BIZOMAT MAKEOS · Mechanics
Shoe Brake Stop Check (Stopping Torque, Lever Force, Lining Pressure, Heat)
What braking torque stops this rotating load in the time I want, what lever force does my shoe brake need, and are the lining pressure and drum temperature rise acceptable?
Check of a single-shoe drum brake stopping a rotating load: the torque to decelerate the inertia in the stopping time less any drag that helps (as the torque to accelerate a rotating load tool), the normal and friction forces on the shoe and the lever force for the pivot geometry, self-energising or not, with the self-locking check (as the shoe brake tool), shoe pressure, kinetic energy per stop, revolutions to stop and the drum temperature rise, checked against the force available, your pressure limit and temperature limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Inertia of the load at the brake shaft | kg·m² | Moment of inertia of everything being stopped, referred to the brake shaft. |
| Speed | rpm | Speed of the brake shaft when the brake is applied. |
| Stopping time wanted | s | Time in which the load must stop. |
| Drag torque helping to stop | N·m | Friction or load torque that also slows the load (0 to ignore). |
| Brake geometry | ||
| Drum diameter | mm | Diameter of the brake drum. |
| Coefficient of friction | Friction coefficient of the lining on the drum. | |
| Pivot to applied force | mm | Distance from the shoe pivot to the applied lever force. |
| Pivot to shoe normal force line | mm | Distance from the pivot to the line of the shoe normal force. |
| Offset of friction force line from pivot | mm | Offset of the friction force line from the pivot. |
| Rotation relative to the pivot | choice | Whether drum rotation helps or opposes the shoe application. |
| Shoe contact area | mm² | Contact area of the lining. |
| Limits | ||
| Lever force available | N | Force the operator, spring or actuator can apply to the lever. |
| Allowable lining pressure | MPa | Allowable pressure for the lining. |
| Drum mass | kg | Mass of the drum that absorbs the heat. |
| Drum specific heat | kJ/kg·K | Specific heat of the drum (cast iron or steel about 0.46 kJ/kg·K). |
| Largest drum temperature rise per stop | K | Largest temperature rise per stop you 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: Inertia of the load at the brake shaft
- What it is
- The combined moment of inertia of everything the brake must stop (rotor, drum, gears, load), referred to the brake shaft through the drive ratios.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0.000001 kg·m² to 1000000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Braking torque and energy per stop are proportional to it.
- Get it right
- Parts on other shafts must be referred to the brake shaft by multiplying by the square of their speed ratio.
What this means: Speed
- What it is
- The rotational speed of the brake shaft at the moment the brake is applied.
- 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 600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Braking torque rises in proportion; energy per stop rises with its square.
- Get it right
- Use the brake shaft speed, not the motor or output speed if they differ.
What this means: Stopping time wanted
- What it is
- The time in which the brake must bring the load from its running speed to rest.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 10000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The torque to decelerate the load is inversely proportional to the stopping time.
What this means: Drag torque helping to stop
- What it is
- A friction or load torque on the brake shaft that also slows the load and so helps the brake. Type 0 to ignore it.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The brake torque needed is reduced one for one by this torque.
- Get it right
- Ignoring drag (0) is the safe case; only include drag that is always present.
Brake geometry
What this means: Drum diameter
- What it is
- The diameter of the brake drum surface the shoe lining rubs on.
- 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 friction force and lever force needed for the same torque.
What this means: Coefficient of friction
- What it is
- The friction coefficient between the shoe lining and the drum, from the lining maker’s data for the operating temperature.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 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
- A higher coefficient reduces the shoe normal force and the lever force.
- Get it right
- Friction can fall when the lining is hot, wet or oily; use a value you can rely on.
What this means: Pivot to applied force
- What it is
- The distance from the shoe lever pivot to the line of the applied lever force, measured at right angles to that force.
- 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 arm reduces the lever force in proportion.
What this means: Pivot to shoe normal force line
- What it is
- The distance from the shoe lever pivot to the line of action of the normal force 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.
What this means: Offset of friction force line from pivot
- What it is
- The perpendicular offset of the friction force line (tangent to the drum at the shoe) from the pivot. It decides how much the friction moment helps or opposes 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.
- Get it right
- If the pivot lies on the friction force line, the offset is zero.
What this means: Rotation relative to the pivot
- What it is
- Whether the drum’s direction of rotation makes the friction moment help press the shoe on (self-energising) or push it off (de-energising).
- 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
- A self-energising brake needs less lever force but can grab; reverse rotation changes the result.
What this means: Shoe contact area
- What it is
- The contact area of the lining against the drum: lining width times the arc length in contact. The normal force divided by it gives the lining pressure.
- 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.
- Get it right
- Type square millimetres.
Limits
What this means: Lever force available
- What it is
- The force the operator, spring or actuator can apply at the end of the lever arm.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 100000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1500 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable lining pressure
- What it is
- The highest pressure the lining material may take against the drum, from the lining maker’s data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 50 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Drum mass
- What it is
- The mass of the drum metal that absorbs the heat of each stop.
- Units and format
- Enter a number in kg: kilograms. The form accepts 0.000001 kg to 100000 kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A heavier drum lowers the temperature rise per stop in proportion.
- Get it right
- Use only the drum itself, not the hub or shaft unless they share the heat quickly.
What this means: Drum specific heat
- What it is
- The heat needed to warm one kilogram of the drum material by one degree, from material data.
- Units and format
- Enter a number in kJ/kg·K: kilojoules per kilogram per kelvin. The form accepts 0.000001 kJ/kg·K to 5 kJ/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.46 kJ/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Type kJ/kg·K; data in J/kg·K must be divided by 1000.
What this means: Largest drum temperature rise per stop
- What it is
- The largest drum temperature rise you accept from a single stop, set by the lining and the duty.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0.000001 K to 1000 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- A rise in kelvin equals the same rise in °C; repeated stops add up if the drum cannot cool.
Method and formulas
- Brake torque = J ω ÷ t − drag (as the torque to accelerate a rotating load tool, with deceleration).
- Friction force = torque ÷ r; normal force = friction ÷ μ; lever force = N (b ∓ μc) ÷ a, self-locking if b ≤ μc when self-energising (as the shoe brake tool); pressure = N ÷ area.
- Energy per stop = ½ J ω²; revolutions = n t ÷ 120; drum temperature rise = energy ÷ (m c).
- Example: stopping in 3 s needs 167.55 N·m and 1,187.2 N on the lever; each stop puts 15.791 kJ into the drum, 2.2886 K.
Limitations
- Short shoe with uniform pressure; long shoes need the pressure distribution.
- All energy assumed to go into the drum in one stop; repeated stops accumulate heat.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a hand or spring-applied drum brake
- Check a brake for a new stopping time
- Estimate drum heating per stop
Who it is for
- Machine designers
- Maintenance engineers
- Design engineers
What you get
- Stopping torque, energy and revolutions
- Shoe forces, lever force and pressure
- Drum temperature rise
Interpreting the result
- A self-energising shoe needs less lever force but its torque is very sensitive to the friction coefficient.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2455–2459, 176–181. Topic reference; no source tables or recommended settings are reproduced.
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Open the Shoe Brake Stop Check (Stopping Torque, Lever Force, Lining Pressure, Heat) calculator