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Modelling and assembly of the full vehicle 383 LUMPED MASS MODEL EQUIVALENT ROLL STIFFNESS MODEL SWING ARM MODEL LINKAGE MODEL Fig. 6.52 Modelling of suspension systems body. Each of the four road wheel parts has 1 spin degree of freedom relative to the axles making a total of 12 degrees of freedom for the model. When a simulation is run in MSC.ADAMS the program will also report the number of equations in the model. As discussed in Chapter 3 the software will formulate 15 equations for each part in the model and additional equations representing the constraints and forces in the model. On this basis the size of all the models is summarized in Table 6.6.

384 Multibody Systems Approach to Vehicle Dynamics Table 6.6 Vehicle model sizes Model Degrees of freedom Number of equations Linkage 78 961 Lumped mass 14 429 Swing arm 14 429 Roll stiffness 12 265 40.0 LUMPED MASS MODEL – 100 km/h LANE CHANGE Yaw rate (deg/s) 30.0 20.0 10.0 0.0 10.0 20.0 Track test ADAMS __ __ __ __ ___________ 30.0 40.0 1.0 3.0 5.0 0.0 2.0 4.0 Time (s) Fig. 6.53 Yaw rate comparison – lumped mass model and test. (This material has been reproduced from the Proceedings of the Institution of Mechanical Engineers, K2 Vol. 214 ‘The modelling and simulation of vehicle handling. Part 4: handling simulation’, M.V. Blundell, page 80, by permission of the Council of the Institution of Mechanical Engineers) The size of the model and the number of equations is not the only issue when considering efficiency in vehicle modelling. Of perhaps more importance is the engineering significance of the model parameters. The roll stiffness model, for example, may be preferable to the lumped mass model. It is not only a simpler model but is also based on parameters such as roll stiffness that will have relevance to the practising vehicle dynamicist. The roll stiffness can be measured on an actual vehicle or estimated during vehicle design. This model does, however, incorporate rigid axles eliminating the independent suspension characteristics. Note that in this case study an interpolation tyre model of the type described in Chapter 5 has been used with each vehicle model. Measured outputs including lateral acceleration, roll angle and yaw rate can be compared with measurements taken from the vehicle during the same manoeuvre on the proving ground to assess the accuracy of the models. By way of example the yaw rate predicted by simulation with all four models is compared with measured track test data in Figures 6.53 to 6.56.

Modelling and assembly of the full vehicle 383<br />

LUMPED MASS<br />

MODEL<br />

EQUIVALENT ROLL STIFFNESS<br />

MODEL<br />

SWING ARM MODEL<br />

LINKAGE MODEL<br />

Fig. 6.52<br />

Modelling of suspension systems<br />

body. Each of the four road wheel parts has 1 spin degree of freedom relative<br />

to the axles making a total of 12 degrees of freedom for the model.<br />

When a simulation is run in MSC.ADAMS the program will also report the<br />

number of equations in the model. As discussed in Chapter 3 the software<br />

will formulate 15 equations for each part in the model and additional equations<br />

representing the constraints and forces in the model. On this basis the<br />

size of all the models is summarized in Table 6.6.

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