A machine with mass, M'= 1000 kg is mounted on the floor of a building using...

  

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A machine with mass, M'= 1000 kg is mounted on the floor of a building using 4 vibration isolation mounts as shown. The source of vibration is somewhere on the floor and the objective is to isolate the machine from the floor by changing its mass. When the vibration source was on, an accelerometer mounted on the machine determined that the machine was oscillating at 7 Hz and the machine oscillation amplitude was X = 5.0 mm. • As the vibration source frequency was increased to 10 Hz, the machine vibration amplitude was increased to X = 10.0 mm. When the vibration source frequency increased further, the machine oscillation amplitude was found to decrease (i.e. 10.0 mm was the maximum oscillation amplitude observed). (a) What is the frequency ratio r when f = 10 Hz? (b) Determine the damping factor, , of the machine system, and the floor oscillation amplitude, Y, when the machine was oscillating at 7Hz. (Hint: Solve 2 equations for the 2 unknowns, Y and, assuming they stay the same as the input frequency changes. Note that r= 1 when f = 10 Hz.) (c) Determine the machine's overall stiffness, K [N/m] (d) Assume that the vibration source is running at 7Hz, as an attempt to reduce the machine oscillation amplitude, X, someone suggested to reduce the mass of the machine to M = 800 kg, calculate the new 3 due to this mass change. Calculate the machine oscillation amplitude at this new mass (with the new (). Will this reduction in mass help reduce X? Partial Answer (a) r = 1, (b) ( = 0.139 kw accelerometer www. Machine Floor X X=10 mm X = 5 mm f = 7 Hz ww f = 10 Hz Vibration Source Building Y = ? 5 = ? A machine with mass, M'= 1000 kg is mounted on the floor of a building using 4 vibration isolation mounts as shown. The source of vibration is somewhere on the floor and the objective is to isolate the machine from the floor by changing its mass. When the vibration source was on, an accelerometer mounted on the machine determined that the machine was oscillating at 7 Hz and the machine oscillation amplitude was X = 5.0 mm. • As the vibration source frequency was increased to 10 Hz, the machine vibration amplitude was increased to X = 10.0 mm. When the vibration source frequency increased further, the machine oscillation amplitude was found to decrease (i.e. 10.0 mm was the maximum oscillation amplitude observed). (a) What is the frequency ratio r when f = 10 Hz? (b) Determine the damping factor, , of the machine system, and the floor oscillation amplitude, Y, when the machine was oscillating at 7Hz. (Hint: Solve 2 equations for the 2 unknowns, Y and, assuming they stay the same as the input frequency changes. Note that r= 1 when f = 10 Hz.) (c) Determine the machine's overall stiffness, K [N/m] (d) Assume that the vibration source is running at 7Hz, as an attempt to reduce the machine oscillation amplitude, X, someone suggested to reduce the mass of the machine to M = 800 kg, calculate the new 3 due to this mass change. Calculate the machine oscillation amplitude at this new mass (with the new (). Will this reduction in mass help reduce X? Partial Answer (a) r = 1, (b) ( = 0.139 kw accelerometer www. Machine Floor X X=10 mm X = 5 mm f = 7 Hz ww f = 10 Hz Vibration Source Building Y = ? 5 = ?