The core mechanism of mechanical loosening is nonlinearity and impact. Loosening introduces a gap in the machine, which changes the support stiffness of the system from linear to highly nonlinear. In the linear region, the rotor moves freely within the gap and the stiffness decreases; In the nonlinear region, when the components come into contact with the constraint surface, the stiffness instantly becomes very high. This "soft hard" switching or "collision" effect is the root cause of all complex spectral features.

The typical frequency spectrum is 1:1 times the rotational speed frequency, while the harmonics are very small

Loose early faults. Although there is a gap, the rotor has not (or rarely) had strong periodic collisions with the constraint surface during operation. At this time, the nonlinear impact effect of the system is not yet obvious, mainly manifested as changes in static characteristics (stiffness reduction). The static position of the rotor's axis will shift, causing the original mass imbalance force to be significantly amplified in the direction of stiffness reduction, manifested as a sharp increase in 1 × speed frequency vibration. The spectrum is mainly dominated by the fundamental frequency, which often occurs when the anchor bolts are slightly loose.

Typical spectrum: 2:1 times the speed frequency and harmonics.

A typical loosening fault. The gap is already large, and the components undergo clear and stable periodic collisions with the constraint surface during the rotation of the rotor. At this point, nonlinear shock effects dominate the vibration characteristics. The amplitude of the spectrum decreases gradually from 1 times the frequency conversion, and this type of spectrum often occurs in the gap fitting area due to the coupling between gaps and imbalances; The spectrum arrangement is uneven, mostly caused by the movement of rotating components.

Typical spectrum: 3:1 times the speed frequency and odd harmonics.

Many sources cite the main characteristic of looseness, but it is rare in reality, and this is an idealized theoretical model. Assuming the rotor is in a pure radial gap, only one symmetrical unilateral impact occurs per rotation (for example, only one impact occurs at the bottom of the gap). The time-domain waveform of this "half wave shock" is mathematically half wave symmetric, and after its Fourier series expansion, the coefficients of even cosine terms are zero, leaving mainly the fundamental frequency (1 ×) and odd harmonics (3 ×, 5 ×...).

In reality, due to factors such as misalignment, gravity, or bidirectional gaps, the impact becomes asymmetric, leading to the introduction of strong even harmonics (2 ×, 4 ×). Therefore, "rich harmonics" are more common than "pure odd harmonics".

Typical spectrum: 4:1 times the speed frequency and harmonics, with a higher harmonic as the main frequency.

This type of spectrum is often seen in reality, such as the number of components multiplied by the rotational speed. In mechanical loosening, local resonance often occurs when a harmonic frequency is close to or equal to a certain natural frequency in the mechanical system, resulting in abnormally large amplitudes of this order of harmonic, even exceeding 1 ×.

Typical spectrum: 5:1 times the speed frequency and harmonics, subharmonics.

The generation of subharmonics is a sign of severe looseness and strong nonlinearity. Sub harmonic means that the rotor motion is no longer repeated every revolution, but requires multiple rotations to complete a complete vibration cycle. For example, 1/2 x harmonics indicate that the impact motion of the rotor is "repeated every two revolutions". This may be because the rotor bounced off after the initial impact, failed to collide again during the second rotation, and only collided again after the third rotation.

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