Taking the gearbox of an electric orbital grinding work vehicle as the research object, the theoretical analysis of the gear transmission system was carried out. The analytical method was used to calculate the stiffness and meshing impact excitation of the gear system, and the error excitation was simulated. After that, an electric drive axle gearbox vibration test bench was built to carry out the vibration response test. The research results show that the vibration prediction results of the axle gearbox of the electric rail grinding car are in good agreement with the test, which verifies the rationality of the analytical model. This study provides data support for the subsequent development and delivery of gearboxes.
1. Introduction
In recent years, the rapid development of the rail transit industry has led to a daily increase in rail traffic volume and, consequently, an increase in rail maintenance workload. Rail grinding engineering vehicles, as important maintenance equipment for regular grinding and defect repair of rail surfaces, have been widely used in the post-construction maintenance of rail transit lines. The axle gearbox, as a key core transmission component of grinding vehicles, directly affects the overall performance of the grinding vehicles. Therefore, the development of high-performance axle gearboxes for rail grinding engineering vehicles has significant engineering practical value for high-quality rail maintenance.
Early grinding vehicles mainly used diesel engines. However, due to their working environment, the diesel engine’s air intake can easily become clogged, leading to shutdowns and blocking of rail lines. In recent years, to enhance the operational stability of grinding vehicles, electric/diesel hybrid power rail grinding vehicles have been proposed to address the issue of diesel engine shutdowns occupying rail lines [1-5]. Compared to diesel engine axle gearboxes, electric drive gearboxes use direct electric drive, eliminating intermediate transmission shafts, thus effectively improving energy transmission efficiency. However, the rapid response characteristics of electric drives have a significant impact on the shock performance of gearboxes, thereby affecting the vibration characteristics of the gear system [6].
In recent years, researchers have conducted various studies on the vibration response of gearboxes in rail vehicles. Chen et al. [7-9] proposed a general time-varying mesh stiffness model. Based on this model, a vehicle-track dynamic model was established to analyze the dynamic characteristics under internal gear excitations. He et al. [10] comprehensively considered the effects of internal and external excitations, established a gearbox dynamics model, and analyzed the vibration impact of the gear transmission system on traction motors and wheelsets. These scholars used the lumped mass method to calculate the vibration response of the gear transmission system. However, the lumped mass method finds it difficult to couple the structural system with the transmission system to solve the overall vibration characteristics of the gear system.
Huang Guanhua et al. [11] calculated the internal and external excitations of high-speed train gearboxes based on the finite element method and solved the vibration response of the gearbox casing. Taking the metro drive gearbox as the research object, a coupled finite element dynamics model of gear transmission and the structural system was established, and the gearbox vibration response was obtained through the step-by-step integration method [12]. However, there have been few reports on establishing a coupled vibration characteristic analysis model for the structural system and gear transmission system of electric rail grinding vehicle axle gearboxes, studying system vibration response, building electric drive axle gearbox vibration test benches, and conducting vibration response tests.
Therefore, this paper takes the electric drive rail grinding vehicle axle gearbox as the research object. By using the analytical method to obtain gear pair stiffness, errors, and meshing impact forces and synthesizing internal excitation forces, a coupled vibration characteristic analysis model of the structural system and gear transmission system is established. The internal excitation forces are applied as load boundary conditions to the model, and the vibration response of the gearbox is solved using the direct integration method. Additionally, a full-load operation test of the physical entity is conducted, and the rationality of the calculation method is verified by comparing test and numerical simulation data.
2. Finite Element Mesh Model of the Gearbox
The electric drive grinding vehicle gearbox adopts a two-stage involute helical gear structure, with gear parameters shown in Table 1. The drive motor is connected to the input shaft of the first-stage gear through a coupling, driving the wheelset to operate and transmit torque. The axle is connected to the second-stage output gear, driving the vehicle forward. The gearbox adopts a vertical suspension structure. The input end is securely connected to the crossbeam of the bogie through a rotatable suspension rod, and the output end is fixedly supported on the axle through two bearings. The physical parameters of the gearbox are shown in Table 2. A finite element dynamic analysis model including gear pairs, shafts, bearings, and the casing is established using Ansys software. The bearings are simplified into equal-mass inner and outer ring models, connected by Combin14 spring elements to simulate the bearing support capacity. The components in the finite element model are all meshed using Solid45 element types. The finite element mesh model is shown in Figure 1, with a total of 1,866,898 elements and 403,642 nodes. The labeled positions in Figure 1 correspond to the positions of the corresponding test measurement points in the finite element model.
Table 1. Gear Parameters
| Item | First-Stage Gear | Second-Stage Gear |
|---|---|---|
| Number of teeth | 28, 53 | 23, 66 |
| Module (mm) | 5 | 7 |
| Tooth width (mm) | 82 | 112 |
| Pressure angle (°) | 20 | 20 |
| Helix angle (°) | 8 | 2 |
Table 2. Gearbox Physical Parameters
| Item | Casing | Gear Pair |
|---|---|---|
| Elastic modulus (Pa) | 1.69×10^11 | 2.10×10^11 |
| Poisson’s ratio | 0.3 | 0.3 |
| Density (kg/m³) | 7.01×10³ | 7.85×10³ |
Figure 1. Finite Element Mesh Model of the Gearbox
3. Internal Dynamic Excitation of the Gearbox
3.1 Gear Mesh Stiffness
The analytical method is used for theoretical calculations of the transmission gear pairs. By comprehensively considering the contact, bending, shear, axial compression, and base body elastic stiffness of the gear teeth meshing, the comprehensive mesh stiffness is calculated as:
k_t = 1/(1/k_h + 1/k_t1 + 1/k_t2) (1)
1/k_ti = 1/k_bi + 1/k_si + 1/k_ai + 1/k_fi (i=1, 2)
In the formula, k_h is the contact stiffness; k_b is the bending stiffness; k_s is the shear stiffness; k_a is the axial compression stiffness; k_f is the base body stiffness; subscript 1 represents the driving gear, and subscript 2 represents the driven gear.
3.2 Gear Deviation
A harmonic function is used to simulate the combined transmission error of the gears, and the gear deviation value is determined according to the gear’s design accuracy grade. The tooth profile error and base pitch error of the gear teeth can be represented by a half-sine function:
e(t) = e0 + e_r sin(πt/T_z + φ) (2)
In the formula, e(t) is the combined error of the gear; e0 and e_r are the constant and amplitude values of the tooth error, respectively; T_z is the meshing period of the gear, T_z = 60ε_r/n_z; ε_r is the contact ratio; n is the rotational speed; φ is the phase angle.
3.3 Gear Mesh Impact
3.3.1 Determination of Mesh Impact Point Position
The position of the mesh impact point C is obtained by using the reversal method based on the reversal angles θ1 and θ2 of the driving and driven gears. The reversed position is shown in Figure 2. An equation is established based on φ = φ’, and solved together to determine r_C, establishing the position of the mesh impact point.
According to geometric relationships, the relationship formula for the geometric clearance angle φ with the impact radius at the driving gear end face as the independent variable is:
φ = arccos((r_2a^2 + a^2 – r_O1C^2) / (2ar_2a – θ2 – γ2)) (3)
In the formula, a is the center distance of the gear pair; γ2 is the difference between the tooth tip circle pressure angle and the pitch circle pressure angle of the driven gear, γ2 = α_a2 – α0.
From the gear elastic deformation theory, the loaded deformation angle φ’ of the gear teeth is obtained, i.e.,
φ’ = δ_∑ / r_
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