Dr A. Cookson Department of Mechanical Engineering
2020/2021 University of Bath
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Assignment 3: Simulink Modelling of Dynamic Systems
ME40064: System Modelling & Simulation
ME50344: Engineering Systems Simulation

The overall aim of this assignment is to develop, verify, and use a model of a ½
car system, building on the ¼ model in the tutorials.


Figure 1: Representation of the 1/2 car model
Having completed Tutorial 9 you will have developed the suspension and wheel
models. The main changes will be in the body model, which now represents ½ a
car, and couples together the front and rear wheel assemblies. The equations of
motion of the 1⁄2 car body are as follows:




where sB and θ are vertical (positive up) and pitch (anti-clockwise)
displacements about the centre of mass, and Ffront, Frear are the upward forces
exerted by the suspension systems on the body, at the front and rear,
respectively. The equations for the wheel and suspension models are as before.

The parameters for this model are given below:

Wheel: mW = 20 kg, kT = 14 x 104 N/m
Dr A. Cookson Department of Mechanical Engineering
2020/2021 University of Bath
Page 2 of 3

Suspension: kS = 2 x 104 N/m, cS = 600 Ns/m (under contraction) & 1200 Ns/m
(under extension). Spring hardening parameters: kSstiff = 20kS, x0 = 0.2.

Body: mB = 500 kg, I = 600 kg/m2, a = 1.25m, b = 1.4m
Part 1: Model Construction & Verification

(a) Create an icon block for the 1⁄2 car body with suitable inputs (forces) and
outputs (including vertical displacements/velocities at suspension points).
Verify that your 1⁄2 car body model is correct and explain the reasoning behind
your verification tests. [15%]

(b) Connect the suspension and wheel models to the 1⁄2 car body. Verify that
the complete 1⁄2 car model is correct and explain the reasoning behind your
verification tests. [25%]
Part 2: Investigation of Car Performance

(c) Simulate the vehicle’s transient response over a sinusoidal road of
wavelength 1 m and a range of amplitudes from 0.01 m upwards. Choose a range
of speeds for your simulations and explain your results and their relevance to
car design. [25%]

(d) Now examine how this performance is affected by changing various
parameter values of the car model and discuss the results in the context of car
performance optimisation. [35%]

The assignment should be written up as a concise report showing your Simulink
models, model verification tests, simulation results, and conclusions. All the
results should be presented clearly and properly explained. Simulink diagrams
should be neatly organised and easy to read. You should demonstrate that your
simulation results are converged.

See Lecture 21 slides for further details on the model and what is required.

Submission

Submit your report & the Simulink model files using the online submission on
the unit’s Moodle page. As before this is an anonymous submission; therefore,
do not include your name in the report, Simulink models, or filenames, but do
include your candidate number. There is a word limit of 2000 words.

Dr A. Cookson Department of Mechanical Engineering
2020/2021 University of Bath
Page 3 of 3

Your report will be marked against the following criteria:

• Correctness of model & numerical results
• Clarity of written explanations
• Clear presentation of report content, results plots, and Simulink diagrams
• Rigour of model verification and simulation convergence testing
• Thoroughness and real-world relevance of the performance investigations

Deadline: 4pm on Monday 11th January 2021.