BIZOMAT MAKEOS · Manufacturing
Grinding Equivalent Diameter and G-Ratio
What is the equivalent wheel diameter for this cylindrical grind, and what G-ratio was achieved?
Equivalent wheel diameter for external, internal or surface grinding, the geometric contact length for a depth of cut, and the grinding ratio (G-ratio) from metal removed and wheel worn.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Grinding | choice | Grinding configuration. |
| Wheel diameter | mm | Current wheel diameter. |
| Work diameter | mm | Work diameter (ignored for surface grinding). |
| Depth of cut | mm | Depth of cut per pass. |
| Work material removed (0 = skip G-ratio) | mm³ | Volume of work material removed during the test. |
| Wheel volume worn | mm³ | Volume of wheel worn in the same period (from wheel diameter loss). |
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: Grinding
- What it is
- How the wheel meets the work: on the outside of a cylinder, inside a bore, or on a flat surface. It sets how the equivalent wheel diameter is worked out.
- Units and format
- Choose one of 3 options from the list: External cylindrical; Internal cylindrical; Surface (flat).
- Example
- The form opens with “External cylindrical” selected as a worked example. Choose the option that matches your case.
What this means: Wheel diameter
- What it is
- The present outside diameter of the grinding wheel, measured or read from dressing records.
- 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.
- Get it right
- Wheels shrink with dressing; use the current diameter, not the new-wheel size.
What this means: Work diameter
- What it is
- The diameter of the workpiece surface being ground: the outside diameter for external work or the bore for internal work. Ignored for surface grinding.
- 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 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For internal grinding the wheel must be smaller than the bore.
What this means: Depth of cut
- What it is
- The depth of material the wheel removes in one pass, measured radially (into the surface), as set on the infeed.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Contact length rises with the square root of the depth of cut.
- Get it right
- For cylindrical grinding this is the radial infeed per pass, which is half the change in diameter.
What this means: Work material removed (0 = skip G-ratio)
- What it is
- The volume of workpiece material removed during the wear test or production run used for the G-ratio. Zero skips the G-ratio.
- Units and format
- Enter a number in mm³: mm³. The form accepts 0 mm³ or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50000 mm³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The G-ratio rises in direct proportion to the volume removed.
- Get it right
- Work it out from stock removed and the part dimensions, in cubic millimetres.
What this means: Wheel volume worn
- What it is
- The volume of abrasive worn from the wheel during the same run, worked out from the measured loss of wheel diameter and the wheel width. Zero skips the G-ratio.
- Units and format
- Enter a number in mm³: mm³. The form accepts 0 mm³ or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 mm³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The G-ratio is inversely proportional to wheel wear.
- Get it right
- Exclude wheel removed by dressing unless your G-ratio definition includes it.
Method and formulas
- External: De = ds dw ÷ (dw + ds); internal: De = ds dw ÷ (dw − ds); surface: De = ds.
- Contact length lg = √(ae De).
- G-ratio = work volume removed ÷ wheel volume worn.
- Example: a 400 mm wheel on 50 mm work has De = 44.444 mm and a contact length of 0.94281 mm.
Limitations
- Geometric contact length; real contact is longer due to wheel and work deflection.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Compare grinding conditions between external and internal work
- Track wheel wear performance
- Estimate contact length for burn risk
Who it is for
- Grinding machinists
- Manufacturing engineers
What you get
- Equivalent wheel diameter
- Geometric contact length
- G-ratio
Interpreting the result
- Larger equivalent diameters (internal grinding) mean longer contact, more heat and more burn risk.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1199–1268. Topic reference; no source tables or recommended settings are reproduced.
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Open the Grinding Equivalent Diameter and G-Ratio calculator