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Transcript of Engdyn Rover Kseries
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Crankshaft Durability of Rover K-Series Engine:
Comparison of ENGDYN Analysis with DynamicMeasurements
Roger B. Dailly David J. BellBMW Group, Birmingham, UK Ricardo Consulting Engineers
Figure 1: MGF with 1.8L K-series VVC engine
Abstract
This paper describes the technique used to perform a dynamic simulation of the Rover K-
Series crankshaft with the aim of predicting multi-axial stresses and Fatigue Factors of Safetyusing ENGDYN from Ricardo. This production crankshaft had been previously analysed andvalidated using in-house software techniques and contracted instrumentation work.ENGDYN was used to predict bearing loads and oil film thicknesses across the runningrange of the engine. Torsional vibration predictions were then compared to actual dynamicmeasurements of the crankshaft and in-house software results. Multi-axial stresses andF ti F t f S f t th d t t i t ENGDYN
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1 Introduction
The Rover K-Series engine has now been in
production for over 10 years, initially of 1.4 L
capacity. Since then 1.1L, 1.6L, 1.8L and 1.8L
VVC (Variable Valve Control) have beenintroduced with an accumulative build of two
million engines since 1989. The 1.8L engine is
also built under official licence for Lotus andCaterham, and also in the MGF motorsport
series. The K-Series is an attractive buy due toits reduced cost and low weight, which is anecessity for sport cars.
This report aims to validate Ricardo ENGDYN
software with respect to Rover K-Series 1.8
Litre VVC crankshaft durability. The softwarewill be used to output the behaviour of thecrankshaft under as realistic conditions as
possible. The oil film thickness and bearingload characteristics of the crankshaft throughthe running range of the engine will be
compared to results obtained from in-house
software. The torsional and bending vibrationoutput from ENGDYN will then be compared
with results obtained from dynamic
measurements. Finally, the crank stress anddurability results from ENGDYN will be
compared to strain gauge measurements at
comparative points on the crankshaft.
ENGDYN is a computer program used foranalysing the dynamics of the engine, and in
particular the crankshaft and its interaction with
the cylinder block. In this analysis the software
will be used to predict the time-domainresponse of the 3-dimensional vibration of the
crankshaft coupled to the block by way of a
non-linear oil film. When this loading andmotion has been calculated the software can
perform a fast Fourier transform to break down
2 Method of Analysis
2.1 Engine Specifications
Configuration: in-line 4
Fuel: GasolineCylinder bore: 80 mm
Piston stroke: 89.3 mm
Swept volume: 1.8L Crankpin
Peak Power: 107 KW @ 7000 rpmPeak Torque: 174 N/m @ 4500 rpm
Engine running range: 750-7200 rpm
2.2 Component Modelling
2.2.1 Crankshaft
To perform the analysis within ENGDYN two
crankshaft models were created. These
included a complete stiffness representation of
the crank (excluding the crank nose hub and theflywheel), and a detailed model of the crank
from main bearing 4 to main bearing 5, with
mesh density increased around the fillets.
ENGDYN can however perform crank analysisof any portion of the crank as long as the model
incorporates at least two main journal bearings.Features such as bolt holes and oil drilling were
omitted on both models, which were meshed
using solid tetrahedral elements.
The stiffness model of the crank as shown in
Fig. 2 was used to generate the mass andstiffness matrices of the crank within
ENGDYN. The flywheel and torsional
vibration damper assemblies were added withinENGDYN as lumped masses concentrated at
the appropriate points. The detailed crank
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was treated as a lumped mass which did not
contribute to the stiffness of the crank.
The torsional vibration damper was defined inENGDYN by the hub and annulus properties.
This flywheel and vibration damper areeffectively added to the FE model of the
crankshaft so that ENGDYN can generate mass
and stiffness matrices of the full crank. It ismore accurate to define these components in
the FE model, but for this analysis these
components were not previously modelled.
2.2.2 Cylinder Block
The cylinder block was received as an IDEAS
model file and required some modification
before being read into ENGDYN. The modelof the block was very large and it was
necessary to create a master-degree-of-freedomset, which represented a condensed mass andstiffness matrix of the engine block. These
matrices were derived in MSC/Nastran by
static condensation performed in a normal
modes solution.
2.2.3 ENGDYN Solution Technique
The software previously used by CAE Design
Analysis for analysing engine bearing
behaviour was Engine Bearing Analysis(EBA). This software represented a rigid
cranktrain with appropriate lumped masses
modelled within a rigid block. The oil film
being modelled using the Booker MobilityMethod. For direct comparison it was therefore
necessary to solve an indeterminate solution
within ENGDYN(1)
against a rigid block. Forthis analysis the oil characteristics and cylinder
firing pressure maps across the speed range
the journal bearings. The centrifugal effects
were also taken into account due to the mass
and inertia of the crankshaft. 10W30 oil wasused along with pressure maps for a full load
engine condition. A no-load condition ismore detrimental to crank life since the inertia
torque is not relieved by the gas torque,
however accurate cylinder pressure maps werenot available for this load case and hence a
full-load condition was used for comparison.
Bearing force and eccentricity results were thenoutput and compared with EBA for full load
and inertia only running conditions.
With the FE models of the crank and block
defined in ENGDYN, a dynamic/compliantsolution was then performed to evaluate the
torsional and bending response of the
crankshaft. The dynamic solution generatesmass and stiffness matrices of the crank andincludes the non-linear gyroscopic effects in
the solution. The reactions and journal bearing
orbits are then calculated for each pin and journal bearing, with the 3-dimensional
vibration behaviour also evaluated. The block
was set to compliant, which considered only
the stiffness of the block. This means the blockwas modelled such that the natural mode
shapes did not contribute to its interaction with
the crankshaft. The results from this solutionwould then be compared to those from
experimentally measured results. A dynamic
solution of the crank against a rigid block wasalso done so that the results could be compared
with the Rover Torsional Vibration (TV)program. The TV software uses a mass-elasticsystem to represent the inertia and stiffness
between each web and journal along the crank.
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was already known that the fillet in main
bearing five closest to web 8 suffered the
greatest loading. Failure had occurred in thisregion during durability tests at 7500 rpm.
Since the stress model used in this analysisconsisted of webs 7 and 8, then stresses were
only resolved in this area. ENGDYN splits the
model at cut planes through the journal centres.Each split would extend from the centre of a
main journal bearing to the centre of the next
immediate pin journal bearing. Taking eachsplit part in turn ENGDYN applies unit force
loads in the four orthogonal directions (+Y,-
Y,+Z,-Z) at both the main and pin journal
centres. In addition unit moment loads in thefour orthogonal directions are applied at the
main journals. For this dynamic solution, which
takes into account bending vibration, additional
unit moment loads were applied at the mainbearing centres. Unit torsional and axial loads
were applied at what would be the nose of thecrank. In this case the nose is represented by
the start of main bearing 4, as shown in Fig.3.
A body load equivalent to a constant angular
velocity about the crankshaft axis was alsoapplied so as to include the centrifugal effects
of the crankshaft. For the model analysed here,
the total number of unit loads amounted to 23.
ENGDYN then writes out a file, which can beconverted to an MSC/Nastran deck and solved
to produce stress per unit loading. The stresses
due to quasi-static (a snap shot in the timecycle of crank rotation) bending, torque and
vibration loading are calculated such that anumber of combined loadcases are created ateach crank angle. It is the variation of the
bearing loads through the crank cycle that
causes the stress to change, and hence a newfactor is required so that the unit loads can be
speed and Goodman diagrams to be created.
The resulting file containing all of the factored
stresses for each fillet can then be convertedand read into IDEAS for post-processing the
stress and FSF plots. For this solution the FFSwere calculated for the speed range 5000 rpm
to 7000 rpm.
3 Results & Discussion
3.1 Normal Modes
Table 1 shows the frequencies and mode shapedescriptions for a free-free crank with
conventional flywheel attached as produced by
the Lanczos method using MSC/Nastran. Theflywheel was attached to the crank palm with a6 degree-of-freedom spring with stiffness
equivalent to that of the flywheel. The
installed modes were calculated with thecrankshaft fitted with the torsional vibration
damper, flywheel and masses equivalent to the
con-rod big-end mass plus piston mass addedto the centre of the pin journals. The entire
crank was then grounded with linear springs of
5x108
N/mm stiffness at all four of the main
journal bearing centres.
Natural
Frequency
Mode Shape Description
175 Hz Vertical Bending224 Hz Lateral Bending
358 Hz 2nd
Vertical Bending
509 Hz Torsional Vibration
547 Hz 2nd
Lateral Bending
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Table 2 shows that the torsional vibration
damper created two smaller torsional vibrations
at 321 Hz and 541 Hz. Without the TV damperthe torsion mode would create a larger peak
and in this case was excited at 509 Hz.
NaturalFrequency
Modes Shape Description
213 Hz Crank Nose Bending
238 Hz Crank Nose Bending
321 Hz 1st
Torsional Vibration
349 Hz Crank Palm Bending
394 Hz Crank Palm Bending
478 Hz 2nd Vertical Bending
541 Hz 2nd
Torsion Vibration
644 Hz Flywheel Axial
778 Hz Swashing of Flywheel
786 Hz Swashing of Flywheel
Table 2: Installed modes of crankshaft
3.2 Bearing Loads & Oil Film EccentricitiesFig. 4a illustrates the ENGDYN solution for
the characteristics of main bearing 5 under afull load condition at 4000 rpm. Fig. 4b shows
how the EBA results for the same bearing
compare It can be seen from the graphs that
of the oil film whereas the EBA calculation
performs a more simple calculation. A similar
comparison was made for an inertia onlycondition at an engine speed of 7500 rpm. Fig.
5a/b show results for main bearing 4 for aninertia only engine condition. As the no load
pressure maps were not available the
ENGDYN solution was run with only theinertia loading of the crankshaft. This would
account for some differences in the bearing
eccentricities as EBA is a no load solution.However the maximum bearing load compares
exactly.
3.3 Torsional Vibrations
The ENGDYN results for a dynamic solution
of the crankshaft supported in a compliantblock are shown in Fig. 6. Node 1 represents
the node at the centre of the hub on the crank
nose. The figure shows the response of thisnode in the rotational direction along the crank
axis. The main orders of vibration are plotted
and these are relative to a rotating axis set. Thespeeds at which these resonant peaks occur
compare quite well to those obtained throughexperimental measurement as shown in Fig. 7.The amplitudes of these peaks depends very
much on the damping coefficient of the damper
rubber and the overall cylinder damping withinthe engine. For this analysis the damping
coefficient of the damper rubber was calculated
to be 1.77 N.m.s/rad and the cylinder damping
was set to 1000 Nms/rad (default inENGDYN). The torsional vibration results are
tabulated in Table 3 and shows how the
predicted values compare to the measured andin-house results. It can be seen that the
amplitudes of the predicted harmonic peaks
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order peak. This indicates that the FE model of
the crankshaft does not represent the real
crankshaft accurately enough.
Improved results can be obtained by
incorporating actual FE models of the torsional
vibration damper and flywheel to moreaccurately model these components in the
solution.
HarmonicOrder ENGDYNResults MeasuredResults
4.0th Order
Speed (rpm)
Freq. (Hz)
Amp. (Deg.)
4400
293
0.15
4750
317
0.15
6.0th Order
(I,II)
Speed (rpm)
Freq. (Hz)
Amp. (Deg.)
3000 & 5000
300 & 500
0.07 & 0.06
3400 & 5125
340 & 512
0.09 & 0.07
3.5 Order
Speed (rpm)
Freq. (Hz)
Amp. (Deg.)
5000
292
0.10
5625
328
0.10
Table 3: Comparisons of measured and
predicted torsional vibrations.
Fig. 8b shows the ENGDYN results for adynamic/rigid solution. The dominant orders
of vibration are plotted and show that 4.0 th
order vibration is greatest around 4400 rpm.
The sixth order peaks occur at 3000 rpm and
3.4 Bending Vibration & Strain Gauge
Measurements
The motion of the node representing mainbearing 5 (closest to crankshaft palm) was
analysed. The results provided a comparison of
bending vibration to the strain gaugemeasurements. Fig. 9a shows the axial
displacement of this node in the X-direction.
The graph shows that 2.0 order (relative to the
crank) vibration is dominant at high engine
speed and reaches a maximum around 7000rpm. This amplitude equates 0.185 mm 2.0order and 0.228 mm in the time domain. At a
lower engine speed the crank is excited at 5400
rpm by 2.5 order and 6100 rpm by 1.5 order. Asimilar result was obtained for the movement
of the same node in the vertical Y-direction as
shown in Fig. 9b. Inspection of the results
relative to the fixed datum show that the 1.5and 2.0 order resonances correspond to the
forward flywheel whirl mode whilst the 2.0
order resonance corresponds to the reversewhirl mode of the flywheel. A photograph of
the instrumented crankshaft is shown in Fig.10a. The location of the strain gauge is
illustrated in Fig. 10b. The precise location ofthe gauge corresponds to the area of highest
stress in the fillet, found from previous
analysis. Areas of high strain will coincidewith areas of high stress and hence low factors
of safety. The strain gauge measures
predominantly axial and vertical strain causedby bending of the fillet, the results of which are
shown in Fig. 11. Fig. 12 compares the 1.5 and2.0 order measured strain amplitudes ofFig. 11with those derived from the ENGDYN
analysis. This shows good correlation of the
resonant frequencies for each of these harmonicorders. Inspection of the measured 1.5 order
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thought that this vibration absorber mechanism
may be due either to the effect of the oil film at
the adjacent main bearing, the flexibility of thecrankshaft web counterweight or more likely
the flexibility of the flywheel which was notincluded in this model (but can be included in
ENGDYN if required.) The correlation of the
1.5 order strain amplitude therefore requiressome further investigation. The predicted 2.0
order strains correlate well with the
measurements although the predicted amplitudeis lower than the measured value.
3.5 Crankshaft Durability
The stresses due to quasi-static and vibration
loading for every 10 through a cycle of 720
were calculated for each engine speed underfull load. These stresses were then combined
using an Alternative Goodman Criterion toproduce the fatigue safety factors through the
desired speed range, as shown in Fig. 13.These results are shown for the fillet at the rear
of web 8, closest to the crankshaft palm. Under
full engine load at 7000 rev/min the maximum
stress was found at 570 of crank rotation, witha value of 198 MN/m2. The stress distribution
at this condition is shown in Fig. 14a and themaximum stress corresponds to a fatiguesafety factor of 1.283. Similarly at 5000
rev/min as shown in Fig. 14b the maximum
stress occurs at 20 crank rotation. It can beseen therefore at higher engine speeds the shear
stress due to the gas torque rotates the high
stress region in the direction of crank rotation.
The ENGDYN factor of safety results compare
very well with those obtained throughexperimental measurement and follow a similar
trend. The general decrease in fatigue safety
factor with increasing engine speed is due to
rev/min.. The discrepancy at the lower engine
speeds is not easily explained since the
measured and predicted strains for thedominant 1.5 order resonance at these speeds,
as shown in Fig.12, correlate well. Howeverthe predicted 2.0 order strains at these speeds
are lower than the measured values. Further
work is required to explain the differences infatigue safety factor at these speeds. The
discrepancy in fatigue safety factors at speeds
between 6000 and 6500 rev/min is consistentwith the comparison of measured and predicted
strains as shown in Fig.12. As previously
discussed, this showed that the 1.5 order strain
amplitudes were over-predicted by ENGDYN.
4 Conclusions The results have shown that ENGDYN couldbe used with confidence to predict the bearing
load and oil film eccentricities of pin and main
journal bearings. The mathematics behind theoil flow rate calculation within ENGDYN is
more accurate than the EBA solution.
With respect to the torsional vibrationsENGDYN predicted slightly lower frequenciesfor 6.0 and 3.5 order vibration when compared
to measured data. However, when compared to
in-house software the frequencies matched for
all orders of vibration. The analysis did showhowever that the damping values used in the
model were a good approximation. The
amplitudes of the predicted peaks were close tothe measured values.
The ENGDYN results describing the motion
of main bearing 5 compared well with the
experimental results, in that both showed aid i i 2 0 d ib ti t d
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measurement and follow a similar trend. The
most significant discrepancy is the over
prediction of the 1.5 order strain amplitudewhich results in lower predictions of fatigue
safety factor. Further work is required toinvestigate this difference.
5 References
(1) Ricardo Software: Engine Dynamics
Simulation ENGDYN Users Manual,Revision 1.2
(2) Perkins Technology Consultancy:Predication of Durability for a 1.8L I4
Crankshaft Using Three Flywheel
Models, March 20, 1998
(3) Perkins Technology Consultancy: AnInvestigation into 1.8L K-SeriesFlywheel Whirl Activity, June 16, 1998
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Figure 2: FE Model of crankshaft for Mass and Stiffness Matrix Formulation
X
Y
Z
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Figure 7: Torsional vibrations measured at TV damper on running crankshaft(2)
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Main bearing 5, closest
to crankshaft palm.
Strain gauge location at
predicted high stress region
Figure 10a: Photograph of Crankshaft Instrumented with Strain Gauges(2)
Pin bearing 4
Gauge 1 and Gauge 2
(backup)
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Figure 11: Strain gauge results for web 8 fillet on main bearing 5(3)
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Figure 13: Fatigue Factor of Safety resolved for the worst stress in the fillet at eachcrankshaft speed
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5th Ricardo Software International User Conference 23
Figure 14a: Stress plot around fillet,
showing maximum stress at 570 crankangle at 7000 rpm full load
Figure 14b: Stress plot around fillet,
showing maximum stress at 20 crankangle at 5000 rpm
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5th Ricardo Software International User Conference 24