4 Versus 8 Counterweights for an I4 Gasoline Engine Crankshaft

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SAE TECHNICALPAPER SERIES 2008-01-0088

4 Versus 8 Counterweights for an I4 GasolineEngine Crankshaft - Analytical Comparison

Naji Zuhdi and Fadhlan Nik Abdul AzizPETRONAS Malaysia

Phil Carden and David BellRicardo UK

Reprinted From: Advanced Concepts, 2008(SP-2180)

2008 World CongressDetroit, MichiganApril 14-17, 2008

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2008-01-0088

4 Versus 8 Counterweights for an I4 Gasoline Engine Crankshaft – Analytical Comparison

Naji Zuhdi and Fadhlan Nik Abdul Aziz PETRONAS Malaysia

Phil Carden and David Bell Ricardo UK

Copyright © 2008 SAE International

ABSTRACT

This paper presents results of an analytical comparison between two alternative versions of a crankshaft for a 2.2L gasoline engine. The first version had 8 counterweights and a bay balance factor of 80.3%. The second had 4 (larger) counterweights giving a bay balance factor of 56.6% and a crankshaft mass reduction of 1.42 kg.

The results presented in this paper relate to the main bearings in terms of specific loads, oil film thickness and shaft tilt angle under full load and no load conditions across the speed range. Torsional vibration analysis and crankshaft stress analysis were also performed but the results are not presented here.

The differences in bearing force and oil film thickness were very small and the only major difference in terms of shaft tilt angle occurred at Mains 2 and 4 (increase of ~20% compared with 8 counterweight version). This increase could result in extra edge wear of the bearing shells but the crankshaft mass reduction achieved by using the 4 counterweight version was significant. It is not currently possible to determine with certainty the acceptability of the bearing durability at Mains 2 and 4 by analysis. Testing of both versions is planned and may be the subject of a further SAE paper.

The highest value of shaft tilt angle was predicted to occur at Main 5 at high speed and this was caused by whirling of the flywheel to be used for testing (this is heavier and has larger overhang than flywheel intended for production).

INTRODUCTION

Crankshaft counterweights cannot be used to reduce engine reciprocating shaking force or moment for an in-line 4 cylinder engine (as explained in Reference 1). The primary reciprocating and rotating forces and moments are naturally balanced. However, most engines with this

configuration have counterweights on some or all crank webs to reduce bearing forces/moments and to improve the bearing oil film thickness. 8 counterweights (one on each crank web) are often used for gasoline engines with rated speed around 6000 revolutions/minute (rpm) and it is sometimes quoted that this gives the best possible control of bending moments within the crankshaft and so results in better NVH. However crankshaft mass can be significantly reduced if just 4 counterweights are used (one per crank bay) and many current production engines use this strategy. Some researchers (References 2 and 3) suggest that NVH is not strongly affected by the choice of number of counterweights.

The objectives of the work described in this paper were as follows. • To make a detailed quantitative comparison

between an 8 counterweight and a 4 counterweight version of the same crankshaft in terms of the critical parameters affecting main bearing performance.

• To show the differences between results obtained by statically determinate calculations (used during the early stages of design) and dynamic calculations (possible only when FE models are available).

CRANKSHAFT ANALYSIS OVERVIEW

Classical analysis methods are often employed during the concept design phase to support the choice of crankshaft dimensions including counterweight sizes.

In this case initial classical analysis was performed assuming that the crankshaft was rigid and reaction forces were calculated at each main bearing by the statically-determinate method. The key assumption in this case was that the force at each main bearing was influenced by • the gas pressure from the adjacent cylinders only • the inertial effects of the pistons and rods from the

adjacent cylinders only • the centrifugal effects of the adjacent crank webs

only



The crank was assumed to be effectively pin-jointed at each main bearing and so the effects of more distant crank bays were ignored and so load sharing was not accounted for. The Mobility Method of Booker using the short bearing approximation (see Reference 4) was used for all calculations of bearing oil film thickness. This technique enabled preliminary assessment of bearings and has been developed to include effects of oil grooves and the effect of increased oil temperature due to oil shear heating on the oil viscosity. These methods were very useful for assessment of many different crankshaft designs but some important aspects of the performance (such as the effect of crankshaft vibration and load sharing between bearings) cannot be determined by their use.

Advanced dynamic analysis of the selected 4 and 8 counterweight crankshaft designs was also performed. In this case the dynamics of the crankshaft and flexibility of the cylinder block were represented using finite element models. The 3D vibratory behaviour of the crankshaft (including non-linear gyroscopic effects) was calculated and used to determine reaction forces and moments at the main bearings. For this analysis the torsional vibration damper and the flywheel were also modeled as these can influence the vibratory behaviour of the crankshaft significantly. The shaft tilt angle at each bearing was also recorded using this dynamic analysis technique.

The mobility method was also used to analyse the bearings under the influence of dynamic loadings. For rotational motion the short bearing approximation was also used to determine the stiffness and damping of the oil film. This is based on the work of Kikuchi (See Reference 5).

CRANKSHAFT DESIGN PHILOSOPHY

The bearing sizes for the 8 counterweight crankshaft were chosen by using benchmark data from other similar engines followed by an iterative process of design and classical analysis methods described above. The crank webs were designed by a similar process and were refined following analysis of torsional vibration and concept level analysis of stress and safety factor at critical locations on the crankshaft.

The required counterweight MR (mass x distance from crankshaft axis to counterweight centre of mass) was chosen such that the worst case minimum oil film thickness at main bearing No.3 at overspeed of 6600 rpm under no load (no combustion) condition was limited to 0.5 micron. This is typically the worst case for oil film

thickness and the limit has been developed over many years by making identical calculations on other I4 crankshafts under similar conditions. For this analysis the cold mean main bearing clearance was used and the oil viscosity was determined (assumed 10W40 grade oil) from the effective bearing temperature obtained using a thermal balance. The oil supply temperature and pressure were assumed to be 130°C and 3.5 bar, respectively, but the calculated effective temperature under this condition was ~200°C.

The counterweights were designed to meet the packaging constraints of the particular engine (limit on clearance between counterweight radius and piston and cylinder block). For the 8 counterweight version the resultant bay balance factor was calculated to be 80.3% with a counterweight outer radius of 74 mm. The 8 counterweight crankshaft is shown in Figure 1.

Figure 1 Crankshaft with 8 counterweights

The 4 counterweight version was identical to the 8 counterweight version in most respects and was defined by the following process. The counterweights were removed from Webs 2, 3, 6 and 7 and a 20 degrees cut was performed relative to the lands of Mains 2 and 4 (as shown in Figure 2). The radius of the remaining 4 counterweights (on Webs 1, 4, 5 and 8) was increased until the same minimum oil film criteria was met at main bearing No. 3 at no load overspeed. This time the criterion was met with a significantly reduced bay balance factor of 57.6% and the required counterweight radius (on Webs 1, 4, 5 and 8) was 77 mm.

Figure 2 Crankshaft with 4 counterweights

The sensitivity of the worst case minimum oil film thickness to variation of bay balance factor for both the 8 counterweight and the 4 counterweight versions of the crank is shown in Figure 3.



Figure 3 Minimum oil film thickness against balance factor

The remaining counterweights on Webs 4 and 5 were ideally placed to control the oil film at the worst case bearing (No.3). Thus although these weights needed to be larger than those on the 8 counterweight version it was not necessary to make them so large as to achieve the same bay balance factor as the 8 counterweight version in order to meet the oil film criteria.

The reduced bay balance factor was expected to give worse conditions at the other bearings, particularly Nos. 2 and 4 as the shaft will bend more at these locations. One reason for performing this analysis was to quantify this effect.

ANALYSIS INPUT DATA

Some key input data for the main bearing analysis are presented in Table 1.

Table 1 Basic input data Parameter Value Bore (mm) 86.0 Stroke (mm) 94.6 Firing order 1-3-4-2 Rod length (mm) 145.7 Piston assembly mass (kg) 0.46 Rod assembly mass (kg) 0.56 Distance from crank pin to rod centre of mass (mm)

38.59

Main bearing diameter (mm) 55.0 Main bearing shell effective length (mm) 18.8 Main bearing groove extent (deg) 180.0 Main bearing groove width (mm) 4.15 Main bearing mean diametral clearance - hot (μm)

66.0

Oil grade 10W40 Oil supply pressure (bar) 3.5 Oil supply temperature (°C) 130 The analysis presented in the remainder of this paper was performed using hot main bearing clearance. A thermal balance simulation option was used to elevate

the temperature of the oil due to shear forces at each main bearing.

The analysis was performed using Ricardo Software ENGDYN, a computer software primarily used for the analysis of the dynamics of an engine, particularly of the cranktrain and the reactions of the cylinder block to the cranktrain.

CRANKSHAFT FINITE ELEMENT MODEL

ENGDYN requires a finite element (FE) model of each crankshaft as input data for dynamic analysis so stress quality models of both the 4 and 8 counterweight crankshafts were created using Altair HyperMesh. Stress quality model is an FE model with increased element density around the critical areas. Oil holes and journal fillets were included in the FE model for stress analysis and fatigue safety factor assessments (results are not presented in this paper). The models are displayed in Figures 4 and 5.

FE models of the damper hub and sprockets were included with the crankshaft. The TV damper ring was modeled as a lumped inertia connected to the damper by a torsional stiffness. An FE model of the flywheel was also made and this was used to determine the mass properties and stiffness data for the flywheel. The flywheel was then modeled in ENGDYN using these data.

Figure 4 Crankshaft FE model with 4 counterweights

Figure 5 Crankshaft FE model with 8 counterweights



CYLINDER BLOCK FINITE ELEMENT MODEL

A stress quality FE model of the cylinder block was used and this was reduced by the static condensation method to derive a stiffness representation of the cylinder block structure (see Figure 6).

Figure 6 Cylinder block FE model

EXCITATION

The ENGDYN model was run using full load cylinder pressure between 1000 rpm and 6500 rpm at 100 rpm intervals. The rated speed for the engine was 6000 rpm. ENGDYN was also run using no load (no combustion) cylinder pressure between 1000 rpm and 7000 rpm at 100 rpm intervals. The fuel cut speed was 6600 rpm. The cylinder pressure data used in each case was generated using Ricardo WAVE engine performance simulation software. Figure 7 shows the variation in peak cylinder pressure with engine speed.

Figure 7 Peak cylinder pressure

MAIN BEARING ANALYSIS RESULTS

DIFFERENCES BETWEEN PREDICTED RESULTS DUE TO ALTERNATIVE CALCULATION METHODS

It is useful to examine the differences in predicted bearing force between the statically determinate analysis method (rigid crank) and the dynamic method (flexible crank and cylinder block). Peak specific bearing load (bearing force divided by projected area) for each bearing of the 8 counterweight version at full load are presented in Figures 8 to 12.

Figure 8 Peak specific load at Main 1







These results revealed the following features.

• Peak specific loads at Mains 1, 3 and 5 showed a transition in the speed range when calculated by both methods – gas forces dominated at low speed and inertia forces dominated at high speed.

• The transition speed of Main 3 bearing load was lowest as this bearing was adjacent to 2 crank bays with the same angular alignment so both bays contribute inertial force at high speed.

• The peak bearing load at Mains 2 and 4 was increased significantly across the speed range when calculated dynamically compared with statically determinately. This was due to the stiffening effect of the central part of the crankshaft compared with the ends. Mains 2 and 4 feel the influence of a restoring moment due to crankshaft stiffness and this acts to increase the specific load at these bearings while reducing it at Mains 1 and 5.

• The peak bearing force at Mains 1 and 5 was reduced at low speed when calculated dynamically compared with statically-determinate method but at high speed an increase was predicted and this was greater on Main 5. The increase in peak specific load at high speed on Main 5 was indicative of flywheel whirl that cannot be included in the statically determinate method.

It was also interesting to compare the predictions of bearing specific load and minimum oil film thickness at Main 3 at under no load conditions since this can be the worst case at high engine speed. These results are plotted in Figures 13 and 14.


Figure 14 Minimum oil film thickness at Main 3

Under no load conditions the transition to inertia dominated force at Main 3 occurred at an even lower speed than under full load. The bearing specific load at no load overspeed of 6600 rpm was predicted to be 30.2 N/mm2 by dynamic analysis (46% higher than the value predicted by statically determinate method) but this was not as high as the peak specific load on Mains 2 and 4 under full load conditions in the mid speed range. The minimum oil film thickness predicted by the dynamic calculations under no load conditions at 6600 rpm with hot clearance was 0.512 μm (18% lower than the value predicted by statically determinate method) and this was the worst case film thickness under all conditions analysed.



COMPARISON BETWEEN 4 COUNTERWEIGHT AND 8 COUNTERWEIGHT CRANKSHAFTS USING DYNAMIC ANALYSIS

The peak specific loads at each main bearing of both 4 and 8 counterweight versions (as calculated by the dynamic analysis under full and no load conditions) are shown in Figures 15 to 19.

Figure 15 Peak specific load at Main 1 against speed





The most remarkable feature of these graphs was that in terms of peak specific load at the bearings there was almost no difference between the 8 counterweight and 4 counterweight versions.

The predicted minimum oil film thickness values were also equally similar as shown in Figures 20 to 24.








The similarity of the specific load and oil film thickness between the 4 and 8 counterweight versions is a consequence of the design strategy adopted in this case. If the 4 counterweight version had used the same size counterweights as the 8 counterweight version (lower balance factor) this would have given different results. Also if the 4 counterweight version had used larger counterweights such that it had the same bay balance factor as the 8 counterweight version the results would also have been different.

The merit of the strategy proposed in this paper is that it enables the center main bearing to meet its known durability-related constraint at overspeed while not increasing the peak forces or reducing the oil film thickness at the other main bearings in the normal operating speed range.

Using the dynamic analysis method it was also possible to calculate the peak resultant shaft tilt angle at each main bearing as shown in Figure 25 to 29.

Figure 25 Peak resultant shaft tilt angle at Main 1







These graphs showed some interesting trends.

• Shaft tilt angle at Mains 1, 3 and 5 are very similar for both 4 and 8 counterweight versions and the peak value was sensitive to engine load.

• Shaft tilt angle at Mains 2 and 4 was significantly increased on the 4 counterweight shaft as compared with the 8 counterweight shaft and the increase was greatest (~20%) at high engine speed

• Shaft tilt angle at Mains 2 and 4 was not sensitive to engine load

• Shaft tilt at Main 5 reached the highest value of all the bearings at high engine speed under both full and no load conditions for both crankshaft versions.

To gain a better understanding of the conditions at Main 2 the specific load, oil film thickness and resultant shaft tilt angle were plotted against crank angle at 6000 rpm under full load conditions as shown in Figures 30 to 32.

Figure 30 Specific load at Main 2 at 6000 rpm



Figure 31 Oil film thickness at Main 2 at 6000 rpm

Figure 32 Shaft tilt angle at Main 2 at 6000 rpm

Figure 32 shows that the high tilt angle at Main 2 at high speed occurs throughout most of the cycle and was mainly caused by inertial effects. In fact the two firing events on the adjacent cylinders (1 at 15 deg and 2 at 555 deg) act to straighten the shaft reducing tilt. So the highest values of force and smallest oil film thickness did not occur at the same time as the highest shaft tilt angle.

It is important to remember that the oil film thickness values calculated in this paper are central values calculated by the mobility method. As such they are useful for comparative purposes but they do not account for the effect of shaft tilt or distorted shape of the housing.

At high speed at Main 5 under no load conditions the predicted peak shaft tilt reached the highest value of any bearing. This required some further explanation because it was so different from the shaft tilt at Main 1 (to which it might be expected to be similar by symmetry). Figure 33 shows the shaft tilt at Main 5 at 7000 rpm with no load plotted against crank angle.

Figure 33 Shaft tilt at Main 5 at 7000 rpm

The flywheel whirl behaviour can be seen in Figures 34 and 35 which show the Y and Z components of flywheel angular displacement relative to Main 5 against engine speed. The total values and the major order content are indicated. Flywheel whirl is excited by the inertia forces of the engine. These graphs show the order content relative to ground and indicate excitation of the flywheel by 1st and 2nd order inertia forces. This result is indicative of the flywheel used for testing being heavier and with a larger overhang than the flywheel intended for production.

Figure 34 Y-component of angular displacement between flywheel and Main 5



Figure 35 Z-component of angular displacement between flywheel and Main 5

CONCLUSIONS

Analysis presented in this paper suggested that it was possible to meet known criteria for good design of the main bearings of an in-line 4 cylinder gasoline engine using just 4 counterweights instead of 8. In making this change crankshaft mass was reduced by a significant amount (~9% in this case).

To achieve the significant mass reduction with the 4 counterweight version it was necessary to reduce the bay balance factor compared with the 8 counterweight version but, following the design philosophy described in this paper, this reduction gave the 4 counterweight version almost identical values of peak bearing specific loads and minimum oil film thicknesses as the 8 counterweight version.

The shaft tilt (particularly at Mains 2 and 4) was increased by up to ~20% for the 4 counterweight version but since acceptable oil film thickness was present at these bearings it was hoped that the increase in shaft tilt would not result in unacceptable edge wear.

In fact the bearing showing the largest shaft tilt angle and so largest risk of edge loading was Main 5 (for both 4 and 8 counterweight versions of the crankshaft) at high speed. This was due to whirling of the prototype flywheel used for this analysis (and intended for initial testing).

In the near future it is planned to test both versions of the crankshaft and to compare bearing shell wear. It is also planned to perform a more rigorous main bearing analysis including elastohydrodynamic effects and using finite volume bearing models.

ACKNOWLEDGMENTS

The authors would like to thank senior management at PETRONAS for providing permission to publish this paper.

REFERENCES

1. A characteristic parameter to estimate the optimum counterweight mass of a 4 cylinder in-line engine. Stanley, R., Taraza,D. SAE 2002-01-0486

2. The influence of the counterweight on the vibrational behaviour of a crankshaft. Grasso, C. Martorelli, M. 2nd International Conference on Advanced Measurement Techniques and Sensory Systems for Automotive Applications - Accuracy and Reliability, Ancona, Italy, 13-14 Sep 2001, ATA, Session 1, 8pp.

3. The effect of cranktrain design on powertrain NVH. Querengaesser, J., Meyer, J. Schaefer, E. and Wolschendorf, J. SAE 971994

4. Dynamically loaded journal bearings – Mobility method of solution. Booker, J.F. Trans. ASME. Journal of Basic Engineering. Sept 1965.

5. Analysis of Unbalance Vibration of Rotating Shaft System with Many Bearings and Disks. K.Kikuchi. Bulletin of the JSME, 1970.

CONTACT

Naji Zuhdi Powertrain Technology, Block E, PETRONAS Research Sdn. Bhd., LOT 3288 & 3289 Kawasan Institusi Bangi 43000 Kajang, Selangor Darul Ehsan Malaysia Phone : +603-89244539 Fax : +603-89244548 e-mail [email protected] Phil Carden Ricardo UK Shoreham Technical Centre Shoreham-by-sea BN43 5FG UK Tel +44 1273 794959 e-mail [email protected]

DEFINITIONS, ACRONYMS, ABBREVIATIONS

Bay balance factor: This is defined as the mass x radius product of all the out-of-balance elements on the counterweight side of 1 crank bay (counterweights if present) divided by the mass x radius product of all out-of-balance elements on the crank pin side of the bay (including 1 crank pin, 2 crank webs and 1 connecting rod big end).



Documents

4 Versus 8 Counterweights for an I4 Gasoline Engine Crankshaft