BIZOMAT MAKEOS · Mechanics
Single Shoe (Block) Brake
What lever force does this block brake need, and is it self-energising or self-locking?
Normal force, lever force and shoe pressure of a short single-shoe brake on a drum, for either direction of rotation, with the self-locking check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Braking torque required | N·m | Braking torque required. |
| Drum diameter | mm | Drum diameter. |
| Coefficient of friction | Lining friction coefficient. | |
| Pivot to applied force | mm | Lever length from pivot to the applied force. |
| Pivot to shoe normal force line | mm | Perpendicular distance from the pivot to the line of the shoe’s normal force. |
| Offset of friction force line from pivot | mm | Perpendicular distance from the pivot to the line of the friction force (tangent at the shoe). |
| Rotation relative to the pivot | choice | Whether friction drags the shoe onto the drum (self-energising) or off it, for this rotation direction. |
| Shoe contact area | mm² | Contact area of the shoe 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 shoe brake must hold or absorb at the drum, including your design service factor.
- 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 200 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Normal force, lever force and shoe 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 shoe contact surface.
- 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 larger drum lowers the forces needed for the same torque.
- Get it right
- Use the diameter at the friction surface.
What this means: Coefficient of friction
- What it is
- The coefficient of friction between the shoe 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 0.35 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 normal force needed and moves the brake towards self-locking.
- Get it right
- Use a conservative value; the self-locking check depends on it.
What this means: Pivot to applied force
- What it is
- The distance along the lever from its pivot to 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 500 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 applied force.
What this means: Pivot to shoe normal force line
- What it is
- The perpendicular distance from the lever pivot to the line along which the shoe presses on the drum.
- 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 200 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.
- Get it right
- Measure at right angles to the line of the normal force through the shoe centre.
What this means: Offset of friction force line from pivot
- What it is
- The perpendicular distance from the lever pivot to the line of the friction force, which acts along the drum tangent at the shoe.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 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 offset lowers lever force when self-energising and raises it when de-energising.
- Get it right
- Measure at right angles to the tangent at the shoe; it decides how much friction helps or hinders.
What this means: Rotation relative to the pivot
- What it is
- Whether, for the drum’s rotation direction, the friction on the shoe pulls it onto the drum or pushes it away, relative to the lever pivot.
- Units and format
- Choose one of 2 options from the list: Friction moment helps apply the shoe (self-energising); Friction moment opposes the shoe (de-energising).
- Example
- The form opens with “Friction moment helps apply the shoe (self-energising)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Check both directions if the drum can turn either way; the brake must work in the harder one.
What this means: Shoe contact area
- What it is
- The area of the shoe lining in contact with the drum, used for the average pressure on the lining.
- Units and format
- Enter a number in mm²: square millimetres. The form accepts 0.000001 mm² to 100000000 mm². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6000 mm² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger area lowers shoe pressure.
- Get it right
- Use the contact area, lining width times arc length, not the shoe plate area.
Method and formulas
- Friction force = T ÷ r; normal force N = T ÷ (μ r).
- Lever force: self-energising F = N(b − μc) ÷ a; de-energising F = N(b + μc) ÷ a.
- Self-locking when b ≤ μc in the self-energising direction; shoe pressure = N ÷ area.
- Example: 200 N·m on a 300 mm drum needs N = 3,809.5 N and a lever force of 1,417.1 N.
Limitations
- Short-shoe assumption (uniform pressure); long shoes need integration over the shoe arc.
- Heat capacity not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a shoe brake for a drum or wheel
- Check the effect of rotation direction
- Avoid unintended self-locking
Who it is for
- Design engineers
- Maintenance engineers
- Machine builders
What you get
- Normal force on the shoe
- Lever force
- Shoe pressure
- Self-locking check
Interpreting the result
- Avoid self-locking geometry unless it is deliberate; it makes the brake grab.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2455–2459. 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
Shoe brakes
In Clutches and Brakes by the Numbers
What it covers: How a shoe brake's lever, pivot and friction combine: normal and lever forces, self-energising and de-energising directions, self-locking, shoe pressure and the side load on the drum shaft.
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