BIZOMAT MAKEOS · Mechanics
Rotary Index Table Drive Sizing
What torque and motor does this rotary index table need to index in time, and what holding torque during machining?
Sizing of a servo or geared index table: table and fixture inertia, index angle from the number of stations, peak speed and acceleration for a cycloidal or trapezoidal move, table and motor torque through the reducer, motor speed, dwell time in the cycle, and the holding torque the clamp or brake must provide against machining forces.
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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 round table plate. |
| Table plate radius | mm | Radius of the table plate. |
| Stations | Number of stations (indexes per revolution). | |
| Mass of each fixture and part | kg | Mass of one fixture with its part. |
| Radius of fixture centres | mm | Radius at which fixtures sit. |
| Index time | s | Time allowed for each index move. |
| Total cycle time | s | Total time per station including the index. |
| Motion profile | choice | Motion profile of the index. |
| Bearing and seal friction torque | N·m | Friction torque at the table. |
| Reducer ratio | Speed reduction between motor and table. | |
| Reducer efficiency | % | Reducer efficiency. |
| Motor inertia | kg·m² | Motor rotor inertia. |
| Machining force at the fixture (tangential) | N | Tangential machining force at the fixture radius during dwell. |
| Safety factor on holding | Factor on the 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
- Mass of the round table plate itself, treated as a solid disc turning about its centre.
- 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
- Plate inertia is proportional to its mass.
What this means: Table plate radius
- What it is
- Outside radius of the table plate, half its diameter, used for the plate’s 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
- Plate inertia rises with the square of radius.
- Get it right
- Radius, not diameter.
What this means: Stations
- What it is
- Number of stations around the table; each index turns the table on by one station.
- 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
- For the same index time, more stations mean a smaller index angle and lower peak speed and acceleration.
What this means: Mass of each fixture and part
- What it is
- Mass of one fixture with its part loaded, treated as a point mass at the fixture radius.
- 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.
- Get it right
- Per station, not for all stations together.
What this means: Radius of fixture centres
- What it is
- Distance from the table axis to the centre of each fixture. The machining force is also taken to act at this radius.
- 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.
- Get it right
- A radius from the axis, not the pitch circle diameter.
What this means: Index time
- What it is
- Time allowed for the table to move from one station to the next, from start of motion to stop.
- 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 quadruples the angular acceleration and its torque.
What this means: Total cycle time
- What it is
- Total time per station: the index move plus the dwell for work. It is used to report the dwell 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.
What this means: Motion profile
- What it is
- Shape of the speed curve during the index: smooth cycloidal motion, or a trapezoidal profile with equal accelerate, cruise and decelerate 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.
What this means: Bearing and seal friction torque
- What it is
- Torque needed to turn the table against bearing and seal drag alone, from the bearing maker or measured.
- 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.
What this means: Reducer ratio
- What it is
- Speed reduction between the motor and the table, motor speed ÷ table speed.
- 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.
- Get it right
- Include every stage between the motor and the table, such as a gearbox plus a worm or cam unit.
What this means: Reducer efficiency
- What it is
- Efficiency of the reducer between the motor and the table, from its maker.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 20% 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.
What this means: Motor inertia
- What it is
- Rotor inertia of the motor, from its data sheet; the inertia of a brake or coupling on the motor shaft can be added.
- 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.
- Get it right
- kg·m², not kg·cm²: 1 kg·cm² = 0.0001 kg·m².
What this means: Machining force at the fixture (tangential)
- What it is
- Tangential cutting or pressing force at the fixture radius during the dwell, 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
- Holding torque needed is proportional to this force.
What this means: Safety factor on holding
- What it is
- Multiplier on the torque from the machining force, used to size the clamp or brake that holds the table still during the dwell.
- Units and format
- Enter a plain number with no unit. The form accepts 1 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.
Method and formulas
- J = ½ M R² + stations × m_f r_f² (fixtures as point masses).
- Index angle θ = 360° ÷ stations; cycloidal: ω_max = 2θ ÷ t, α_max = 2π θ ÷ t²; trapezoidal (⅓ each): ω_max = 1.5 θ ÷ t, α = 4.5 θ ÷ t².
- Table torque = J α + friction; motor torque = table torque ÷ (i η) + J_m α i; motor speed = ω_max i.
- Holding torque = SF × F_m × r_f.
- Example: a 6-station table indexing in 0.6 s needs 139.34 N·m at the table and 3.7354 N·m at the motor.
Limitations
- Rigid table; reducer backlash and stiffness affect settling time.
- Unbalanced fixtures add gravity torque on tilted tables.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Choose a motor and reducer for a dial table
- Check whether an index time is achievable
- Specify the table clamp or brake for machining loads
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Table inertia and index motion
- Table and motor torque and motor speed
- Dwell time and holding torque
Interpreting the result
- Cycloidal motion needs more peak torque than trapezoidal but settles more smoothly.
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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