BIZOMAT MAKEOS · Power Transmission
Step Cone Pulley Design (Geometric Speed Steps, Step Diameters, Crossed Belt Length)
For a pair of step (cone) pulleys giving a range of output speeds, what speeds should the steps give and what diameter is each step, so one belt fits every step?
Design of matched step (cone) pulleys driven by a crossed belt: output speeds in geometric progression between the lowest and highest speed with the step ratio fitted to the number of steps (as the progression tool), the driver and driven diameter of each step with a constant diameter sum so the same crossed belt fits every step, and the belt length and wrap (as the crossed belt length tool), against the smallest pulley diameter you allow.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Driver (input) speed | rpm | Speed of the driving shaft. |
| Lowest output speed | rpm | Slowest output speed wanted. |
| Highest output speed | rpm | Fastest output speed wanted. |
| Number of steps | steps | Number of steps on each pulley. |
| Sum of driver and driven diameters | mm | Driver plus driven diameter, the same for every step with a crossed belt. |
| Centre distance | mm | Distance between the shaft centres. |
| Smallest pulley diameter allowed | mm | Smallest diameter the belt can bend round without damage. |
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: Driver (input) speed
- What it is
- The speed of the driving shaft carrying the driver cone pulley, which stays the same whichever step the belt is on.
- 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 400 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the shaft speed under load, after any reduction before the cone pulley.
What this means: Lowest output speed
- What it is
- The slowest output speed wanted, given by the first step of the driven cone.
- 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 100 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the driven shaft speed, not the driver speed.
What this means: Highest output speed
- What it is
- The fastest output speed wanted, given by the last step of the driven cone.
- 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 800 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be higher than the lowest output speed.
What this means: Number of steps
- What it is
- The number of steps on each cone pulley, which is also the number of output speeds. Speeds are spaced in geometric progression between the lowest and highest.
- Units and format
- Enter a number in steps: steps. The form accepts 2 steps to 10 steps. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 steps as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More steps give a smaller ratio between neighbouring speeds.
- Get it right
- Count steps on one pulley; the matching pulley has the same number.
What this means: Sum of driver and driven diameters
- What it is
- The driver diameter plus the driven diameter, which is the same on every step so that one crossed belt fits all of them.
- 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 sum makes every step larger and lengthens the belt.
- Get it right
- It is a sum of two diameters, not a radius or a single pulley size.
What this means: Centre distance
- What it is
- The distance between the centres of the driver and driven shafts.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 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 centre distance lengthens the belt.
- Get it right
- It must be more than half the diameter sum, or a crossed belt cannot fit.
What this means: Smallest pulley diameter allowed
- What it is
- The smallest pulley diameter you allow on any step, set by how tightly the belt can bend without damage.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the belt maker’s minimum pulley diameter for your belt.
Method and formulas
- Step ratio r = (n_max ÷ n_min)^(1 ÷ (k − 1)); speeds n_i = n_min r^i (as the progression tool).
- Driver d₁ = S n_i ÷ (n_in + n_i); driven d₂ = S n_in ÷ (n_in + n_i), so d₁ + d₂ = S on every step.
- Crossed belt length depends only on the diameter sum, so one belt fits every step (as the crossed belt length tool).
- Example: step ratio 2; the smallest step is 80 mm and the belt 1,895.6 mm long.
Limitations
- Crossed belt for exact equal lengths; with an open belt the diameter sums differ slightly between steps.
- Belt slip of a few per cent lowers each output speed.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out step pulleys for a drill press or lathe
- Replace a worn cone pulley pair
- Choose speeds for a belt-driven machine
Who it is for
- Machine builders
- Restorers
- Design engineers
What you get
- Speed ratio and output speeds
- Diameters of each step
- Belt length and smallest pulley
Interpreting the result
- Speeds in geometric progression give the same percentage step everywhere, which suits cutting speeds on a range of diameters.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 37–39, 2473–2490. Topic reference; no source tables or recommended settings are reproduced.
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