モーターの電気的欠陥頻度計算機

2× line frequency (2FL) is 100 Hz for 50 Hz systems and 120 Hz for 60 Hz systems. It is the vibration frequency generated by the alternating magnetic attraction in the motor air gap (the magnetic field reverses twice per cycle, creating a force at 2× the supply frequency).

It is always present in motor vibration at some level. Elevated 2FL can indicate:

• Stator eccentricity (uneven air gap)
• Shorted stator laminations
• Unbalanced supply voltage or phase problems
• Loose stator iron

Broken rotor bars produce characteristic patterns in both vibration and current spectra:

• Current spectrum (MCSA): Sidebands at f_line ± n × f_{pole pass} around the supply frequency peak
• Vibration: Rotor bar pass frequency with sidebands at 2× line frequency
• Amplitude modulation: The 1× vibration amplitude varies at pole pass frequency rate
• Speed variation: Slight cyclic speed fluctuation at pole pass frequency

The severity is judged by the amplitude difference (dB) between the line frequency peak and the pole-pass sidebands in the current spectrum.

Both electrical and mechanical unbalance produce vibration at or near 1× shaft speed. The key tests:

• Power-off test: Turn off power and observe. If vibration drops instantly at disconnect, it's electrical. If it coasts down with speed, it's mechanical.
• Frequency precision: Electrical unbalance peaks appear at exact line frequency or 2× line. Mechanical unbalance appears at shaft running speed.
• Sidebands: Electrical problems show sidebands at slip frequency or pole pass frequency around line frequency harmonics.

Slip frequency is the electrical frequency corresponding to the difference between synchronous and actual rotor speed:

f_slip = s × f_line

where s = (N_s − N) / N_s

Slip is essential for torque production in induction motors — without slip, no current is induced in the rotor. Typical full-load slip values:

• Large motors (>100 kW): 1–2%
• Medium motors (10–100 kW): 2–4%
• Small motors (<10 kW): 3–5%

Systematic approach to identifying fault origin:

• Step 1 — Power-off test: Instantly disappearing vibration = electrical source
• Step 2 — Frequency analysis: Peaks at exact multiples of line frequency = electrical; peaks at shaft speed multiples = mechanical
• Step 3 — Sideband analysis: Slip-related sidebands = rotor electrical fault; bearing frequencies = mechanical
• Step 4 — Current analysis: Use MCSA to identify rotor bar, eccentricity, or stator faults independently of vibration
• Step 5 — Phase analysis: Electrical 2× line is typically in-phase across all measurements; mechanical unbalance shows phase shift between positions