## 2017/2018

systems modelling代写 building a simulation model, based on the mathematical model, usinga continuous system simulation tool

### Objectives

This assignment is designed to give you experience in:

a）deriving a mathematical model of a dynamical engineeringsystem;

b）building a simulation model, based on the mathematical model, usinga continuous system simulation tool;

c）using the simulation model to study the behaviour of the dynamicalengineering system under a variety of

### Problem systems modelling代写

A road with a flat and horizontal surface incorporates a hump with a rectangular cross section of height 0.1 m, relative to the flat horizontal surface, and a width of 0.5 m. An automobile travels along the road at a nominal speed of 15ms-1. Representative values for the physical parameters of the vehicle are given in table 1.

Develop a mathematical model to represent the transient behaviour of the pitch and heave (vertical) motion of the vehicle. Implement your mathematical model as a dynamic system simulation model using the SIMULINK continuous system simulation tool. Use your simulation model to predict the behaviour of the vehicle as it traverses the road hump and obtain estimates of the:

i. maximum vertical displacements ofthe:

a. sprung mass centre ofgravity,

b. front un-sprung mass centre ofgravity,

c. rear un-sprung mass centre ofgravity;

ii. the maximum pitch angle of the sprungmass;

iii. the frequencies ofthe:

a. vertical motion of the sprung mass,

b. vertical motion of the front un-sprung mass,

c. vertical motion of the rear un-sprungmass,

d. pitch motion of the sprung mass;

iv. The maximum variation inthe:

a. front suspension spring force,

b. rear suspension springforce,

c. front suspension damper force,

d. rear suspension damperforce,

e. vertical force of the fronttyres,

f. vertical force of the rear

### Submission of work systems modelling代写

The work to be submitted for assessment should consist of:

. (1) a listing and brief explanation of the equations defining your mathematical model of the pitch and heave motion of the vehicle;

. (2) your SIMULINK simulation model of the vehicle (including any parameter files);

. (3) the graphs generated using your SIMULINK simulation model of the pitch and heave motion of the vehicle;

. (4) an Assignment Submission Proforma (attached) containing entries of the estimates of the vehicle characteristics derived from the graphs generated using your SIMULINK simulation model;

. (5) a half page summary of your conclusions.

#### Note:

• A report is notrequired and should not be
• Your work must be submitted electronically via
• Ensure that you define all mathematical variables (using a diagram if necessary).
• Ensure that the SIMULINK model is neatly laid out and clearlylabelled:
• Use sub-system blocks ifnecessary
• All blocks and variables appropriately named
• No unnecessarycomponents/connections
• Components and connections neatly laidout

### Assessment systems modelling代写

Your submitted work will be assessed against the level of: achievement (30%); presentation and discussion of results (30%); understanding and intellectual quality of analysis (30%), quality of submitted SIMULINK model (10%).

 Sprung Mass Weight (kg) 1500 Pitch moment of inertia (kg m2) 2000 Front Suspension Horizontal distance to centre of gravity (m) 1.4 Spring rate, per axle (kN m-1) 40 Damping rate, per axle (kN s m-1) 5.6 Rear Suspension Horizontal distance to centre of gravity (m) 1.6 Spring rate, per axle (kN m-1) 54 Damping rate, per axle (kN s m-1) 8 Un-sprung masses Weight, per axle (kg) 150 Tyre vertical stiffness, per axle (kN m-1) 400

Table 1 – Vehicle Parameters.

## Assignment Submission Proforma

Enter below the estimates that you predicted using your simulation model.

 Vehicle characteristic Estimated value Maximum vertical displacement Sprung mass centre of gravity Front un-sprung mass centre of gravity Rear un-sprung mass centre of gravity Maximum angle Maximum pitch angle of the sprung mass Frequencies Vertical motion of the sprung mass Vertical motion of the front un-sprung mass Vertical motion of the rear un-sprung mass Pitch motion of the sprung mass Maximum force variation Front suspension spring Rear suspension spring Front suspension damper Rear suspension damper Front tyres Rear tyres

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