Components of load torque with examples

For matching a motor to a load, the load torque $T_l$ that the motor must overcome is split into components. With inertia, the motor torque equation is

$$T = T_l + J\frac{d\omega_m}{dt}, \qquad T_l = T_F + T_W + T_L$$

Components of load torque

1. Friction torque $T_F$ (present in all machines, at bearings, gears, couplings, brushes). Its parts:

• Static friction (stiction) $T_s$: present only at standstill; must be overcome to start. Large for some loads (e.g. loaded conveyor, rolling mill).
• Coulomb friction $T_C$: constant, independent of speed.
• Viscous friction $T_v = B\omega_m$: proportional to speed, due to lubricant.

2. Windage torque $T_W$: due to air (or fluid) resistance of moving parts, approximately proportional to speed squared: $T_W = C\omega_m^2$.

3. Torque for useful mechanical work $T_L$: depends on the nature of the load:

 TL
  |\  1/w (constant power)
  | \          w^2 (fan)
  |  \        /
  |___\______/________ constant (hoist)
  |    '.  /
  |      /'-..___
  |    /  w (linear)
  +-------------------> speed

Total friction characteristic

 TF
  | Ts (stiction)
  |*.
  |   '.  ___----- Tv + Tc (rises with speed)
  |     '--
  |  Tc
  +--------------> w

At very low speed the total friction is high (stiction) and then dips before rising with speed. Usually the friction and windage are combined with the useful load torque in one load characteristic $T_l(\omega)$.

Active and passive load torques

• Active torques: produced by gravity, tension, compression or torsion; keep their sign when the drive reverses (hoist, lift, locomotive on a gradient).
• Passive torques: always oppose motion, so change sign with speed (friction, cutting, windage).

Knowing these components and their dependence on speed lets the designer check starting (stiction), steady-state stability and the motor rating.