WORKDONE AND MASS-SPRING-DAMPER SYSTEM

AIM:

1. To determine the workdone of the shaping machine as the tool moves from 0 - 100 mm at a certain force.

2. To evalute the equation by using array datas and store the datas using To File block in simulink.

3. Study the Mass-Spring-Damper system in simulink.

KEYWORDS: Shaping machine, To File, Damper.

SOFTWARE: Matlab, Simulink

OBJECTIVE:

Study 1:- Calculation of workdone by using given data and create a simulink block.

Study 2:- Evaluate equation by using set of array datas and store the results.

Study 3:- Study the Spring-mass-damper system and the modify the data and obtain the result.

INTRODUCTION:

Study 1:-

In the above model, it consists of Signal builder, integrator, scope and display. These block are effective to calculate the workdone for the given data. When a force causes a body to move, work is being done on the object by the force. Work is the measure of energy transfer when a force (F) moves an object through a distance (d). So when work is done, energy has been transferred from one energy store to another, and so: energy transferred = work done. Here, the shaping machine tool is used to remove the material on the work surface of 100mm length which is placed at fixed position and the tool is moving from 0 to 100mm of length at a certain froce in kN. Signal builder block is used to input the values to the The integrator block outputs the value of the integral of its input signal wrt time. Formula to calculate the workdone is,

W = F * D * cos(theta)

where, in this case theta = 0 (the tool is perpendicular to the workpiece)

F = force (k-Newton)

D = distance (mm)

W = workdone (K-Joule)

The above figure shows as input from signal builder according to the force and distance, and sends to the integrator which integrats wrt to the time. From this workdone will be calculated and obtained the result as 5780.5 kJ.

Study 2:-

Input from command window:

In this study, we need to evaluate the equation by given set of array datas for 'x' and 'y' variables, which should be call from workspace command window and calculate in simulink. In this model consists of From workspace block, product, square, adder, display and To File. 'From workspace' block is used to initialize the value in command window workspace, To File block is used to store all the values in file format. Display block shows the result of the equation in element-wise.

Study 3:-

Input values for simulink and simscape:

In this model consists of spring, damper, mass, integrator, gain, motion sensor, scope and display bolcks are used in simscape and simulink model respectively. In this system, study the vibration in model by varying damper coefficient (b) , spring constant (k), displacement and mass for simscape and simulink model. The governing equation for this model is shown below,

mx2+bx1+kx=0 ------------------------( 1 )

where,

m = mass (kg)

b = damping coefficient (N/m/s)

k = spring constant (N/m)

x2 = acceleration (m/s2)

x1 = velocity (m/s)

x = displacement (m)

mx2+bx1+kx=0">In this study, the simulink model value for spring constant ( k ), damping coefficicent (b) and mass ( m ) as shown in input values above figure. The simscape model value for spring constant ( k1 ), damping coefficicent ( b1 ) and mass ( m ) as shown in input values above figure. The mass value is given as 25kg for both the model and varies the spring constant, damping coefficient and displacement which shows the simscape model result is more efficient than simulink model result. As the damping coefficient increases, the oscillation of the vehicle reduces and forms steady rate. By decreasing the spring constant which gives the smooth ride over the velocity and mass. By changing the displacement value to 2, there is no much variation in oscillation, it mainly depends on the mass, spring constant and damping coefficient.

OUTPUT:

Study 1:-

Figure 1

Study 2:-

Figure 2

Study 3:-

Figure 3

CONCLUSION:

1. The value of workdone is calculated and shown in figure 1.

2. The evaluated equation result is stored and shown in figure 2.

3. The variation of oscillation in simulink and simscape model is shown in figure 3.