Abstract
Spiral bevel gear is widely used in mechanical equipment due to their high load-bearing capacity and smooth transmission. Quenching is an indispensable process in the manufacturing of spiral bevel gear. However, the design of quenching processes for spiral bevel gear often employs a trial-and-error method, which is time-consuming and costly. Therefore, numerical simulation techniques, which offer advantages such as shorter cycle times and lower costs, have become important means for contemporary quenching process design.
In the numerical simulation study of quenching processes, the heat transfer coefficient is an important input parameter. Due to its complex influencing factors, the determined results lack universality and significantly increase the complexity and errors in the numerical simulation process. This paper proposes a new numerical simulation method for quenching processes by expanding the simulation domain, introducing the coupling heat transfer between the liquid quenching medium and the workpiece, and replacing the role of the heat transfer coefficient in the numerical simulation of quenching processes.
The method is applied to the numerical simulation of quenching in spiral bevel gear, effectively avoiding the process of experimentally obtaining heat transfer coefficients. This method provides a better solution to the problem of varying heat transfer coefficients in different parts of spiral bevel gear due to their shape and size. The paper’s approach provides guidance for determining the quenching process parameters of spiral bevel gear.
The main research findings of this paper are as follows:
- Research on the numerical simulation method for thermo-fluid-solid coupling during the quenching process.
- Numerical simulation and experimental study of thermo-fluid-solid coupling during the quenching process.
- Study of the effect of quenching medium flow parameters on the quenching process.
- Numerical simulation study of thermo-fluid-solid coupling during quenching of spiral bevel gear.
1. Introduction
1.1 Research Background and Significance
1.1.1 Source of the Research Topic
The research topic of this paper is derived from the project “Research on the Formation Mechanism and Control Technology of Heat Treatment Distortion of Spiral Bevel Gear” supported by the National Natural Science Foundation of China (Grant No. 52165005).
1.1.2 Research Status and Significance
Spiral bevel gear is important components in mechanical transmission systems, widely used in aerospace, automotive, shipbuilding, and other fields due to their high load-bearing capacity, smooth transmission, and high transmission efficiency. The heat treatment process, especially the quenching process, plays a crucial role in improving the mechanical properties and service life of spiral bevel gear.
However, the quenching process of spiral bevel gear is complex and involves multiple physical fields such as temperature, stress, and microstructure. Traditional quenching process design relies heavily on empirical methods, which are time-consuming, costly, and difficult to optimize. Therefore, numerical simulation technology has gradually become an important means to study and optimize the quenching process of spiral bevel gear.
The numerical simulation of the quenching process mainly involves solving the heat transfer equation, phase transformation kinetic equation, and stress-strain equation. Among them, the heat transfer coefficient between the quenching medium and the workpiece surface is a key parameter affecting the accuracy of the simulation results. However, due to the complex influencing factors of the heat transfer coefficient, such as the flow state of the quenching medium, the shape and size of the workpiece, and the temperature changes during quenching, it is difficult to obtain accurate heat transfer coefficients through experiments.
Therefore, this paper proposes a new numerical simulation method for the quenching process of spiral bevel gear based on the thermo-fluid-solid coupling model. This method expands the simulation domain to include the quenching medium and realizes the coupling simulation of the quenching medium and the workpiece. By doing so, it avoids the need to experimentally obtain heat transfer coefficients and improves the accuracy and efficiency of quenching process simulation.
1.2 Research Status at Home and Abroad
1.2.1 Research Status of Numerical Simulation of Quenching Cooling Process
The simulation of the quenching cooling process began in the 1970s. Japanese scholars Inoue et al. first proposed a temperature-organization coupling model and later added a stress model to realize the coupling simulation of the three physical fields of temperature, organization, and stress. They also developed numerical simulation software such as HEARTS and COSMAP for various quenching process simulations [1-3].
Subsequently, scholars from various countries have further improved the theoretical models and simulation tools for quenching simulation. For example, Lee S J combined a new phase transformation kinetic model with ABAQUS and its subroutines to establish the relationship between deformation and phase transformation [4]. Sugianto improved the thermal-elastic-plastic model and conducted secondary development of the DEFORM software to obtain more accurate quenching stress-strain results [5].
Compared with foreign countries, domestic research on quenching simulation started later in the 1980s. To better develop numerical simulation in China, scholar Liu Zhuang developed the NSTH (Numerical Simulation of Heat Treatment) software package to simulate the quenching of large forgings, which was verified by projects from Tsinghua University and Shanghai Heavy Machinery Plant [6-7].
Shanghai Jiao Tong University has been committed to research on heat treatment process simulation. Academician Pan Jiansheng added the treatment of interface condition changes to quenching simulation, successfully simulating the temperature, organization, and stress during quenching of workpieces of various shapes [8-9].
1.2.2 Research Status of the Effect of Quenching Medium on Quenching Cooling Process
With the increasing demand for quenching quality, scholars have gradually focused on the influence of quenching medium flow parameters on the quenching effect. In the early 20th century, scholars such as Chen Suyu combined computational fluid dynamics (CFD) with quenching tank structure design to analyze the influence of different flow states of quenching oil on the cooling characteristics of the quenching process [10-11].
Subsequently, scholars such as Barren and Colburn further studied the heat transfer characteristics and flow state of quenching oil and proposed methods to improve the uniformity of quenching oil flow and the cooling effect of the quenching process [12-13].
In recent years, with the continuous development of computer technology and numerical simulation methods, scholars have gradually shifted their research focus to the multi-field coupling simulation of the quenching process. By combining fluid dynamics, heat transfer, and solid mechanics, a more comprehensive understanding of the quenching process has been achieved.
1.2.3 Research Status of Heat Treatment of Spiral Bevel Gear
Spiral bevel gear is widely used in various mechanical equipment due to their high load-bearing capacity and smooth transmission. The heat treatment process, especially the quenching process, has a significant impact on the performance and service life of spiral bevel gear.
However, due to the complex shape and manufacturing process of spiral bevel gear, there are still many challenges in the heat treatment process. For example, the quenching distortion of spiral bevel gear is difficult to control, and the quenching process parameters need to be optimized to ensure the hardness and toughness of the gears.
In recent years, with the continuous development of numerical simulation technology, scholars have gradually applied it to the heat treatment process of spiral bevel gear. For example, scholars such as Zhang Yifeng and Wang Leigang have studied the phase transformation and deformation of spiral bevel gear during quenching and proposed methods to control quenching distortion [14-15].
However, the current research on the heat treatment of spiral bevel gear is still relatively limited, and there is a lack of systematic research on the quenching cooling process of spiral bevel gear. Therefore, this paper proposes a new numerical simulation method based on the thermo-fluid-solid coupling model to study the quenching cooling process of spiral bevel gear, aiming to provide theoretical support and technical guidance for the optimization of the quenching process of spiral bevel gear.
1.3 Research Methods and Content of This Paper
This paper proposes a new numerical simulation method for the quenching process of spiral bevel gear based on the thermo-fluid-solid coupling model. The main research contents are as follows:
- Research on the numerical simulation method for thermo-fluid-solid coupling during the quenching process: Analyze the discrete principles and numerical analysis methods of the quenching medium fluid domain and the quenched workpiece solid domain. Establish a thermo-fluid-solid coupling model and solve the evolution laws of the flow field, temperature field, microstructure field, and stress field during the quenching process using the finite element-finite volume coupling method.
- Numerical simulation and experimental study of thermo-fluid-solid coupling during the quenching process: Build a numerical simulation platform for the quenching cooling process based on the thermo-fluid-solid coupling model. Conduct water quenching experiments on 45 steel rods to verify the accuracy of the simulation results.
- Study of the effect of quenching medium flow parameters on the quenching process: Design quenching tank structures to change the flow state of the quenching medium and study the influence of quenching medium flow parameters on the quenching effect using numerical simulation.
- Numerical simulation study of thermo-fluid-solid coupling during quenching of spiral bevel gear: Apply the proposed numerical simulation method to the quenching process of spiral bevel gear and study the influence of different quenching process parameters on the quenching effect.
2. Research on Numerical Simulation Method for Thermo-Fluid-Solid Coupling During Quenching Process
2.1 Introduction
In the quenching process, the heat transfer between the quenching medium and the workpiece is a complex physical phenomenon involving fluid dynamics, heat transfer, and solid mechanics. Traditional numerical simulation methods often simplify this process by using a heat transfer coefficient to characterize the heat transfer intensity between the quenching medium and the workpiece surface. However, due to the complex influencing factors of the heat transfer coefficient, it is difficult to obtain accurate values through experiments, which affects the accuracy of the simulation results.
To overcome this limitation, this paper proposes a new numerical simulation method based on the thermo-fluid-solid coupling model. This method expands the simulation domain to include the quenching medium and realizes the coupling simulation of the quenching medium and the workpiece. By doing so, it avoids the need to experimentally obtain heat transfer coefficients and improves the accuracy and efficiency of quenching process simulation.
2.2 Finite Element-Finite Volume Coupling Heat Transfer Mathematical Model
2.2.1 Fluid-Solid Coupling Heat Transfer Model
In the quenching process, the quenching medium and the workpiece constitute a fluid-solid coupling system. The heat transfer between the two involves complex physical phenomena such as convection, conduction, and phase transformation. To accurately simulate this process, it is necessary to establish a fluid-solid coupling heat transfer model.
The fluid-solid coupling heat transfer model in this paper is based on the conservation laws of mass, momentum, and energy. For the fluid domain, the finite volume method is used to discretize and solve the governing equations. For the solid domain, the finite element method is used to discretize and solve the heat conduction equation, phase transformation kinetic equation, and constitutive equation.
2.2.2 Finite Element-Finite Volume Coupling Calculation Method
In the fluid-solid coupling heat transfer model, the discrete methods for the fluid domain and the solid domain are different. Therefore, it is necessary to adopt an appropriate coupling calculation method to realize the data exchange between the two domains.
In this paper, the wall function method and Gaussian integral interpolation method are used to realize the coupling calculation between the fluid domain and the solid domain. The wall function method is used to calculate the heat flux at the fluid-solid interface, and the Gaussian integral interpolation method is used to interpolate the temperature and other physical quantities between the two domains.