hw7soln

hw7soln - ME 375 HOMEWORK #7 SOLUTION Fall 2009 PROBLEM 1:...

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1 ME 375 HOMEWORK #7 SOLUTION Fall 2009 PROBLEM 1 : (30%) GIVEN : An industrial sewing machine (having mass m ) is mounted on springs (with stiffness k ) and dampers (with damping coefficient b ) to decrease the force transmitted to the floor. The input force acting on the sewing machine during operation is denoted by F ( t ), while the vertical motion of the machine is denoted by y ( t ). The sewing machine mass is 150 kg. Suitable spring and damper values must be selected so that the vertical motion of the machine is sufficiently small. FIND : (a) Draw a schematic diagram that describes this system. (b) Generate the transfer function between input force F ( t ) and vertical displacement y ( t ). (c) The excitation force is given by () 5s in (30) Ft t = N and the following springs and dampers are available: 55 1.35 10 , 5.4 10 k × N/m, and 2250,12000 b = N/(m/s), select the best combination of one spring and one damper so that the steady-state amplitude of y is 5 1.0 10 × m or less. Please explain how you arrived at your answer. SOLUTION : (a) Schematic diagram: (b) Transfer function: 22 () 1 1 / / / Ys m Gs Fs m s b s k s bms k m == = ++ + + (c) For ( ) 5sin(30 ) t = N, the steady-state response amplitude is given by 5( ) Gj ω . From part (b), we get: 2 2 2 1/ // m km b m ωω = −+ k m b y F ( t )
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2 Plugging in the numbers, and using both choices for k and b , we get: Steady-state amplitude 5 1.35 10 k 5 5.4 10 k 2250 b = 5 7.41 10 m × 5 1.22 10 m × 12000 b = 5 1.39 10 m × 6 9.23 10 m
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hw7soln - ME 375 HOMEWORK #7 SOLUTION Fall 2009 PROBLEM 1:...

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