BIZOMAT MAKEOS · Mechanics
Band Brake Torque and Lever Force
What band tensions and lever force does this simple band brake need for the braking torque?
Tight and slack band tensions, lever force and maximum lining pressure of a simple band brake from the braking torque, drum size, wrap angle and friction.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Braking torque required | N·m | Torque the brake must hold or absorb, including your service factor. |
| Drum diameter | mm | Drum diameter at the lining. |
| Wrap angle | ° | Angle of band contact on the drum. |
| Coefficient of friction | Lining friction coefficient from the maker (use a conservative value). | |
| Lever length (pivot to applied force) | mm | Distance from the lever pivot to where the force is applied. |
| Pivot to slack-end attachment | mm | Distance from the pivot to the slack-side band attachment (simple band brake with the tight end anchored at the pivot). |
| Band width | mm | Width of the band lining. |
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: Braking torque required
- What it is
- The torque the brake must hold or absorb at the drum, including the service factor your design uses.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 400 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Band tensions, lever force and lining pressure rise in direct proportion.
- Get it right
- Apply your service factor before entering it.
What this means: Drum diameter
- What it is
- The diameter of the brake drum at the surface the band lining touches.
- 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 400 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 drum lowers band tensions and lever force for the same torque.
- Get it right
- Use the diameter at the lining contact, not the drum’s outside flange.
What this means: Wrap angle
- What it is
- The angle of the drum circumference the band is in contact with, from the band anchor point round to the slack end.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 720°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 270° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More wrap raises the tension ratio and lowers the lever force.
- Get it right
- Enter degrees; a band covering three quarters of the drum is 270°.
What this means: Coefficient of friction
- What it is
- The coefficient of friction between the band lining and the drum, from the lining maker’s data.
- Units and format
- Enter a plain number with no unit. The form accepts 0.000001 to 2. 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.
- Effect on the result
- Higher friction lowers the lever force.
- Get it right
- Use a conservative value; friction falls when the lining is hot or wet.
What this means: Lever length (pivot to applied force)
- What it is
- The distance along the brake lever from its pivot to the point where the operating force is applied.
- 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 600 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 lever lowers the lever force in direct proportion.
- Get it right
- Measure at right angles to the line of the applied force.
What this means: Pivot to slack-end attachment
- What it is
- The distance from the lever pivot to the point where the slack end of the band is attached, with the tight end anchored at the pivot.
- 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 60 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 distance raises the lever force in direct proportion.
- Get it right
- Measure at right angles to the band’s slack-side line of pull.
What this means: Band width
- What it is
- The width of the band lining in contact with the drum.
- 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 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A wider band lowers the maximum lining pressure.
- Get it right
- Use the lining width, not the steel band width if they differ.
Method and formulas
- Net band force T₁ − T₂ = 2T ÷ D; T₁ ÷ T₂ = e^(μθ).
- T₂ = (T₁ − T₂) ÷ (e^(μθ) − 1); lever force = T₂ b ÷ a.
- Maximum pressure p = T₁ ÷ (r w).
- Example: 400 N·m on a 400 mm drum needs a 64.284 N lever force, with T₁ = 2,642.8 N.
Limitations
- Simple band brake rotating so the anchored end is the tight side; reversing the drum greatly increases lever force.
- Heat dissipation and lining wear are not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a band brake for a winch or hoist drum
- Check lever or actuator force
- Check lining pressure
Who it is for
- Design engineers
- Maintenance engineers
- Machine builders
What you get
- Tight and slack tensions
- Lever force
- Maximum lining pressure
Interpreting the result
- Keep peak pressure within the lining maker’s limit and check heat for repeated stops.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2455–2457. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Method explained here · BIZOMAT original book
Band brakes and controlled lowering
In Clutches and Brakes by the Numbers
What it covers: How a band brake multiplies a small lever force by friction round the drum: band tensions, lever force, lining pressure, the direction that matters, stops, and the heat of a controlled lowering.
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