In industrial applications, the gear shaft is a critical component for power transmission in heavy machinery such as mining equipment, transportation systems, and agricultural machinery. The gear shaft operates under severe conditions, including high cyclic loads and impact stresses, necessitating robust material selection and heat treatment processes. The 17CrNiMo6 steel, a Cr-Ni-Mo alloy, is widely used for gear shaft manufacturing due to its high strength, compressive resistance, and hardenability. However, the high hardenability of this steel often leads to significant distortion during carburizing and quenching processes, which adversely affects machining precision, assembly accuracy, and service life. To mitigate distortion, pre-heat treatment before carburizing is commonly applied in practice, but the process parameters are typically based on empirical knowledge, lacking quantitative analysis. This study employs finite element simulation to quantitatively analyze the effects of pre-heat treatment on the distortion of a 17CrNiMo6 steel gear shaft, comparing direct carburizing with pre-heat carburizing processes. The temperature fields, stress fields, and distortion behaviors are investigated to optimize pre-heat treatment parameters.
The gear shaft under consideration has a module of 9 mm, 28 teeth, a pressure angle of 20°, and a pitch diameter of 252 mm. The geometry of the gear shaft is symmetric, allowing for a simplified model to reduce computational complexity. The carburizing and quenching process parameters include strong carburizing at 920°C for 21,600 s with a carbon potential of 1.05%, diffusion at 920°C for 10,800 s with a carbon potential of 0.75%, cooling to 840°C in 3600 s, air cooling to 30°C in 3600 s, heating to 840°C for quenching in 10,800 s, and finally quenching in oil at 60°C for 3600 s. Pre-heat treatment involves heating the gear shaft to a specific temperature (e.g., 400°C) and holding for a duration (e.g., 3 h) before carburizing. The finite element model is developed to simulate these processes, incorporating diffusion, heat transfer, stress-strain, and phase transformation phenomena.
The carburizing process is governed by non-steady-state diffusion, following Fick’s second law. The carbon concentration evolution can be described by the partial differential equation:
$$ \frac{\partial C}{\partial t} = \frac{\partial}{\partial x_i} \left( D \frac{\partial C}{\partial x_i} \right) $$
where \( C \) is the carbon concentration in kg/m³, \( t \) is time in seconds, \( x_i \) is the spatial coordinate in meters, and \( D \) is the diffusion coefficient in m²/s. The diffusion coefficient depends on temperature and carbon content, expressed as:
$$ D(T, C) = D_{0.4} \exp \left( -\frac{Q}{RT} \right) \exp[-B(0.4 – C)] $$
Here, \( D_{0.4} = 25.5 \, \text{mm}^2/\text{s} \) is the diffusion constant at 0.4% carbon content, \( B = 0.8 \) is a constant, \( Q = 141 \, \text{kJ/mol} \) is the activation energy for carbon diffusion, \( R \) is the gas constant, and \( T \) is temperature in Kelvin. The boundary condition for carbon diffusion at the gear shaft surface is given by:
$$ -D \frac{\partial C}{\partial x_i} = -\beta (C_e – C_s) $$
where \( C_e \) is the ambient carbon potential, \( C_s \) is the surface carbon concentration, and \( \beta \) is the carbon transfer coefficient, defined as:
$$ \beta = \beta_0 \exp \left( -\frac{E}{RT} \right) $$
with \( \beta_0 = 0.00347 \, \text{mm/s} \) and \( E = 34 \, \text{kJ/mol} \).
The temperature field during heat treatment is modeled using the three-dimensional heat conduction equation based on Fourier’s law and energy conservation:
$$ \lambda \left( \frac{\partial^2 T}{\partial r^2} + \frac{1}{r} \frac{\partial T}{\partial r} + \frac{\partial^2 T}{\partial x^2} \right) + Q = \rho c_p \frac{\partial T}{\partial t} $$
where \( T \) is the temperature in °C, \( t \) is time in seconds, \( \lambda \) is the thermal conductivity in W/(m·°C), \( \rho \) is the density in kg/m³, \( c_p \) is the specific heat capacity in J/(kg·°C), \( Q \) represents heat sources from plastic work and phase transformations in J/kg, and \( r \) and \( x \) are radial and axial coordinates. The initial condition assumes a uniform temperature distribution:
$$ T|_{t=0} = T_0(x_i) $$
The boundary condition for convective heat transfer is:
$$ -\lambda \frac{\partial T}{\partial n} = H(T – T_f) $$
where \( H \) is the convective heat transfer coefficient, \( T_f \) is the ambient temperature, and \( n \) is the normal direction.
The stress-strain field accounts for elastic, plastic, thermal, and phase transformation strains. The total strain rate tensor is given by:
$$ \dot{\varepsilon}_{ij} = \dot{\varepsilon}_{ij}^t + \dot{\varepsilon}_{ij}^e + \dot{\varepsilon}_{ij}^p + \dot{\varepsilon}_{ij}^{tr} + \dot{\varepsilon}_{ij}^{tp} $$
where the superscripts denote thermal (\( t \)), elastic (\( e \)), plastic (\( p \)), transformation (\( tr \)), and transformation plasticity (\( tp \)) components. The plastic flow stress is a function of strain, strain rate, and temperature:
$$ \bar{\sigma} = \bar{\sigma}(\varepsilon, \dot{\varepsilon}, T) $$
Phase transformations during heat treatment include diffusion-based transformations (e.g., austenite to ferrite, pearlite, bainite) and non-diffusive martensitic transformation. The austenitization kinetics are described by:
$$ \xi_A = 1 – \exp \left[ A \left( \frac{T – Ac_1}{Ac_3 – Ac_1} \right)^D \right] $$
where \( \xi_A \) is the volume fraction of austenite, \( Ac_1 \) and \( Ac_3 \) are the start and finish temperatures for austenitization, and \( A = -4 \) and \( D = 2 \) are material constants. The martensitic transformation follows the Koistinen-Marburger equation:
$$ \xi_M = 1 – \exp[-\alpha(M_s – T)] $$
with \( \xi_M \) as the martensite volume fraction, \( M_s \) as the martensite start temperature, and \( \alpha = 0.011 \, \text{K}^{-1} \).
The finite element model of the gear shaft is created using a 1/14 symmetric segment to leverage symmetry, reducing computational effort. The mesh consists of 40,280 elements and 9,464 nodes, ensuring accuracy in capturing temperature and stress gradients. The diffusion coefficients for carbon in austenite are temperature and carbon content-dependent, as summarized in Table 1.
| Carbon Content (wt%) | 1203 K | 1100 K | 1050 K | 1010 K | 1000 K |
|---|---|---|---|---|---|
| 0.2 | 16.390 | 4.3780 | 2.1010 | 1.1082 | 0 |
| 0.4 | 19.233 | 5.1377 | 2.4656 | 1.3005 | 0 |
| 0.6 | 22.571 | 6.0291 | 2.8934 | 1.5262 | 0 |
| 0.8 | 26.487 | 7.0752 | 3.3954 | 1.7910 | 0 |
| 1.0 | 31.082 | 8.3021 | 3.9846 | 2.1017 | 0 |
For quenching, the heat transfer coefficient between 17CrNiMo6 steel and KR128 oil is critical and varies with temperature, as shown in Figure 1. This coefficient influences the cooling rate and subsequent phase transformations.
Simulation results for direct carburizing without pre-heat treatment reveal significant distortion in the gear shaft. The radial distortion ranges from -0.364 mm to 0.480 mm, with contraction at the tooth ends and expansion at the core, particularly in the gear section. The maximum distortion occurs at the center of the teeth, leading to non-uniform machining allowances and increased residual stresses. The average stress distribution shows high tensile and compressive stresses, contributing to potential failure risks. For instance, the residual stress can exceed 500 MPa in critical regions, emphasizing the need for distortion control.
To evaluate pre-heat treatment effects, various pre-heating parameters are tested, as listed in Table 2. The radial distortion is measured for each case, and the optimal parameters are identified based on minimal distortion.
| Process No. | Pre-Heat Temperature (°C) | Pre-Heat Time (h) | Radial Distortion Range (mm) |
|---|---|---|---|
| 1 | 350 | 2 | -0.305 to 0.421 |
| 2 | 400 | 2 | -0.291 to 0.398 |
| 3 | 450 | 2 | -0.312 to 0.435 |
| 4 | 350 | 3 | -0.284 to 0.385 |
| 5 | 400 | 3 | -0.189 to 0.126 |
| 6 | 450 | 3 | -0.275 to 0.401 |
| 7 | 350 | 4 | -0.298 to 0.412 |
| 8 | 400 | 4 | -0.231 to 0.345 |
| 9 | 450 | 4 | -0.320 to 0.445 |
Process 5 (400°C for 3 h) exhibits the smallest distortion range, from -0.189 mm to 0.126 mm, indicating that pre-heat treatment at 400°C for 3 h is optimal. The radial distortion and average stress distributions for this case are compared with direct carburizing. After pre-heat treatment, the radial distortion reduces significantly, with the maximum distortion decreasing from 0.480 mm to 0.126 mm. The average stress also shows a reduction, with peak stresses lowering by approximately 20-30%, enhancing the gear shaft’s dimensional stability.
A detailed analysis along the gear shaft axis and teeth is conducted by sampling points. For the axis, 300 points are evaluated, and for the teeth, 100 points are assessed. The radial distortion curves for direct carburizing and pre-heat carburizing are plotted. Along the axis, the maximum distortion in direct carburizing is 0.143 mm at 160 mm from the end, whereas pre-heat treatment reduces it to 0.126 mm. The overall distortion range for direct carburizing is 0.016 mm to 0.143 mm (range: 0.127 mm), and for pre-heat treatment, it is 0.018 mm to 0.126 mm (range: 0.108 mm). In the teeth region, direct carburizing shows a distortion range of -0.218 mm to 0.072 mm (range: 0.290 mm), while pre-heat treatment narrows it to -0.189 mm to 0.061 mm (range: 0.250 mm). These results confirm that pre-heat treatment effectively minimizes distortion in the gear shaft.
The temperature field during heating is critical for understanding distortion mechanisms. In direct carburizing, the gear shaft is heated rapidly to 920°C, creating a large temperature gradient between the surface and core. The maximum temperature difference reaches 485°C initially, inducing high thermal stresses. In contrast, pre-heat treatment involves heating to 400°C first, holding for 3 h, and then proceeding to carburizing. This step reduces the initial temperature gradient during carburizing, with the maximum difference dropping to 285°C. The reduced gradient lowers thermal stresses, as evidenced by the average stress analysis. For example, at the tooth tip and core, the stress evolution during heating shows that pre-heat treatment results in lower peak stresses (e.g., 150 MPa vs. 250 MPa in direct carburizing). The stress history can be modeled using the strain rate equation, incorporating thermal and phase transformation effects.
The phase transformations during quenching contribute to distortion through volumetric changes. The martensitic transformation, in particular, introduces expansion, which combined with thermal contraction, leads to complex stress states. The volume fraction of martensite \( \xi_M \) can be calculated using the Koistinen-Marburger equation, and the associated strain \( \varepsilon^{tr} \) is proportional to the transformation volume change. For 17CrNiMo6 steel, the martensite start temperature \( M_s \) is approximately 350°C, and the transformation strain rate \( \dot{\varepsilon}^{tr} \) is derived from the phase kinetics. Pre-heat treatment moderates these effects by reducing the cooling rate and promoting more uniform phase transformation.
Experimental validation from literature supports the simulation findings. For instance, studies on similar gear shafts show that pre-heating at 400°C for 3 h before carburizing reduces radial runout from 0.58-0.69 mm to 0.31-0.47 mm, aligning with the distortion reduction observed in simulations. This consistency underscores the reliability of the finite element model in predicting gear shaft behavior during heat treatment.
In conclusion, pre-heat treatment before carburizing is an effective strategy to control distortion in 17CrNiMo6 steel gear shafts. The optimal parameters—400°C for 3 h—minimize radial distortion and residual stresses by reducing temperature gradients and thermal stresses during heating. The finite element analysis provides a quantitative basis for optimizing heat treatment processes, enhancing gear shaft performance and longevity. Future work could explore the effects of cooling rates and alternative pre-heat temperatures on microstructural evolution and fatigue properties.
The mathematical models and simulation approach presented here can be extended to other components and materials, contributing to advanced manufacturing practices. The integration of diffusion, thermal, and mechanical models enables comprehensive analysis of heat treatment distortions, facilitating the design of more reliable gear shafts for demanding applications.