BIZOMAT MAKEOS · Power Transmission
Motor and Gearbox Selection
What gear ratio, motor rating and starting torque does this load need, and is the inertia match reasonable?
Selection of an induction motor and gearbox for a load: ratio from the motor speed (pole count and slip) and load speed, running torque and power through the gearbox efficiency, reflected inertia and the acceleration torque to reach speed in the time required (the same method as the reflected inertia tool), the next standard IEC motor rating with a service factor, and its starting torque against the starting requirement.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load torque | N·m | Torque the load needs at its own shaft. |
| Load speed | rpm | Required load speed. |
| Load inertia | kg·m² | Load inertia at the load shaft. |
| Acceleration time | s | Time allowed to reach speed. |
| Motor poles (50 Hz synchronous speed) | choice | Motor pole count (synchronous speed at 50 Hz). |
| Full-load slip | % | Slip at full load (from the motor data). |
| Gearbox efficiency | % | Gearbox efficiency. |
| Motor rotor inertia | kg·m² | Motor rotor inertia (from the motor data; estimate first and re-check). |
| Service factor | Service factor applied to the running power. | |
| Motor starting torque ÷ rated torque | Locked-rotor (starting) torque as a multiple of rated torque, from the motor data. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Load torque
- What it is
- Steady torque the driven machine needs at its own shaft while running, which the tool also assumes during the start.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Running torque, power and starting torque needed rise with it.
- Get it right
- Enter torque at the load shaft, before the gearbox, not at the motor.
What this means: Load speed
- What it is
- Speed the driven machine must run at. With the motor speed it sets the gearbox ratio.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Power rises in proportion; a lower speed needs a higher ratio.
- Get it right
- Enter the load shaft speed, not the motor speed.
What this means: Load inertia
- What it is
- Rotational inertia of the driven machine at its own shaft. The gearbox reduces it by the square of the ratio as seen by the motor.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 1000000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More inertia raises the acceleration torque needed.
- Get it right
- Enter inertia at the load shaft; the tool reflects it to the motor.
What this means: Acceleration time
- What it is
- Time allowed for the motor and load to accelerate from rest to running speed.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 600 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shorter times raise the acceleration torque needed.
- Get it right
- Direct-on-line starts are short; soft starters and drives lengthen them.
What this means: Motor poles (50 Hz synchronous speed)
- What it is
- Number of magnetic poles of the induction motor, which fixes its synchronous speed on a 50 Hz supply.
- Units and format
- Choose one of 4 options from the list: 2-pole (3000 rpm); 4-pole (1500 rpm); 6-pole (1000 rpm); 8-pole (750 rpm).
- Example
- The form opens with “4-pole (1500 rpm)” selected as a worked example. Choose the option that matches your case.
- Get it right
- On a 60 Hz supply the speeds are higher; the tool assumes 50 Hz.
What this means: Full-load slip
- What it is
- Percentage by which the motor’s full-load speed falls below its synchronous speed, from the motor data.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 15%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the nameplate: (synchronous − full-load speed) ÷ synchronous × 100.
What this means: Gearbox efficiency
- What it is
- Efficiency of the gearbox: output power divided by input power.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 30% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 94% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lower efficiency raises the running torque and power at the motor.
- Get it right
- Worm gearboxes can be much less efficient than helical ones; take it from the gearbox maker.
What this means: Motor rotor inertia
- What it is
- Rotational inertia of the motor’s own rotor, from the motor data. It must be accelerated along with the load.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 1000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.04 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds to the acceleration torque needed.
- Get it right
- Estimate first, then re-check with the chosen motor’s data sheet value.
What this means: Service factor
- What it is
- Multiplier on the running power before the next standard motor rating is chosen, covering overloads and duty.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher factor can push the choice to the next motor size.
- Get it right
- Take it from your practice or the driven machine maker; the gearbox needs its own service factor.
What this means: Motor starting torque ÷ rated torque
- What it is
- Locked-rotor (starting) torque of the motor as a multiple of its rated torque, from the motor data sheet.
- Units and format
- Enter a plain number with no unit. The form accepts 0.5 to 5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Available starting torque rises in proportion.
- Get it right
- Take it from the motor data for the starting method used; reduced-voltage starting lowers it.
Method and formulas
- Motor speed = synchronous speed × (1 − slip); ratio i = motor speed ÷ load speed.
- Running torque at the motor = T_L ÷ (i η); power = T_L ω_L ÷ η.
- Reflected inertia J_L ÷ (i² η); acceleration torque = (J_m + J_r) α_m; starting torque needed = running + acceleration torque.
- Motor rating = next standard IEC output ≥ SF × power; starting torque available = multiple × rated torque.
- Example: 200 N·m at 150 rpm with a 4-pole motor needs a 9.7:1 gearbox and a 5.5 kW motor.
Limitations
- Constant load torque during start; fans and pumps (torque rising with speed) start more easily.
- Supply frequency of 50 Hz assumed for the pole speeds.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a gearmotor for a conveyor, mixer or turntable
- Check that a motor can start a high-inertia load
- Compare 4-pole and 6-pole motor options
Who it is for
- Design engineers
- Electrical and mechanical engineers
- Maintenance engineers
What you get
- Gear ratio and motor speed
- Running power and chosen motor rating
- Starting torque check and inertia ratio
Interpreting the result
- A high inertia ratio is acceptable for induction motors on simple drives, but servo drives usually need it below about 10:1.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2569–2580, 3408–3412. Topic reference; no source tables or recommended settings are reproduced.
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