How to Calculate Critical Speed for Optimal Grinding Mill Performance?

Czas: 4 October 2025

Calculating the critical speed of a grinding mill is essential for determining its optimal operational performance. Critical speed refers to the rotational speed at which the mill operates such that the centrifugal force causes the grinding media (balls or rods) to remain pinned to the wall, preventing any motion relative to the mill shell. Operating a mill slightly below the critical speed allows grinding media to cascade, promoting efficient grinding. Here’s how to calculate critical speed:

Formula for Mill Critical Speed:

The critical speed ((N_c)) is calculated using the following formula:

\[N_c = \frac{76.6}{\sqrt{D}}\]

Gdzie:

• (N_c) = Critical speed in revolutions per minute (rpm)
• (D) = Internal diameter of the mill in meters (measured between liners)

Steps to Calculate Critical Speed:

1. Measure Internal Mill Diameter:

   • Determine the internal diameter ((D)) of the grinding mill. Ensure the measurement is taken from liner to liner in meters.

2. Plug the Value Into the Formula:

   • Substitute the mill diameter (D) into the formula.

3. Perform the Calculation:

   • Use basic arithmetic or a calculator to solve for (N_c). The result represents the critical speed in rpm.

4. Adjust Operating Speed:

   • Most mills operate between 65% and 80% of their critical speed for optimal grinding behavior. Multiply the critical speed by the desired operational percentage. For example, if targeting 75%:\[N_{\text{operating}} = 0.75 \times N_c\]

Example Calculation:

Assume a mill has an internal diameter of 4 meters. The critical speed would be:

\[N_c = \frac{76.6}{\sqrt{4}} = \frac{76.6}{2} = 38.3 \, \text{rpm}\]

If you want to operate at 75% of the critical speed:

\[N_{\text{operating}} = 0.75 \times 38.3 = 28.725 \, \text{rpm}\]

Important Considerations:

1. Grinding Media:

   • The choice and size of grinding media (balls or rods) also impact grinding efficiency and should complement the mill speed.

2. Ore Type and Milling Process:

   • Adjust speed depending on ore characteristics, mill design, and desired particle size outcomes.

3. Power and Torque Constraints:

   • Ensure the mill motor can sustain the calculated operating speed without overloading.

By understanding and applying the principles of critical speed, you can maximize the efficiency and performance of a grinding mill.

Contact Us

Shanghai Zenith Mineral Co., Ltd. is a leading manufacturer of crushing and grinding equipment in China. With more than 30 years of experience in the mining machinery industry, Zenith has built a strong reputation for delivering high-quality crushers, mills, sand-making machines, and mineral processing equipment to customers around the world.

Headquartered in Shanghai, China, Zenith integrates research, production, sales, and service, providing complete solutions for aggregates, mining, and mineral grinding industries. Its equipment is widely used in metallurgy, construction, chemical engineering, and environmental protection.

Committed to innovation and customer satisfaction, Shanghai Zenith continues to advance in intelligent manufacturing and green production, offering reliable equipment and comprehensive after-sales service to help clients achieve efficient and sustainable operations.

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