Summary
Torque is an important parameter in ensuring motors are well suited to their intended service. This article demonstrates how to calculate torque for a given motor or drive, and provides a brief introduction to motors and torque.
Definitions
| $D$ | : | Distance from axis of rotation |
| $F$ | : | Force |
| $I$ | : | Moment of inertia |
| $N$ | : | Rotational speed |
| $P$ | : | Power |
| $t$ | : | Time to accelerate load |
| $\tau$ | : | Torque |
| $\tau_{av}$ | : | Average torque over time to accelerate load |
Torque and Machinery
Torque is the rotating force supplied from a motor to a load. In order to move a stationary load torque must be applied, likewise a rotating load may be accelerated or decelerated by applying torque in the suitable rotational direction.
Generally torque may be viewed as a measure of turning force on an object rotating about an axis and as such may be defined as force multiplied by the distance from the axis of rotation as demonstrated below.
It is important to match motor or drive torque with the intended application as motor damage is frequently caused by a mismatch between the two. There are three main torque measures which must be considered; breakaway torque, running torque and high inertia loads.
$$ \displaystyle \tau = F \times D $$
Breakaway Torque
Breakaway torque is the torque required to start moving a stationary load. It is typically much higher than the torque required once a load is rotating, but is however, only required for a short initial period to get the load moving with motors often being able to operate at this elevated torque requirements during start up.
Depending on the nature of the machinery and the types of bearings used the breakaway torque can be anywhere from 120% to 600% and above of running torque. The table below provides some typical ranges:
| Machinery Type | Breakaway Torque (as % Running Torque) |
|---|---|
| Typical with ball or roller bearings | 120-130% |
| Typical with sleeve bearings | 130-160% |
| Conveyors and machines with significant sliding actions | 160-250% |
| Machines with high load points, typical of some cams and cranks | 250-600% |
Running Torque
Running torque is the torque that is required to sustain the machine at the normal operating rotational speeds. Running torque may be calculated if the power requirement and the motor speed are known as shown below.
$$ \displaystyle \tau=\frac{30 P}{\pi N}$$
Where $N$ is in rpm, $P$ is in kW and $\tau$ is in kN.m.
In imperial units:
$$ \displaystyle \tau=\frac{5252 P}{N}$$
Where $N$ is in rpm, $P$ is in Hp and $\tau$ is in lbf.ft.
High Inertia Loads
In addition to the breakaway and running torque the inertia of the load must be considered when selecting a motor or drive. Unlike breakaway torque, if a load has a high moment of inertia it may take a significant period of time to accelerate or decelerate. This will lead to an extended period of time for which the motor must run at an elevated torque increasing the risk of motor will fail or be damaged during start up.
The time to accelerate a load can be calculated using the formula below if the inertia of the load is known. Otherwise the equipment manufacturer should be consulted.
$$ \displaystyle t=\frac{IN}{9.523\tau_{av}}$$
Where $I$ is in kg.m2, $N$ is in rpm, $t$ is in s and $\tau_{av}$ is in kN.m.
In imperial units:
$$ \displaystyle t=\frac{IN}{308\tau_{av}}$$
Where $I$ is in lb.ft2, $N$ is in rpm, $t$ is in s and $\tau_{av}$ is in lbf.ft.
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