Grinding Cutting Data Calculator
Determine cutting speed v_c, speed ratio q, specific material removal rate Q'w and equivalent chip thickness h_eq for external cylindrical grinding or surface (peripheral) grinding - either from the wheel speed n_s or directly from v_c, with a traffic-light guideline rating for grinding-burn and roughness risk.
Calculation
Traffic-light rating is a rough guideline: wheel specification, dressing condition, coolant supply and material-specific grindability are not accounted for here.
Cutting data
- Cutting speed v_c
- 39.794 m/s
- Wheel speed n_s
- 1,900 1/min
- Speed ratio q
- 119.4
Material removal rate and contact length
- Specific material removal rate Q'w
- 6.667 mm³/(mm·s)
- Equivalent chip thickness h_eq
- 0.168 µm
- Contact length l_k
- 0.943 mm
Q'w regime: Transition finishing/roughing
Sketch: grinding wheel engaging the workpiece (schematic)
Sketch is schematic, not to scale - the depth of cut a_e is shown greatly enlarged.
Your inputs stay in your browser - all calculations run locally, nothing is sent to a server.
Formulas and fundamentals
Cutting speed and wheel speed
As with turning or milling, the cutting speed at the grinding wheel follows from its diameter and speed:
The calculator accepts either input: given the wheel speed n_s, v_c follows; given v_c directly (e.g. a manufacturer recommendation for the wheel), the calculator back-calculates the corresponding speed n_s = 60000·v_c/(pi·d_s).
Speed ratio q
The speed ratio relates the wheel's cutting speed to the workpiece speed (surface speed for external cylindrical grinding, or table speed for surface grinding):
Typical values for external cylindrical grinding are q = 60...125; for surface grinding, with its usually lower table speed, q is often considerably higher. Too low a q (workpiece too fast relative to the wheel) produces a coarser surface and higher wheel wear; a very high q increases the thermal load in the contact zone.
Specific material removal rate Q'w
The specific material removal rate normalizes the removed volume per unit time to the grinding width, making it comparable independent of wheel width - the key parameter for productivity and thermal load in grinding:
With the depth of cut a_e in mm and the workpiece speed v_w in m/min, the unit conversion (m/min -> mm/s) gives Q'w in mm³/(mm·s). Finishing operations typically stay up to about Q'w = 4 mm³/(mm·s); roughing operations go well beyond that, up to several tens - depending on material, wheel specification and coolant.
Equivalent chip thickness h_eq
The equivalent chip thickness combines material removal rate and cutting speed into a single indicator for the average grain load:
h_eq correlates with achievable roughness and grinding-burn risk: typical values range from 0.1 µm (fine finishing) to about 10 µm (roughing); above that, the risk of thermal damage to the surface layer rises sharply - see also the surface roughness calculator.
Contact length
The geometric contact length between wheel and workpiece follows approximately from the depth of cut and the effective diameter:
For surface grinding, or when the workpiece diameter is not given, the wheel diameter d_s is used directly. Contact length feeds into more advanced thermal models (e.g. contact time, peak temperature) that this calculator does not cover.
Conventional grinding versus high-speed grinding (HSG)
Conventional grinding operates at v_c of roughly 25 to 45 m/s. High speed grinding (HSG) uses substantially higher cutting speeds of roughly 60 to 140 m/s (and beyond with CBN wheels), which - at the same Q'w - yields a lower equivalent chip thickness and therefore better surfaces and lower grinding-burn risk, provided the machine, spindle and wheel bond are designed for it.
Worked example
Reference example, external cylindrical grinding: wheel diameter d_s = 400 mm, wheel speed n_s = 1900 rpm, workpiece speed v_w = 20 m/min, depth of cut a_e = 0.02 mm, workpiece diameter d_w = 50 mm. The cutting speed is v_c = pi·400·1900/60000 = 39.79 m/s - within the conventional guideline range (25...45 m/s), so the rating is green.
The speed ratio is q = 39.79/(20/60) = 119.4 - within the guideline range (40...150) and close to the typical external-cylindrical range of 60...125. The specific material removal rate is Q'w = 0.02·20·1000/60 = 6.67 mm³/(mm·s) (transition zone between finishing and roughing), and the equivalent chip thickness h_eq = 6.67/39.79 = 0.168 µm is well below the 10 µm guideline - unremarkable regarding roughness and grinding-burn risk.
With workpiece diameter d_w = 50 mm, the equivalent diameter is d_eq = 400·50/450 = 44.4 mm, giving a contact length l_k = sqrt(0.02·44.4) = 0.94 mm. If v_c = 40 m/s were given directly instead of the speed, the back-calculated speed would be n_s = 60000·40/(pi·400) ≈ 1910 rpm - both input paths lead to the same result.
If the depth of cut is increased to a_e = 0.1 mm and the workpiece speed to v_w = 40 m/min, Q'w rises to 66.7 mm³/(mm·s) (clearly in the roughing range) and h_eq to 1.68 µm - still below the warning threshold, but with a noticeably higher thermal load. Increasing a_e or v_w further without adjusting v_c or coolant supply triggers a warning once h_eq exceeds 10 µm, flagging elevated grinding-burn and roughness risk.
Frequently asked questions
What cutting speed is used for grinding?
Conventional grinding typically operates at v_c = 25...45 m/s. High speed grinding (HSG) uses 60...140 m/s, and even more with CBN wheels, but requires a machine designed for it (spindle power, balancing, guarding) and a suitable wheel bond. The actual maximum permissible speed of a grinding wheel must always be taken from the manufacturer's rating printed on the wheel.
What is the specific material removal rate Q'w and what is it used for?
Q'w = a_e·v_w normalizes the removed material volume per unit time to the grinding width (unit mm³/(mm·s)), making it comparable independent of wheel or workpiece width. It is the key parameter for comparing processes of different scale in terms of productivity and thermal load, and for distinguishing roughing from finishing operations.
What does the equivalent chip thickness h_eq mean for roughness and grinding burn?
h_eq = Q'w/v_c approximates the average chip thickness per grain engagement. The larger h_eq, the coarser the achievable surface and the higher the thermal load in the contact zone - above a material-dependent threshold (guideline around 10 µm), the risk of grinding burn (tempering zones, tensile residual stress, cracking) rises sharply.
What does the speed ratio q indicate?
q = v_c/v_w shows by what factor the grinding wheel moves faster than the workpiece. Too low a q leads to a coarser surface, uneven grain wear and higher load on the workpiece per engagement; a very high q increases frictional heat in the contact zone. Typical values for external cylindrical grinding are 60...125, and often higher for surface grinding.
How do you avoid grinding burn?
Grinding burn results from excessive thermal load in the contact zone - usually from too large a depth of cut a_e or workpiece speed v_w at a given cutting speed (high h_eq). Countermeasures: reduce Q'w or h_eq (smaller depth of cut, more dressing passes), ensure sufficient and well-targeted coolant supply, use a sharper/more open wheel bond instead of a loaded wheel, and if needed switch to high-speed grinding with a higher v_c. When in doubt, verify with an etch test (nital etching) or Barkhausen noise inspection.
What distinguishes conventional grinding from high-speed grinding (HSG)?
Conventional grinding uses v_c = 25...45 m/s with standard grinding wheels. High speed grinding (HSG) operates at v_c = 60...140 m/s or more, usually with high-strength bonds (e.g. CBN, vitrified) and correspondingly designed machine technology. At the same Q'w, h_eq decreases as v_c increases, so HSG enables a substantially higher material removal rate (higher productivity) at equal or better surface quality.
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