7 Steps to Help You Choose the Most Suitable Harmonic Gear Rotary Actuator

How do you choose the harmonic gear rotary actuator that best suits your needs?

This article introduces the selection and calculation process from the perspectives of confirming the reduction ratio, torque calculation, bearing load calculation, load inertia confirmation, and driver matching.

1. Calculate Load Torque

1) Load gravity torque calculation formula:

TG = M × g × L × cosΘ

Θ = the angle between the direction of gravity and the lever arm L

2) Load acceleration torque calculation formula:

Ta = J × α

Load inertia J: measured using 3D modeling software (material properties must be included, and attention should be paid to the coordinate system origin position during measurement)

Angular acceleration α: determined according to actual user requirements (for example, rotating 180 degrees in 1 second, with 0.1 second required for the acceleration phase)

3) Confirm the comprehensive peak torque during start and stop of the reducer:

∑T = (TG + Ta) × safety factor

Safety factor: 1.2 for slight impact, 1.5 for medium impact, 2.0 for heavy load impact

Start-stop peak torque ∑T ≤ maximum acceleration torque T2B

2. Product Selection Process – Torque Calculation

1) Establish the rotation coordinate system

2) Select the corresponding coordinate system

3) Observe the value determined by the output coordinate system (Izz shown in the figure)

T = J × α + TG

T: peak torque

J: moment of inertia

α: angular acceleration

TG: static load torque

Tip: Angular acceleration can be simply planned linearly.

Example:

The motor accelerates from 0 rpm to 3000 rpm in 0.12 s, reduction ratio 101, and load inertia simulated in SolidWorks is 0.88 kg·m².

α = (3000/60 × 2π) / 101 / 0.12 = 25.9 rad/s²

Ignoring static torque, peak torque T = J × α = 0.88 × 25.9 = 22.8 N·m

3. Product Selection Process – Torque Calculation

T = J × α + TG

Example:

The motor accelerates from 0 rpm to 3000 rpm in 0.5 s, reduction ratio 101.

α = (3000/60 × 2π) / 101 / 0.5

Ignoring static torque, peak torque T = J × α

Example:

The motor accelerates from 0 rpm to 3000 rpm in 0.12 s, reduction ratio 101, and load inertia simulated in SolidWorks is 0.88 kg·m².

α = (3000/60 × 2π) / 101 / 0.12 = 25.9 rad/s²

Ignoring static torque, peak torque T = J × α = 0.88 × 25.9 = 22.8 N·m

4. Product Selection Process – Bearing Verification

Bending moment load torque

The static load moment calculation method is as follows:

Mmax = Frmax × Lr + Famax × La

In particular, when the load swings rapidly, centrifugal force must be included. At this time, the comprehensive radial force on the bearing is:

∑Fr = Frmax + m × r × ω²

5. Product Selection Process – Inertia Verification

Motor inertia matching

To achieve better system responsiveness and more precise control between the motor and the load, inertia matching calculations are required for the load inertia, reducer input rotor inertia, and motor rotor inertia.

Since the client’s load shape and density distribution are often non-uniform, the load inertia can be quickly obtained directly from 3D modeling software.

Load inertia ratio calculation formula:

Load inertia / i² / motor rotor inertia

This result should be controlled within 5 for better servo system response.

(i = reduction ratio)

If the initially selected reduction ratio is not suitable after calculation, increase the reduction ratio or select a medium- or high-inertia motor.

6. Product Selection Process – Accuracy Calculation

Reducer positioning accuracy calculation

When using a rotary actuator for absolute positioning, the error at the outermost circle of the load rotation can be calculated using the following formula (this formula does not include torsional rigidity error caused by load torque):

δ = positioning accuracy (arcsec) / 3600 / 57.3 × R (rotation radius)

Example:

For HAT20-100, the single-direction positioning accuracy is 60 arcsec, and the rotation radius R = 200 mm.

Transmission error ≤ 60 / 3600 / 57.3 × 200 = 0.058 mm

7. Product Selection Process – Accuracy Calculation

Other considerations:

For outdoor applications: pay attention to starting torque and replace with low-temperature grease.

For acid and alkali corrosion environments: secondary protection of the reducer output end is required.

For special high-precision requirements: customized ultra-high rigidity harmonic reducers are needed.

Special requirements for end face runout and radial runout in machine tool machining.

For extremely compact installation space requirements: standard reducers may not meet the requirements; customized production is required.

If you still have questions about selecting a harmonic drive rotary actuator, please contact us.