BIZOMAT MAKEOS · Fasteners
Pinned Hub Drive Check (Cross Pin Size, Pin Shear, Shaft Bearing and Torsion)
For a hub or collar driven by a pin through the shaft, is the pin big enough, and do the bearing pressure and the weakened shaft stay within limits?
Check of a hub, collar or lever driven through a cross (taper or straight) pin: the torque from torque or power and speed, the pin diameter needed and the pin shear stress in double shear (as the taper pin torque tool), the bearing pressure of the pin on the shaft bore, the torsional stress in the shaft raised by the cross-hole stress concentration, and the pin-to-shaft size ratio, against your allowable stresses.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load given as | choice | Whether the load is entered as a torque or as power and speed. |
| Torque | N·m | Torque through the pin. |
| Power | kW | Power through the pin. |
| Speed | rpm | Shaft speed (power mode). |
| Shaft diameter | mm | Diameter of the shaft where the pin passes through. |
| Pin mean diameter | mm | Mean diameter of the pin in the shaft. |
| Allowables | ||
| Safe shear stress of the pin | MPa | Safe shear stress for the pin material and duty. |
| Allowable bearing pressure on the shaft | MPa | Allowable bearing pressure of the pin on the shaft material. |
| Stress concentration at the cross hole | Torsional stress concentration factor for a transverse hole in a shaft. | |
| Allowable shaft shear stress | MPa | Allowable torsional shear stress in the shaft. |
| Largest pin ÷ shaft diameter | Largest pin diameter as a share of the shaft diameter you will accept. | |
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: Load given as
- What it is
- Whether the load through the pin is entered directly as a torque, or worked out from power and shaft speed. Only the inputs for the chosen option are used.
- Units and format
- Choose one of 2 options from the list: Torque; Power and speed.
- Example
- The form opens with “Torque” selected as a worked example. Choose the option that matches your case.
- Get it right
- In torque mode the power and speed are ignored; in power mode the torque is ignored.
What this means: Torque
- What it is
- The twisting moment the cross pin must transmit between the shaft and the hub, collar or lever. Used only in torque mode.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Pin shear, bearing pressure and shaft stress all rise in direct proportion to the torque.
- Get it right
- Use the peak torque the drive sees, such as starting or jamming torque, if it is higher than running torque.
What this means: Power
- What it is
- The power transmitted through the pinned joint, from the motor rating or the driven load. Used with the speed in power mode to find the torque.
- 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 3 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The torque, and so every stress, rises in direct proportion to the power.
- Get it right
- Enter it in kW; a rating in horsepower must be converted.
What this means: Speed
- What it is
- The rotational speed of the shaft carrying the pin, used with the power in power mode to find the torque.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 1000000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 500 rpm 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 power a lower speed means a higher torque and higher stresses.
- Get it right
- Use the speed of this shaft, not the motor speed if a reduction stage sits between them.
What this means: Shaft diameter
- What it is
- The diameter of the shaft where the cross pin passes through it. It sets the pin shear, the bearing pressure on the bore and the torsional stress in the shaft.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 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 shaft lowers pin shear, bearing pressure and shaft stress.
- Get it right
- Use the shaft diameter at the pin hole itself, not a larger shoulder nearby.
What this means: Pin mean diameter
- What it is
- The diameter of the cross pin within the shaft; for a taper pin, its mean diameter over the length inside the shaft. The pin is taken as being in double shear.
- 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.
- Effect on the result
- Pin shear stress falls with the square of the pin diameter.
- Get it right
- For a taper pin take the average of its diameters at the two shaft surfaces, not the nominal small-end size.
Allowables
What this means: Safe shear stress of the pin
- What it is
- The shear stress you allow in the pin for its material and duty, from your design code, engineer or material data with your safety margin.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower safe stress raises the pin diameter needed.
- Get it right
- Use a shear value, not the tensile strength of the pin material.
What this means: Allowable bearing pressure on the shaft
- What it is
- The pressure you allow between the pin and the sides of the hole through the shaft, from your design data for the shaft material.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 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
- Base it on the weaker of the pin and shaft materials, as set by your design rules.
What this means: Stress concentration at the cross hole
- What it is
- The factor by which the transverse pin hole raises the torsional stress in the shaft above the nominal value, from a stress concentration chart for a shaft with a cross hole.
- 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.
- Effect on the result
- The shaft stress at the hole rises in direct proportion to this factor.
- Get it right
- It depends on the hole size relative to the shaft; read it for your pin-to-shaft ratio.
What this means: Allowable shaft shear stress
- What it is
- The torsional shear stress you allow in the shaft at the pin hole for its material and duty, from your design code or engineer.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use a shear stress; the tool compares it with the nominal stress raised by the stress concentration factor.
What this means: Largest pin ÷ shaft diameter
- What it is
- The largest pin diameter, as a fraction of the shaft diameter, that your design rules allow, to stop the hole weakening the shaft too much.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 0.6. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter a plain ratio, not a percentage: a quarter of the shaft diameter is 0.25, not 25.
Method and formulas
- Torque from T or 9549 P ÷ n; pin needed d = 1.13 √(T ÷ (D S)); pin shear τ = 4T ÷ (π d² D) (as the taper pin torque tool).
- Bearing pressure of the pin on the shaft = 6T ÷ (d D²).
- Shaft stress = K_t × 16T ÷ (π D³).
- Example: a 5.65 mm pin is the least; the 8 mm pin runs at 39.789 MPa shear and the shaft at 22.635 MPa.
Limitations
- Steady torque; reversing or shock loads loosen pins and need lower allowables.
- Shaft net-section effect is in the stress concentration factor you enter.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the pin for a pinned collar or gear
- Check a pinned handwheel or lever
- See whether the cross hole weakens the shaft too much
Who it is for
- Design engineers
- Maintenance engineers
- Machinists
What you get
- Torque and pin size needed
- Pin shear and bearing pressure
- Shaft stress at the cross hole
Interpreting the result
- A pin that shears before the shaft yields acts as a shear pin; a pin over about a third of the shaft size weakens the shaft too much.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 220, 1714–1720. Topic reference; no source tables or recommended settings are reproduced.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Pinned Hub Drive Check (Cross Pin Size, Pin Shear, Shaft Bearing and Torsion) calculator