In this study, we address a critical issue in automotive transmission systems: the deformation of internal threads in reverse idler gear shafts after carburizing and quenching of 20CrMoH material, which leads to low qualification rates. To resolve this, we propose substituting the current material with 45 steel, utilizing a normalizing plus high-frequency local quenching process. Through joint simulation using JMatPro and ANSYS software, we optimize the heat treatment parameters and evaluate the mechanical performance under operational conditions. Our approach integrates theoretical calculations, numerical simulations, and experimental validation to ensure the gear shaft meets all design requirements while improving production efficiency.
The reverse idler gear shaft is a pivotal component in manual transmissions, supporting the idler gear that facilitates reverse motion. Its performance directly impacts transmission quality, with surface hardness being a key indicator of wear resistance. Traditional methods like carburizing enhance hardness but often cause distortions, especially in threaded areas, necessitating additional anti-seepage treatments that complicate manufacturing. Our investigation focuses on the gear shaft’s operational loads, material properties, and thermal processing to develop a robust alternative.
We begin with theoretical calculations to determine the forces acting on the gear shaft. The shaft experiences circumferential and radial forces from the input and output gears, as well as an axial force from the shift fork. However, the axial force is negligible due to its short duration and low magnitude. The circumferential force \( F_t \) is calculated using the formula:
$$ F_t = \frac{2000 T_1}{d_1} $$
where \( T_1 = 103 \, \text{Nm} \) is the input torque and \( d_1 = 32.4 \, \text{mm} \) is the pitch diameter. This yields \( F_t = 6358.02 \, \text{N} \). The radial force components are derived from the pressure angle \( \alpha = 20^\circ \):
$$ F_{r1} = F_t \tan \alpha $$
and the resultant radial force \( F_r \) is:
$$ F_r = 2 F_{r1} \cos 30^\circ = 11012.41 \, \text{N} $$
with components \( F_{rx} = 5506.21 \, \text{N} \) and \( F_{ry} = 9537.03 \, \text{N} \). The deflection of the gear shaft, modeled as a cantilever beam, is given by:
$$ y = \frac{F L^3}{3 E I} $$
where \( L = 50 \times 10^{-3} \, \text{m} \) is the length, \( E = 205 \, \text{GPa} \) is the elastic modulus, and \( I = \pi D^4 / 64 = 5150.39 \, \text{mm}^4 \) is the moment of inertia. The total deflection is \( y_{\text{total}} = 4.42 \times 10^{-5} \, \text{m} \), and the deflection in the y-direction is \( y_y = 3.83 \times 10^{-5} \, \text{m} \).
For the induction hardening process of 45 steel, the current penetration depth \( \Delta \) is estimated using the empirical formula:
$$ \Delta_{800} \approx \frac{500}{\sqrt{f}} \, \text{mm} $$
with a frequency \( f = 100 \, \text{kHz} \), resulting in \( \Delta_{800} = 1.61 \, \text{mm} \). This depth ensures adequate surface hardening for the gear shaft.
We selected 45 steel as the alternative material due to its cost-effectiveness and mechanical properties. The chemical composition is summarized in Table 1.
| C | Si | Mn | Cr | P | S | Ni | Cu |
|---|---|---|---|---|---|---|---|
| 0.45 | 0.24 | 0.64 | 0.17 | 0.013 | 0.005 | 0.03 | 0.01 |
Using JMatPro software, we simulated the heat treatment processes for 45 steel. The phase transformation during heating, as shown in Figure 3, indicates that austenitization begins at 720°C, with 50% ferrite and austenite at 735°C, and complete austenite above 780°C. The CCT cooling curve (Figure 4) demonstrates that air cooling at 1°C/s from 860°C to 560°C, followed by holding for 90 minutes and further cooling, results in a ferrite-pearlite microstructure with a hardness of approximately 225 HBS.
We performed transient thermal analysis in ANSYS to model the normalizing heating process. The finite element model, meshed as shown in Figure 5, assumes constant material properties: density \( \rho = 7.85 \times 10^3 \, \text{kg/m}^3 \), and temperature-dependent thermal conductivity \( \lambda \), specific heat capacity \( C_p \), and thermal expansion coefficient \( \alpha \) (Table 2). Convective boundary conditions with a coefficient of 35 W/(m²·°C) were applied.
| Temperature (°C) | λ [W/(m·°C)] | C_p [J/(kg·°C)] | α (×10⁻⁵ /°C) |
|---|---|---|---|
| 20 | 47.68 | 472 | 1.291 |
| 100 | 43.53 | 480 | 1.167 |
| 200 | 40.44 | 498 | 1.038 |
| 300 | 38.13 | 524 | 0.930 |
| 400 | 36.02 | 560 | 0.822 |
| 500 | 34.16 | 615 | 0.710 |
| 600 | 31.98 | 700 | 0.584 |
| 700 | 28.66 | 854 | 0.429 |
| 755 | 25.14 | 1064 | 0.302 |
| 800 | 26.49 | 806 | 0.420 |
| 900 | 25.92 | 637 | 0.520 |
| 1000 | 24.02 | 602 | 0.510 |
The simulation results, depicted in Figure 6, show that the core temperature reaches 860°C after 2400 seconds of heating, confirming the suitability of the normalizing parameters.
For static analysis, we constructed a finite element model of the gear shaft using SOLID45 elements, as illustrated in Figure 7. Constraints were applied to the fixed end (Φ45 mm), and a load of \( F = 9537.03 \, \text{N} \) was applied vertically to the Φ18 mm section. The stress and strain distributions (Figure 8) reveal a maximum stress of 765,952 Pa at the groove base, below the yield strength of normalized 45 steel, and a maximum strain of \( 0.614 \times 10^{-6} \, \text{m} \), which is lower than the theoretical deflection limit. These results validate the structural integrity of the gear shaft under operational loads.
Experimental validation involved manufacturing gear shaft blanks from 45 steel, as per the specifications in Figure 9. Normalizing was conducted in an ITN-500 isothermal normalizing line at 860°C for 120 minutes, followed by air cooling for 300 seconds, isothermal holding at 560°C for 80 minutes, and final air cooling. High-frequency quenching was performed on a GP-100 machine at 100 kW and 100 kHz, with a traverse speed of 400 mm/min and water cooling, followed by tempering at 200°C for 120 minutes.
We assembled transmission units with both 20CrMoH and 45 steel gear shafts and conducted endurance tests on a BSG-0000 dynamometer (Figure 10). The test conditions included an input speed of 1000 rpm and torque of 103 Nm for 1440 minutes. Post-test analysis involved measuring the outer diameter of the Φ18 mm section using a G-90C coordinate measuring machine.
Metallographic examination of normalized 45 steel (Figure 11) showed a microstructure of small blocky ferrite and pearlite, with a hardness of 228 HBS, consistent with JMatPro predictions. After high-frequency quenching and tempering, the surface microstructure (Figure 12) comprised tempered acicular martensite and residual austenite, with a surface hardness of 55 HRC and a hardened layer depth of 1.65 mm (at 450 HV), closely matching the theoretical value of 1.61 mm (error 2.4%).
Wear measurements from the endurance tests are summarized in Table 5. The 45 steel gear shaft exhibited a wear amount of 0.0011 mm, slightly higher than the 0.0010 mm for 20CrMoH, but within acceptable limits for practical applications.
| Material | Before Test (mm) | After Test (mm) | Wear Amount (mm) |
|---|---|---|---|
| 45 Steel | 17.994 | 17.9929 | 0.0011 |
| 20CrMoH | 17.993 | 17.9920 | 0.0010 |
Our findings demonstrate that the 45 steel gear shaft, processed with normalizing and high-frequency local quenching, meets all design requirements for strength, deformation, and wear resistance. The elimination of thread heat treatment ensures a 100% qualification rate for the M10 × 1.25 internal threads. Additionally, the revised heat treatment process reduces the heating time per gear shaft by 37.93%, significantly enhancing production efficiency without compromising performance.
In conclusion, the integration of JMatPro and ANSYS simulations provides a robust framework for optimizing gear shaft materials and heat treatment processes. The proposed 45 steel alternative effectively addresses deformation issues while maintaining mechanical performance, offering a viable solution for automotive transmission applications. Future work could explore other material systems and processing techniques to further improve the durability and efficiency of gear shafts.