174 J.P. De Clerck and J.S. De Clerck 16.5 Lab Activity 3: Tuned Absorber to Reduce Steering Wheel Vibration The scenario for the multiple degree of freedom (MDOF) experiment is to design a tuned absorber for the steering wheel of a luxury automobile. The problem is that engine firing frequency at idle is the same as the natural frequency of the steering column causing excessive vibration. The Chief Engineer asks the students to investigate using a tuned absorber to reduce the steering column vibration. The student engineers are asked to recommend a design (mass and stiffness) for a tuned absorber and provide quantitative evidence of the reduction in vibration. The pre-lab activity begins with a brief lecture on the basics of two degree of freedom free vibration analysis. Frequency response functions for one and two degrees of freedom are compared. The key concept is that anti-resonance is a special case where the specific degree of freedom will not move even when a high amplitude force is applied at that frequency. The PhET Resonance [5] is used to demonstrate how system can have multiple natural frequencies. This tool is also used to demonstrate how a reed tach works. The PhETNormal Modes [6] is used to demonstrate mode shapes and natural frequencies. In the lab, the first step is to identify the natural frequency of the simulated steering column. The surrogate engine is a Modal Shop Model 2002E Miniature Electrodynamic Inertial Shaker [7] attached to a piezo-electric load cell which is attached to the surrogate test structure, as shown in Fig. 16.7. Because the shaker is part of the system, the pluck test cannot be used to estimate the natural frequency. Student engineers must use skills from the previous activity to estimate the accelerance and compliance using a series of measurements at discrete frequencies. Once the natural frequency is identified, the excitation frequency is set at resonance. The students then attach the tuned absorber (mass and spring steel) and adjust the stiffness by moving the mass in and out until the simulated steering column stops moving. Students also notice that the added mass has high amplitude of vibration. The student engineers use two methods to validate their solution. The first requires inserting a stiff block between ground and the surrogate steering column and measuring the free response of just the tuned absorber. The natural frequency of the tuned absorber should match the frequency that they wanted to cancel. The second method is to repeat measuring accelerance to demonstrate that the proposed solution results in a system has two natural frequencies and anti-resonance at the frequency they wanted to cancel. A sample plot is shown in Fig. 16.8. In their test report to the Chief Engineer, students recommend adding a tuned absorber to the steering column and specify values for the mass and stiffness to guide the design of the tuned absorber. Fig. 16.7 Surrogate steering column with tuned absorber shown as a mass attached to slotted spring steel
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