# 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 (T_{F}) 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 (kgm
^{2}) - Time (sec)
- Angular Velocity (radsec
^{-1}) - Angular Accel/Decel (radsec
^{-2})

## 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 T_{F} opposes acceleration but assists deceleration.

## 2. Calculate Acceleration Torque T_{A}

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 T_{R}

T_{R} is the torque required to overcome T_{F} to maintain constant Run Speed. T_{F} may be measured using a torque wrench or calculated.

\(T_R=T_F\ Nm\)

## 4. Calculate Deceleration Torque T_{D}

This step is very similar to the calculation of T_{A} except T_{F} aids deceleration.

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

\(T_D=J_T\ast\alpha-\ T_F\ Nm\)

## 5. Calculate Hold Torque T_{H}

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

\(T_H=0\ Nm\)

## 6. Calculate Cycle Time t_{C}

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 T_{PK}

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

## 8. Calculate Continuous Torque T_{RMS}

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 T_{A} and T_{D} is an adequate approximation for the calculating of T_{RMS}.

If there are a sequence of moves rather than a single repeated move, the calculation must include all the T^{2}t segments. The cycle time will be the time for the entire sequence.

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