BIZOMAT MAKEOS · Power Transmission
Torque Arm Reaction Check (Output Torque, Arm Reaction, Anchor Pin Joint)
For a shaft-mounted gearbox held by a torque arm, what reaction does the arm put on its anchor, and is the anchor pin joint strong enough?
Check of the torque arm of a shaft-mounted gear reducer: the output torque from power and speed with a service factor, the reaction at the arm anchor from the torque and the arm length, then the pin bending, shear and bearing, the eye net tension and tear-out of the arm’s pin joint (as the clevis pin joint tool), against the allowable stresses.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Motor power | kW | Rated power of the motor driving the reducer. |
| Output (shaft) speed | rpm | Speed of the reducer output shaft. |
| Service factor (starting and shock) | Factor for starting torque, shock and jams. | |
| Arm length (shaft centre to anchor pin) | mm | Distance from the shaft centre to the anchor pin, measured perpendicular to the arm’s line of reaction. |
| Anchor pin joint | ||
| Pin diameter | mm | Diameter of the anchor pin. |
| Arm eye thickness | mm | Thickness of the arm’s eye. |
| Thickness of each bracket plate | mm | Thickness of each plate of the anchor bracket (fork). |
| Gap between eye and each plate | mm | Gap between the eye and each plate. |
| Eye edge distance | mm | Distance from the eye hole centre to the end of the arm. |
| Allowable pin bending stress | MPa | Allowable pin bending stress. |
| Allowable pin shear stress | MPa | Allowable pin shear stress. |
| Allowable bearing stress | MPa | Allowable bearing stress. |
| Allowable eye tensile stress | MPa | Allowable eye net-section tensile stress. |
| Allowable eye tear-out shear stress | MPa | Allowable eye tear-out shear stress. |
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: Motor power
- What it is
- The rated power of the motor driving the shaft-mounted reducer whose reaction the torque arm holds.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Output torque and the arm reaction rise in direct proportion.
- Get it right
- Use the motor nameplate power, in kW.
What this means: Output (shaft) speed
- What it is
- The rotational speed of the reducer output shaft that the torque arm’s reducer is mounted on.
- 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 50 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lower output speed means higher torque and reaction for the same power.
- Get it right
- Use output shaft speed, not motor speed.
What this means: Service factor (starting and shock)
- What it is
- A multiplier on the rated torque to cover starting torque, shock loads and jams the arm must hold.
- 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 1.5 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All forces and stresses rise in direct proportion.
- Get it right
- Take it from the reducer maker’s service factor tables for the driven machine.
What this means: Arm length (shaft centre to anchor pin)
- What it is
- The lever arm from the shaft centre to the anchor pin, taken at right angles to the line along which the anchor pin pushes or pulls.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 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
- A longer arm lowers the reaction force and every pin and eye stress.
- Get it right
- If the arm is not at right angles to its reaction link, use the perpendicular distance, not the arm length.
Anchor pin joint
What this means: Pin diameter
- What it is
- The diameter of the anchor pin that joins the arm eye to the fixed bracket.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pin bending stress falls with the cube of the diameter and shear with its square.
- Get it right
- Use the pin diameter at the shear planes, not the head or thread size.
What this means: Arm eye thickness
- What it is
- The thickness of the arm’s eye, the part of the arm that the pin passes through between the bracket plates.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the eye thickness where the pin bears.
What this means: Thickness of each bracket plate
- What it is
- The thickness of each of the two bracket (fork) plates either side of the arm eye.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter one plate, not both together.
What this means: Gap between eye and each plate
- What it is
- The clearance between the face of the arm eye and each bracket plate. It lengthens the pin span and raises bending.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger gap raises the pin bending moment.
- Get it right
- Enter the gap on one side; the tool counts both sides.
What this means: Eye edge distance
- What it is
- The distance from the centre of the pin hole in the arm eye to the end of the arm, which resists the pin tearing out.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure from the hole centre to the outer edge along the line of the load; it must exceed the pin radius.
What this means: Allowable pin bending stress
- What it is
- The bending stress you allow in the anchor pin.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the pin material’s strength and your design code’s safety factor.
What this means: Allowable pin shear stress
- What it is
- The shear stress you allow across the anchor pin at each shear plane.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 120 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the pin material’s strength and your design code.
What this means: Allowable bearing stress
- What it is
- The bearing stress you allow where the pin presses on the arm eye and on the bracket plates. The same limit is used for both.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 3000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the value for the weaker of the eye and plate materials.
What this means: Allowable eye tensile stress
- What it is
- The tensile stress you allow on the net section of the arm eye beside the pin hole.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the arm material’s strength and your design code.
What this means: Allowable eye tear-out shear stress
- What it is
- The shear stress you allow along the paths by which the pin could tear out through the end of the eye.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Set it from the arm material’s strength and your design code.
Method and formulas
- Output torque = 9549 P ÷ n × service factor.
- Arm reaction = torque ÷ arm length (taken perpendicular to the arm).
- Pin bending, shear, eye and fork bearing, eye net tension and tear-out (as the clevis pin joint tool).
- Example: 1,145.9 N·m gives a 3.8197 kN reaction; the joint is at 36.025% of its allowables.
Limitations
- Arm perpendicular to the line to the shaft centre; an inclined arm adds a component along the arm.
- Reaction from torque only; belt pull or overhung loads on the reducer are not included.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check the torque arm on a conveyor drive
- Size the anchor pin and bracket
- Check a torque arm after fitting a larger motor
Who it is for
- Maintenance engineers
- Design engineers
- Millwrights
What you get
- Output torque
- Arm reaction
- Pin joint stresses and utilisation
Interpreting the result
- Doubling the arm length halves the anchor reaction; a rubber bush at the anchor cushions starting shocks.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1535, 1720–1735, 2122–2160. Topic reference; no source tables or recommended settings are reproduced.
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Open the Torque Arm Reaction Check (Output Torque, Arm Reaction, Anchor Pin Joint) calculator