6 720 SECTION B- Attempt any TWO Questions from this Section. 4 An air compressor experiences exc...
6 720 SECTION B- Attempt any TWO Questions from this Section. 4 An air compressor experiences excessive vibrations when running at 1100 rpm. It is fitted with a tuned dynamic absorber in order to reduce these vibrations. The mass of the compressor, me, is 80 kg and the total stiffness of its supports, kc, is 1075 kN/m. The amplitude of the out of balance force, P, is 30 N The compressor with the absorber in place is shown in Figure Q4 below. (a) Derive equations for the amplitudes of the motion of the compressor and absorber masses. (14) (b) The amplitude of the vibrations of the air compressor needs to be zero when the compressor is running at 1100 rpm. The amplitude of vibration of the absorber mass when the compressor is running at 1100 rpm should be less than, or equal to 1 mm. What mass and spring stiffness should be selected for the absorber? (c) What is the mass ratio of a tuned dynamic absorber? Describe how the mass ratio affects the performance of a tuned dynamic absorber. (d) The compressor can run at a range of frequencies. At the upper and lower ends of the operating range, the amplitude of the vibrations of the compressor with the absorber in place, are deemed to be too large. Explain how the design of the absorber could be altered in order to reduce the vibrations at these frequencies. too e to (2) mc Psin(ut) xe k, kd2 k./2 J.
6 720 SECTION B- Attempt any TWO Questions from this Section. 4 An air compressor experiences excessive vibrations when running at 1100 rpm. It is fitted with a tuned dynamic absorber in order to reduce these vibrations. The mass of the compressor, me, is 80 kg and the total stiffness of its supports, kc, is 1075 kN/m. The amplitude of the out of balance force, P, is 30 N The compressor with the absorber in place is shown in Figure Q4 below. (a) Derive equations for the amplitudes of the motion of the compressor and absorber masses. (14) (b) The amplitude of the vibrations of the air compressor needs to be zero when the compressor is running at 1100 rpm. The amplitude of vibration of the absorber mass when the compressor is running at 1100 rpm should be less than, or equal to 1 mm. What mass and spring stiffness should be selected for the absorber? (c) What is the mass ratio of a tuned dynamic absorber? Describe how the mass ratio affects the performance of a tuned dynamic absorber. (d) The compressor can run at a range of frequencies. At the upper and lower ends of the operating range, the amplitude of the vibrations of the compressor with the absorber in place, are deemed to be too large. Explain how the design of the absorber could be altered in order to reduce the vibrations at these frequencies. too e to (2) mc Psin(ut) xe k, kd2 k./2 J.