vibration design problem
vibration design problem
(OP)
A step cone pulley with a belt drive is used to change the cutting speeds in a lathe. the speed of driving shft is 350 rpm and speeds of output shaft are 87.5, 250, 450 and 750 rpm. the diameters of the driving and the driven pulleys corresponding to 150 rpm output speeds are 250mm and 1000mm, respectively. center distance between the shafts is 5m. the mass moments of inertia of the driving and the driven pulley are 0.1 and 0.2 kg-m^2, respectively. how can i find the cross sectional area of the belt to avoid resonance with any of the input/output speeds of the system? assume the Young's modulus of the belt material as 10^10 N/m^2.





RE: vibration design problem
If so (or anyway) how far have you got?
Do you have an expression for the resonant modes of the pulley / belt system?
Cheers
Greg Locock
Cheers
Greg Locock
RE: vibration design problem
RE: vibration design problem
I think you'll find that there's only one resonant frequency for a given step up ratio, as the system has a zero Hz mode, and a mode where each pulley rotates in opposition to the other. This makes working the frequency out very easy. Your spring exerts a variable torque on the pulley wheel due to the different drive radius for each ratio.
You need to check that for each step up ratio that this resonant frequency does not match the input speed or the output speed.
I'm a bit surprised by this problem - it is pretty hard, and there are two obvious,useless, solutions that require no calculation at all.
Cheers
Greg Locock
Cheers
Greg Locock