vibration design problem

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.

 

[GregLocock]

Is this a homework 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

 

yes, it is a homework problem. i have done the differential equations of rotational motion for the pulley and found the equation of natural frequencies of pulley one and pulley two. then i dun know what to do next....

 

[GregLocock]

I haven't solved this, I'm just sketching it out in my head.

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