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A mathematical model for the simulation of vehicle motions

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Summary

The equations of motion for an idealised vehicle are derived by the use of Lagrange's method. Expressions for those variables which affect the forces applied to the vehicle are derived in terms of the vehicle motion parameters. Extensions to the model and its particular usefulness are considered.

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Abbreviations

M s :

vehicle sprung mass

m u :

unsprung mass per wheel

I xs :

body moment of inertia aboutOX

I ys :

body moment of inertia aboutOY

I zs :

body moment of inertia aboutOZ

C xzs :

product of inertia of body with respect toOX, OZ

I xu :

cambering moment of inertia of each unsprung mass

I yu :

polar moment of inertia of each unsprung mass

I zu :

yawing moment of inertia of each unsprung mass

a :

distance fromO to plane of front suspension

b :

distance fromO to plane of rear suspension

t :

lateral distance fromO to each wheel centre

t of,t or :

values oft at front and rear respectively for vehicle at rest

R :

wheel radius

h 0 :

value of (−z0) for vehicle at rest

I u :

unsprung mass inertia approximately equal toI xu,I zu,I yu/2

δ 1,δ 2,δ 3,δ 4 :

road wheel steer angles

References

  1. H. B. Pacejka,Study of the lateral behaviour of an automobile moving on a flat, level road, and of an analog method of solving the problem, Cornell Aeronautical Laboratory Report YC-857-F-23, 1958.

  2. F. N. Beauvais, C. Garelis and D. H. Iacovani, An improved analog for vehicle stability analysis.Society of Automotive Engineers 295C, (1961).

  3. W. Bergman, The basic nature of vehicle understeer-oversteer.Society of Automotive Engineers 957 B, (1965).

  4. A. Chiesa and L. Rinonapoli, Vehicle stability studied with a non-linear, seven-degree model.Society of Automotive Engineers 670476, (1967).

  5. I. D. Nielson, The motion and stability of a vehicle moving over surfaces which are bumpy, sloping, or cambered.Proc. Instn. Mech. Engrs., 183, Part 3A, (1968–69).

  6. F. D. Hales, A theoretical analysis of the lateral properties of suspension systems.Proc. Instn. Mech. Engrs., 179, Part 2A, (1964–65).

  7. R. E. D. Bishop and D. C. Johnson,The mechanics of vibration, Cambridge Univ. Press, 1960.

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Authors and Affiliations

  1. The Birmingham Small Arms, Co. Ltd., Birmingham, England

    R. S. Sharp

  2. The Motor Industry Research Association, Lindley, Nuneaton, Warwickshire, England

    J. R. Goodall

Authors
  1. R. S. Sharp
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  2. J. R. Goodall
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Additional information

Formerly of The Advanced School of Automobile Engineering, College of Aeronautics, Cranfield, Bedford, England.

Formerly of The Advanced School of Automobile Engineering.

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Sharp, R.S., Goodall, J.R. A mathematical model for the simulation of vehicle motions. J Eng Math 3, 219–237 (1969). https://doi.org/10.1007/BF01535170

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  • DOI: https://doi.org/10.1007/BF01535170

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