Confusion About Oscillating Mass

[Nidum]

No need for numbers . Algebra variables are what we will use . We can keep the actual maths quite simple .

Getting a bit late now here in UK so I'm signing off pro tem .

Nos dda .

 

[jbriggs444]

No need for numbers . Algebra variables are what we will use . We can keep the actual maths quite simple .

Seems simple enough. Finite mass on the piston, rigidly mounted crank-case/engine block. Frictionless bearings and frictionless piston rings. Watch what happens as the mass of the crankshaft and connecting rod decrease toward zero. There is always an increase in crankshaft angular velocity near top dead center and bottom dead center. As the mass of the crankshaft and connecting rod decrease toward zero, the peak angular velocity diverges toward infinity.

There is no convergence toward a physically reasonable limiting behavior. Something will break first.

 

[person123]

Seems simple enough. Finite mass on the piston, rigidly mounted crank-case/engine block. Frictionless bearings and frictionless piston rings. Watch what happens as the mass of the crankshaft and connecting rod decrease toward zero. There is always an increase in crankshaft angular velocity near top dead center and bottom dead center. As the mass of the crankshaft and connecting rod decrease toward zero, the peak angular velocity diverges toward infinity.

There is no convergence toward a physically reasonable limiting behavior. Something will break first.

All right. My train of thought before making the thread was this:
I know that when the mass is momentarily still, the acceleration is at its maximum. I can find that acceleration, and then find what the angular acceleration would be at that point. This would allow me to find the maximum torque. It did give me an equation (τ=ω^2l^2m) which passes dimensional analysis and seems reasonable, but I never considered the mass of the rod. Does this calculation make any sense to do, or should I go back to the drawing board completely?

 

[person123]

Also what is exactly meant by:

There is no convergence toward a physically reasonable limiting behavior. Something will break first.

What is meant by something breaking? Is this meant in a physical sense?

 

[jbriggs444]

Also what is exactly meant by: What is meant by something breaking? Is this meant in a physical sense?

How are you going to manage infinite acceleration with a material with a finite strength to mass ratio?

 

[person123]

How are you going to manage infinite acceleration with a material with a finite strength to mass ratio?

I see what you meant.