suspenssion system comparision

1.plot the function Y(x)=(x-1)⋅(x-3)2⋅(x-9)2">Y(x)=(x−1)⋅(x−3)2⋅(x−9)2Y(x)=(x-1)⋅(x-3)2⋅(x-9)2 using basic Simulink blocks.

SIMULINK basic blocks used for the above function.

1.CONSTANT:-

The constant symbol is used in Simulink to assign a constant value.

2.Ramp:-

Ramp symbol is used in Simulink to assign a variable concerning time.

3. Add:-

Add symbol is used in Simulink to assign to subtract or addition two constants or variables, but the size of the variables must be the same.

4.Square:-

used to square the constants, it may single or an array.

5.Product:-

The product is used in Simulink to multiply or divide the two or more constants or variables.

6.Scope:-

The scope is used to plot the graphs and visualize the results.

7.Display:-

The display is used to see the results at the last time step.

SIMULINK model for Y(x)=(x-1)⋅(x-3)2⋅(x-9)2">Y(x)=(x−1)⋅(x−3)2⋅(x−9)2Y(x)=(x-1)⋅(x-3)2⋅(x-9)2

EXPLANATION:-

1. In the block diagram, 3 constants and 3 ramps (named as x-variable) blocks are taken to assign the constant values and variable 'x' in the formula. change the constant values as per the formula.

2. 3 add(named as subtracting) blocks are taken and changed the symbols by editing the block, constants and variables are connected to as per their position in the formula for every Add block.

3.2 square blocks are taken, squared the subtract value as per the formula.

4.in product block changed the number of inputs to 3, connected all 3 outputs from the blocks to product block as shown in the block diagram.

5.the product block is connected to display(named as End value display) and scope(named as plot).

6.setup time limit is 10.00 sec and runs the simulation. results are showing as a plot in scope, end time (at 10.00 sec)shows in the display.

Y(x)=(x-1)⋅(x-3)2⋅(x-9)2">Y(x)=(x−1)⋅(x−3)2⋅(x−9)2Y(x)=(x-1)⋅(x-3)2⋅(x-9)2 function plot

The X-axis is the time(x), Y-axis is the value of function Y(x).

for the Simulink model clock on this link https://drive.google.com/drive/u/0/folders/1XxwlFGuIMXoNRDT7CXXurZH9wCzadue0

2. Run the Simulink example "suspension system comparison" and answer the following.

SIMULINK BLOCK DIAGRAM OF "suspension system comparison"

1.what are the objectives of simulation? what are the similarities and differences between the three systems understudy?

objectives:- the main objective of this simulation is the calculation of the amplitude at the sprung mass under three types of suspension by using the input displacements(road profile).

similarities:-For all three systems input force, tire stiffness, unsprung mass and sprung mass properties are the same.

The input force will explain in a later question.

Tire stiffness:- which is indicated with the below symbol.

The stiffness value assigned for the tire is 200000 n/m, the variable is the only deformation is selected because, in results we need the amplitude at the sprung mass, deformation is depending on the sprung weight and unsprung weight units are in meters.

unsprung mass:-it is indicated with the below figure in the block diagram.

the unsprung mass is 50Kg and gravity is 9.8 ms2">ms2ms2. this mass is below the spring so its called unsprung mass. its total weight of the vehicle which has below the suspension.

sprung mass:-it is indicated with the below figure in the block diagram.

the sprung mass is 350Kg and gravity is 9.8 ms2">ms2ms2. this mass is above the spring so its called sprung mass. its total weight of the vehicle which has above the suspension.

differences:-

there are three types of suspension systems

1.shock absorber:-

A shock absorber or damper is a mechanical or hydraulic device designed to absorb and damp shock impulses. It does this by converting the kinetic energy of the shock into another form of energy (typically heat) which is then dissipated. Most shock absorbers are a form of dashpot(a damper which resists motion via viscous friction).

the properties of the shock absorber are shown below.

2.non-linear shock absorber:-

A linear spring one with a linear relationship between force and displacement, meaning the force and displacement are directly proportional to each other. A graph showing force vs. displacement for a linear spring will always be a straight line, with a constant slope.

A nonlinear spring has a nonlinear relationship between force and displacement. A graph showing force vs. displacement for a nonlinear spring will be more complicated than a straight line, with a changing slope.

properties of the non-linear shock absorber are shown below

3.variable suspension:-

variable suspension properties are varied according to time (depends on given input).properties are shown below.

from the above image, only stiffness is assigned as 1 and damping is 0.

the sub Simulink model is inside the 'BK' block.shown in the below figure.

here stiffness and damping vary concerning time as shown in the below graph.

and damping is calculated

2C=(KM)0.5">2C=(KM)0.52C=(KM)0.5

2. What is your observation from the results?

results1:-

my observations from the results are

1. The bottom subplot 2 is the input velocity, the x-axis is the time variable and y-axis the input velocity.

2. Red, orange, and blue in subplot 1 defines the amplitude at the sprung mass which is the body of the vehicle.

3. here we can the behavior of three suspension systems, suggest the best for as per requirement.

results2:-

1.above graph is showing power spectral density(PSD) up to 100Hz, PSD is very dangerous to vibrations the optimum PSD is best for the suspension.

3. How the oscillating velocity is created?

the oscillating velocity sub Simulink model is shown in the below figure.

by using the sine wave and pulse generator a periodic sine wave is created until some time, repeated this process for different time intervals with different lengths of the sine wave. Added these waves to generate a single wave and derivated concerning time. finally, we have got the input velocity as shown in the results figure.