Dynamic simulation and fatigue life prediction of locomotive traction drive system

Abstract

In this work, a rigid-flexible coupling dynamic model has been established to describe a specific type of locomotive traction drive system, by a parametric modeling method utilizing Creo, Ansys, and RecurDyn software systems comprehensively. With this model, the dynamic characteristics, stress, and deformation results of the system under various working conditions were evaluated via dynamic simulation and modal analysis. These results enable the prediction of contact fatigue strength of driving gear tooth surface for the estimation of its service life. On the basis of theoretical analysis, combined with the performance test of the laboratory bench, the working condition of the test gear pair’s tooth surface under the condition of equivalent load was tested, and the pitting position of the tooth surface was found to be consistent with the simulation analysis. Through the dynamic simulation and fatigue life prediction of the transmission system, it provides a theoretical basis for reasonably improving the efficiency of transmission system parts and setting up the inspection and maintenance cycle.

Keywords

traction drive system fatigue life prediction multi-body dynamics simulation rigid-flexible coupling

Introduction

Gears are fundamental and important part in the field of machinery, widely used in aviation, wind turbines, ships, automobiles, and other fields of power transmission. Fatigue reliability in gear transmission is a decisive factor to maintain good mechanical performance and service life under high-speed loads.^1–5 The bending fatigue strength and contact fatigue strength of gears decrease with the continuous cycling of loads,⁶ and the research on contact fatigue of gears mainly focuses on the fatigue damage and wear process during operation.^7–10

The calculation of gear contact stress is based on the traditional Hertz contact model, which is the basic model for studying contact body collision. Its assumptions mainly include the following: the instantaneous contact of meshing gears is considered as pure rolling of two cylinders without relative sliding on the surface; the contact surface is continuously smooth.

Hertz contact model only reflects the macroscopic characteristics of contact surfaces. For a long time, gear fatigue performance evaluation mainly relies on classical mechanics and fatigue life test, and reliability analysis is carried out based on Weibull, exponential distribution, or logarithmic normal distribution hypotheses.^11–14 The traditional fatigue test analysis method is based on the classical statistical theory of large samples, which not only requires a large amount of test input but also consumes huge manpower and material resources. Gear life prediction methods are mostly based on fatigue cumulative damage theory for life prediction, or on the basis of fatigue cumulative damage theory, combined with finite element analysis or multi-model co-simulation technology.

At present, fatigue analysis methods of various components have been more widely used with the rapid development of modern computer technology and finite element technology.^15–18 In the design stage of various products, designers can compare the quality of fatigue life of different design schemes with these technologies, which can not only check whether the fatigue life of products meets the design requirements but also carry out relevant anti-fatigue design. Before the test and operation of the product, the key parts of monitoring during the fatigue test can be determined by fatigue analysis. Compared with the traditional test method, the finite element fatigue simulation calculation can provide the fatigue life distribution of components, judge the weak position of fatigue life of components, and avoid unreasonable life distribution in advance by modifying the design. With this technology, the number of test prototypes and development cost can be reduced, the development cycle of products can be shortened, and the market competitiveness of products can be improved.¹⁹

Therefore, this paper analyzes and predicts the fatigue life of locomotive transmission system by combining rigid-flexible coupling dynamics simulation and transmission system performance test in laboratory.

Solid model modeling

The locomotive traction gear transmission device has a relatively simple structure, usually composed of a driving gear and a driven gear. The active gear rotates under the motor drive and drives the driven gear mounted on the axle to complete the load and motion transmission. The structure of the driving gear and the motor shaft are installed through interference fit connection.²⁰ The modeling of the gear adopts the method of parametric design, and the gear model is generated by inputting the basic parameters of the gear and the tool parameters on the software interface, as shown in Figure 1(a). The driven gear and the axle are connected by interference fit, and the gear model is shown in Figure 1(b). After completing the modeling of the motor shaft and the axle, each model is assembled, and the assembled model is shown in Figure 1(c).

Dynamic modeling

Computational multi-body dynamics analysis covers two stages: modeling and solving. Modeling includes two processes: physical modeling which forms physical model from geometric model and mathematical modeling which forms physical model from physical model. In the solving stage, corresponding solvers should be selected according to the solving type for numerical operation and solving. The geometric model is equivalent to the component model of mechanism and machine, which can be established in the software system, or can be modeled, exported, and imported from other CAD software. The mechanical model of the mechanical structure is established by endowing the geometric model with physical attributes such as mass and inertia, while applying kinematic motion pairs, force loads, and initial motion conditions to establish a dynamic model similar to the actual working state.

The components of the model can be rigid body or flexible body. The force relationship in the multi-body system includes the interaction force between components and the external force exerted on the internal object of the system. Through the modeling and solving process, the motion and force variation of multi-body system can be obtained. Dynamic stress analysis and fatigue life prediction can be carried out by rigid-flexible coupling dynamics simulation.^21,22

Rigid body modeling

In this work, multi-body dynamics software RecurDyn is used for dynamic modeling and simulation analysis. Create a rigid body model in MMKS and import the assembled model in Creo software system into RecurDyn software system.

Firstly, the kinematic pair relationship was set in the system. In order to simulate the real motion condition of the transmission system and avoid the unnecessary loss between gear and shaft affecting the simulation data, the fixed kinematic pair was selected to fix the motor shaft and driving gear. Then, the same operation process was used to set the fixed hinge between axle and driven gear.

Then, all tooth profile surfaces of the driving and slave gear models were selected, and two FaceSurface sets were set, respectively. The contact relationship between the surfaces was generated by using Geosurface command to select the FaceSurface sets of the generated main and driven gear.

Finally, spline curves of driving gear speed and driven gear torque were established by software system to control the movement and traction torque between driving and slave gears. The final rigid body dynamics model is modeled as shown in Figure 2.

Modeling of rigid-flexible coupling dynamics model

In order to better reflect the law of stress changes on the tooth surface during the working process of the tooth pair, it is impossible to achieve only by establishing the rigid body dynamic model of the system. Therefore, this paper makes the driving gear flexible to establish the rigid-flexible coupling dynamics model of the system. The finite element model of the driving gear is generated in ANSYS software environment, and the Solid185 hexahedral element is used for meshing. Mass21 mass units generate mass nodes instead of the axis function of the entity. The generated finite element model of driving gear is shown in Figure 3(a), and the rigid-flexible coupling dynamic model is shown in Figure 3(b).

Application of load and drive

The linear movement process of the transmission system is simulated according to the maximum driving speed of the vehicle at 142 km/h, and the specific speed change is set according to the parameters in Table 1.

Table 1.

Law of load change.

time(s)	Motor shaft speed (rad/s)	Gear traction moment (N·m)
0∼0.05	0∼21.6	0∼5.24 × 10⁴
0.05∼0.1	21.6∼436.8	5.24 × 10⁴
0.1∼0.3	436.8∼10488.6	5.24∼1.05 × 10⁴
0.3∼1	10,488.6	1.05 × 10⁴

The Rotational Axial torque is applied to the driven gear, and the load applied on the axle is converted according to the speed of the vehicle and the power of the motor. The specific load size is shown in Table 1.

Comparative analysis of simulation results

Simulation results

The simulation running step was set as 0.17 ms/ step, and the calculation results under various working conditions were obtained by simulation calculation. Taking the 142 km/h working condition as an example, the average speed of the output shaft under this condition is n₂ ≈ 32.90 rad/s. The calculation error of the transmission ratio between the average transmission ratio of the simulation analysis i₂ ≈5.31337 and the total transmission ratio of the theoretical mechanism i₁ ≈ 5.3125 is 0.01638%. The simulation model well reflects the working state of the traction drive system, and the speed comparison between the gear groups is shown in Figure 4.

Dynamic performance analysis

The angular acceleration variation curve of the output driven gear at the speed of 142 km/h is shown in Figure 5(a); Fourier change was performed on the calculated result data, and the frequency domain variation curve was obtained, as shown in Figure 5(b). The angular acceleration of the gear pair fluctuates significantly in the frequency range of 444.9 Hz, 1211.7 Hz, and 1424.7 Hz, which will cause the change of load and force state of the gear transmission system during the working process and cause the change of dynamic load. Among them, 444.9 Hz is the rotation angle frequency corresponding to the driving gear, and the other main frequency points are its frequency multiplication or division frequency.

The contact force curve between the output tooth pairs is shown in Figure 6(a). Fourier transform is applied to the contact force variation curve, and the frequency domain variation curve is shown in Figure 6(b). There are load mutations in the frequency ranges of 444.9 Hz, 889.8 Hz, and 1424.7 Hz. Under other speed conditions, the transmission system has similar dynamic characteristics.

Combined with ANSYS software, modal frequency analysis of the established finite element model of the tooth pair was carried out to analyze the first 10 modes of the master and driven gears. The calculation results are shown in Table 2. The driving gear is an integral structure with a large modal frequency, which is not prone to vibration caused by modal frequency. The driven gear is a web structure, so the calculated result of modal frequency is lower than that of the driving gear. The 444.9 Hz frequency causes a certain fluctuation of the contact force between the teeth in the contact state, as shown in Figure 6(b).

Table 2.

Modal analysis results.

Order number	Frequency (Hz)
Order number	Driving gear	Driven gear
1	0	0
2	5.29E-04	0
3	8.38E-04	4.73E-04
4	1.03E-03	5.79E-04
5	1.13E-03	6.66E-04
6	1.45E-03	7.65E-04
7	9933.2	120.25
8	10,003	120.25
9	10,003	251.41
10	12,106	251.41

Fatigue life analysis and prediction

Fatigue life analysis

The calculated results are analyzed by using the fatigue subroutine function of RecurDyn software system to determine the dangerous node locations of the gear surface nodes under different working conditions, so as to predict the contact fatigue life.

Fatigue life analysis of driving gear

According to the gear material, the S-N data of the corresponding steel was selected for fatigue life analysis, and the S-N curve of the material is shown in Figure 7. As the load of traction drive system is maximum at the starting condition, the calculated fatigue life is the shortest. The fatigue stress distribution cloud diagram of the output starting condition is shown in Figure 8. The element at node 11,679 on the flexible body has the maximum cumulative damage effect, and the maximum stress value in the working process of the node is determined as 964 MPa according to the dynamic display. Simulation analysis of starting conditions shows that the life calculation result is 16,053,928 cycles, as shown in Figure 9. Other working conditions were analyzed according to the analysis time shown in Table 3, and the calculation results are recorded in Table 3.

Table 3.

Analysis results of fatigue life of driving gear.

Simulation cycle time(s)	Simulated working condition (km/h)	Cycle life (secondary cycle)
0∼0.05	0∼0.29	1.E + 36
0.05∼0.1	0.29∼5.90	1.E + 36
0.1∼0.3	5.90∼142.10	16,053,928
0.3∼1.0	142.10	690,176,800

Fatigue life analysis of driven gear

The material of the driven gear is the same as that of the driving gear. The element at node 2204 on the flexible body has the maximum cumulative damage effect, and the maximum stress value in the working process of the node is determined as 1361 MPa according to the dynamic display. Simulation analysis of starting conditions shows that the life calculation result is 453,872,358 cycles, as shown in Figure 10. Other working conditions were analyzed according to the analysis time shown in Table 4, and the calculation results are recorded in Table 4.

Table 4.

Analysis results of fatigue life driven gear.

Simulation cycle time(s)	Simulated working condition (km/h)	Cycle life (secondary cycle)
0∼0.05	0∼0.29	1.E + 36
0.05∼0.1	0.29∼5.90	58,609,717
0.1∼0.3	5.90∼142.10	453,872,358
0.3∼1.0	142.10	134,737,713,525,182

Fatigue life prediction

The fatigue life of locomotive traction drive system must be different under different working conditions and routes. In this paper, a locomotive operating condition is simulated, and its operating interval distance is 1207 km, in which the starting and low-speed operating conditions account for about 10% of the total operating time, the continuous acceleration conditions account for about 20% of the total operating time, and the 142 km/h high-speed operating conditions account for about 70% of the total operating time (Figure 11).

Due to the limitation of computer computing ability, it is impossible to simulate the model during the whole operation of the traction drive system. Therefore, the flexible body dynamics simulation and fatigue life analysis are carried out for each working condition according to the simulation cycle time in Table 3, and the whole life calculation is carried out according to the linear damage accumulation theory:

\sum_{i = 1}^{z} \frac{n_{i}}{N_{i}} = 1

(1)

in this paper, according to the specific working conditions of the traction drive system, a total of four working conditions were set up for simulation analysis. According to the fatigue damage accumulation theory, the load in each working condition will cause a certain degree of damage to the driving gear tooth surface. According to the characteristics of cyclic variation of each working condition, the total damage of operation under each working condition is summed, which is the total damage of single operation of traction drive system in the working interval, and its reciprocal is the total number of operation times before fatigue failure, which can be calculated by formula (2), that is:

L = \frac{1}{\sum_{j = 1}^{8} a_{j} \cdot \sum_{i = 1}^{z} \frac{n_{i}}{N_{i}}}

(2)

Among them:

a_j is the number of cycles in the j operating condition;

L-t is the total number of interval runs before part failure;

$\sum_{i = 1}^{z} \frac{n_{i}}{N_{i}}$ is the single working condition simulation damage.

Taking the calculated data into formula (2), the damage rate is calculated to be 1.56 × 10⁻⁵, and the number of cycles L = 6.4 × 10⁴. If the damage rate is 10%, the fatigue life of driving gear tooth surface is predicted to be 7.7 × 10⁶ km. Meanwhile, the distribution cloud diagram of tooth surface fatigue damage was obtained, as shown in Figure 12.

Fatigue test

Due to the difficulty in monitoring and tracking the gear transmission system, in order to verify the rationality of the theoretical analysis, the test gear and gear box structure with reduced size can be used to simulate the operation of the traction drive system in the actual working process, and the gear performance bench test can be carried out in the laboratory. The structure of the test device is shown in Figure 13(a). The main structural equipment includes the following: 1. auxiliary gear box, 2. test gear box, 3. drive shaft, 4. input torque and speed sensor, 5. test gear box, 6. output torque and speed sensor, 7. torque and speed meter, and 8. Internal helical gear hydraulic loading equipment. The power is provided by the motor and auxiliary gearbox, and the dynamic load is applied by the internal bevel gear hydraulic loading device. The torque speed sensor and efficiency instrument are used to collect and control the application of load and the real-time monitoring of working conditions. In order to simulate the working conditions of the traction drive system in the laboratory, two groups of measured gearboxes with the same transmission parameters are used to realize the load transmission and ensure the constant speed transmission of the whole transmission chain. The experimental platform is shown in Figure 13(b).

In order to ensure that the contact strength and bending strength of the test gear and the traction gear are basically consistent, the load transmitted by the tested gear is one-eighth of the load in Table 2. After equivalent to the locomotive traction drive system running 5 × 10⁵ km, the tooth surface working state inspection is shown in Figure 14. It can be seen that there are small initial pitting micro-cracks on the surface of the driving and driven gear, and their relative positions on the tooth surface are consistent with the virtual failure positions on the tooth surface as shown in Figure 12. The contact state of the tooth surface of the driven gear is better than that of the driving gear, and the microcracks are less. The results show that the state of the tooth surface of both driving and driven gears is ideal, and there is no large area of tooth surface spalling phenomenon. Compared with the calculated life of 7.7×10⁶ km, there is a certain life margin, indicating that the theoretical calculation has certain reference value and practical significance for predicting the life of gears.

Conclusion

This paper takes traction gear transmission system of a locomotive as the research object and comprehensively uses Creo, ANSYS, and RecurDyn software systems to establish rigid-flexible coupling dynamic model of the transmission system by parametric modeling method. The system simulation results under various working conditions were obtained through dynamic analysis and modal analysis, and the fatigue strength life prediction was carried out based on the big data platform. Finally, through the laboratory bench test, the actual working state of gear under equivalent working condition is obtained, which provides comparative analysis for theoretical analysis. In this paper, the following conclusions are obtained through simulation analysis and experimental verification:

1. According to the analysis of the frequency domain variation curve of the contact force and the acceleration of the slave gear, there are load mutations in the frequency ranges of 444.9 Hz, 889.8 Hz, and 1424.7 Hz during the contact process of the tooth pair, which are corresponding to the rotation frequency and the natural frequency of the part.

2. The element of node 11679, node 2204, and other node parts on the flexible body was determined to have the largest cumulative damage effect, and the maximum stress value of the node was determined to be 1687 MPa according to the dynamic display, which was the location of the dangerous node in the weak position of the fatigue strength of the tooth surface, and the distribution of the dangerous parts of the damage was obtained.

3. By simulating a complete process of traction working interval, the cumulative damage rate was calculated to be 1.56 × 10⁻⁵, the number of cycles L = 6.4 × 10⁴, and the predicted equivalent fatigue life of driving gear tooth surface was about 7.7 × 10⁶ km.

4. After running 5 × 10⁵ km under equivalent load condition, it can be seen that initial pitting micro-cracks appear on the surface of the main and slave gear used in the test, but the state of the tooth surface is ideal, which has a certain life margin with the theoretical calculated life of 7.7 × 10⁶ km, indicating that the theoretical calculation has a certain reference value. It is of practical significance to predict the life of gears and make reasonable maintenance cycle.

Statements and declarations

Footnotes

Conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

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