Contact Length in Cylindrical Grinding
Computes the geometric contact arc length between wheel and workpiece in cylindrical grinding, l_c = √(a_e × d_e), where d_e = d_s × d_w ÷ (d_s + d_w) is the equivalent diameter that replaces the two real diameters with a single one. It is the stretch over which each abrasive grain stays cutting, and it governs how much heat enters the part: at constant work speed, doubling the contact length doubles how long the same area is exposed to the grinding zone. In external grinding the two diameters add up in the denominator and the contact shortens, whereas in surface grinding the part is flat and the contact tends to √(a_e × d_s), the largest value this formula reaches. Enter the depth of cut, the wheel diameter and the workpiece diameter.
Result
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Contact Length in Cylindrical Grinding
When a part leaves the grinder with a burn mark or a surface crack, heat is the suspect, and heat depends on how long each point of the surface spends inside the cutting zone. That time is the contact arc length divided by the workpiece speed. Anyone chasing burn, comparing an external plunge with a surface grinding pass, or feeding a thermal model needs this length before anything else — and it does not follow from the wheel diameter alone, because the workpiece is curved too.
Two steps. First the equivalent diameter, d_e = d_s × d_w ÷ (d_s + d_w), which combines wheel and workpiece the way two parallel resistors combine; then l_c = √(a_e × d_e). With the default values — a_e of 0.02 mm, a 400 mm wheel and a 50 mm part — the equivalent diameter drops to 44.44 mm and the contact measures 0.9428 mm. To see the limiting behaviour, type a huge workpiece diameter such as 1e9 mm: the answer rises to 2.8284 mm, exactly the square root of 0.02 times 400, which is the flat case. External grinding always shortens the contact against surface grinding on the same wheel.
The value is purely geometric: it assumes a rigid wheel and workpiece, perfect contact and no deflection. In practice the wheel surface flattens under load, and the real length usually lands between 1.5 and 2 times the geometric one — models such as Rowe add the elastic share in quadrature with the geometric share. The implemented expression is also the external cylindrical case, with the diameters added in the denominator; in internal grinding the part wraps around the wheel, the denominator becomes the difference of the diameters and the arc gets longer, a case this page will not handle. There is no temperature, power or specific energy output here.
Frequently asked questions
How do I use this for surface grinding?
Does the page handle internal grinding?
Is the real contact length equal to the geometric one?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.