# Meshing modulation of gear vibration in practical work of tractor gears

Various defects will inevitably occur in the process of gear processing, installation and use, such as crack, tooth surface fatigue, wear, scratch, uneven gear indexing, unbalanced quality and improper installation. On the one hand, these defects change the load on the tooth contact surface and the external exciting force of meshing vibration. For example, a large tooth has large peeling, and a pulse excitation is generated when the defective tooth participates in the meshing transmission every revolution of the gear. This pulse excitation has a certain influence on the meshing vibration of the gear and changes the amplitude. This phenomenon is called amplitude modulation. On the other hand, gear defects can change the stiffness of gear teeth. If the gear has cracks, it not only increases the vibration, but also changes the phase and produces frequency modulation. Most gear defects produce both frequency modulation and amplitude modulation. Frequency modulation and amplitude modulation are collectively referred to as modulation. The gear vibration dynamic equation with modulation phenomenon is:

E2 (T) is the relative displacement between two gears caused by gear error or fault, or the relative displacement caused by other faults such as shaft bending.

According to the above formula, the vibration source of the gear comes from two parts: one part is the conventional vibration part k (T) E1 (T), which is the vibration arched by the normal alternating load; Part k (T) E2 (T) is that it depends on the comprehensive stiffness and fault function of the gear.

If y (T) = XG (T) DG (T) = K (T) E2 (T). Then XG (T) is the carrier signal, which includes the gear meshing frequency and its high-order harmonic frequency, and DG (T) is the modulation frequency, which reflects the error and fault of the gear itself and the gear transmission error caused by the fault of other parts. DG (T) changes once every revolution of the gear, including the rotation frequency and high-order harmonic of the shaft. By analyzing the spectrum, several groups of sidebands with frequency conversion and frequency doubling around the meshing frequency and its higher harmonic are formed on the spectrum, which is the phenomenon of meshing frequency modulation. This modulation phenomenon can be caused by tooth profile error, pitting corrosion, broken teeth, misalignment of coupling and slight bending of transmission shaft in gearbox, but its sideband distribution is different.

At this time, the vibration signal measured in the gearbox is:

Where:

G (T) is the vibration signal with lower frequency related to each frequency conversion;

Σ XG (T) DG (T) is the gear meshing frequency modulation signal;

Σ XB (T) dB (T) is the abnormal vibration signal of rolling bearing;

N (T) is other vibration and interference signals;

X (T) is the carrier signal;

D (T) is the modulation signal.

Generally, the modulation sideband caused by broken teeth and large shedding is wide and flat, that is, there are many sidebands and the amplitude is uniform. The amplitude of modulation sideband caused by uniform defects such as pitting and scratch changes greatly. The amplitude of side frequency component close to meshing frequency is high, and the amplitude of other side frequency components decreases in turn. Modulation sideband asymmetry caused by faults such as imbalance, misalignment and mechanical looseness. It can be seen that the characteristics of sideband are important information for gear fault diagnosis. Extracting and analyzing sideband information is the key to gear fault diagnosis. In the test environment with high signal-to-noise, it is easy to extract the gear modulation information. The general signal processing methods, such as power spectrum, cepstrum and time-domain average, can make a more accurate diagnosis of the detected gear. However, in the test environment with low signal-to-noise ratio, the gear vibration signal is submerged in a large amount of environmental noise, and the sideband becomes blurred or even invisible, which makes it difficult to make a correct diagnosis of the test object.

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