A Single-Degree-of-Freedom Rotational Mass–Spring–Damper System Consider the simple disk–shaft system in Example 5.8. A single-degree-of-freedom rotational mass–spring–damper system can be used to approximate the dynamic behavior of the disk–shaft system. The parameter values are I = 0.01 kg·m²,

Question

A Single-Degree-of-Freedom Rotational Mass-Spring-Damper System

Consider the simple disk-shaft system in Example 5.8. A single-degree-of-freedom rotational mass-spring-damper system can be used to approximate the dynamic behavior of the disk-shaft system. The parameter values are [latex]I=0.01 \mathrm{~kg} \cdot \mathrm{m}^{2}, B=1.15 \mathrm{~N} \cdot \mathrm{m} \cdot \mathrm{s} / \mathrm{rad}[/latex], and [latex]K=4150 \mathrm{~N} \cdot \mathrm{m} / \mathrm{rad}[/latex].

a. Assume that a torque [latex] au=10 \sin (600 t)[/latex] is acting on the disk, which is initially at rest. Build a Simscape model of the physical system and find the angular displacement output [latex] heta(t)[/latex].

b. Assuming that the external torque is [latex] au=0[/latex] and the initial angular displacement is [latex] heta(0)=0.1[/latex] rad, find the angular displacement output [latex] heta(t)[/latex].

Accepted Answer

a. The Simscape block diagram and the angular displacement output of the system are shown in Figures 5.111 and 5.112, respectively. Comparing Figure 5.111 with Figure 5.31, which is the Simscape model of a single-degree-of-freedom translational mass-spring-damper system, reveals the similarity of these two Simscape diagrams. The main difference is that the blocks in this example are all related to rotational motion instead of translational motion.

b. The Simscape model in Figure 5.111 can also be used to simulate the system in Part (b). To specify a zero external torque, we can either define the Amplitude of the Sine Wave as 0 or delete the blocks related to input generation, including Sine Wave, Simulink-PS Converter, Ideal Torque Source, and Mechanical Rotational Reference blocks. To specify a nonzero initial angle, double-click on the Rotational spring block, type 0.1 for the Initial deformation, and choose the unit as rad. This implies that the spring is initially twisted by [latex]0.1 \mathrm{rad}[/latex]. Also, double-click on the IdeaI Rotational Motion Sensor block, type 0.1 for the Initial angle, and choose the unit as rad. The corresponding angular displacement of the system is shown in Figure 5.113.

Question 5.20: A Single-Degree-of-Freedom Rotational Mass–Spring–Damper Sys...

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