# How to Calculate Torque – Peak and Continuous

The basic methodology is to calculate the individual torques required for all segments of a motion profile. The largest of the individual torque values is the Peak Torque. Each torque value is combined to determine continuous torque.

Consider a rotary move unaffected by gravity. Speed independent static friction torque (TF) is present as the load turns, opposing motion. There is no viscous friction or tension.

It is critical to use consistent units:

• Torque (Nm)
• Inertia (kgm2)
• Time (sec)

## 1. Velocity & Torque Profile

The application may have a variety of moves. Consider the fastest move with the shortest hold time between moves. It is helpful to sketch a representation of the torque required to execute the move velocity profile, see the example below. The acceleration torque is larger than deceleration torque as TF opposes acceleration but assists deceleration.

## 2. Calculate Acceleration Torque TA

After calculating angular acceleration and total inertia (direct drive is assumed), acceleration torque can be determined by applying the rotary version of Newton’s Second Law of Motion.

$$Angular\ Velocity\ \left(\omega\right)=Run\ {Speed}_{RPS}\ast2\ast\pi\ rad{sec}^{-1}$$

$$Angular\ Acceleration\ (\alpha)=\ \omega/{t_A\ rad{sec}^{-2}}$$

$$Total\ Inertia\ \left(J_T\right)=J_{MOTOR}+J_{LOAD}\ kgm^2$$

$$T_A=J_T\ast\alpha+\ T_F\ Nm$$

## 3. Calculate Run Torque TR

TR is the torque required to overcome TF to maintain constant Run Speed. TF may be measured using a torque wrench or calculated.

$$T_R=T_F\ Nm$$

## 4. Calculate Deceleration Torque TD

This step is very similar to the calculation of TA except TF aids deceleration.

$$Angular\ Deceleration\ (\alpha)=\ \omega/{t_D\ rad{sec}^{-2}}$$

$$T_D=J_T\ast\alpha-\ T_F\ Nm$$

## 5. Calculate Hold Torque TH

As there is no gravity to oppose or tension to maintain:

$$T_H=0\ Nm$$

## 6. Calculate Cycle Time tC

Cycle time includes all the time periods of the velocity profile and the hold time between moves:

$$t_C=t_A+t_R+t_D+t_H\ sec$$

## 7. Determine Peak Torque TPK

Peak torque in this example is the torque to accelerate, TA. If the velocity profile was a pure S-curve, TPK would be 2 x TA. In most applications a modified S-curve is used which smooths profile discontinuities while increasing TPK by just 10-20 %.

## 8. Calculate Continuous Torque TRMS

Continuous torque can be calculated as follows:

$$T_{RMS}=\sqrt{\frac{T_A^2t_A+T_R^2t_R+T_D^2t_D+T_H^2t_H}{t_C}}\ Nm$$

If an S-curve velocity profile is used, the trapezoidal derivation of TA and TD is an adequate approximation for the calculating of TRMS.

If there are a sequence of moves rather than a single repeated move, the calculation must include all the T2t segments. The cycle time will be the time for the entire sequence.

TRMS must fall in the continuous region of the motor torque/speed curve. An application dependent safety margin (10% is typical) is recommended for both TRMS and TPK.