Due to some characteristics of structure and working principle, the vibration signal of gear is more complex. When diagnosing the vibration fault, it is often necessary to analyze it in time domain and frequency domain at the same time. The characteristic frequency of gear fault is basically composed of two parts: one is carrier signal composed of gear meshing frequency and its harmonic; the other is modulation signal composed of amplitude and phase change of low frequency component (mainly speed frequency). The modulation signal includes amplitude modulation and frequency modulation.
The characteristic of gear transmission is that the position of meshing point and the number of teeth participating in meshing change periodically in the process of meshing, which results in periodic changes in the force and stiffness of gear teeth. The vibration caused by this change must contain periodic components, which reflects the periodic characteristic information of meshing frequency and its higher harmonic.
In the process of meshing, the tooth surface has both relative rolling and relative sliding. As shown in the figure below, the engagement point on the driving wheel moves from the tooth root to the tooth top, and the speed increases gradually with the increase of the engagement radius; while the engagement point on the driving wheel moves from the tooth top to the tooth root, and the speed decreases gradually. The difference in speed between the two wheels results in relative sliding. At the node, the speed of the two wheels is equal and the relative sliding speed is zero. On the driving wheel, the speed of the mesh point between the dedendum and the node is lower than that on the driven wheel, so the sliding direction is downward; on the other hand, the speed of the mesh point between the node and the tooth top is higher than that of the driven wheel, and the sliding direction is upward. The driving wheel and driven wheel have changed the sliding direction at the node, that is to say, the direction of friction force has changed at the node, forming a pitch line impact.
In the process of gear meshing, in addition to the pitch line impact caused by the change of the position of the meshing point, the more important is the meshing impact caused by the change of the number of teeth participating in the meshing. For the involute spur gears with the overlap coefficient between 1 and 2, the single tooth meshing is near the node, and the double tooth meshing is near the tooth root and the tooth top. Obviously, the load is small and the rigidity is large when two teeth are engaged, and large and the rigidity is small when one tooth is engaged, as shown in the right figure. That is to say, even if the constant torque is transmitted by the gear, when each pair of teeth is out of engagement or into engagement, the load and stiffness on the teeth will suddenly increase or decrease, thus forming engagement impact. For the straight teeth with low overlap coefficient, the meshing impact is particularly significant, and the change of force and stiffness basically presents a rectangular wave, as shown in the right figure. For oblique teeth, because the meshing point moves along the tooth width direction, the change of meshing process is relatively gentle, and the change of stiffness is close to sine wave. Therefore, the change of meshing impact and meshing stiffness depends on the type of gear and the overlapping coefficient.
Obviously, the change of meshing impact, pitch line impact and meshing stiffness of gears is periodic, and the frequency of this periodic change is the product of speed frequency f and tooth number Z (the number of change cycles per second is determined by speed frequency, the number of change cycles per circle is determined by tooth number, and the product is the number of change cycles per second), that is, meshing frequency FM, that is
fm＝f1•z1＝f2•z2
In the formula, F1, F2 ~ rotating speed frequency of driving wheel and driven wheel; Z1, Z2 ~ number of teeth of driving wheel and driven wheel.
Meshing frequency is very important in gear fault diagnosis.
In fact, in a 1 / FM meshing cycle, there are many impact processes such as entering meshing, disengaging, pitch line impact, etc. Therefore, the vibration signal of the gear must contain the meshing frequency FM and its high-order harmonics 2fm, 3FM Ingredients.
No matter whether the gear is in normal or fault state, the vibration component of meshing frequency FM always exists in the vibration signal of the gear, but the amplitude value of the two states is different. The meshing frequency and harmonic amplitude are relatively low. The increase of meshing frequency and harmonic amplitude is not only related to the load variation, but also to the improper backlash. There are various reasons for the improper side clearance. Besides the manufacturing and installation, the tooth surface wear is also one of the main reasons.
In particular, it should be pointed out that not only the side clearance becomes larger, but also the shape of tooth profile (involute teeth, circular arc teeth) is damaged after the tooth surface is evenly worn, which will increase the impact and reduce the meshing stiffness during meshing, and will increase the amplitude of the pass frequency, among which the increase of the meshing frequency and harmonic amplitude is the most obvious. What’s more, the amplitude of higher harmonic of engagement frequency increases faster than that of fundamental wave, as shown in the right figure. When the wear is serious, the amplitude of the second harmonic may exceed the meshing fundamental. Therefore, the wear degree of tooth surface can be reflected from the relative increase of meshing frequency and harmonic amplitude.