Chassis Stiffness

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SAE TECHNICAL PAPER SERIES

2000-01-3554

The Effect of Chassis Stiffness on Race Car Handling Balance Andrew Deakin, David Crolla, Juan Pablo Ramirez and Ray Hanley School of Mech. Eng., The University of Leeds

Reprinted From: Proceedings of the 2000 SAE Motorsports Engineering Conference & Exposition (P-361)

Motorsports Engineering Conference & Exposition Dearborn, Michigan November 13-16, 2000 400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A.

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2000-01-3554

The Effect of Chassis Stiffness on Race Car Handling Balance Andrew Deakin, David Crolla, Juan Pablo Ramirez and Ray Hanley School of Mech. Eng., The University of Leeds Copyright © 2000 Society of Automotive Engineers, Inc.

ABSTRACT

LT =

This paper looks at the fundamental issues surrounding chassis stiffness. It discusses why a chassis should be stiff, what increasing the chassis stiffness does to the race engineer’s ability to change the handling balance of the car and how much chassis stiffness is required. All the arguments are backed up with a detailed quasi static analysis of the problem. Furthermore, a dynamic analysis of the vehicle’s handling using ADAMS Car and ADAMS Flex is performed to verify the effect of chassis stiffness on a race car’s handling balance through the simulation of steady state handling manoeuvres.

(1)

where LT is the lateral load transfer for an axle, LATacc is the lateral acceleration, ma is the mass supported by that relevant axle, hCG is the centre of gravity height and t is the track width. This assumes a flexible chassis. 3000

Maximum lateral force generated, N

It is often quoted that to be able to make a race car handle ‘properly’ by tuning the handling balance, the chassis should have a torsional stiffness of ‘X times the suspension stiffness’ or ‘X times the difference between front and rear suspension stiffness’ [1].

ma Latacc hCG t

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Vertical load, N

Figure 1 – Non-linear behaviour of a typical Formula SAE tyre, max. lateral force produced for a vertical load.

INTRODUCTION It is well known that to make a race car handle correctly, it must be possible to tune the handling balance. Tuning the handling balance means adjusting the level of grip available from either the front or the rear of the vehicle. When both the front and rear axles can produce a force to give the same lateral acceleration, the chassis can be said to be balanced. Figure 1 illustrates the non-linear behaviour of a typical tyre used with Formula SAE racing cars. Figure 2 shows the Leeds University Formula SAE car. It can clearly be seen that if a pair of tyres on an axle had the same vertical load, then they could both produce the same maximum lateral force. If for example, the vehicle was cornering, then the lateral acceleration would cause a load transfer, equation 1. This lateral acceleration would increase the vertical load on the outside tyre and decrease the vertical load on the inside tyre by the same quantity. The result of this load transfer is that the two tyres combined can produce less lateral force.

Therefore a car understeers (a car that has too little grip at the front), the grip can be increased at the front by reducing the load transfer at the front and increasing the load transfer at the rear.

Figure 2 – Leeds University Formula 1999 SAE car Being able to control the load transfer distribution is therefore the key to being able to obtain a good handling balance. The lateral load transfer distribution can only be controlled however, if the chassis is stiff enough to transmit the torques.

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The question that is then raised is how stiff is stiff enough. The objective of this work was to go some way towards answering that question.

MODELLING

The real vehicle is much more equivalent to that shown in figure 5, where the mass is evenly distributed along the body. As long as the chassis is equally torsionally stiff at all points along the chassis then it can be shown that the idealised model still represents the actual chassis.

There are two sections of modelling within this paper. The first is a simple static analysis to determine the effects of chassis torsional stiffness on being able to maintain the desired lateral load transfer distribution. The second is a dynamic analysis of the effect of a flexible chassis using the ADAMS and ADAMS Flex. STATIC ANALYSIS OF CHASSIS STIFFNESS – A model calculating the static forces present in the chassis under steady state conditions has been developed. This considers the racing car to consist of two point masses, mf and mr for the front and rear respectively, connected by a torsional spring, Kch, and a suspension at each end of the vehicle represented by a roll stiffness, Krollf and Krollr, figure 3.

mr Krollr

Figure 5 – Chassis model with uniformly distributed mass The real vehicle however, does not have an evenly distributed mass with all mass having the same moment arm and each segment of the chassis having an equal torsional stiffness. In reality, figure 6 is something like an actual vehicle’s mass distribution. Heavier objects such as the engine, the driver safety cell and the driver are located close to the centre of gravity of the car. Also, the torsional springs may not be along the same axis as shown in figure 6. Therefore there are likely to be discrepancies between results from the idealised model and a real vehicle.

mf Kch Krollf Figure 3 – Static model of the effect of chassis torsional stiffness on lateral load transfer distribution

Figure 6 – Mass distribution of real vehicle

From this model, equations 2, 3 and 4 were derived. φ1, φ2 and φ3 are the front suspension roll angle, the rear suspension roll angle and the chassis torsional twist respectively. Mf and Mr are the front and rear moments due to the lateral acceleration of the body masses.

Additionally, there are compliances in the suspension, commonly referred to as the installation stiffness, which reduce the chassis torsional stiffness as seen at the wheels. These should also be considered as possible errors between the idealised model which has been proposed and the real vehicle.

Mf = Krollfφ1 − Kchφ 3

(2)

Mr = Krollrφ 2 + Kchφ3

(3)

φ1 + φ 3 = φ 2

(4)

These equations represents a very much idealised model of the vehicle as shown in figure 4.

MULTI-BODY HANDLING MODEL – A model of the Leeds University Formula SAE car has been developed in ADAMS to understand further the effect of a flexible chassis on handling. The basic model configuration with a rigid chassis is shown in figure 7. Two extensions to this model were created which included; a chassis separated into a front and rear section joined by a torsional spring along an axis at the wheel centre height, and a flexible chassis incorporated into the ADAMS model using ADAMS Flex. In theory, the model containing a torsional spring could be used to validate the static model results. The results from the model incorporating an ADAMS Flex, flexible chassis, could be used to understand the effect on a real vehicle.

Figure 4 – Idealised chassis model with two masses connected by a torsional spring Author:Gilligan-SID:3681-GUID:30311078-129.16.65.19

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The model with the torsional spring was developed to enable evaluation of multiple chassis torsional stiffnesses on the vehicle’s handling performance, as this just requires a single model parameter to be changed. ADAMS Flex takes a modal neutral file format which is produced using the finite element method in a software package such as ANSYS, figure 8. This model is loaded such that a torsional force is put onto the chassis at the suspension rocker mounts. Ideally it should be loaded such that all the suspension wishbone and track rod forces load the ADAMS Flex model, however, this would increase the complexity significantly. As it was, there were 18 mode shapes represented in the model, eight of which were rigid body modes. The nominal torsional stiffness of the ADAMS Flex model was 1,300 Nm/deg.

Subsystem Value rear susp. 17.93 front susp. 16.70 rr. antiroll 1.99 frt. antiroll 1.99 steering 5.90 frt. wheels 21.00 rr. wheels 21.00 chassis with driver 250.00 Chassis Inertias Ixx (roll) 7.33E+06 Iyy (pitch) 3.56E+07 Izz (yaw) 3.94E+07 Chassis C.G. Location

kg kg kg kg kg kg kg kg [kg*mm^2] [kg*mm^2] [kg*mm^2]

frt. weight 46.5 % rr. weight 53.5 % height 300 mm Spring Rates frt. spring rate 61.5 [N/mm] rr. spring rate 87.9 [N/mm] frt. antiroll bar rate 150 [Nm/deg] rr. antiroll bar rate 125 [Nm/deg] Table 1 – Data for Formula SAE Car model

RESULTS Results were produced to indicate how chassis stiffness effects, set up of the desired lateral load transfer. This was conducted both through static analysis and dynamic analysis. Figure 7 – ADAMS model of the Leeds University Formula SAE Car.

STATIC ANALYSIS RESULTS – The static analysis results were performed for a range of vehicle, total suspension roll stiffnesses representing different vehicles. Dixon [2], gives a range of data values, table 2, for different types of racing vehicle. Total roll stiffnesses for typical Formula SAE cars are also included. Car type Saloon Sports car Sports prototype

Total roll stiffness, Nm/deg 300 – 800 2000 18,000

Formula One

20,000 – 25,000

Formula SAE

500 – 1,500

Table 2 – Typical total vehicle roll stiffness, Nm/deg

Figure – 8 ADAMS Flex chassis template. The overall vehicle parameter data used in the ADAMS model is shown in table 1.

Figures 9, 10, 11 and 12 show the difference in front to rear lateral load transfer distribution for different roll stiffness distributions. This is calculated for a range of chassis stiffnesses and for total roll stiffnesses of 500, 1500, 5000 and 15000 Nm/deg respectively. All of these results assume that both the static load distribution is 50:50 and the front and rear centre of gravity heights are the same.

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90 80 70 60 50 Chassis stiffness 100 Nm/deg Chassis stiffness 300 Nm/deg Chassis stiffness 600 Nm/deg Chassis stiffness 1000 Nm/deg Chassis stiffness 2000 Nm/deg Chassis stiffness 4000 Nm/deg Chassis stiffness 8000 Nm/deg Chassis stiffness 16000 Nm/deg

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Front roll stiffness as % of total roll stiffness

Figure 10 – Lateral load transfer from a racing car with roll stiffness of 1500 Nm/deg 100 90 80 70 60 50 Chassis stiffness 100 Nm/deg Chassis stiffness 300 Nm/deg Chassis stiffness 600 Nm/deg Chassis stiffness 1000 Nm/deg Chassis stiffness 2000 Nm/deg Chassis stiffness 4000 Nm/deg Chassis stiffness 8000 Nm/deg Chassis stiffness 16000 Nm/deg

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Front roll stiffness as % of total roll stiffness

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Figure 11 – Lateral load transfer from a racing car with roll stiffness of 5000 Nm/deg

60 50 Chassis stiffness 100 Nm/deg Chassis stiffness 300 Nm/deg Chassis stiffness 600 Nm/deg Chassis stiffness 1000 Nm/deg Chassis stiffness 2000 Nm/deg Chassis stiffness 4000 Nm/deg Chassis stiffness 8000 Nm/deg Chassis stiffness 16000 Nm/deg

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Front roll stiffness as % of total roll stiffness

Figure 9 – Lateral load transfer from a racing car with roll stiffness of 500 Nm/deg With a total suspension roll stiffness of 1,500 Nm/deg, the modelled chassis stiffness required to produce a front to rear lateral load difference of 80%, of the roll stiffness distribution difference, is approximately 1000 – 2,000 Nm/deg, figure 10. Similarly, when the roll stiffness is increased to 5,000 Nm/deg, a modelled chassis torsional stiffness greater than approximately 6000 Nm/deg is required, figure 11. For the vehicle with a roll stiffness of 15,000 Nm/deg, using the same 80% guideline, a modelled chassis stiffness of greater than 10,000 Nm/deg is required, figure 12.

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Front load transfer as % of total load transfer

Front load transfer as % of total load transfer

It is clear from figure 9 that all but the least stiff of chassis shown, (100Nm/deg torsional stiffness), produces a load transfer distribution of 34:66 or greater at the point where the roll stiffness distribution is 30:70. Therefore if the criterion is that the difference between front and rear lateral load transfer is to be 80% of the difference between front and rear roll stiffness, then for softly sprung cars, (roll stiffness