ToolnozaInputs and measurement basis
Enter effective inside diameter after liners in meters and representative ball diameter in millimeters. Choose an operating percentage to calculate RPM; enter measured RPM to compare the actual speed with the theoretical limit.
Effective inside diameter (m); Ball diameter (mm); Target critical-speed fraction (%); Measured operating speed (RPM).
Formula and calculation
Nc (RPM) = (60/2π) × √[2g/(D − d)]; g = 9.80665 m/s²; d (m) = d (mm)/1000; Ntarget = Nc × fraction/100.
Estimate theoretical mill critical speed and operating RPM from internal diameter, grinding-ball size and selected critical-speed percentage.
Worked example
D = 4 m; d = 50 mm → Nc = 21.28 RPM; 75% → 15.96 RPM.
How to interpret the result
Critical speed is the ideal speed at which a ball at the shell can remain held against it by centrifugal acceleration. Grinding normally requires relative charge movement, so critical speed is a reference rather than a target.
A liner replacement changes effective diameter. Use internal dimensions rather than the outside shell diameter, and compare using the same ball-size convention.
Assumptions and limits
Ideal single-ball gravity/centrifugal balance. D must exceed ball diameter. Charge shape, lifters, slurry and wear are excluded. The selected percentage is an input, not an operating recommendation.
Frequently asked questions
Can I use the outside mill diameter? No. Use effective inside diameter at the liner surface. Outside shell dimensions overstate the available radius.