Decoding Machinery Vibrations: Excitation Frequencies and Their Role

Decoding the Hidden Symphony: Understanding Excitation Frequencies in Vehicles & Machines

Beneath the roar of an engine, the whine of a transmission, or the hum of an industrial pump lies a complex world of vibrations. These vibrations aren't random noise; they are the signatures of forces acting upon the machinery – its excitation frequencies.

Understanding these frequencies is crucial for engineers, technicians, and analysts involved in design, diagnostics, and predictive maintenance. They are the key to;

• Unlocking performance
• Identifying faults, and
• Ensuring longevity.

In this post, we'll look at the following:

1. What are Excitation Frequencies
2. Key Examples of Excitation Frequencies
   1. Engine Firing Frequency (Combustion Frequency)
   2. Bearing Frequencies
   3. Gear Mesh Frequency (GMF)
3. The Bigger Picture: Vibration Analysis
4. Conclusion

What are Excitation Frequencies?

An excitation frequency is the specific rate (measured in Hertz - Hz, or cycles per second) at which a periodic force is applied to a mechanical system, causing it to vibrate. These forces originate from the fundamental physics of the machine's operation:

1. Inertia Forces: Masses accelerating and decelerating (e.g., pistons in an engine).
2. Combustion Forces: Explosions within cylinders.
3. Impact Forces: Gear teeth meshing, bearings rolling over defects.
4. Fluid Forces: Pressure pulsations in pumps, fans, or hydraulic systems.
5. Electromagnetic Forces: Unbalance in motors or generators.

Every rotating or reciprocating component generates characteristic excitation frequencies based on its geometry and operating speed. When these frequencies coincide with a system's natural frequencies (its inherent resonant frequencies), vibrations can amplify dramatically, leading to excessive noise, accelerated wear, fatigue failure, or even catastrophic breakdown.

Key Examples of Excitation Frequencies:

Let's explore three critical types found in almost all rotating machinery:

I. Engine Firing Frequency (Combustion Frequency):

• Source: The fundamental excitation comes from the combustion events within each cylinder.
• Calculation: The firing frequency depends on the engine speed (RPM), the number of cylinders, and the engine cycle (2-stroke or 4-stroke).
  • Firing Frequency (Hz) = (Engine RPM × Number of Cylinders) / (120 × Number of Strokes per Cycle)
  • *For a 4-stroke engine:* Firing Freq (Hz) = (RPM × N_cyl) / 120
  • *For a 2-stroke engine:* Firing Freq (Hz) = (RPM × N_cyl) / 60
• Harmonics: Significant vibration also occurs at multiples (harmonics) of this fundamental firing frequency (2x, 3x, etc.), especially in diesel engines with sharp pressure rises.
• Examples:
  • 4-Cylinder, 4-Stroke Car Engine @ 3000 RPM: Firing Freq = (3000 * 4) / 120 = 100 Hz. Harmonics at 200 Hz, 300 Hz, etc.
  • 6-Cylinder, 4-Stroke Truck Engine @ 1800 RPM: Firing Freq = (1800 * 6) / 120 = 90 Hz
  • V-Twin Motorcycle Engine (Harley Davidson), 4-Stroke @ 2500 RPM: Firing Freq = (2500 * 2) / 120 ≈ 41.7 Hz. (Note: Firing order in a 45° V-twin creates an uneven firing pulse, adding complexity).

Fig 1: Inline 6 Cylinder Engine

• Diagnostic Importance: Misfires, injector problems, or combustion instability will directly alter the amplitude and pattern of the firing frequency and its harmonics.

II. Bearing Frequencies:

• Source: As rolling elements (balls or rollers) travel over raceway defects (inner race, outer race, cage, or rolling element itself), they generate distinct impact forces. Each defect location creates a unique frequency.
  
• Calculation: Bearing frequencies depend on the bearing geometry (Pitch Diameter P_d, Ball/Roller Diameter B_d, Number of Elements N_b, Contact Angle α) and rotational speed (Shaft RPM - f_r). Manufacturers provide formulas or databases. Key frequencies are:
  • Ball Pass Frequency Outer Race (BPFO): Rate balls/rollers pass a defect on the outer race. (f_bpfo ≈ (N_b / 2) * f_r * (1 - (B_d / P_d) * cosα))
  • Ball Pass Frequency Inner Race (BPFI): Rate balls/rollers pass a defect on the inner race. (f_bpfi ≈ (N_b / 2) * f_r * (1 + (B_d / P_d) * cosα))
  • Ball Spin Frequency (BSF): Rotational rate of a ball/roller itself. (f_bsf ≈ (P_d / (2 * B_d)) * f_r * (1 - (B_d² / P_d²) * cos²α))
  • Fundamental Train Frequency (FTF - Cage Frequency): Rotational rate of the cage/retainer. (f_ftf ≈ (f_r / 2) * (1 - (B_d / P_d) * cosα))
  • (N_b=Number of Balls/Rollers, B_d=Ball/Roller Diameter, P_d=Pitch Diameter, α=Contact Angle)
• Examples (Approximate - Always use exact bearing specs):
  • Common Deep Groove Ball Bearing (6205): N_b=8, P_d≈39mm, B_d≈7.9mm, α=0°. @ 1800 RPM (f_r=30 Hz):
    • BPFO ≈ 3.05 x f_r = 91.5 Hz
    • BPFI ≈ 4.95 x f_r = 148.5 Hz
    • BSF ≈ 1.99 x f_r = 59.7 Hz
    • FTF ≈ 0.38 x f_r = 11.4 Hz
• Diagnostic Importance: The presence and amplitude of these specific frequencies (and their harmonics/sidebands) directly indicate bearing fault location and severity. A high BPFO points to an outer race defect, BPFI to an inner race defect, etc. Sidebands spaced at shaft speed (f_r) around BPFI/BPFO are classic indicators.

III. Gear Mesh Frequency (GMF):

• Source: The fundamental excitation comes from the periodic impact of gear teeth engaging and disengaging as the gears rotate.
  
• Calculation: Multiply the rotational speed (Hz) of a gear by its number of teeth.
  • Gear Mesh Frequency (Hz) = Gear Shaft Speed (Hz) × Number of Teeth on the Gear
  • Since both gears contribute, GMF = f_pinion * N_pinion = f_gear * N_gear
• Harmonics & Sidebands: Significant vibration occurs at multiples of GMF (2xGMF, 3xGMF). Crucially, modulation occurs due to shaft speeds, creating sidebands spaced at the rotational frequencies (f_pinion, f_gear) around the GMF and its harmonics. E.g., GMF ± f_pinion, GMF ± f_gear, 2xGMF ± f_pinion, etc.
• Examples:
  • Car Transmission: Pinion gear (input): 20 teeth @ 3000 RPM (f_p=50 Hz). Ring gear (output): 80 teeth.
  • GMF = 50 Hz * 20 = 1000 Hz (also = (3000/60 * 80/4) * 80
  • f_ring = (20/80)*50 Hz = 12.5 Hz; GMF = 50*20 = 1000 Hz or 12.5*80=1000 Hz). Sidebands at 1000 ± 50 Hz, 1000 ± 12.5 Hz, etc.
  • Industrial Gearbox: Input Shaft: 1800 RPM (30 Hz), 25 teeth. Output Shaft: 450 RPM (7.5 Hz), 100 teeth.
    • GMF = 30 Hz * 25 = 750 Hz (or 7.5 Hz * 100 = 750 Hz). Sidebands at 750 ± 30 Hz, 750 ± 7.5 Hz.
  • Wind Turbine Gearbox (High Speed Stage): Input (Planet Carrier) ~20 RPM (~0.33 Hz), Sun Gear: 30 teeth. GMF = 0.33 Hz * 30 = ~10 Hz.
• Diagnostic Importance: The GMF amplitude indicates overall meshing condition (wear, load). Increased sidebands indicate problems like eccentricity, misalignment, gear tooth damage (e.g., a chipped tooth), or shaft unbalance/bending modulating the mesh pattern.

The Bigger Picture: Vibration Analysis

Understanding these excitation frequencies is the foundation of Vibration Analysis (VA), a core predictive maintenance technique:

1. Data Acquisition: Sensors (accelerometers) measure vibration on machine housings/bearings.
2. Signal Processing: Fast Fourier Transform (FFT) converts the time-domain vibration signal into a frequency spectrum.
3. Identification: Analysts look for peaks in the spectrum corresponding to known excitation frequencies (firing, bearing faults, GMF).
4. Diagnosis: The amplitude, presence of harmonics/sidebands, and comparison to baselines reveal the machine's health:
   • Is the firing frequency abnormally high? (could signify combustion issue)
   • Are bearing fault frequencies (BPFI, BPFO) present with sidebands? (Bearing defect)
   • Has GMF amplitude increased with strong sidebands? (Gear damage/misalignment)
   • Is an excitation frequency coinciding with a structural natural frequency? (Resonance - a major concern!)

Conclusion

Excitation frequencies are the fundamental "voices" in the mechanical symphony of vehicles and machines. The rhythmic pulse of engine combustion, the characteristic tones of rolling bearings, and the dominant whine of meshing gears each tell a story.

By mastering the calculation and identification of these frequencies – like the firing frequency of an engine, the precise fault frequencies of a bearing, or the mesh frequency and sidebands of gears – engineers and analysts gain a powerful diagnostic lens.

This understanding enables proactive maintenance, prevents costly failures, optimizes performance, and ultimately ensures the smooth, reliable, and efficient operation of the mechanical world around us. Listening to these frequencies isn't just about noise; it's about understanding the very heartbeat of machinery.