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Equal belt speed makes pulley speeds inversely proportional to their effective diameters.
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Formula
n in min−1; D in consistent length units
| Symbol | Meaning | Unit |
|---|---|---|
| n1, n2 | Input and output pulley speeds | min−1 |
| D1, D2 | Effective pitch diameters of input and output pulleys | m |
\frac{n_1}{n_2}=\frac{D_2}{D_1}The ratio follows from v=πD1n1/60=πD2n2/60. It assumes no slip and a common belt speed; elastic creep and load can change real output speed. Open and crossed belts change direction, not this magnitude ratio.
The ratio follows from v=πD1n1/60=πD2n2/60. It assumes no slip and a common belt speed; elastic creep and load can change real output speed. Open and crossed belts change direction, not this magnitude ratio.
Equal belt speed makes pulley speeds inversely proportional to their effective diameters.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Speed ratio of slip-free belt pulleys” and check its unit and magnitude.
A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: n in min−1; D in consistent length units.
Formula cluster
Equal belt speed makes pulley speeds inversely proportional to their effective diameters.
A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm.
Determine ideal speed change from pulley sizes.
Here is how to work through a typical Speed ratio of slip-free belt pulleys (n₁/n₂ = D₂/D₁) task step by step:
Task
Work through the numerical example for “Speed ratio of slip-free belt pulleys” and check its unit and magnitude.
Solution path
A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm.
Both pulleys share belt speed without slip. A larger pulley moves more belt per revolution and must rotate more slowly to maintain that linear speed. This is a magnitude ratio for a no-slip belt; use effective diameters. Application: Determine ideal speed change from pulley sizes. The numerical example A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm anchors the idea in a concrete measurement case. The corresponding units are n in min−1; D in consistent length units. A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm. This checks that the reference quantities are compatible.
No, speed magnitudes keep the same ratio if the belt transmits motion without slip. A crossed belt reverses output direction. Its geometry and reduced wrap can affect power capacity. This is a magnitude ratio for a no-slip belt; use effective diameters. The corresponding units are n in min−1; D in consistent length units. A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm. This checks that the reference quantities are compatible. Scope: The ratio follows from v=πD1n1/60=πD2n2/60. It assumes no slip and a common belt speed; elastic creep and load can change real output speed. Open and crossed belts change direction, not this magnitude ratio. A practical application is Determine ideal speed change from pulley sizes.
The ideal kinematic ratios look similar, but belts transmit by friction and can slip while gears mesh positively. Torque, efficiency and limits differ despite similar speed equations. This is a magnitude ratio for a no-slip belt; use effective diameters. Scope: The ratio follows from v=πD1n1/60=πD2n2/60. It assumes no slip and a common belt speed; elastic creep and load can change real output speed. Open and crossed belts change direction, not this magnitude ratio. A practical application is Determine ideal speed change from pulley sizes.
Write the quantity and unit from the variable list next to every value: n in min−1; D in consistent length units. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A 100 mm driver at 1,800 rpm ideally drives a 300 mm pulley at 600 rpm. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. This is a magnitude ratio for a no-slip belt; use effective diameters.
The background states this starting condition: The ratio follows from v=πD1n1/60=πD2n2/60. It assumes no slip and a common belt speed; elastic creep and load. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. This is a magnitude ratio for a no-slip belt; use effective diameters.
Quanta exam set
Curated exam set for "Speed ratio of slip-free belt pulleys":
Question (front)
Which formula describes Speed ratio of slip-free belt pulleys?
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Question (front)
How do you rearrange Speed ratio of slip-free belt pulleys for Base equation for the target quantity?
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Question (front)
Which common mistake happens with Speed ratio of slip-free belt pulleys?
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