Unbalance in rotating machinery is one of the main causes of
vibration. A simplified model of such a machine is shown below. The
total mass of the machine is M, and there are two eccentric masses
m/2 rotating in opposite directions with a constant angular
velocity . The centrifugal force 𝑚 𝑒 𝜔2 2 due to each mass will
cause excitation of the mass M. We consider two equal masses 𝑚 2
rotating in opposite directions in order to have the horizontal
components of excitation of the two masses cancel each other.
However, the vertical components of excitation add together and act
along the vertical axis of symmetry.
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- Unbalance In Rotating Machinery Is One Of The Main Causes Of Vibration A Simplified Model Of Such A Machine Is Shown Be 1 (85.44 KiB) Viewed 11 times
Unbalance in rotating machinery is one of the main causes of vibration. A simplified model of such a machine is shown below. The total mass of the machine is M, and there are two eccentric masses m2 rotating in opposite directions with a constant angular velocity c. The centrifugal due to each mass will cause excitation of the mass M. We consider two equal masses rotating in opposite directions in order to have the horizontal components of excitation of the two masses cancel each other. However, the vertical components of excitation add together and act along the vertical axis of symmetry. force : 2016 O escos cw cosas car casinot * c. woos • . newcos en M sinal cw If the angular position of the masses is measured from a horizontal position, the total vertical component of the excitation is always given by F(t)=me sin(at). What is the equation of motion of the system? show that the solution of this equation can be expressed as X(t) = X sin(wt - 0) =, where mewa and = tan Vk - Mw2)2 + (cm) :-MW using the definitions of C and Cerit, the precedent expression can be written as : MX 2ĘT (1-2)2 + (2&r)? r and = tan me 5 Use excel or matlab to plot the variation of MX/me versus r, for different values of damping. Same thing for Observations: 1. regarding the amplitude at the resonance : why is it interesting to introduce damping purposely? 2. at very high speeds, what is the impact of the damping? 3. for 0 <<<1/17, what is the maximum value of (MX/me)? 4. same
question for > 1/12