BIZOMAT MAKEOS · Power Transmission
Band Brake Stopping Design
Can this band brake stop the load in the time required, what lever force does it need, and how hot does it get?
Design of a simple band brake to stop a rotating inertia: braking torque to stop in the target time against a load that resists or overhauls (as in hoist lowering), design torque with a service factor, band tensions from the Euler relation, lever force and lining pressure, actual stopping time and angle, energy per stop, drum temperature rise and average heat.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Duty | ||
| Inertia at the brake drum | kg·m² | Inertia of everything being stopped, referred to the drum shaft. |
| Speed at the start of braking | rpm | Drum speed when braking starts. |
| Required stopping time | s | Time within which it must stop. |
| Load torque | N·m | Torque from the load (friction or gravity). |
| Load torque | choice | Whether the load torque resists rotation or drives it (overhauling loads make stopping harder). |
| Service factor | Factor on torque for lining variation. | |
| Brake | ||
| Drum diameter | mm | Brake drum diameter. |
| Wrap angle | ° | Angle of drum covered by the band. |
| Friction coefficient | Lining friction coefficient. | |
| Lever length to the applied force | mm | Lever arm from the fulcrum to the applied force. |
| Lever length to the band slack end | mm | Lever arm from the fulcrum to the band’s slack end. |
| Band width | mm | Width of the band. |
| Lever force available | N | Force the operator, spring or actuator can apply at the lever (about 250–300 N for a hand lever). |
| Allowable lining pressure | MPa | Allowable pressure for the lining material. |
| Heat | ||
| Drum mass absorbing heat | kg | Mass of the drum that soaks up the heat. |
| Drum specific heat | J/kg·K | Specific heat of the drum (460 J/kg·K for steel). |
| Stops per hour | How often the brake stops the load. | |
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.
Duty
What this means: Inertia at the brake drum
- What it is
- Total rotational inertia the brake must stop, referred to the drum shaft: drum, shafts, gears, couplings and the driven load.
- 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 5 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More inertia raises the braking torque, band tensions and energy per stop.
- Get it right
- Refer inertia through gearing by multiplying by the square of the speed ratio to the drum shaft.
What this means: Speed at the start of braking
- What it is
- Rotational speed of the drum at the moment braking starts.
- 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
- Higher speed raises the torque needed and the stopping energy steeply.
- Get it right
- Use drum speed, after any gearing from the motor.
What this means: Required stopping time
- What it is
- Longest time allowed for the drum to come to rest after the brake is applied.
- Units and format
- Enter a number in s: seconds. The form accepts 0.000001 s to 1000 s. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 s as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Shorter times raise the inertia part of the braking torque.
- Get it right
- A very short stop demands high torque; a longer stop is gentler on the load and the lining.
What this means: Load torque
- What it is
- Size of the steady torque the load exerts on the drum shaft during the stop, from friction, process load or gravity on a suspended load.
- 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 50 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Raises the braking torque needed when it drives the motion, and lowers it when it resists.
- Get it right
- Enter the magnitude only; choose in the next field whether it helps or opposes stopping.
What this means: Load torque
- What it is
- Whether the load torque opposes rotation and so helps stop the drum, or drives rotation (an overhauling load, such as lowering) and so must also be overcome.
- Units and format
- Choose one of 2 options from the list: Resists motion (helps stop); Drives motion (overhauling, e.g. lowering).
- Example
- The form opens with “Drives motion (overhauling, e.g. lowering)” selected as a worked example. Choose the option that matches your case.
- Get it right
- Hoists and lowering duties are usually overhauling; get this right, as it changes the torque needed a lot.
What this means: Service factor
- What it is
- Multiplier on the torque needed, to allow for variation in lining friction, wear and wet or glazed linings.
- 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 1.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Design torque, band tensions, lever force and lining pressure rise in proportion.
- Get it right
- Take it from your design practice or the brake maker.
Brake
What this means: Drum diameter
- What it is
- Diameter of the brake drum surface the band wraps around.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 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 in proportion, and lining pressure more strongly.
- Get it right
- Use the drum’s braking surface diameter, not the flange or hub.
What this means: Wrap angle
- What it is
- Angle of drum circumference covered by the band, from the anchored end to the lever end.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 30° to 340°. 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, lowering the slack tension and lever force.
- Get it right
- Measure the contact arc in degrees, not the angle of the gap left uncovered.
What this means: Friction coefficient
- What it is
- Friction coefficient between the band lining and the drum surface.
- Units and format
- Enter a plain number with no unit. The form accepts 0.05 to 1. 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 raises the tension ratio and lowers the lever force.
- Get it right
- Use the lining maker’s design value; oil or water on the drum lowers it sharply.
What this means: Lever length to the applied force
- What it is
- Distance from the brake lever’s fulcrum to the point where the operator, spring or actuator applies force.
- 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 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 arm lowers the lever force needed in proportion.
- Get it right
- Measure square to the line of the applied force, not along a bent lever.
What this means: Lever length to the band slack end
- What it is
- Distance from the lever’s fulcrum to where the slack end of the band is attached.
- 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
- The lever force needed rises in proportion to this arm.
- Get it right
- This is the short arm to the slack (lever) end, not to the anchored tight end.
What this means: Band width
- What it is
- Width of the band and its lining in contact with the drum, across the drum face.
- 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 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 lining pressure in proportion.
- Get it right
- Use the lining width in contact, not the steel band width if it is wider.
What this means: Lever force available
- What it is
- Largest force the operator, spring or actuator can apply at the end of the lever. The force needed is checked against it.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For hand levers use a force a typical operator can apply repeatedly, from ergonomic guidance, not a one-off maximum.
What this means: Allowable lining pressure
- What it is
- Highest contact pressure the lining material may carry, from the lining maker. Pressure is highest at the tight end of the band.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 20 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.5 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter megapascals (1 MPa = 1 N/mm²).
Heat
What this means: Drum mass absorbing heat
- What it is
- Mass of the drum metal that absorbs the heat of one stop before it is carried away.
- 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 20 kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More mass lowers the temperature rise per stop in proportion.
- Get it right
- Count only the rim and nearby metal that heats during the stop, not the whole hub.
What this means: Drum specific heat
- What it is
- Specific heat capacity of the drum material: the energy needed to raise one kilogram by one kelvin.
- Units and format
- Enter a number in J/kg·K: J/kg·K. The form accepts 0.000001 J/kg·K to 5000 J/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 460 J/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Temperature rise falls in proportion as specific heat rises.
- Get it right
- Take it from the material data sheet for the drum material.
What this means: Stops per hour
- What it is
- Number of stops the brake makes per hour under this duty. It sets the average heat the drum must get rid of.
- Units and format
- Enter a plain number with no unit. The form accepts 0 to 10000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Average heat rises in proportion.
- Get it right
- Use the busiest hour, not a daily average.
Method and formulas
- Torque to stop in time T = J ω ÷ t ± load torque (+ when overhauling); design torque = SF × T.
- Band brake: net pull = T ÷ r; slack tension T₂ = net ÷ (e^(μθ) − 1); tight T₁ = T₂ + net; lever force = T₂ b ÷ a; peak pressure = T₁ ÷ (r w) (handbook band brake formulas).
- Actual stopping time = J ω ÷ (T_design ∓ T_L); angle = ω t ÷ 2.
- Energy = ½ J ω² ± T_L × angle; temperature rise = energy ÷ m c_p.
- Example: stopping 5 kg·m² from 600 rpm in 2 s needs 258.85 N·m and 41.6 N on the lever.
Limitations
- Anchored end is the tight side for the rotation shown; reverse rotation needs much more lever force.
- Constant friction; fade at high temperature is not modelled.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a band brake for a winch, hoist or flywheel
- Check stopping time and heating at a new duty
- Find the lever force an operator or actuator must apply
Who it is for
- Design engineers
- Maintenance engineers
- Power transmission engineers
What you get
- Braking torque and design torque
- Band tensions, lever force and lining pressure
- Stopping time, energy and heat
Interpreting the result
- For hoists, size for the overhauling case with the heaviest load lowering at full speed.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2455–2458. 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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