Reference ID: MET-0AF8 | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
The Lockout‑Tagout (LOTO) calculation for a grinding mill provides the quantitative basis for selecting mechanical restraints (brakes, chocks, or lockout devices) and electrical isolation equipment that will safely secure the mill during maintenance. By evaluating the stored rotational energy, the required holding torque, and the electrical in‑rush characteristics of the drive motor, engineers can verify that the chosen hardware meets industry‑required safety factors and that the power distribution system can tolerate the transient conditions when the motor is de‑energized.
This analysis is typically applied in process‑plant environments where large rotating equipment such as ball mills, SAG mills, or roller mills must be isolated before personnel access the interior for inspection, repair, or component replacement.
Methodology & Formulas
The calculation proceeds through a series of physics‑based steps, each directly derived from the mill’s physical parameters and operating conditions.
Moment of Inertia – Approximating the mill shell as a solid cylinder:
\[
I = \tfrac{1}{2}\,m\,r^{2}
\]
where \(m\) is the shell mass and \(r\) is the shell radius.
Angular Speed – Converting the rotational speed from revolutions per minute to radians per second:
\[
\omega = \frac{2\pi N}{60}
\]
with \(N\) representing the speed in rpm.
Stored Rotational Kinetic Energy – Energy stored in the rotating mass:
\[
E_{k} = \tfrac{1}{2}\,I\,\omega^{2}
\]
Required Holding Torque – Torque needed to decelerate the mill at the specified angular deceleration \(\alpha\):
\[
T_{\text{req}} = I\,\alpha
\]
Safety Factor – Ratio of the selected hardware’s rated torque \(T_{\text{rated}}\) to the required torque:
\[
\text{SF}_{\text{ach}} = \frac{T_{\text{rated}}}{T_{\text{req}}}
\]
Electrical In‑rush Power – Estimated from the motor’s rated power \(P_{\text{motor}}\) and an in‑rush multiplier \(k_{\text{inrush}}\):
\[
P_{\text{inrush}} = k_{\text{inrush}} \, P_{\text{motor}}
\]
In‑rush Current (Three‑Phase) – Derived from the three‑phase power relationship:
\[
I_{\text{inrush}} = \frac{P_{\text{inrush}}\times 10^{3}}{\sqrt{3}\,V_{\text{line}}}
\]
where \(V_{\text{line}}\) is the line‑to‑line voltage.
Power Verification – Re‑computing power from voltage and current to confirm consistency:
\[
P_{\text{check}} = \frac{\sqrt{3}\,V_{\text{line}}\,I_{\text{inrush}}}{10^{3}}
\]
Validity Checks & Design Criteria
Criterion
Condition
Typical Limit / Target
Action
Rotational Speed
\(N\)
\(\le 30\ \text{rpm}\) for low‑speed mills
Issue warning if exceeded
Angular Deceleration
\(\alpha\)
0 < \(\alpha\) ≤ 0.5 rad s\(^{-2}\)
Warn if non‑positive or above typical brake capability
Target Safety Factor
\(\text{SF}_{\text{target}}\)
\(\ge 2.0\)
Warn if below industry minimum
Achieved Safety Factor
\(\text{SF}_{\text{ach}}\)
\(\ge \text{SF}_{\text{target}}\)
Warn if hardware does not meet requirement
Torque Rating
\(T_{\text{rated}}\)
\(\ge T_{\text{req}}\)
Warn if rated torque is insufficient
In‑rush Power
\(P_{\text{inrush}}\)
\(< 200\ \text{kW}\) (example threshold)
Note if high; verify isolation device ratings
Result Summary (Symbolic)
The following symbolic results are obtained from the above calculations:
Identify all energy sources (electrical, hydraulic, pneumatic, mechanical, thermal).
Notify all affected personnel that a lockout is about to occur.
Isolate each energy source using the appropriate isolation device (breaker, valve, disconnect).
Apply lockout devices and attach a tag that includes the employee’s name, date, and reason for lockout.
Verify that the equipment is de‑energized by attempting to start it or using a calibrated test instrument.
Secure the lockout devices so that only the authorized employee can remove them.
Locate the main disconnect for the shared panel and lock it out first.
Identify downstream isolation points for each individual source (e.g., hydraulic pump, motor starter).
Apply separate lockout devices to each downstream point, tagging them with the same work order reference.
Perform a sequential verification: test each source after its lockout to confirm isolation.
Document the lockout sequence in the mill’s LOTO log for audit purposes.
Immediately stop the lockout process and notify the shift supervisor.
Obtain a replacement lockout device that meets the mill’s approved specifications.
Re‑apply the lockout using the new device, ensuring the tag includes the original work order number.
Record the incident in the LOTO deviation log, noting the missing or damaged device and corrective action taken.
Conduct a brief toolbox talk to reinforce the importance of maintaining a complete lockout inventory.
No. The lockout tag must remain in place until the equipment is inspected, all tools are removed, and the area is declared safe.
Only the employee who applied the lock may remove it, and only after a formal de‑energization verification.
Complete a **"Lockout Removal Checklist"** that includes:
Verification that all work is finished.
Confirmation that all personnel are clear of the equipment.
Re‑inspection of the equipment for any residual energy.
Document the removal in the mill’s LOTO log, signing off with the date and time.
Worked Example – Sizing the Lockout Brakes for a Ball-Mill During LOTO
A process engineer is preparing the Lockout-Tagout procedure for a 2.5 t ball-mill that must be held stationary while the liner plates are replaced. The mill is normally driven by a 75 kW, 400 V motor that reaches 12 rpm at full speed. To prevent any possibility of rotation while personnel are inside, a spring-applied brake is to be installed on the mill shell. The brake must be able to hold the loaded mill against a worst-case torque caused by an unbalanced load, with a minimum safety factor of 2.0. The following calculation confirms the brake size and checks the motor inrush current that will be locked out.
Knowns
Mass of mill charge, \(m = 2500\) kg
Effective radius, \(r = 1.000\) m
Rotational speed, \(N = 12\) rpm
Angular acceleration during unbalanced start-up, \(\alpha = 0.100\) rad/s²
Compute rotational kinetic energy stored in the mill:
\[
E_k = \frac{1}{2} I \omega^2 = \frac{1}{2} \times 1250 \times (1.257)^2 = 986.960 \text{ J}
\]
Determine the torque required to hold the mill against the unbalanced load:
\[
T_{required} = I \alpha = 1250 \times 0.100 = 125 \text{ Nm}
\]
Check achieved safety factor against the motor’s rated torque:
\[
SF_{achieved} = \frac{T_{rated}}{T_{required}} = \frac{250}{125} = 2.0
\]
The brake must therefore supply at least 125 Nm; the existing motor torque capability meets the 2× safety requirement.
Verify the electrical inrush that will be locked out:
\[
P_{inrush} = k \times P_{motor} = 6 \times 75 = 450 \text{ kW}
\]
\[
I_{inrush} = \frac{P_{inrush} \times 1000}{\sqrt{3} \times V_{line}} = \frac{450000}{\sqrt{3} \times 400} = 649.519 \text{ A}
\]
Final Answer
The brake must provide a minimum holding torque of 125 Nm. With the motor’s rated torque of 250 Nm, the achieved safety factor is exactly 2.0, satisfying the LOTO requirement. During lockout, the motor supply will be isolated at an inrush level of 450 kW (650 A), confirming that the selected disconnect and LOTO devices are adequately rated.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise."— Charles de Gaulle
