Centerless Grinding Through-Feed Calculator
Calculate regulating wheel forward feed velocity, optimize tilt angles and RPM, set work-rest blade heights to eliminate tri-lobing, and forecast hourly part output.
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Centerless Through-Feed Cylindrical Grinding Kinematics
Centerless grinding supports cylindrical workpieces without mechanical chucks or center holes. The workpiece floats between a high-speed vitrified grinding wheel, a rubber-bonded regulating wheel, and an angled work-rest blade.
1. Forward Through-Feed Velocity Formula
The regulating wheel rotates slowly and is tilted at a small inclination angle (\alpha) (typically 1° to 5°) relative to the horizontal plane. This tilt imparts both rotation and an axial forward thrust vector to the workpiece:
$$V_f = \pi \cdot D_r \cdot N_r \cdot \sin(\alpha) \cdot \eta$$
Where (D_r) is regulating wheel diameter, (N_r) is regulating wheel RPM, (\alpha) is the tilt angle, and (\eta) is the frictional driving efficiency (~0.95).
2. Work-Rest Blade Height & Tri-Lobing Prevention
If the workpiece center sits exactly on the line connecting the grinding wheel and regulating wheel centers, any high spot will push the opposite side deeper into the grinding wheel, producing a three-lobed constant-diameter polygon (tri-lobing) that appears round on a 2-point micrometer but fails roundness on a roundness gage.
To ensure true roundness, the workpiece center must be elevated above the wheel centerlines by roughly one-half the workpiece diameter ((h \approx D_w / 2), not exceeding 12 to 15 mm to prevent chatter).
3. Workpiece Rotational Speed
The regulating wheel governs workpiece rotation via frictional traction:
$$N_w = N_r \cdot \frac{D_r}{D_w} \cdot \cos(\alpha)$$
Frequently Asked Questions
What causes workpiece chatter in centerless grinding?
Setting the workpiece too high above the centerlines causes instability and chatter vibrations. Setting it too low causes out-of-roundness. Lower the work-rest blade height slightly or increase blade bevel angle to 30°-40° to stabilize the part.
Why must the regulating wheel be dressed with a hyperbolic profile?
Because the regulating wheel is tilted at an angle α, a cylindrical wheel would only touch the cylindrical workpiece at a single point. Dressing the wheel at the tilt angle generates a hyperboloid of revolution, providing a full line of contact across the entire wheel width.