Vibration Analysis for Mill Maintenance

Introduction & Context

ISO 10816-3 overall velocity is the de-facto screening tool used by maintenance crews to decide whether a large, rigidly-mounted machine (hammer-mills, fans, compressors, etc.) is still fit for service. A single-point velocity spectrum, integrated to v_rms, is compared with an empirically-derived limit that depends on machine class and rotational speed. The method is purely empirical—no structural or mass-flow models are required—so it is robust enough for daily work-order decisions.

Methodology & Formulas

1. Verify operating speed lies within ±5 % of the nominal value:
\[ (1 - \text{RPM\_TOLERANCE}) \cdot \text{nominal\_rpm} \leq \text{measured\_rpm} \leq (1 + \text{RPM\_TOLERANCE}) \cdot \text{nominal\_rpm} \]
2. Collect raw acceleration signal band-limited 10 Hz–1 kHz and compute velocity v(t) via integration. The overall vibration severity is:
\[ v_{\text{rms}} = \sqrt{\frac{1}{T} \int_0^T v(t)^2 \: dt} \quad [\text{mm/s}] \]
3. Establish zone thresholds based on the applicable ISO 10816-3 limit for the machine's class and speed:

Zone	Multiplier applied to ISO limit	Algebraic form
GOOD	0.7	\text{good\_threshold} = \text{GOOD\_MUL} \cdot \text{ISO\_LIMIT}
CAUTION	1.0	\text{caution\_threshold} = \text{CAUTION\_MUL} \cdot \text{ISO\_LIMIT}

4. Determine status:
\[ \begin{cases} \text{GOOD} & \text{if } v_{\text{rms}} \leq \text{good\_threshold}\\[4pt] \text{CAUTION} & \text{if } \text{good\_threshold} < v_{\text{rms}} \leq \text{caution\_threshold}\\[4pt] \text{DANGER} & \text{if } v_{\text{rms}} > \text{caution\_threshold} \end{cases} \]
5. Range checks for correlation validity (typical bounds):

Parameter	Lower bound	Upper bound
RPM	\text{MIN\_RPM} (=120)	\text{MAX\_RPM} (=15000)
Power (kW)	\text{MIN\_POWER\_KW} (=15)	\text{MAX\_POWER\_KW} (=300)
vrms (mm/s)	\text{MIN\_V\_RMS} (=0.4)	\text{MAX\_V\_RMS} (=45)