Cyndi Nyberg
EASA Technical Support Specialist
The basic definition of torque is the measure of the force applied to produce rotational motion, usually measured in pound-feet or Newton-meters. Torque is determined by multiplying the applied force by the distance from the pivot point to the point where the force is applied.
Torque = Force x Radius
Figure 1 illustrates the relationship between force and torque.
Obviously, if the force is increased, the torque will increase. If the magnitude of the force is maintained, but the radius is increased, then the torque is also increased.
When this principle is applied to a sheave, chain or belt system, the effect of increasing the radius is to slow down the driven load, while increasing the torque. The basic torque equation is:
Torque = Horsepower x 5252/rpm
Speed and torque have an inverse linear relationship, which means that however much the speed is decreased, the torque will increase by the same percentage. For a motor system with sheaves, the horsepower in the above equation stays constant, but by lowering the final speed of the driven equipment, the final output torque can be increased without a change in the driving motor’s power rating.
Torque and speed
Very often, motors run at too high a speed for the final driven load. By using speed reduction, the driven load can be slowed down to the desired speed, but without a loss of torque. This is why sheaves, chains, and belts are often called torque multipliers. By this, we mean that you can increase the torque delivered to a load without requiring an increase in the torque the motor has to deliver. The torque is increased in proportion to the amount that rotational speed is reduced.
Theoretically, the amount of torque available from even the smallest of motors is limited only by our ability to increase the sheave ratio. Practical limitations include diminishing belt contact of a smaller sheave when gross mismatches of diameters occurs. And as sheave size increases, so does the cost! However, some modifications are possible to change the speed or increase the torque on most applications.
A smaller drive sheave is connected to the motor shaft, while a larger diameter sheave is attached to a parallel shaft that will, as a result, operate at a lower speed. Think of the larger sheave radius as a longer distance in which you are transmitting the same force— hence, a higher torque—as compared to the shorter radius of the smaller sheave.
In a case where a very large reduction in speed is necessary, gear reducers are used because they can typically accomplish large reductions in speed in a small package. And the sheave diameter mismatch reduces the belt contact, limiting the speed ratio obtainable with sheaves. Gear reducers are available at specific speed ratios, so it may be necessary to tweak the final output speed by using sheaves in addition to the gearbox.
For lower-speed, high-torque applications, it is common to see chain drives and sprockets used rather than simple belts, which are more flexible.
Sheave calculations
Typical motor sheave systems consist of a motor with a sheave attached to the shaft, connected by a belt to a second sheave. The sheave on the motor shaft is the driving sheave and the second sheave is the driven sheave. The speed of the driving sheave is obviously the speed of the motor. The speed of the driven sheave depends on the speed of the motor shaft, as well as the diameters of both the sheaves.
The most basic sheave equation is this:
S x D = s x d
where
- S = the speed of the driving sheave (rpm)
- s = the speed of the driven sheave (rpm)
- D = the diameter of the driving sheave*
- d = the diameter of the driven sheave*
* The diameters can be expressed in any unit of measurement as long as both D and d are in the same unit.
The diameter is the effective diameter, termed “pitch diameter,” not the outside diameter. Manufacturer catalogs for sheaves provide the pitch diameters and outside diameters. Use the pitch diameters to calculate speed ratios.
To determine the value needed, the equation can be manipulated so you can solve for what you need.
Example: Motor speed = 1780 rpm Driving sheave = 4.75 inches Driven sheave = 8.5 inches How fast is the driven sheave turning?
S x D = s x d or
s = (1780 x 4.75)/8.5
s = 995 rpm
Here is a simple example of a modification made to a crusher application. A crusher is an example of a common application where belts and sheaves are used.
The crusher is currently operating at 875 rpm. The motor that is being used is a 300 hp, 8-pole motor running at 875 rpm.
This motor drives the crusher via belt and sheave, with a one-to-one ratio.
The end user wants to drive the crusher at 1150 rpm with 1750 rpm (4-pole) motor.
Calculate the power required of the 1750 rpm motor to drive the crusher.
Increasing power rating
Currently, the crusher is operating at the same speed as the motor, 875 rpm. It will be necessary for the 4-pole motor to deliver the same amount of torque to drive the crusher, but at a higher speed.
Consequently, the power rating of the motor will have to increase:
Torque at 875 rpm
= Horsepower x 5252/rpm
= 300 x 5252/875
= 1800 lb-ft of torque.
Now, at 1150 rpm, the horsepower required to deliver the same amount of torque is: hp at 1150 rpm
= 1800 lb-ft x 1150/5252
= 394 hp
You would therefore need a 400 hp motor at 1750 rpm to develop the needed torque. Note: Make sure that the new motor is crusher duty rated, probably NEMA Design C. When calculating the crusher speed, keep in mind that higher slip is often characteristic of the Design C or D motor. Since the sheave diameters were originally equal (one-to-one ratio), it may be necessary to replace one of the sheaves to obtain the desired final speed.
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