BIZOMAT MAKEOS · Mechanics
Rotary Index Table Drive Check (Table Inertia, Motor Torque and Speed, Inertia Ratio, Holding)
For a rotary index table driven by a servo or geared motor, can the motor index it in the time I want, is the inertia match acceptable, and will the drive hold the table against the process force?
Check of a rotary indexing table drive against the motor: table and fixture inertia, index angle, peak speed and acceleration for a cycloidal or trapezoidal move, table and motor peak torques through the reducer, motor speed, the holding torque needed against the process force and the load-to-motor inertia ratio (as the rotary index table sizing tool), against the motor’s peak torque, top speed, your inertia ratio limit and the brake torque multiplied through the reducer.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Table plate mass | kg | Mass of the table plate. |
| Table plate radius | mm | Radius of the table plate. |
| Stations | Number of stations (index positions). | |
| Mass of each fixture and part | kg | Mass of each fixture with its part. |
| Radius of fixture centres | mm | Radius at which the fixtures sit. |
| Index time | s | Time for one index move. |
| Total cycle time | s | Time for a full cycle, index plus dwell. |
| Motion profile | choice | Cam-like cycloidal motion or a trapezoidal velocity profile. |
| Bearing and seal friction torque | N·m | Friction torque of the table bearing and seals. |
| Reducer ratio | Reduction ratio between motor and table. | |
| Reducer efficiency | % | Efficiency of the reducer. |
| Motor rotor inertia | kg·m² | Inertia of the motor rotor. |
| Process force at the fixture radius | N | Tangential process force on a fixture during the dwell. |
| Holding safety factor | Factor on the holding torque. | |
| Motor | ||
| Motor peak torque | N·m | Peak torque the motor can give. |
| Motor top speed | rpm | Highest motor speed. |
| Largest inertia ratio accepted | Largest load-to-motor inertia ratio you accept for good control (reflected through the reducer). | |
| Motor brake torque | N·m | Holding torque of the motor brake (or the drive’s holding torque). |
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: Table plate mass
- What it is
- The mass of the round table plate (the rotating top) on its own, without fixtures or parts. The tool treats it as a solid disc for its inertia.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Table inertia rises in proportion to it, raising the torque needed to accelerate the table.
- Get it right
- Weigh it or take it from the CAD model; include any adaptor plate that turns with it.
What this means: Table plate radius
- What it is
- The outer radius of the table plate, from the centre of rotation to its edge, used to work out its disc inertia.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Table plate inertia rises with the square of the radius.
- Get it right
- Enter the radius, not the diameter: halve the table diameter.
What this means: Stations
- What it is
- The number of index positions per revolution of the table, which is usually the number of fixtures. The index angle is one full turn divided by this number.
- Units and format
- Enter a plain number with no unit. The form accepts 2 to 72. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More stations give a smaller index angle, so peak speed and acceleration fall for the same index time, but more fixtures add inertia.
- Get it right
- Count positions, including any empty or load stations, because each one is a separate index move.
What this means: Mass of each fixture and part
- What it is
- The mass of one fixture together with the part it holds, treated as a point mass at the fixture centre radius. Every station is assumed to carry the same.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0 kg to 10000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Table inertia rises in proportion to it.
- Get it right
- Include the heaviest part the fixture will carry, and any clamps or valves mounted on it.
What this means: Radius of fixture centres
- What it is
- The radius from the table axis to the centre of mass of each fixture and part. It sets the fixture inertia and the lever arm of the process force.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Fixture inertia rises with its square and the holding torque needed rises in proportion to it.
- Get it right
- Measure to the combined centre of mass of fixture and part, which may differ from the fixture’s bolt circle.
What this means: Index time
- What it is
- The time allowed for one index move, from the table starting to turn to it stopping at the next station.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 100 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.6 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Halving the index time doubles the peak speed and quadruples the peak acceleration and inertia torque.
- Get it right
- Do not include the dwell; enter only the moving time.
What this means: Total cycle time
- What it is
- The time for one full cycle, the index move plus the dwell during which work is done at the stations. The tool reports the dwell as cycle time minus index time.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 10000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be longer than the index time or the tool will not calculate.
What this means: Motion profile
- What it is
- The shape of the speed curve during each index. Cycloidal motion starts and stops smoothly like a cam; trapezoidal accelerates, cruises and decelerates in equal thirds.
- Units and format
- Choose one of 2 options from the list: Cycloidal; Trapezoidal (⅓ accel, ⅓ cruise, ⅓ decel).
- Example
- The form opens with “Cycloidal” selected as a worked example. Choose the option that matches your case.
- Get it right
- Choose the profile your controller or cam indexer will actually run; the two give different peak speed and acceleration.
What this means: Bearing and seal friction torque
- What it is
- The torque needed to turn the table against its bearing and seal drag alone, measured at the table axis. It is added to the inertia torque.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Table torque rises by this amount, and the motor torque by it divided by ratio and efficiency.
- Get it right
- Take it from the bearing or table maker, or measure it with a torque wrench on the table with the drive disconnected.
What this means: Reducer ratio
- What it is
- The speed reduction between the motor and the table: motor revolutions per table revolution, including the gearbox and any belt stage.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher ratio lowers motor torque and inertia ratio but raises motor speed in proportion.
- Get it right
- Multiply the ratios if there are several stages; enter 50 for a 50:1 reducer, not 0.02.
What this means: Reducer efficiency
- What it is
- The share of motor power the reducer passes to the table, after gear and bearing losses.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 85% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The table torque reflected to the motor is divided by it, so a lower efficiency raises motor torque.
- Get it right
- Type the percentage itself, not a fraction; worm reducers can be much less efficient than helical ones, so use the maker’s figure.
What this means: Motor rotor inertia
- What it is
- The mass moment of inertia of the motor’s own rotor, from the motor data sheet. It must be accelerated along with the load and sets the inertia ratio.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 100 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0005 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger rotor inertia lowers the inertia ratio but adds torque to accelerate the motor itself.
- Get it right
- Check the unit: data sheets often give kg·cm²; divide by 10 000 to get kg·m². Include the brake inertia if it is listed separately.
What this means: Process force at the fixture radius
- What it is
- The tangential force the process puts on a fixture during the dwell, for example a pressing, drilling or screwing force, acting at the fixture centre radius and trying to turn the table.
- Units and format
- Enter a number in N: newtons. The form accepts 0 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The holding torque needed rises in proportion to it.
- Get it right
- Use the component that acts around the table, not a vertical force pushing down on it.
What this means: Holding safety factor
- What it is
- The multiplier applied to the process torque to get the holding torque the brake must provide at the table.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 10. 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
- The holding torque needed rises in proportion to it.
- Get it right
- Choose it from your design standard or company practice; it is not a material property.
Motor
What this means: Motor peak torque
- What it is
- The highest torque the motor and drive combination can deliver for short acceleration periods, from the motor and drive data sheet.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 100000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the peak torque for your actual drive current, which may be lower than the motor’s own peak rating.
What this means: Motor top speed
- What it is
- The highest speed the motor is rated to run, from its data sheet or the drive’s speed limit, compared with the motor speed at peak index speed.
- 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 3000 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If the drive voltage is lower than the motor’s rated voltage, the usable top speed is lower too.
What this means: Largest inertia ratio accepted
- What it is
- The largest ratio of load inertia reflected to the motor shaft to motor rotor inertia that you accept for stable, responsive control.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take the limit from the servo maker’s sizing guidance or your own practice; the tool does not suggest one.
What this means: Motor brake torque
- What it is
- The holding torque of the motor brake, or the drive’s holding torque if it holds position electrically. The tool multiplies it by the reducer ratio to get the holding torque at the table.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 100000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Holding torque at the table rises in proportion to it.
- Get it right
- Use the static holding torque of the brake, not the dynamic stopping torque, and note that the tool ignores reducer losses here.
Method and formulas
- J = ½ M R² + stations × m_f r_f²; index angle 2π ÷ stations; cycloidal ω_max = 2θ ÷ t, α_max = 2πθ ÷ t² (as the rotary index table sizing tool).
- Motor torque = (J α + T_f) ÷ (i η) + J_m α i; motor speed = ω_max i; inertia ratio = J ÷ i² ÷ J_m.
- Holding torque needed = SF × F × r_f; brake holds brake torque × i at the table.
- Example: the motor needs 3.7354 N·m at 1,666.7 rpm with an inertia ratio of 5.88.
Limitations
- Rigid drive; backlash and compliance in the reducer cut the usable stiffness.
- Brake holding taken through the reducer without efficiency loss.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a motor for a dial table
- Find whether a faster index is possible
- Check the brake holds the table during pressing
Who it is for
- Automation engineers
- Machine designers
- Controls engineers
What you get
- Table inertia, speed and acceleration
- Motor torque, speed and inertia ratio
- Holding against the process force
Interpreting the result
- A larger reducer ratio cuts the reflected inertia by its square but raises the motor speed in proportion.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 171, 2284–2290. Topic reference; no source tables or recommended settings are reproduced.
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