BIZOMAT MAKEOS · Manufacturing
Machine Spindle Speed Range Design (Geometric Series and Speed Loss)
What spindle speed range covers my diameters and cutting speeds, what step ratio do my number of speeds give, and how much cutting speed is lost between steps?
Design of a stepped spindle speed range for a machine tool: lowest and highest speeds needed from the work diameter range and cutting speed range, the geometric step ratio for the number of speeds (as the speed series tool), the nearest preferred-number series, the largest cutting speed loss between neighbouring speeds, the number of speeds needed for your largest acceptable loss, and the list of speeds.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Smallest work (or tool) diameter | mm | Smallest diameter machined (with the highest cutting speed). |
| Largest work (or tool) diameter | mm | Largest diameter machined (with the lowest cutting speed). |
| Lowest cutting speed | m/min | Lowest cutting speed needed (tough materials, large diameters). |
| Highest cutting speed | m/min | Highest cutting speed needed. |
| Number of speeds | Number of spindle speeds the gearbox gives. | |
| Largest acceptable speed loss between steps | % | Largest loss of cutting speed you accept when the ideal speed falls between two steps. |
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: Smallest work (or tool) diameter
- What it is
- The smallest work diameter (turning) or tool diameter (milling, drilling) the machine must cut. With the highest cutting speed it sets the top spindle speed.
- 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 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Largest work (or tool) diameter
- What it is
- The largest work or tool diameter the machine must cut. With the lowest cutting speed it sets the lowest spindle speed.
- 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 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be larger than the smallest diameter.
What this means: Lowest cutting speed
- What it is
- The lowest surface cutting speed any planned job needs, typically for tough materials or large diameters, from your tooling data.
- Units and format
- Enter a number in m/min: metres per minute. The form accepts 0.000001 m/min to 5000 m/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 m/min as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Highest cutting speed
- What it is
- The highest surface cutting speed any planned job needs, typically for finishing easy-cutting materials, from your tooling data.
- Units and format
- Enter a number in m/min: metres per minute. The form accepts 0.000001 m/min to 5000 m/min. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 m/min 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 cutting speed.
What this means: Number of speeds
- What it is
- How many separate spindle speeds the gearbox provides from the lowest to the highest.
- Units and format
- Enter a plain number with no unit. The form accepts 2 to 60. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More speeds give a smaller step ratio and a smaller speed loss between steps.
What this means: Largest acceptable speed loss between steps
- What it is
- The largest drop in cutting speed you accept when the ideal speed falls between two steps and the lower step has to be used.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 60%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 21% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- n_min = 1000 v_min ÷ (π d_max); n_max = 1000 v_max ÷ (π d_min); range R = n_max ÷ n_min.
- Step ratio φ = R^(1/(z − 1)) (as the speed series tool); largest loss = 1 − 1 ÷ φ.
- Speeds needed for a loss limit: z = 1 + ln R ÷ ln[1 ÷ (1 − loss)], rounded up.
- Example: 95.493–4,774.6 rpm in 18 speeds gives φ = 1.2587 (nearest R10) and up to 20.556% speed loss.
Limitations
- Constant step ratio; many gearboxes merge or overlap steps at the ends.
- Cutting speed limits only; power and torque limits at low speed need their own check.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Lay out the speeds of a lathe or drill gearbox
- Check whether a stepped drive is fine enough
- Compare the speed loss of 12 and 18 speeds
Who it is for
- Machine tool designers
- Manufacturing engineers
- Process planners
What you get
- Lowest and highest spindle speeds
- Step ratio and nearest preferred series
- Speed loss and speeds needed
Interpreting the result
- Ratios of 1.26 (R10) suit general turning; 1.12 (R20) suits production machines where speed loss costs tool life.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 37–39. Topic reference; no source tables or recommended settings are reproduced.
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