Evaluating a Function and Comparison of various Suspension Systems using SIMULINK

COMPARISION OF VARIOUS SUSPENSION SYSTEMS USING SIMULINK :-

AIM :-

To compare and study the results of various suspension systems using Simulink.

PLATFORM USED :-

1. Software – Simulink (MATLAB)

SYSTEM SPECIFICATIONS :-

1. Manufacturer - DELL
2. Model – Vostro 3478
3. Operating System - Windows 10
4. Processor - Intel(R) Core(TM) i5-8250U CPU @ 1.60GHz 1.80GHz
5. RAM – 8 GB

OBJECTIVES :-

1. Evaluate and plot the given function using Simulink.
2. Comparison of various suspension systems.

EVALUATION OF THE FUNCTION USING SIMULINK

GIVEN FUNCTION :-

`y(x) = (x-1)*(x-3)^2*(x-9)^2`

SIMULINK MODEL :-

For plotting the function we are varying the ‘x’ value from 0 – 12.

BLOCKS USED :-

1. Ramp – For varying the ‘x’ value to plot the function f(x).
2. Constant – To represent the values of ‘1, 3 & 9’.
3. Subtract – For solving the equation.
4. Square – For squaring the solved equation.
5. Product – To evaluate and generate the function output.
6. Display – To show the evaluated value.
7. Scope – To trace the change in values during increment in ‘x’ value and plot the function graph.

FLOW PROCESS :-

1. Initially the ‘x’ value is taken and sent to (x-1), (x-3) and (x-9) blocks to solve with the constants.
2. Then the (x-3) and (x-9) blocks values are squared.
3. Then the values from (x-1), (x-3)^2 and (x-9)^2 blocks are sent to product block for multiplication.
4. Then the output is taken as display for showing the evaluated value and scope block for tracing the changes in the function when ‘x’ value changes.
5. All the above steps are run like a loop till ‘x’ value reaches the desired run seconds given by the user.

VERIFICATION :-

Always the Simulink displays the last timer value '12' evaluation for the function.

So,

`x =12`

Now,

`y(x) = (x-1)*((x-3)^2)*((x-9)^2)`

`y(12) = (12-1)*((12-3)^2)*((12-9)^2)`

`y(12) = (11)*((9)^2)*((3)^2)`

`y(12) = (11)*(81)*(9)`

`y(12) = 8019`

OUTPUT :-

The evaluated value as ‘8019’.

COMPARISION OF VARIOUS SUSPENSION SYSTEMS USING SIMULINK

SIMULINK MODEL :-

In this model three different types of spring and damping for arresting the vibrations generated by the velocity source.

MODEL FLOW :-

1. Initially we provide the velocity source to the tire spring and then it gets transferred through the un-sprung mass.

2. From the un-sprung mass, it get passed to sprung mass via spring and damper arrangements. The damping co-efficient (B) and spring constant is varied for variable spring suspension system.

3. The motion sensor is connected to capture the movement and position of the spring during change in velocity.

This model is based on the following real suspension system used in the automobiles,

QUESTION & ANSWERS :-

1. What is the objective of the simulation? What are the similarities and differences between the three systems understudy?

Objective of the Simulation,

To provide certain range of velocity input and analyze the sprung mass position during vibrations in all the three different types of spring mass arrangement.

Three Damping Systems,

In this model we are using three different arrangement of spring and damper,

1. Shock Absorber (Linear Arrangement of Spring and Damper)
2. Non-Linear Translational arrangement of Spring and Damper
3. Variable Translational Spring and Damper

Shock Absorber,

In the shock absorber both spring and damper are arranged linear and type used is Linear Translational.

Non-Linear Arrangement,

In this the spring and damper are arranged in non-linear (parallel) method and type used is Non-Linear Translational.

Variable Type,

In this the spring and damper used are variable translational w.r.t stiffness ‘K’ and damping co-efficient ‘B’.

2. What are your observations from the results?

The observations after simulating the model is the vibrations of the three systems and the position of the sprung mass during the vibration frequency variation.

Result I :-

In this plot we can observe that the position of the sprung mass during the change in velocity and vibration of the spring. Initially the spring gets vibrated during the input velocity and gets damped out by the damper.

1. Till time (t=20 sec) the vibration of all the three systems are same and them gets damped out.
2. From time (t=40 – t=60) the variable spring vibrates and damps out. But the suspension and linear one vibrates till (t=70 sec) and then gets damped out.
3. Further there are very small vibrations in between (t=80 – t=100) interval in suspension and linear one then gets damped out where the input velocity is high.

RESULT II :-

From this plot we can observe the vibration frequency of the springs in all the three systems from the noise in (dB) during the input velocity.

3. How the oscillating velocity source is created?

The oscillating velocity is created using sine wave and pulse generator block.

MODEL FILE :-

1. Function Model (Simulink)

REFERENCES :-

1. https://in.mathworks.com/help/physmod/sdl/examples/suspension-system-comparison.html

CONCLUSION :-

From the above simulation we are able to solve a function using Simulink and simulate the three suspension system to understand their behavior (vibration, damping & frequency) during change in velocity (different road conditions).