recordings. This may have been due to unavoidable lack of circularity of the test bearing and to possible local distortion under high loads. Some change in viscosity due to local temperature effects and even to local shear rate and/or pressure effects may also have played its part. This increased film thickness was reflected in measured dynamic pressures lower than predicted, as discussed in the following section.
the test rig. All comparisons indicate good agreement in respect of phasing, but poor to fair agreement in respect of amplitUdes, the peak numerical predictions always being higher than the experimental recordings, for the possible reasons mentioned in the previous section. Also the pressure transducers used were large, occupying about 10° of atc and about half the land width, thus spreading the pressure and reducing the peak. A 6-cylinder ASRl/6LTS engine was also tested for the purpose of again comparing predicted and experimental hydrodynamic pressures in its no 1 big-end bearing. The engine was located at the Admiralty Engineering Laboratory, West Drayton, its specification being described in Ref 9. Its load pattern is similar to (but not equal to) that of the 6VEB engine (Fig 2(a». Data transmission was achieved through a mechanical linkage while the engine was running. The bottom half of the bearing, that is the half adjacent to the cap, was grooved to provide two lands of width 2.3437" (59.53 mm) and three pressure transducers, T 1 , T 2 and T 3 were located in the top half of the bearing (Fig 4(a». The engine was run under no-load conditions at a speed of 750-760 r/min, and the pressure signals were displayed on an oscilloscope. Figs 4(b), (c), show, respectively, predicted and experimental pressure recordings; As expected, the maximum positive pressure occurs at the inner location T 1 , being about 2000 Ibf/in 2 gauge (13.8 MN/m 2 ). The corresponding predicted value is about 2100 Ibf/in 2 (14.5 MN/m 2 ) and for both predictions and measurements, three peaks per cycle are dis-
Comparisons of dynamic oil film pressures Bearing pressure recordings were taken from the same testrig and from an actual diesel engine. In the former pressure transducers were proVided at four locations situated around the circumference of the bearing. In the latter three axial locations were used. Using the 6VEB engine load pattern of Fig 2(a), (Ref 8), Fig 3 shows comparisons between predicted and experimental dynamic pressures at each of the four locations on
a
b
c
d
e
f
Fig 2: (a) The 6 VEE engine big-end bearing load pattern with crank angles after TDC firing; (b) measured journal-centre orbit, full circumferential groove; (c) numerically-predicted journal-centre orbit, full circumferential groove, with crank angles after TDC firing; (d) the 16 VMS engine big-end bearing load pattern; (e) measured journal-orbit, full circumferential groove; (f) numerically-predicted journal-centre orbit, full circumferential groove. (All load and bearing data appear in NEL report No. 688 8 )
254
October 1984 Vol17 No 5
Dede and Holmes - assessment of engine-bearing performance
played. As far as shape and spacing are concerned agreement is seen to be good, despite measured deformation of the bearing under 10ad3 .
The squeeze-film bearing A squeeze film is an annulus of oil supplied between the outer race of a rolling-element bearing (or the bush of a sleeve bearing) and its housing. It is used as a multidirectional damping element for the control of engine vibrations. Such a squeeze fihn is often placed in parallel with a soft flexible element to comprise a vibration isolator. By this means the natural frequencies of the x 10 2,----5000 50
N
c "'>-
engine are artificially reduced so that they may be traversed well before the normal operating speeds are reached. The purpose of the damper in this application is to reduce to acceptable levels the amplitudes of vibration and transmitted force due to unbalance as these low natural frequencies are traversed. The performance of squeeze-film bearings may be investigated by putting w = 0 in the factor B of Eq (1). Although the mechanism of cavitation is quite different from that in an ordinary journal bearing, it is often broadly assumed that it occurs when the dynamic pressure drops below absolute zero (-14.7 lbf/in 2 gauge). To investigate this xI02, -
---,
5000
e*: o'
;;c-
e*
50
45
45
40
40
35
35
30 25
30 25
---,
e*: 90
-0 Q)
:J V> V>
2500
:" 0.-
2500
20
20
15
15
10
10 5 00
b
a 5000 N
c
x 10 50
2 ~
e*:
5000
180'
xl0 2 50
45
45
40
40
-0
35
35
:"
30 25
"-
e*: 270'
'>-
-. :J V> V>
2500
:"
2500
20
0.-
Predicted Experimenta I
30 25 20
15
15 10 5 0
c
0
202530354045 5055 60657
I
360
d
Crank angle
Cronk angle
Fig 3. Measured (dashed) and predicted pressure recordings for bearing with a full circumferential groove using the 6 VEB engine load pattern ofFig 2(a). Pressure in Ibf/in 2 versus crank angles in degrees after TDC firing. (() * denotes position of pressure transducers)
Crank angle
b
Cronk ong!e
c
Fig 4: (a) Big-end bearing of the 6LTS engine showing location of the pressure transducers (L' = 65 mm, D = 159 mm, C= 0.0925 mm, maximum load = 130 kN); (b) predicted pressure recordings; (c) measured pressure recordings (1 div = 1100 Ibf/in 2 (7585 kN/m 2 )) Crank angle after TDC firing
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255
Dede and Holmes - assessment of engine-bearing performance
assumption and the general performance of the squeezefilm bearing, tests were carried out on a rig consisting of a squeeze-film in parallel with a spring beam. Typical predicted and measured pressure waveforms for concentric circular orbits of journal-centre motion are shown in Fig 5. The measured dynamic eccentricity ratios were 0.31 and 0.73, and the values of other nondimensional groups are indicated. The predicted pressures were calculated on the assumption of a full 360° film and show good agreement with the measured recordings. Indeed peak pressures predicted from a wide range of tests using circular concentric orbits compared well with those found experimentally. In Fig 6 theoretical and experimental vibration orbits are shown for non-concentric operation, in which static eccentricity ratios of 0.4 and 0.8 were set. Again, to obtain numerical predictions, a full 360° squeeze film was first assumed. The agreement between numerical predictions and experimental recordings is good, particularly in respect of orbit shape and disposition. However, in Fig 6(c), the predicted orbit (shown as a continuous line) is much
smaller than that obtained experimentally. In seeking an explanation for this, the recording (Fig 7(a)) from a pressure transducer at the base of the squeeze film was examined. It indicates that the negative pressure was sometimes curtailed at allout the absolute-zero level. At other times, however, J:J.'egative pressures were much lower than this, which was indicative of the fact that the lubricant could sustain tensile stresses for a short period, during which the pressure changed rapidly from positive to negative. Evidence of tensile stresses has also been encountered by several other workers in the fields of squeeze-film bearings and journal bearings. In the present work, it can be seen from Fig 7(a) that the lowest recorded negative pressure was about -30 Ibf/in 2 g (-207 kN/m 2 ). This suggests that the numerical method of solution should be modified in such a way that it can accommodate some negative pressure, although not its maximum uncavitated value. The value of this negative pressure is not, however, known precisely for any given application, unless this is measured experimentally. To give an idea of the sensitivity of the orbit to the assumed limit of negative pressure, Fig 6(c) shows, in addition to the small continuous orbit (corresponding to a full film) two dashed orbits, marked (1) and (2), corresponding to negative-pressure curtailment at (1) -16 Ibf/in 2 g (-110 kN/m 2 ) and (2) -30 lbf/in 2 g (-207 kN/m 2 ) before
b
c b Fig. 5 Comparison ofpredicted and measured squeeze-film pressure (Scale: 1 small division = 10 kN/m 2 ): (a) E = 0.31, Qc = 1. 07, A = 1. 764: (b) E = O. 73, Qc = 1.60, A = 0.456
256
Fig. 6 Non-concentric journal-centre orbits (Left-predicted; Right-measured): (a) Eo := 0.4, Qc = 1.12, A=: 0.456; (b) Eo = 0.8, Q c = 1.12, A= 0.456; (c) Eo = 0.8, Q c = 2.25, A= 0.456
October 1984 Vol 17 No 5
Dede and Holmes - assessment of engine-bearing performance
integration to obtain the squeeze-film forces. The effect can be seen to be quite profound and serves to explain why experimental and theoretical orbits for squeeze-film bearings do not always agree. The corresponding predicted pressure waveform at the base of the clearance circle agreed fairly well with the measured pressure but its peak positive value was appreciably greater than that measured. The unique form of cavitation present in the squeeze-film may have been in some part responsible. By replacing the steel bearing by a bearing made of perspex, the cavitation region was observed. This consisted of a myriad of tiny bubbles, as distinct from the streamer-like cavitation observed in normal journal bearings, in which the rotating member plays a significant role in pressure generation. These bubbles were generated in the lowpressure region of the squeeze'film but persisted in the high-pressure period at high dynamic eccentricity ratios. They were probably responsible for the limited positive pressure observed experimentally. Curtailment of the positive pressure as well as the negative pressure at the experimentally-recorded limits of 40 lbf/in 2 g (276 kN/m 2 ) and -30 lbf/in 2 g (-207 kN/m 2 ), respectively, produced the dashed orbit (3) of Fig 6(c), and the pressure waveform of Fig 7(b). Orbit (3) shows considerable improvement when compared with the experimental orbit, and the corresponding pressure waveform of Fig 7(b) shows fair agreement with Fig 7(a). It may thus be that, in the absence of an adequate supply pressure to flush away the cavities, the oil film containing these cavities remains almost stationary, while the pressure field moves through it 10. This is a state of affairs quite different from that pre-
I atmosphere
--Absolute zero level
vailing in ordinary journal bearings. The fact that the formation of tension spikes is intermittant may well be indicative of the presence of a different number of bubbles at the same instant in each cycle, due to the partial success of the supply pressure in flushing some bubbles away. Finally, for certain values of relevant nondimensional groups, the nonlinear frequency response of the squeezefilm damper assembly was determined (Fig 8(a) and this agrees fairly well with numerical predictions (Fig 8(b» based on the curtailment of the hydrodynamic pressure at the absolute zero level when this was attained.
Conclusions This work has shown that a fast semi-analytical prediction method, adopted for the determination of journal-centre loci and oil film pressures, gives results commensurate with those using a full two-dimensional solution, the time saving being of the order of 90 %_ Also, numerical predictions show fairly good agreement with experimental results from test rigs and from an operating engine. The major differences were that predicted pressures were in general greater than experimental for both piston engine bearings and squeeze-film bearings for moderate to high loads. Some explanations for these differences have been put forward.
Acknowledgements The authors acknowledge with thanks the financial support provided by the SERC to carry out this work. Thanks are also due to Mr. F.A. Martin of Glacier Metal Co. Ltd., Mr. W. L. Cooke, late of NEL East Kilbride and Mr. Les Lawrence of MoD West Drayton, Middx. for the use of their test facilities and for useful discussions. Dr. G. Good-
~'O
~1i'-~
:+:
k =0.6
a
a 40
20I-
o
o
f.
Ai
k = 40 j,
I
r Sr 'flvo
Aj
If
TV' s('
wtlxl0 2 )
20
-20, -
-40
.--._----------_..
b Fig 7. Pressure waveforms (eo = 0.8, Qc = 2.25, A = 0.456): (a) Measured, 1 div = 8lbf/in 2 (55 kN/m 2 ); (b) Predicted
TRIBOLOGY international
k = 0.6
b Fig 8. Frequency responses (eo = 0.8, Q c = 0.22, A = 0.02) (a) Predicted, with sample applied force vectors; (b) Measured.
257
Dede and Holmes - assessment of engine-bearing performance
win is to be thanked for carrying out the experimental programme which led to the recording of Fig 4(c).
References
journal bearings. Wear, 1970, 16,221-228 6.
Black H.F. and Brown R.D. Fast dynamic calculations for non-circular bearings. L Mech. E., Tribology Convention, Durham, April 1976
7.
Cooke W.L. Performance of dynamically loaded journal bearings, Part 1: Effect of varying bearing geometry and oil supply conditions. NEL Report No 683, March 1983
1.
Martin F.A. Developments in engine bearing design. Trib. Int. June, 1983, 16(3)
2.
Goodwin G. and Holmes R. Determination of oil film thickness in a crankshaft main bearing. J. Automot. Engng, June 1975, 6(3),6-10
8.
Cooke W.L. Performance of dynamically loaded bearings, Part 2: Measurements of oil film pressure in dynamically loaded bearings. NEL Report No 688, 1983
3.
Goodwin G. and Holmes R. On the continuous monitoring of oil-film thickness in an engine bearing. Proc. L Mech. E., 1978,192(31),371-376
9.
Goodwin G. and Holmes R. On the continuous temperature monitoring of an engine bearing. Proc. L Mech. E., 191, Paper (12/77), 161-167
4.
Ritchie S. The prediction of journal loci in dynamically loaded internal combustion engine bearings. Wear, 1975, 35,291-297
5.
Shelley B. and Ettles C. Tractable solution for medium-length
10. Marsh H. Cavitation in dynamically loaded journal bearings. Proc. Leeds-Lyon Symp. entitled Cavitation and Related Phenomena in Lubrication, Sept 1974,91-95
ESDU software A range of software for engineering design and analysis has been introduced by ESDU International. Suitable for use on the IBM PC, the packages include: • Analysis of forced-damped vibrating systems (cost £150) • Hydrodynamic.journal bearing design (£400) • Rolling element bearing selection (£400) • Design of parallel-axis spur and helical gears (£400) • Hydrodynamic thrust bearing design (£400) • Elastohydrodynamic ffun thickness (£200) • Rotor dynamics - rolling bearings (£400) • Rotor dynamics - general systems (£400) • Rotor dynamics - hydrodynamic journals (£400) ESDU claims the user's manual to be the most comprehensive on the market. For further information contact ESDU International Ltd, 251/9 Regent Street, London WIR 7AD, UK
New materials for automobiles Vehicle manufacturers are concentrating much of their resources on development and application of 'new' materials. They see this as the route to more efficient, smaller and lighter vehicles which take less energy to produce. At Toyota, composite aluminium alloy pistons have been cast with ceramic
258
fibre preform, thus making use of the ability of ceramic fibre and aluminium alloy to suppress heat expansion and maintain adequate clearance between piston and cylinder wall. This ensures better resistance to seizure. Molybdenum sintered alloy has been used by Toyota to form the cams on an integralsteel tube camshaft, research having shown this material to exhibit the optimum combination of wear resistance and sintering properties. These are just two examples of many novel materials applications contained in 'New Materials and the Automobile', a 32-page brochure produced recently by Toyota. The booklet gives a brief appraisal of the materials currently used in automobile manufacture, runs through a history of materials research and application in the company and links the development of vehicles running on 'alternative energy' and in accordance with modern demands, to the need for new materials in sensors
and actuators. The bulk of the contents comprises brief descriptions of individual applications of new materials in modern vehicles. Further information or a copy of the brochure are available from Toyota (GB) Ltd, The Quadrangle, 108-118 Station Road, Redhill, Surrey, RHI IPX, UK
Condition monitoring conference The third IMEKO Seminar on 'Condition Based Maintenance and Technical Diagnostics of Machines' is to be held on 17-27 September 1985 in Zagreb, Yugoslavia. Topics to be considered include: measuring, methods and diagnostic equipment; technical diagnostics in accomplishing progressive maintenance methods; and formulation of test procedures and standards. Institute for Developing Countries, PO Box 303, 41001 Zagreb, Yugoslavia.
14-18 April 1985, Vancouver, BC, Canada
Wear of Materials Eighteen technical sessions are planned, and based on a review of the 184 abstracts received by July the organizers expect: three or four sessions on wear of metals; two or three sessions each on abrasive wear, wear theory, and case studies on wear of devices; one or two sessions on erosion; up to one session each on wear of polymers, wear of composite materials, wear of coatings and wear of ceramics. Further information on the above
sessions can be obtained from the Programme Chairman, Mr R. G. Bayer, IBM Corporation, PO Box 6, Endicott, NY 13760, USA. One post-deadline session is planned as well, at which short presentations are sought on practical problems, new ideas and late developments. To arrange a place in this session, contact Professor S. Bahadur, Mechanical Engineering Department, Iowa State University, Ames, IA 50011, USA.
October 1984 Vol17 No 5
Semi-analytical methods of predicting journal loci and dynamic oil film pressures in engine bearings are discussed and methods are described utilizing simplifying features in the solution of the Reynolds equatidn. These are similar to, but more accurate than, the analytic short- or long-bearing solutions and it is shown that the results predicted by computer programs based on these new methods agree well with the results given by more 'exact' methods. Comparisons of journal-centre orbits and of oil film p.ressures with results taken from test rigs and from an operating engine are given. Keywords: engine bearing, journal loci, oil film pressure
The prediction of journal-centre loci and dynamic oil film pressures in engine bearings has been approached in a number of ways which have been extensively reviewed in Ref 1. Broadly speaking, these methods divide into two categories: (1) analytical methods, using certain simplifying assumptions to solve the Reynolds equation, such as the short and long-bearing approximations and, (2) methods involving the storage in a computer of a large number of basic solutions of the Reynolds equation, using as parameters eccentricity ratio, attitude angle and journal velocities. By the use of such methods the journal-centre locus is marched out using a time-marching routine, such as the Runge-Kutta method, or Hammings predictor-corrector method. The advantage of methods in the first category is the simplicity of analysis but their disadvantage is poor accuracy at the usual operating conditions of many engines, often at high eccentricity ratios. For methods in the second category this disadvantage is overcome in that accurate solutions of the Reynolds equation can be used. However, the need for high computer storage capacity can be a major problem and this makes these methods much less attractive. Also in practice, it is not easy to specify the oil temperature or its variation in the clearance space of the bearing and with many engines elastic distortion of the bearing shell 2 ,3 leads to departure from established theoretical models. New models would have to be evolved comprising complicated lubrication analysis involving the simultaneous solution of the lubrication equation, the energy equation and the elasticity equations. These requirements make the use of pre-computed data even more complicated and demanding of computer storage 4 • There is thus a need to develop analytic methods which preserve the simplicity of the earlier analytic methods but which give more accurate results at high eccentricities. Such methods are considered here. *Dept. ofMechanical Engineering, University ofSouthampton ' Highfield, Southampton S09 5NH, UK
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Improved analytical methods of solution A comm0l! way of obtaining a fast yet not too inaccurate solution of a partial differential equation such as the Reynolds equation is to use Galerkin's variational method. We first of all recognise that the well known Ocvirk shortbearing solution, say, is likely to give a meaningful shape to the hydrodynamic pressure distribution in a journalbearing oil film 4 • Hence if a multiplication factor can be deduced to correct the level of oil pressure to a reasonably accurate value then we have achieved considerable improvement in the short-bearing analytic approximation. This multiplication factor would in general have to be allowed to take on different values at different points in 'the journal locus. Consider the Reynolds equation for an aligned journal bearing in standard notation: 1
R2
a ae
2 ap* 3 a p* (h ae)+h ~ 3
= 6/1 {(w- 21/1) ah/ae + 2ah/ at} = 6/1B, say
(1)
where
B=(w-2~) ah + 2ah
ae
at
In the conventional Ocvirk solution the first term on the left-hand side is neglected, leaving the equation integrable in z. Putting p* = 0 at z = ± Z/2 (l being the land length) gives
p* = po* = -
3J.1B z2
h3 2
2z 2 (1 - (-Z-) )
(2)
in which the film thickness h is a function of e. It is now assumed that p* = exPo*, where ex is a multiplying factor to be determined. Thus Eq (1) may be rewritten: 1
ex' R 2
a ae
3
h apo* (--ae)+ h
3
a2 po*
ex . ~ = 6/1B
0301-679X/84/050251-08 $03.00 © 1984 Butterworth & Co (Publishers) Ltd
251
Dede and Holmes - assessment of engine-bearing performance
The error E in the above equation may be written as:
Nomenclatu re A 1TIJ.R(1/c)3.jkm b 6tJ.B/Pch3 , . 3h 2ah B (w-21J;) 30 +at
a 3 h 3 3po* 32 Po* E= - 2 - ( - - )+h 3 a - -61J.B R 30 30 3z 2 and an optimum value of a found by requiring that:
f
1/2 f (J. Epo* dO dz = -1/2 0 1
a
By this means we make the error E orthogonal to p *. This has the effect of minimizing the error in a kind of least squares fashion, provided Po* is a fairly good approximation to the solution in the first place. We could adopt a cruder approach by noting that: 3
2
h 3 po*
= 6IJ.B (the short bearing approximation)
3z 2
h 3 3po*
a
a
Thus R 2
h30p*
I 0 or a = [ - - • - C o ) + 1]
.
6IJ.BR 2
30
-1
30
radial clearance journal diameter journal eccentricity
G
oPc -aeo [h ae ]IPc h
(3)
k
k
k/mw 2
K 1
multiplying factor journal-land length journal mass per land maximum pressure in axial direction long·bearing pressure average pressure in axial direction oil film pressure oil film pressure using Ocvirk short-bearing approximation dynamic load per land
P p*
HaVing found a at a given point on the locus, the pressure distributionp(O, z)can be found, from which the sub· ambient pressure region is usually curtailed before integration to form the oil film forces. If we used a still cruder approximation we could even assume that a were not a function of z, but the results would be expected to be only a little more accurate than the Ocvirk solutions.
3
oil film thickness = c(l + € cosO) stiffness ofparallel spring support
h
Pc p...
Although Po* isa parabolic function of z (Eq (2)), p* = apo* will no longer be a parabolic function of z.
Po*
Pc lmcw 2
z
Alternatively, but in the same vein, we may argue that the long·bearing solution gives an adequate form of circumferential pressure distribution, while retaining a parabolic form in the axial direction 6 • Thus we might postulate by comparison with Eq (2), that: 2z
3
m
(---a7J ) = 61J.B (1 - a)
30
•
c D e
w
journal radius time axial coordinate eccentricity ratio static eccentricity ratio circumferential coordinate oil film limits lubricant viscosity attitude angle rotational speed of journal
2
p* = Pc{O) [1 - ( - ) ] 1 K
whence:
R2
02 p *
8
=-
3z2
[2 Pc (0)
3 h 3 0p...(0) 30 ( ao
12h 3
)- J2 KP...(O) = 6IJ.B
and K found by minimizing the error as before. But using the long-bearing approximation:
Thus, Eq (1) becomes
6 B= ~ ~ ( h p...(0) ) IJ. R 2 00 30 3
1 0 h 30p* 8h 3 R 2 00 (---ae) "/2 Pc ((f) = 6IJ.B
(4)
we can achieve a crude estimate by writing: Now the average pressure p(O) in the axial direction is given by:
p(O)
=j
6IJ.B (K - 1) =
Pc(O) where K = [1 -
and so Eq (4) becomes:
I R2
0
ao
3
h 0p* (----ae)- r12h
3
p (0) =' 6IJ.B
(5)
in which p(O) is constant in the axial direction. As such it can be compared with the long-bearing pressure p...(O), and indeed we may again use the variational approach by writing p(O) = KpOo(O). Eq (5) may thus be written:
252
r12h
3 K·p...(O)
2h3p...(0) 2
1 IJ.B
-1 ]
(6)
This compares with Eq (3) for the variational method applied to the short·bearing pressure Po*(O, z), but Eq (6) has the advantage that p... (O) is not now a function of z and so the utilization of K is that much easier. Furthermore, boundary conditions in 0 can still be accommodated if axial grooves are to be considered. HaVing found K at a given point in the journal·centre locus, we can write:
October 1984 Vol 17 No 5
Dede and Holmes - assessment of engine-bearing performance
c
b
a
d
.Fig 1: (a) The 1800 cc engine load pattern; (b) journal-centre orbit, plain bearing; (c) journal-eentre orbit, bearing with single supply hole, approximated as an axial groove; (d) journal-centre orbit, bearing with a halfcircumferential groove
p(O):Kp~(O)
and integrate to find the oil film forces, again curtailing the negative pressure at some prescribed value. Yet another semi-analytical solution is obtained by assuming that the pressure distribution in the lubricant film is given by:
p*(O, z): fez) . Pe(O) where Pe(O) is the circumferential pressure around the axial centre line. Under these circumstances Eq (1) becomes: G
Ii. )
b +(
2
d2 f f - dz 2
:
(7)
0
where b : 6J.1BIPeh3 and G 2
:
• ~ [h2 ape]
__ 1_
ao
Peh3
ao
At this stage no prior assumption is made about the forms of fez) and Pe(O). If we employ the usual boundary conditionsf: 0 at z: -112 and z: +112 we obtain:
6J.1B
p*(O, z): -
Y
R
cosh(GzIR)
2
( G) [1 - cosh(G1ID) ]
(8)
If in Eq (7) we observe that dfldz ~ 0 and f ~ 1 as liD ~ 00, then we can write: G
2
2
6J.1BR = --p~h3
for liD ~ 1
in which p~(O) is the long-bearing pressure distribution. Hence Eq (8) becomes: cosh (GzlID) p*(O,z):p~[l- cosh(G1ID) ]
(9)
where z : 2zl1 and G 2 : - 6J.1BR 2 Ip~h3. The term in brackets may be looked upon as a modifying factor applied to the long-bearing pressure distribution p~ and accounting for end leakage. p* may be curtailed as required before integration to allow for cavitation and to find the film forces. Eq (9) compares with the pressure distribution obtained from the solution of Eq (5) using Eq (6), namely _
2
2h3p~
P (0): - Pe(O): p~ [1 - - 2 - ] 3 1 J.1B
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-!
(10)
To the authors' knowledge, neither Eq (9) nor (10) has been previously applied in predictive work on engine bearings and so both were investigated. Of the two, Eq (9) looked the more promising, since it utilized less a priori assumptions about the shape of the pressure profile, without sacrificing computing time. The method leading to Eq (3) was not used as Eq (3) is rather more cumbersome, involving as it does both z and O. The accuracy and speed of the method selected were assessed against solutions of the full two-dimensional Reynolds equation, using typical engine-bearing load patterns and oil-inlet geometries. Finally the numerical results for both journal-centre orbits and dynamic oil film pressures were compared with experimental findings from laboratory test rigs and from an operating diesel engine.
Comparisons with experimental journal-centre orbits The load pattern of the intermain bearing of a 1.8 litre 4-cylinder in-line gasoline engine was first considered, having one of several oil-inlet arrangements. The polar-load diagram for this bearing indicated that most of the load was concentrated in the bottom half of the bearing (Fig 1(a)). Journal-centre orbits were computed for the bearing with a full circumferential groove for different values of effective rotating mass. These illustrated that the inertia force due to the effective mass results in quite different orbits for cases where this mass may playa significant role. For example, for the drive-end main bearing of an engine the mass of the flywheel could be important. It was apparent that the larger the mass, the smaller the orbit, that is the smaller the relative effect of the external forces! . Journal-centre orbits were then compared for a plain bearing (Fig l(b)) and for a bearing with a single supply hole (Fig l(c)), both assuming that cavitation commences at -14.7 lbf/in 2 ( -1 bar) and curtailing the negative pressure region at this value. In both cases the orbits were almost indistinguishable from those obtained by using the full two-dimensional solution ofthe Reynolds equation. Fig 1(d) shows the journal-centre orbit for a bearing which is grooved in its upper half. The lower portion of the orbit remains essentially the same as in Figs 1(b), (c), but the upper portion is of greater eccentricity, owing to the reduced load-carrying capacity arising from the presence of the groove.
253
Dede and Holmes - assessment of engine-bearing performance
The load patterns of the big end bearings of the 6VEB engine 1 and of the ASRI 16 VMS engine have also been used in the past for reference purposes. These load patterns have been simulated on a dynamic bearing test-rig at the National Engineering Laboratory, East Kilbride, Scotland 7,8. They are shown in Figs 2(a) and 2(d), respectively. The experimental and numerically-predicted orbit comparisons for a full-circumferentially grooved bearing are shown for each engine in Figs 2(b), (c) and 2(e), (f), respectively and show good agreement, although the film thickness is generally greater in the experimental recordings. This may have been due to unavoidable lack of circularity of the test bearing and to possible local distortion under high loads. Some change in viscosity due to local temperature effects and even to local shear rate and/or pressure effects may also have played its part. This increased film thickness was reflected in measured dynamic pressures lower than predicted, as discussed in the following section.
the test rig. All comparisons indicate good agreement in respect of phasing, but poor to fair agreement in respect of amplitUdes, the peak numerical predictions always being higher than the experimental recordings, for the possible reasons mentioned in the previous section. Also the pressure transducers used were large, occupying about 10° of atc and about half the land width, thus spreading the pressure and reducing the peak. A 6-cylinder ASRl/6LTS engine was also tested for the purpose of again comparing predicted and experimental hydrodynamic pressures in its no 1 big-end bearing. The engine was located at the Admiralty Engineering Laboratory, West Drayton, its specification being described in Ref 9. Its load pattern is similar to (but not equal to) that of the 6VEB engine (Fig 2(a». Data transmission was achieved through a mechanical linkage while the engine was running. The bottom half of the bearing, that is the half adjacent to the cap, was grooved to provide two lands of width 2.3437" (59.53 mm) and three pressure transducers, T 1 , T 2 and T 3 were located in the top half of the bearing (Fig 4(a». The engine was run under no-load conditions at a speed of 750-760 r/min, and the pressure signals were displayed on an oscilloscope. Figs 4(b), (c), show, respectively, predicted and experimental pressure recordings; As expected, the maximum positive pressure occurs at the inner location T 1 , being about 2000 Ibf/in 2 gauge (13.8 MN/m 2 ). The corresponding predicted value is about 2100 Ibf/in 2 (14.5 MN/m 2 ) and for both predictions and measurements, three peaks per cycle are dis-
Comparisons of dynamic oil film pressures Bearing pressure recordings were taken from the same testrig and from an actual diesel engine. In the former pressure transducers were proVided at four locations situated around the circumference of the bearing. In the latter three axial locations were used. Using the 6VEB engine load pattern of Fig 2(a), (Ref 8), Fig 3 shows comparisons between predicted and experimental dynamic pressures at each of the four locations on
a
b
c
d
e
f
Fig 2: (a) The 6 VEE engine big-end bearing load pattern with crank angles after TDC firing; (b) measured journal-centre orbit, full circumferential groove; (c) numerically-predicted journal-centre orbit, full circumferential groove, with crank angles after TDC firing; (d) the 16 VMS engine big-end bearing load pattern; (e) measured journal-orbit, full circumferential groove; (f) numerically-predicted journal-centre orbit, full circumferential groove. (All load and bearing data appear in NEL report No. 688 8 )
254
October 1984 Vol17 No 5
Dede and Holmes - assessment of engine-bearing performance
played. As far as shape and spacing are concerned agreement is seen to be good, despite measured deformation of the bearing under 10ad3 .
The squeeze-film bearing A squeeze film is an annulus of oil supplied between the outer race of a rolling-element bearing (or the bush of a sleeve bearing) and its housing. It is used as a multidirectional damping element for the control of engine vibrations. Such a squeeze fihn is often placed in parallel with a soft flexible element to comprise a vibration isolator. By this means the natural frequencies of the x 10 2,----5000 50
N
c "'>-
engine are artificially reduced so that they may be traversed well before the normal operating speeds are reached. The purpose of the damper in this application is to reduce to acceptable levels the amplitudes of vibration and transmitted force due to unbalance as these low natural frequencies are traversed. The performance of squeeze-film bearings may be investigated by putting w = 0 in the factor B of Eq (1). Although the mechanism of cavitation is quite different from that in an ordinary journal bearing, it is often broadly assumed that it occurs when the dynamic pressure drops below absolute zero (-14.7 lbf/in 2 gauge). To investigate this xI02, -
---,
5000
e*: o'
;;c-
e*
50
45
45
40
40
35
35
30 25
30 25
---,
e*: 90
-0 Q)
:J V> V>
2500
:" 0.-
2500
20
20
15
15
10
10 5 00
b
a 5000 N
c
x 10 50
2 ~
e*:
5000
180'
xl0 2 50
45
45
40
40
-0
35
35
:"
30 25
"-
e*: 270'
'>-
-. :J V> V>
2500
:"
2500
20
0.-
Predicted Experimenta I
30 25 20
15
15 10 5 0
c
0
202530354045 5055 60657
I
360
d
Crank angle
Cronk angle
Fig 3. Measured (dashed) and predicted pressure recordings for bearing with a full circumferential groove using the 6 VEB engine load pattern ofFig 2(a). Pressure in Ibf/in 2 versus crank angles in degrees after TDC firing. (() * denotes position of pressure transducers)
Crank angle
b
Cronk ong!e
c
Fig 4: (a) Big-end bearing of the 6LTS engine showing location of the pressure transducers (L' = 65 mm, D = 159 mm, C= 0.0925 mm, maximum load = 130 kN); (b) predicted pressure recordings; (c) measured pressure recordings (1 div = 1100 Ibf/in 2 (7585 kN/m 2 )) Crank angle after TDC firing
TRIBOLOGY international
255
Dede and Holmes - assessment of engine-bearing performance
assumption and the general performance of the squeezefilm bearing, tests were carried out on a rig consisting of a squeeze-film in parallel with a spring beam. Typical predicted and measured pressure waveforms for concentric circular orbits of journal-centre motion are shown in Fig 5. The measured dynamic eccentricity ratios were 0.31 and 0.73, and the values of other nondimensional groups are indicated. The predicted pressures were calculated on the assumption of a full 360° film and show good agreement with the measured recordings. Indeed peak pressures predicted from a wide range of tests using circular concentric orbits compared well with those found experimentally. In Fig 6 theoretical and experimental vibration orbits are shown for non-concentric operation, in which static eccentricity ratios of 0.4 and 0.8 were set. Again, to obtain numerical predictions, a full 360° squeeze film was first assumed. The agreement between numerical predictions and experimental recordings is good, particularly in respect of orbit shape and disposition. However, in Fig 6(c), the predicted orbit (shown as a continuous line) is much
smaller than that obtained experimentally. In seeking an explanation for this, the recording (Fig 7(a)) from a pressure transducer at the base of the squeeze film was examined. It indicates that the negative pressure was sometimes curtailed at allout the absolute-zero level. At other times, however, J:J.'egative pressures were much lower than this, which was indicative of the fact that the lubricant could sustain tensile stresses for a short period, during which the pressure changed rapidly from positive to negative. Evidence of tensile stresses has also been encountered by several other workers in the fields of squeeze-film bearings and journal bearings. In the present work, it can be seen from Fig 7(a) that the lowest recorded negative pressure was about -30 Ibf/in 2 g (-207 kN/m 2 ). This suggests that the numerical method of solution should be modified in such a way that it can accommodate some negative pressure, although not its maximum uncavitated value. The value of this negative pressure is not, however, known precisely for any given application, unless this is measured experimentally. To give an idea of the sensitivity of the orbit to the assumed limit of negative pressure, Fig 6(c) shows, in addition to the small continuous orbit (corresponding to a full film) two dashed orbits, marked (1) and (2), corresponding to negative-pressure curtailment at (1) -16 Ibf/in 2 g (-110 kN/m 2 ) and (2) -30 lbf/in 2 g (-207 kN/m 2 ) before
b
c b Fig. 5 Comparison ofpredicted and measured squeeze-film pressure (Scale: 1 small division = 10 kN/m 2 ): (a) E = 0.31, Qc = 1. 07, A = 1. 764: (b) E = O. 73, Qc = 1.60, A = 0.456
256
Fig. 6 Non-concentric journal-centre orbits (Left-predicted; Right-measured): (a) Eo := 0.4, Qc = 1.12, A=: 0.456; (b) Eo = 0.8, Q c = 1.12, A= 0.456; (c) Eo = 0.8, Q c = 2.25, A= 0.456
October 1984 Vol 17 No 5
Dede and Holmes - assessment of engine-bearing performance
integration to obtain the squeeze-film forces. The effect can be seen to be quite profound and serves to explain why experimental and theoretical orbits for squeeze-film bearings do not always agree. The corresponding predicted pressure waveform at the base of the clearance circle agreed fairly well with the measured pressure but its peak positive value was appreciably greater than that measured. The unique form of cavitation present in the squeeze-film may have been in some part responsible. By replacing the steel bearing by a bearing made of perspex, the cavitation region was observed. This consisted of a myriad of tiny bubbles, as distinct from the streamer-like cavitation observed in normal journal bearings, in which the rotating member plays a significant role in pressure generation. These bubbles were generated in the lowpressure region of the squeeze'film but persisted in the high-pressure period at high dynamic eccentricity ratios. They were probably responsible for the limited positive pressure observed experimentally. Curtailment of the positive pressure as well as the negative pressure at the experimentally-recorded limits of 40 lbf/in 2 g (276 kN/m 2 ) and -30 lbf/in 2 g (-207 kN/m 2 ), respectively, produced the dashed orbit (3) of Fig 6(c), and the pressure waveform of Fig 7(b). Orbit (3) shows considerable improvement when compared with the experimental orbit, and the corresponding pressure waveform of Fig 7(b) shows fair agreement with Fig 7(a). It may thus be that, in the absence of an adequate supply pressure to flush away the cavities, the oil film containing these cavities remains almost stationary, while the pressure field moves through it 10. This is a state of affairs quite different from that pre-
I atmosphere
--Absolute zero level
vailing in ordinary journal bearings. The fact that the formation of tension spikes is intermittant may well be indicative of the presence of a different number of bubbles at the same instant in each cycle, due to the partial success of the supply pressure in flushing some bubbles away. Finally, for certain values of relevant nondimensional groups, the nonlinear frequency response of the squeezefilm damper assembly was determined (Fig 8(a) and this agrees fairly well with numerical predictions (Fig 8(b» based on the curtailment of the hydrodynamic pressure at the absolute zero level when this was attained.
Conclusions This work has shown that a fast semi-analytical prediction method, adopted for the determination of journal-centre loci and oil film pressures, gives results commensurate with those using a full two-dimensional solution, the time saving being of the order of 90 %_ Also, numerical predictions show fairly good agreement with experimental results from test rigs and from an operating engine. The major differences were that predicted pressures were in general greater than experimental for both piston engine bearings and squeeze-film bearings for moderate to high loads. Some explanations for these differences have been put forward.
Acknowledgements The authors acknowledge with thanks the financial support provided by the SERC to carry out this work. Thanks are also due to Mr. F.A. Martin of Glacier Metal Co. Ltd., Mr. W. L. Cooke, late of NEL East Kilbride and Mr. Les Lawrence of MoD West Drayton, Middx. for the use of their test facilities and for useful discussions. Dr. G. Good-
~'O
~1i'-~
:+:
k =0.6
a
a 40
20I-
o
o
f.
Ai
k = 40 j,
I
r Sr 'flvo
Aj
If
TV' s('
wtlxl0 2 )
20
-20, -
-40
.--._----------_..
b Fig 7. Pressure waveforms (eo = 0.8, Qc = 2.25, A = 0.456): (a) Measured, 1 div = 8lbf/in 2 (55 kN/m 2 ); (b) Predicted
TRIBOLOGY international
k = 0.6
b Fig 8. Frequency responses (eo = 0.8, Q c = 0.22, A = 0.02) (a) Predicted, with sample applied force vectors; (b) Measured.
257
Dede and Holmes - assessment of engine-bearing performance
win is to be thanked for carrying out the experimental programme which led to the recording of Fig 4(c).
References
journal bearings. Wear, 1970, 16,221-228 6.
Black H.F. and Brown R.D. Fast dynamic calculations for non-circular bearings. L Mech. E., Tribology Convention, Durham, April 1976
7.
Cooke W.L. Performance of dynamically loaded journal bearings, Part 1: Effect of varying bearing geometry and oil supply conditions. NEL Report No 683, March 1983
1.
Martin F.A. Developments in engine bearing design. Trib. Int. June, 1983, 16(3)
2.
Goodwin G. and Holmes R. Determination of oil film thickness in a crankshaft main bearing. J. Automot. Engng, June 1975, 6(3),6-10
8.
Cooke W.L. Performance of dynamically loaded bearings, Part 2: Measurements of oil film pressure in dynamically loaded bearings. NEL Report No 688, 1983
3.
Goodwin G. and Holmes R. On the continuous monitoring of oil-film thickness in an engine bearing. Proc. L Mech. E., 1978,192(31),371-376
9.
Goodwin G. and Holmes R. On the continuous temperature monitoring of an engine bearing. Proc. L Mech. E., 191, Paper (12/77), 161-167
4.
Ritchie S. The prediction of journal loci in dynamically loaded internal combustion engine bearings. Wear, 1975, 35,291-297
5.
Shelley B. and Ettles C. Tractable solution for medium-length
10. Marsh H. Cavitation in dynamically loaded journal bearings. Proc. Leeds-Lyon Symp. entitled Cavitation and Related Phenomena in Lubrication, Sept 1974,91-95
ESDU software A range of software for engineering design and analysis has been introduced by ESDU International. Suitable for use on the IBM PC, the packages include: • Analysis of forced-damped vibrating systems (cost £150) • Hydrodynamic.journal bearing design (£400) • Rolling element bearing selection (£400) • Design of parallel-axis spur and helical gears (£400) • Hydrodynamic thrust bearing design (£400) • Elastohydrodynamic ffun thickness (£200) • Rotor dynamics - rolling bearings (£400) • Rotor dynamics - general systems (£400) • Rotor dynamics - hydrodynamic journals (£400) ESDU claims the user's manual to be the most comprehensive on the market. For further information contact ESDU International Ltd, 251/9 Regent Street, London WIR 7AD, UK
New materials for automobiles Vehicle manufacturers are concentrating much of their resources on development and application of 'new' materials. They see this as the route to more efficient, smaller and lighter vehicles which take less energy to produce. At Toyota, composite aluminium alloy pistons have been cast with ceramic
258
fibre preform, thus making use of the ability of ceramic fibre and aluminium alloy to suppress heat expansion and maintain adequate clearance between piston and cylinder wall. This ensures better resistance to seizure. Molybdenum sintered alloy has been used by Toyota to form the cams on an integralsteel tube camshaft, research having shown this material to exhibit the optimum combination of wear resistance and sintering properties. These are just two examples of many novel materials applications contained in 'New Materials and the Automobile', a 32-page brochure produced recently by Toyota. The booklet gives a brief appraisal of the materials currently used in automobile manufacture, runs through a history of materials research and application in the company and links the development of vehicles running on 'alternative energy' and in accordance with modern demands, to the need for new materials in sensors
and actuators. The bulk of the contents comprises brief descriptions of individual applications of new materials in modern vehicles. Further information or a copy of the brochure are available from Toyota (GB) Ltd, The Quadrangle, 108-118 Station Road, Redhill, Surrey, RHI IPX, UK
Condition monitoring conference The third IMEKO Seminar on 'Condition Based Maintenance and Technical Diagnostics of Machines' is to be held on 17-27 September 1985 in Zagreb, Yugoslavia. Topics to be considered include: measuring, methods and diagnostic equipment; technical diagnostics in accomplishing progressive maintenance methods; and formulation of test procedures and standards. Institute for Developing Countries, PO Box 303, 41001 Zagreb, Yugoslavia.
14-18 April 1985, Vancouver, BC, Canada
Wear of Materials Eighteen technical sessions are planned, and based on a review of the 184 abstracts received by July the organizers expect: three or four sessions on wear of metals; two or three sessions each on abrasive wear, wear theory, and case studies on wear of devices; one or two sessions on erosion; up to one session each on wear of polymers, wear of composite materials, wear of coatings and wear of ceramics. Further information on the above
sessions can be obtained from the Programme Chairman, Mr R. G. Bayer, IBM Corporation, PO Box 6, Endicott, NY 13760, USA. One post-deadline session is planned as well, at which short presentations are sought on practical problems, new ideas and late developments. To arrange a place in this session, contact Professor S. Bahadur, Mechanical Engineering Department, Iowa State University, Ames, IA 50011, USA.
October 1984 Vol17 No 5