The helical gearbox is a key component on the bogie of subway vehicles, used to transfer loads and transmit the torque of the traction motor to the wheelset through a certain transmission ratio to provide power for the forward operation of the subway. It plays a crucial role in the safety and reliability of operation. For the subway vehicles studied in this study, their power bogies were equipped with helical gearboxes. Each power bogie was equipped with two helical gearboxes, and the helical gearboxes on the bogies were symmetrically arranged obliquely.
The driving gear and the driven gear mesh to form a gear pair, and the torque of the traction motor is transmitted to the wheelset through a certain transmission ratio, which has the function of reducing speed and increasing force. The main forms of failure of helical gears include root fracture, tooth surface wear, pitting, bonding, and plastic deformation. The starting and braking stages of subway vehicles occur frequently, and the traction motor has a large torque and speed, which requires the helical gear to have high strength. Therefore, in the design of transmission gears for subway vehicles, it is necessary to combine the current experience of using helical gearboxes for subway vehicles and the level of helical gear manufacturing technology to ensure good meshing smoothness, low noise, and high reliability of helical gears.
Based on the analysis results of the finite element model of single tooth meshing for subway vehicle transmission helical gears, with fatigue performance as the goal, optimization of the subway vehicle transmission helical gears is carried out on the basis of ensuring smooth meshing and low noise of the helical gear pair.
The meshing parameters of helical gears have a direct impact on the quality of involute gear transmission. In terms of selection, good high-speed operation performance is required to ensure continuous transmission and achieve precise and stable gear tooth alternating meshing. The above factors are generally evaluated using the parameter of overlap. And for the transmission of helical gears in subway vehicles, the meshing noise level of the helical gear pair should also be considered in order to provide passengers with a better riding experience.
1. Analysis of the overlap degree of the optimized helical gear pair
We know that when a pair of helical gears mesh together, the contact point between a pair of involute teeth will move along the pressure line. Ensuring that a pair of teeth remain in contact until the next pair of teeth is ready to withstand the load is clearly of great significance. It is not difficult to understand that the longer the time gap between the meshing of one pair of teeth and the lower pair of teeth, the smaller the noise and vibration caused by the helical gear.
The overlap of the helical gear pair optimized by the line graph method according to the principle of equal strength can be calculated using a formula, and the results are shown in the table.
| End face overlap degree 𝜀𝛼 | Vertical overlap degree 𝜀𝛽 | Gear pair overlap ratio 𝜀𝛾 | |
| Equal strength principle 𝑥 1=0.559 𝑥 2=0.603 | 1.3990 | 1.0363 | 2.4353 |
The magnitude of the longitudinal overlap degree 𝜀𝛽 is related to the degree of change in the length of the contact line of the helical gear pair. When the longitudinal overlap degree 𝜀𝛽 is an integer, the length of the contact line will not change during the meshing process of the helical gear pair. However, when the longitudinal overlap degree 𝜀𝛽 is not an integer, especially in the 0-1 range, the length of the contact line will change dramatically. From the table, it can be seen that the longitudinal overlap degree 𝜀𝛽 of the helical gear pair optimized by the line graph method according to the principle of equal strength is 1.0363, which is very close to integer 1 and not within the range of 0-1. Therefore, the length of the contact line during the meshing process of the helical gear pair will not change significantly, that is, the distribution of load and the degree of change in load size during the tooth meshing process will not change significantly. And after optimization, the overlap degree of the helical gear pair is 2.4353, with a large number of teeth engaged, ensuring smooth transmission and meeting the operational requirements of subway vehicles.
2. Analysis of optimized helical gear pair noise
The noise during the meshing process of helical gears is mainly caused by three possible reasons. Three reasons are all influenced by the meshing force of the teeth: during the meshing process, if the magnitude, direction or point of action of the meshing force changes, vibration and noise will be generated. For the reason of the direction of meshing force, as the common normal direction of involute gears is constant, we only need to use involute gears to eliminate the factor of changing the direction of meshing force. In addition, there is another factor that causes a slight change in the direction of the meshing force, namely frictional force. However, compared to the changes in meshing force caused by inaccurate manufacturing of helical gears, the impact of friction is very small. The impact caused by manufacturing errors is much greater than the impact that can be caused by changing the direction of meshing force due to friction. The noise caused by impact at the helical gear node can be ignored due to the inherent characteristics of the helical gears used in subway vehicle transmission, which can counteract this type of noise.
In summary, the optimized helical gear pair using the line graph method based on the principle of equal strength does not show a significant increase in noise compared to the prototype helical gear pair of subway vehicles, meeting the requirements for subway vehicle operation.
Based on the analysis results of the finite element model of single tooth meshing of helical gears in subway vehicles, tooth root stress modification coefficient line diagrams and fatigue life modification coefficient line diagrams were drawn. The accuracy of the line graph method was verified through finite element method. According to the principles of equal strength and equal life, the line graph method was used to optimize the transmission helical gears of subway vehicles with fatigue performance as the objective, and the transmission quality was analyzed. The following conclusions can be drawn:
(1) The line graph method was validated using the finite element method, and the error size of the tooth root stress obtained by the line graph method was the minimum of 0.02% and the maximum of 1.51%; The minimum error in the fatigue life of the obtained helical gear is 0.59%, and the maximum error is 18.76%, indicating that the line graph method can accurately predict the root stress and fatigue life of the helical gear pairs in subway transmission with different displacement coefficients.
(2) The deformation coefficient of the helical gear pair optimized by the line graph method according to the principle of equal strength is 𝑥 1=0.559 𝑥 2=0.603. The comprehensive fatigue life of the helical gear pair is 3.29 times that of the prototype helical gear pair, which is 3.06 times higher than the principle of equal life. When using the line graph method to optimize the modification coefficient of helical gears, priority should be given to optimizing according to the principle of equal strength.
(3) After optimization, the overlap degree 𝜀𝛾 of the helical gear pair is 2.4353. Through noise analysis of the helical gear pair, it can be ensured that the optimized helical gear pair mesh smoothly, has low noise, and meets the requirements of subway vehicle operation.