A SIMULINK Model to Solve a Simple Shaft-Disk Dynamics Problem

The following figure 1 represents pretty simple model where two circular disks of inertia J1 and J2 are mentioned. Torque (T) is applied to the disk 1. The shaft has its own stiffness which is K. 

Fig.1: Showing a very simple model where two disks are connected by a shaft and torque is applied to one of them.

At first, let's find the state variables for this problem and then write the state equations.

State Variables and State Equations:

Next, we assume the following key parameters,

Initial Conditions:

Parameter Values:

J1 = 100, J2 = 100, K = 100, and T = 10000. (All values are considered unitless for simplicity)

The SIMULINK model is formed by implementing the state equations. And, the above parameter values are considered. The following simulation results are for the acceleration, velocity and position of the disks which are essentially the outputs from the SIMULINK block diagram.

Fig.2: SIMULINK model of the shaft-disk system.

Fig.3: Showings the results of angular acceleration, velocity and displacement respectively of disk 1.

Fig.4: Showings the results of angular acceleration, velocity and displacement respectively of disk 2.

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