Advantage of using a bigger pulley in belt drive?

[hihiip201]

Hi :

lets examine the following scenario

1.

M --------- o where M is a mass, o is a pulley with it's outter radius r attached to a mass by the belt drive -------. frictionless.


2.

M ---------O same setup but the radius is now bigger, R.



I was reading somewhere saying, a smaller pulley can move things quicker, so i decided to derive this to see for myself.


the following is the result:


for case 1:

alpha = T/(J+Mr^2)

case 2:

alpha = T/(J+MR^2)


in other word, for the same torque generated from DC motor, alpha is higher for case 1.



also, in the case where the pulley rotates at a constant velocity, constant torque output, case 1 amplify the force on the mass M where as the force on the Mass M in case 2 would be lower.



so my question is, why would anyone choose case 2 at all? what advantage does it have on any applications?


thanks

 

[CWatters]

also, in the case where the pulley rotates at a constant velocity, constant torque output, case 1 amplify the force on the mass M where as the force on the Mass M in case 2 would be lower.

In this contact "constant velocity" means "constant angular velocity". So with the smaller pulley the force available to accelerate the object will be greater but the linear velocity of the belt will be lower.

Changing r is like changing gear on your car.

 

[hihiip201]

In this contact "constant velocity" means "constant angular velocity". So with the smaller pulley the force available to accelerate the object will be greater but the linear velocity of the belt will be lower.

Changing r is like changing gear on your car.

but wouldn't the mass still be able to moved quicker though since for a constant T the force on the mass would be higher?


I know this is related to how if you rotate a disk from its side you apply less force but cover more distance, vice versa, but i don't know how to apply that principle in this case.

 

[CWatters]

When you say "moved" you need to be clear if you mean "moved at a constant velocity" or "accelerated"?

If the system is frictionless and the mass is moving horizontally it takes no power (no torque) to move the mass at a constant velocity. The maximum velocity will depend on the motors angular velocity and the gearing. The radius r is part of the gearing.

If you are accelerating the mass or raising it up an incline then that's a different matter.

 

[PJC01]

There are several advantages to using a bigger pulley in a belt drive. Firstly, a bigger pulley can handle more torque and power, making it suitable for heavier loads and higher speeds. This means that it can be used in a wider range of applications, from small machines to large industrial equipment.

Secondly, a bigger pulley can reduce the strain on the belt and extend its lifespan. With a smaller pulley, the belt has to make more revolutions to achieve the same output, resulting in more wear and tear. A bigger pulley allows the belt to make fewer revolutions, reducing the strain and prolonging its life.

Additionally, a bigger pulley can provide more precise control over the speed and torque of the system. With a smaller pulley, small changes in the motor speed can result in larger changes in the output speed. This can be problematic in applications that require precise control, such as in robotics or conveyor systems. A bigger pulley allows for finer adjustments and smoother operation.

In summary, while a smaller pulley may have a higher acceleration and force output, a bigger pulley offers more versatility, durability, and precision in a variety of applications. It is important to carefully consider the specific requirements and constraints of a system when choosing the appropriate pulley size.