One of the key aims to provide opportunity to gain hands-on practical experience of dynamical response of mechanical systems to externally applied load: Dynamics and Vibration Report, TU

ICA Brief & Laboratory Manual

Lab experiment: Torsional Oscillations of a Rotary system

Assignment Brief

Overview

One of the key aims of the Dynamic and Vibration module is to provide students with the opportunity to gain hands-on practical experience of dynamical response of mechanical systems to externally applied load. The type and magnitude of the response depends on many parameters. Some of them are system parameters and the others are material parameters.

This assignment constitutes 30% of the overall module mark. The report should contain no more than 2,400 words) – about maximum 15 pages including graphs, calculations, references, etc. The report needs to be written and submitted individually (and not as a group work). The assessment
will assess learning outcomes 2, 3 and 4.

Assessment

The assessment has two components. These are the experiment and the report writing.

a) Experiment

A laboratory experiment including two parts (A and B) as demonstrated in Fig. 4, Fig. 5 and Table 2 is employed to determine the value of the shear modulus of rigidity (G) of a circular shaft through an oscillatory experiment. For an initial gauge length of 100 mm in setup A and 250 mm in setup B, a small angle of twist within the shaft elastic deformation region is induced on the shaft and released.

Under the influence of a rotor system shown in Fig. 4 and Fig. 5, the shaft undergoes 20 rotational oscillations. The details of the rotor are presented in Table 2. The time to complete the oscillations is recorded. Some other gauge lengths are employed and for each length, 20 oscillations and their
corresponding time are recorded in each setup. The results are presented in Table 3 and Table 4

b) Report Writing

(a) Note the required parameter values of the rotor system (masses, radius of discs, and offset mass distance from the axis of rotation) according to Table 2.0.

(b) Compute the mass moment of inertia Iz [kg.m2] for each rotary system (setups in Part A and Part B) of the experiment separately.

(c) Compute the second polar moment of area J of the shaft.

(d) Plot the values of frequency, f [Hz] versus the length of shaft, L [m], on a graph sheet via Excel for each part of the experiment (A and B).

(e) Plot the values of 𝜏2[𝑠2] against length L [m] on a graph sheet via Excel for each part of the experiment (A and B).

(f) Determine the slope of the latter graph (after linearization) for each setup of the experiment.

(g) Compute the value of the shear modulus of rigidity G [MPa] of the shaft for each graph.

(h) Compare the value of G resulted from Parts A and B and state the relative error between these two values besides presenting an average value for G.

(i) Give a name for the material of the test shaft and state your reasons.

(j) What deduction(s) can you make on the relationship between the frequency of the system, f [Hz] and the length L?

(k) What deduction(s) can you make on the relationship between the length L and the square of the period, 𝜏2?

(l) How close is your generated G value to the published literature value of the named material?

Explain the possible sources of error in this experiment and suggest how you can mitigate them.

(m) Discuss the assumptions and/or simplifications considered in the experiment or the theoretical development that may have affected the accuracy of results.

(n) Discuss the reasons causing the suppression of oscillations in the rotary systems over time

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