Rotary machines are used both in industry and in many areas of our daily life. Bearings are one of the most important machine elements in rotating machines. Bearings are the elements that carry radial and axial loads in machines and reduces friction between parts. There are various values ​​such as dynamic and static load ratio, fatigue load ratio, working life, which are also included in the datasets of the bearing manufacturers. However, the operational lifetimes realized in practice are earlier than the theoretical operational lifetime. This is due to the operating speed, operating load, oil condition, the way the bearing is mounted etc. These all can be caused by many factors.

Bearing Failure

Failure of bearings can cause long-term downtime of the entire machine and even the production line. Since bearing failures constitute 41% of the failure modes of electric motors and fail much earlier than their estimated working life, continuous monitoring and fault prediction of bearings becomes a great necessity.

The operation of machine components always produces vibration. Bearing failures often cause to change to change vibration to different patterns. These vibrations can be measured with sensors mounted at the right points of the machine. The measured vibration signals are digitized and processed. Through various signal analysis techniques, relevant fault signal components can be extracted and examined. In this way, bearing faults and defects can be detected and isolated.

The main thing in vibration analysis is harmonic analysis. The drive frequency and its harmonics are analyzed by the sidebands of these harmonics. However, it does not coincide with the exact multiples of the drive frequency in bearing failures. Abrasions in bearings caused by reasons such as insufficient lubrication, incorrect assembly, fluting create vibrations at specific frequencies. Since we know that bearings have 4 basic mechanical parts as outer ring, ball, cage and inner ring, each part has its own specific failure frequency. These fault frequencies are BPFO (Ball Pass Frequency Outer), BSF (Ball Spin Frequency), FTF (Fundamental Train Frequency) and BPFI (Ball Pass Frequency Inner).

Envelope Analysis

Envelope analysis, sometimes referred to as “amplitude demodulation”, is a well-known signal processing technique used in electronics and telecommunications. Envelope analysis for bearing failures uses the frictional forces produced by bearings. These forces are affected by surface and lubrication quality, and the broadband generates random vibration. When a fault occurs, the vibration becomes amplitude modulated due to periodic changes in forces. This can be caused by changes in friction, changes in pressure at bearing surfaces, or repetitive impacts due to local surface defects.

An increase in amplitude modulation from both modulating forces (geometric errors) and random stationary forces from friction changes (lubrication problems) will appear in the envelope spectrum. The frequencies generated by these forces also appear in the original spectrum but are much more difficult to extract and identify.

Band Selection

It is necessary to select a frequency range in the vibration spectrum where bearing failure occurs and remove all components outside the band. It is assumed that this selected frequency range relates only to bearing failures and not to other machine failures. The optimum range of the frequency band that combines the characteristic frequency of this bearing failure with the structural resonance of the systems can also be manually selected and put into the Inverse Fourier Transform, and it can also be automated with spectral kurtosis, EMD (Empirical Mode Decomposition) and other optimization algorithms.

Envelope Spectrum

The signal is modulated by selecting the band gap combining the characteristic frequency of the bearing failure with the structural resonance of the systems and taking the Inverse Fourier Transform. Then the modulated signal in time-wave form is enveloped by Hilbert Transform. The Envelope Spectrum is obtained by taking the Fourier Transform of the enveloped signal again. The predominant presence of vibrations at the bearing failure frequencies mentioned above in the Envelope Spectrum will indicate bearing failure.


Based on the evaluation of the amplitude modulation of random vibration and structural resonance, envelope analysis is one of the effective ways to detect and evaluate the condition of a bearing. Using Hilbert Transform instead of filtering and correction in envelope detection provides phase demodulation and frequency demodulation as well as amplitude demodulation for bearing fault diagnosis. Frequency demodulation paves the way for gearbox diagnostics and troubleshooting of problems caused by torsional vibrations.