Vibration Analysis of Gear Transmission System Zhu Weixin (Changzhou Mechanical Workers University, Changzhou 213002) The simplified method of vibration analysis model of gear transmission system is convenient for engineering application and has certain practical application value.
With the rapid development of machinery, the requirements for gear transmission systems are becoming more and more rampant. The main shaft and the branch shaft in the gear transmission system cause the torsional vibration of the rotating shaft due to the periodic change of the external torque, causing large vibration and noise, and shortening the service life of the gear transmission system, especially when the interference frequency causing the torsional vibration is close. And equal to the natural frequency of the torsional vibration system causes mechanical resonance. Therefore, the vibration analysis of the gear transmission system is an indispensable part of the design of the gear transmission system. Due to the error of the gear in the gear transmission system, the mass distribution of the transmission system and the distribution state of the elastic body make the dynamic problem more complicated. If the gear transmission system is simplified into a linear vibration analysis model, the analysis process can be greatly simplified, and the natural frequency can be ensured with sufficient accuracy. The following is a brief discussion on how to simplify the gear transmission system and use the transfer matrix method to analyze the natural frequency of the system.
1 Transfer Matrix Method The transfer matrix method provides an approximate lumped parameter system analysis method, which is especially suitable for large systems composed of several subsystems.
To perform vibration analysis by this method, it is necessary to perform continuous matrix factorial operation on some transfer orders with very low order. In the numerical solution, only the low order transfer matrix and the determinant value are calculated. This greatly saves the computational effort and is also easy to process with a computer.
Taking the multi-disk torsional vibration system as an example, the principle and process of the transfer matrix are briefly described: the multi-disc vibration system diagram la is a multi-disc torsional vibration system, in which the n-th axis and the n-th disc are isolated from the system. come out.
From Figure lb, the transmission relationship from the left to the right of the n-th axis can be obtained: the transfer relationship from the left state of the n discs to the right state can be obtained from the graph lc: or because 呱= is obtained by the formula (a): +(1)2 In this way, the torque relationship between the left and right sides of the A gear is obtained. The matrix is ​​expressed as follows: With the above formula, it is convenient to use the transfer matrix method to solve the natural frequency of the system.
For the multi-i parallel shaft gear transmission system, with the above two simplified foundations, it is easier to handle, and the following is a simplified analysis of several common gear transmission systems.
a is a multi-stage parallel shaft gear transmission system, and the simplified method of the system is similar to the above. First, the equivalent moment of inertia and equivalent stiffness are simplified into a one-to-one gear transmission system as shown in b. Here, the equivalent moment of inertia and the equivalent stiffness are (a) The multi-stage parallel shaft gear transmission system 1 substitutes the above parameters into the equation (5), and the relationship between the torque of the left and right sides of the main shaft gear A can be obtained. In this way, the torsional vibration calculation can be performed on the A-axis as if there is no branch system.
a is also a multi-stage parallel gear transmission system. The system can be simplified as follows. The equivalent moment of inertia and equivalent stiffness are simplified into a series axis and a parallel axis as shown in b. This form is well known. Here, the multi-stage parallel shaft gear transmission system 2 substitutes the parametric heart on the parallel shaft into the equation (4), and uses the boundary condition M=0 to find the relationship between the torques on both sides of the meshing gear, and then twists the series shaft. Vibration calculation.
The above discussion on how to simplify and analyze the vibration in the transmission system is aimed at calculating the natural frequency in the gear transmission system by simple and effective method, so as to avoid resonance and reduce in design or use. Noise and extend the life of the gear drive system. pass. 1 Matrix computer program has matured and been widely used in mechanics. Due to the length of the relationship, the block diagram is not drawn here and the relevant program is written. Users can refer to the relevant materials.
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