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