cyclogramThe energy that comes back
Wherever the motor's torque and its speed point opposite ways, the load is driving the motor. The page integrates that power over the cycle and takes off the motor's and the drive's losses:
E_mech = ∫ max(0, −T(t) · ω(t)) dt over the move and the dwell E_net = E_mech · η_regen η_regen ≈ 0.9The default ball-screw axis brakes with 0.179 N·m from 3600 rpm (377 rad/s) to standstill in 1/6 s: E_mech = 0.179 · 377 / 2 · 1/6 = 5.61 J, of which 5.05 J reaches the bus. The peak braking power, at the start of the ramp, is 60.6 W after the losses.
What the bus can take
A drive absorbs braking energy in its DC-bus capacitors until the voltage reaches the brake chopper's threshold. The data sheet states the energy, or it follows from the capacitance:
E_abs = ½ · C · (V_max² − V_bus²)1000 µF charged from 320 V to 390 V takes ½ · 0.001 · (390² − 320²) = 24.9 J — more than the default axis returns, so it needs no resistor.
When a resistor is needed
If the bus can take only 0.5 J, the remaining 4.55 J of every cycle must go to a resistor. Spread over the 1 s cycle that is an average of 4.55 W, and the resistor's short-time rating must cover the 60.6 W peak.
P_avg = (E_net − E_abs) / t_cycle P_peak = max(−T · ω) · η_regenVertical axes
Which way the axis moves decides a great deal. Climbing, gravity brakes the load for the motor: the default axis stood up vertically returns nothing at all, because even its deceleration needs a positive torque, 0.134 N·m. Coming down, gravity drives the motor through the whole move, and the energy grows with the height.
Based on the motion profile
The energy is worked out for the cycle step 1 defines: the move and the dwell. A longer dwell lowers the resistor's average power; a move back, which the cycle does not include yet, would add its own braking energy. A belt axis brakes the same way: the default belt drive returns 2.23 J per cycle.
Questions
When do I need a brake resistor?
When one cycle returns more energy than the drive's bus can absorb. Heavy loads, high speeds, short ramps and descending vertical axes are the usual causes.
What is the chopper threshold?
The bus voltage at which the drive switches its brake resistor in, a little under its overvoltage trip. Between the normal bus voltage and that threshold, the capacitors store the braking energy.
How do I rate the resistor?
For the average power over the cycle, and with a short-time rating above the peak braking power. Both are in step 5 when a resistor is needed.
Does the regeneration efficiency matter?
Yes. The motor's winding losses and the drive's losses take part of the braking energy before it reaches the bus; 0.9 of it arriving is a common assumption, and you can set it in step 5.
Related guides
- Axis sizing calculatorThe whole guided flow: motion, mechanism, motor, regeneration, and the move as a bar.
- Servo motor sizingPeak torque at speed, RMS over the cycle, maximum speed and inertia ratio, each with its margin.
- Move time and motion profilePeak speed, acceleration and jerk from a distance and a move time; trapezoid, triangle and S-curve.
- Ball screw motor sizingSpeed, reflected inertia, torque per phase, RMS, critical speed and D·N for a ball screw axis.
- Belt drive motor sizingPulley and motor speed, reflected inertia, torque, belt force — and the gearbox a belt axis needs.
Every term on this page, defined: the axis and motor sizing glossary.