Rotary indexing table calculator

Calculate the index angle, cycle time, index ratio and acceleration torque of a rotary indexing table. Enter the number of stations or the index angle and the total inertia, set the index and dwell time, choose the motion profile - the calculator returns angular acceleration, peak angular velocity and the required drive torque M_a = J·α, live with every input.

Calculation

Model: acceleration torque of the table inertia M_a = J_total·α for a triangular or trapezoidal profile. Friction, process and load torques and a gearbox are not included. Sizing tool for automation engineering; the motor is selected from the manufacturer torque-speed curve.

Division and inertia

Number of stations zTotal inertia J_total [kg·m²]

Times

Index time t_index [s]Dwell time t_dwell [s]

Motion profile

Results

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Formulas and fundamentals

Index angle and cycle time

The index angle per step follows from the number of stations z or is entered directly:

φ = 360°/z φ = 2π/z (radians)

The cycle time of one station is the sum of index and dwell time:

t_cycle = t_index + t_dwell

The index ratio t_index/t_cycle describes what share of the cycle is spent moving. The cycle rate is 60/t_cycle cycles per minute.

Acceleration torque and motion profile

The required drive torque during the index is the acceleration torque of the table inertia:

M_a = J_total·α

The angular acceleration α depends on the motion profile: for the symmetric triangular profile half the index time accelerates and half decelerates:

α = 4·φ/t_index² ω_peak = 2·φ/t_index

For the trapezoidal 1/3-1/3-1/3 profile (one third each accelerating, constant, decelerating) the acceleration phase is shorter:

α = 9·φ/(2·t_index²) ω_peak = 3·φ/(2·t_index)

This raises the torque compared with the triangular profile.

Scope of the model

M_a is the pure inertial acceleration torque. Friction in bearings and index mechanism, process and load torques at the stations, and a gearbox between motor and table must be added separately. The motor is selected from the manufacturer torque-speed curve; the peak torque and peak speed computed here are the governing sizing values.

Worked example

A rotary indexing table with 8 stations indexes by φ = 360°/8 = 45° per step (0.7854 rad). The total inertia referred to the table axis including workpiece fixtures is J_total = 2 kg·m², the index time t_index = 0.5 s.

With a triangular profile α = 4·0.7854/0.5² = 12.57 rad/s², giving an acceleration torque M_a = J·α = 2·12.57 = 25.13 Nm; the peak angular velocity is ω_peak = 2·0.7854/0.5 = 3.14 rad/s. A trapezoidal 1/3-1/3-1/3 profile shortens the acceleration phase: α = 9·0.7854/(2·0.25) = 14.14 rad/s², M_a = 28.27 Nm.

With a dwell time of 1.0 s the cycle time is 1.5 s, the index ratio 1/3 and the cycle rate 40 cycles per minute. The trapezoidal profile moves less in the constant segment but demands the higher drive torque - so the profile choice trades torque demand against smooth running.

Frequently asked questions

Why does the trapezoidal profile need more torque than the triangular one?

Because the same index motion is accelerated in less time. With the triangular profile acceleration lasts half the index time, with the trapezoidal 1/3-1/3-1/3 only a third. Shorter acceleration time means higher angular acceleration and therefore higher torque: α = 9φ/(2t²) instead of 4φ/t², a ratio of 9/8.

What belongs in the total inertia J_total?

The inertia of the table plate, the workpiece fixtures and the workpieces, each about the table axis (with a parallel-axis term m·r² for off-centre masses). Motor and gearbox inertia are not included; they are added on the motor side, reduced by the gear ratio, during motor sizing.

Is M_a already the required motor torque?

No. M_a is only the acceleration part of the table inertia. Friction torques, process forces at the stations and a gearbox between motor and table add to it. For a full motor sizing including the effective torque over the cycle, use the drive sizing calculator.

Which profile should I choose?

The triangular profile needs the lowest peak torque and is the simplest approximation. The trapezoidal profile limits the peak velocity and runs more smoothly but costs more torque. For low-vibration motion with limited jerk, S-curve profiles are common in practice; as a conservative estimate the trapezoidal profile usually covers their torque demand.

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