Abstract
Spiral bevel gear, as crucial components in mechanical transmissions, are primarily employed in intersecting or staggered shaft transmissions. Currently, milling remains the dominant method for manufacturing spiral bevel gear, despite its inefficiencies in productivity and material utilization. Moreover, the continuous metal flow lines within the gears are severed during milling, significantly reducing their strength and service life. Precision forging has shown promising results in enhancing the service life of spiral bevel gear driven wheels by nearly 70% compared to traditional milling. However, issues such as difficult die exit, low die life, and inadequate tooth height filling persist in the precision forging of spiral bevel gear pinions. To address these challenges, the roll-extrusion method can be considered for forming the pinion teeth. Near-net-shape rolling technology represents a novel manufacturing process for spiral bevel gear. By utilizing this technology, not only can production costs be reduced, but the bending strength of gear teeth is also significantly improved due to the more rational distribution of metal flow fibers along the tooth profile. This paper proposes a new rolling process for spiral bevel gear pinions based on local induction heating.
1. Introduction
Spiral bevel gear serve as vital components in mechanical transmissions, facilitating power transmission between intersecting or staggered shafts. They are renowned for their smooth transmission, high load-bearing capacity, efficient power transmission, and compact structure, making them widely applicable in automotive drive axles, aerospace main transmissions, and marine applications. Currently, the primary method for manufacturing spiral bevel gear involves milling, which suffers from low productivity, poor material utilization, and the severance of continuous metal flow lines within the gears, leading to a significant reduction in strength and service life .
Precision forging near-net shape technology has demonstrated a remarkable increase in gear service life and processing efficiency when applied to spiral bevel gear driven wheels. For instance, the service life of gears manufactured using this technique is nearly 70% higher, and processing efficiency is enhanced by over 15 times compared to traditional milling . Near-net-shape gears require only finishing operations before use. High Zhenshan has proposed optimization measures to address issues such as high forming loads and inadequate filling of gear tooth corners during the forging of spiral bevel gear. By leveraging numerical simulations and multi-objective orthogonal optimization experiments, he analyzed the influence of design variables on die life, considering forming loads and wear as objective functions . Nevertheless, challenges like difficult die exit, low die life, and inadequate tooth height filling persist in the precision forging of spiral bevel gear pinions, necessitating the continued use of traditional milling for their manufacture.
Near-net-shape rolling technology represents a novel approach in the manufacture of spiral bevel gear. This technology has garnered significant attention and in-depth research from scholars worldwide, particularly in the processing of threads, splines, and straight (helical) cylindrical gears . Based on local induction heating, the near-net-shape rolling of spiral bevel gear involves heating the billet’s forming region using an electromagnetic induction device. This results in a radial temperature gradient within the billet, with the forming region maintaining a high temperature while the inner hole remains cooler. Rolling is then performed under these conditions. Compared to conventional furnace heating, this method enhances heating efficiency, improves the tooth surface quality of the rolled gear, and reinforces the rigidity of the billet’s inner hole.
This paper delves into several key technical aspects of the near-net-shape rolling of spiral bevel gear, including temperature distribution within the billet during rolling, tooth surface quality, tooth tip defects, and tooth filling patterns. It presents quality control strategies for addressing defects encountered during near-net-shape rolling and validates these strategies through experimental research on a rolling test platform.
2. Literature Review
2.1 Research Status of Gear Rolling Forming Technology
Gear rolling forming technology emerged in the early 1950s in Germany, the United States, and Japan. By the 1960s, it had been applied to small-module cylindrical gears and splines. In the 1970s, cold rolling near-net shape technology witnessed rapid development in Japan, leading to the introduction of various rolling methods [12, 13]. In the early 1980s, China also began researching and developing precision cold rolling technology, establishing a bevel gear cold rolling production line at the Shanghai Industrial Sewing Machine Factory .
Recently, with advancements in digital technology and plastic forming theory, an increasing number of researchers globally have employed numerical simulations to study near-net-shape rolling technology. Currently, gear rolling forming faces challenges such as a weak theoretical foundation, the need to improve the accuracy of finite element simulations, and the slow development of experimental equipment.
Zhu Zhenlin and Wang Guangchun have systematically introduced and analyzed the current state of gear rolling technology, highlighting its advantages and existing deficiencies. They also examined the causes of imprecise tooth division and the “rabbit ear” defect during the rolling forming process . Zhu Xiaoxing conducted high-temperature rheological experiments on SAE8620H using a Gleeble-1500D dynamic thermal simulator and performed rolling experiments on cylindrical gears. By optimizing the tool wheel structure, increasing billet temperature, and reducing friction coefficients, he effectively suppressed the “rabbit ear” defect to a certain extent.
Ziyong Ma et al. studied the material flow pattern during the rolling forming process by tracing the flow trajectory of the billet material. They found that end flow occurs at the tooth root of the formed gear, and material located at the neutral plane experiences significant flow resistance, resulting in minimal flow towards the ends . Minchao Cui et al. established an integrated rolling and extrusion process and conducted finite element simulations and experiments. Their findings revealed that during rolling, metal material flow primarily occurs in the forming region on the billet’s outer surface, with negligible plastic deformation observed at the inner hole .
Moriwaki Ichiro et al. investigated material flow during the rolling forming of plastic gears, discussing the effects of friction and sliding speed. Jun Li et al. utilized DEFORM software to analyze the influence of die feed rate, friction coefficient, and die tooth count on the “rabbit ear” defect at the tooth tip of rolled gears. They further validated their findings through experiments. By analyzing the formation mechanism of the “rabbit ear” defect using the point tracking command in DEFORM’s post-processing, they discovered a significant difference in material flow velocity between the tooth flanks and tooth center, which they postulated as a potential cause of the defect.
Dongcheng Li analyzed the effect of process parameters on left and right “rabbit ears” during the rolling forming of spiral bevel gear. Based on the principle that the material area flowing towards the target gear tooth height during each die downward extrusion equals the material area flowing in the tooth height direction, he proposed a method to suppress “rabbit ears” through multiple rolling formations. Ziyong Ma et al. studied the influence of die structural parameters on rolling forming force, tooth root stress of the die, “rabbit ear” defects, and tooth surface scratches during the axial rolling forming of cylindrical gears. By optimizing die structural parameters, they were able to reduce the height of “rabbit ears”, decrease stress at the die tooth root, and eliminate tooth surface scratches to a certain extent.
Khodaee and Melander assessed the quality of formed gears by changing the rotation direction of the die during the rolling forming process. They found that positive and reverse experiments could inhibit the “rabbit ear” defect to a certain extent and analyzed the variations in radial load, axial load, and torque during the rolling forming process. Tao Wu calculated the relationship between the die feed volume and the target gear tooth height using the equal volume method. He proposed a new rolling process that utilizes auxiliary dies to restrict the growth space of “rabbit ear” defects. Numerical simulations and experiments demonstrated a noticeable reduction in “rabbit ear” defects using this process.
Tang Hongyan employed the local synthesis method, gear meshing principle, and equal volume method to establish finite element models of the die and billet. By drawing on domestic and international research on cylindrical gear rolling, she constructed a numerical simulation platform for spiral bevel gear rolling. Zhang Qingjie conducted finite element simulations of the spiral bevel gear rolling process, investigating the impact of different process parameters on rolling forming defects such as “rabbit ears”. Through various combinations of process parameters, he was able to suppress “rabbit ears” to a certain extent.
Liu Saisai utilized orthogonal experiments to study the impact of different process parameters on “rabbit ears” defects and metal flow lines. She obtained the optimal combination of process parameters and validated this combination through experiments on a rolling forming test platform. Seizo Uematsu studied the effect of changes in billet rotation speed on tooth profile errors during the rolling forming process. Alireza Khodaee et al. used DEFORM software to inspect the accuracy of rolled gears with different modules, finding that gears with smaller modules exhibit smaller involute profile errors, while those with larger modules undergo significant total material deformation during rolling.
Neugebauer et al. addressed the issue of decreasing pitch values in the rolled gear as the round die continuously feeds. They proposed adding additional motion compensation to the die during the rolling process to control these variations. Experimental research and validation revealed that this process enhances the pitch accuracy of rolled gears by nearly 50%. Reimund Neugebauer et al. studied the quality of rolled gears, discovering that gear quality depends not only on the geometric accuracy of the die but also on its motion. They attributed the generation of pitch errors to the continuous change in pitch circle diameter of the billet without corresponding compensation in die rotation speed.
Da-Wei Zhang investigated the motion characteristics between the die and workpiece during different stages of rolling. He established a mathematical model relating the centroid, transmission ratio, and instantaneous rotation center during the rolling process, providing a theoretical basis for motion compensation schemes during rolling. Hiroshi Sasaki optimized the rolling process of helical gears using a newly developed double roll mold transverse CNC rolling machine with pitch correction function, thereby enhancing the tooth surface accuracy of rolled gears.
Jun Li et al. studied the slippage defects between the die and billet during the initial stage of rolling through finite element simulations. They analyzed the influence of initial engagement depth, friction coefficient, and die tooth count on slippage. Ma Ziyong established a contact ratio model between the die and rolled gear based on the characteristics of cylindrical gear axial rolling. He studied the relationship between die tooth count, drive gear tooth count, center distance, pressure angle, and initial engagement depth with contact ratio, finding that initial die penetration depth, drive gear tooth count, and friction coefficient between the die and billet significantly impact tooth division accuracy.
Jun Zhao et al. researched the kinematic relationship between the die and rolled gear during the rolling process. Through numerical simulations, they discovered that ensuring an initial engagement depth of no less than 1 mm between the die and billet can guarantee their meshing motion and analyzed the variation in load during the rolling process . Tao Wu et al. studied the axial rolling process of cylindrical gears, establishing formulas for calculating parameters such as die tooth tip diameter, tooth point radius, tooth tip pressure angle, and tooth cone angle. They found that the proposed process improves the accuracy of formed gears to a certain extent.
Youxin Luo et al. studied the tooth filling pattern of the billet during the axial feed rolling of cylindrical gears. Based on the characteristics of rolling, they derived contact stress and sliding ratio models between the billet and die. Through numerical simulations and experiments, they analyzed the influence of billet rotation speed, tooth count, and pressure angle on the effective tooth depth during rolling. Additionally, they found that the tooth tip profile shift coefficient of the die significantly impacts the effective tooth depth of rolled gears .
Amir A. Kamouneh and Jun Li from the University of Michigan proposed a plate rolling process for helical cylindrical gears and employed a combination of finite element simulations and experiments to analyze tooth tip underfilling during the rolling forming process. They addressed this issue by altering the billet shape. Ziyong Ma et al. conducted in-depth research on the structural parameters of cylindrical gear billets, proposing a calculation method and theoretical model for preform billet dimensions. Using DEFORM software, they explored the influence of different tooth counts, modules, pressure angles, and materials on the effective tooth height and defects at the tooth tip of rolled gears. They validated the proposed model through experiments on a rolling test platform.
Xiaobin Fu et al. introduced a new rolling process with a finishing roll, establishing and solving the motion equation of the finishing roll. Through numerical simulations and experiments, they found that this process can enhance the effective tooth height of rolled gears to a certain extent. Min-Chao Cui et al. studied the influence of die structural parameters and temperature on tooth profile filling and forming load during rolling. They identified suitable combinations of process parameters through numerical simulations and validated their findings through experiments on a rolling test platform. Additionally, they modified the tooth root of the die to avoid a rapid increase in forming load due to an excessively large initial billet diameter.
Dawei Zhang et al. studied the contact state between the die and billet using SLFM, deriving a mathematical model relating die feed volume to rolling force. By comparing numerical simulation results of rolling force with analytical results, they found good agreement between the two . Jie Tang et al. conducted error analysis on measured rolling forces during double-die rolling experiments of cylindrical gears, establishing a mathematical model relating rolling force to radial deformation. Through MATLAB calculations and finite element analysis, they found that radial deformation error was only 0.1 μm.
Zhao Jun et al. discovered through orthogonal experiments that equivalent stress in the billet during near-net-shape rolling is most significantly influenced by die feed speed. Both die feed speed and temperature have nearly equal effects on equivalent strain, while billet temperature has the most significant impact on forming load. Additionally, they analyzed the stress experienced by the die at different stages of spiral bevel gear rolling and the influence of billet structural parameters on the rolling process.
Xiaobin Fu et al. conducted secondary development of the commercial software DEFORM, enabling temperature compensation of the billet through local induction heating when its temperature falls below a given threshold during cylindrical gear rolling. After induction heating, a radial temperature gradient is formed in the billet, with temperatures gradually decreasing from the forming region to the inner hole, enhancing the rigidity of the inner hole. Numerical simulations revealed that local induction heating of the billet’s forming region before rolling can reduce rolling force, increase die life, and improve the quality of formed gears.
Bo Peng et al. studied the influence of the involute tooth profile of the die on its strength and rigidity during the rolling process. Through theoretical analysis, they found that adding an elliptical transitional curve at the tooth root can reduce the maximum stress at the tooth root, increasing die strength and rigidity and prolonging its service life. Finite element simulations revealed that the rigidity of the die with an elliptical transitional curve is approximately 10% higher compared to that with a normal transitional curve.
Li Yuxi studied the hardness and strength of gears formed through cold roll beating using different materials. Microscopic analysis revealed significant enhancements in tooth hardness and strength after cold roll beating. Li He conducted research on the microstructure of rolled gears, performing secondary development of the commercial software DEFORM to simulate the evolution of microstructure and metal flow lines in rolled gears under different process parameters. His findings revealed the metal flow pattern during rolling and validated the accuracy of numerical simulations through experiments.
Fu Xiaobin from the University of Science and Technology Beijing studied the microstructure evolution of cylindrical gears rolled using local induction heating. Fengkui Cui et al. investigated metal flow during cold rolling, analyzing metal flow lines, metallographic structure, and grain characteristics at different positions on the formed gear. Their findings indicated that during cold rolling, particles flow in the direction of least resistance.
Zhang Guang studied the equivalent residual stress at different tooth surface positions of face gears rolled using DEFORM software. Numerical simulation results revealed that the maximum equivalent residual stress occurs at the tooth root, with maximum load being proportional to die feed speed and inversely proportional to die rotation speed . Jin Yuanyuan conducted numerical simulations of face gears rolled for aerospace applications using DEFORM, analyzing changes in tooth surface residual stress under different process parameters. She employed the response surface method to analyze residual stress values and depths under various process parameters, obtaining the optimal combination. Finally, she validated the controllability of surface residual stress in face gears rolled through experiments and simulations within the error range.
Z.H. Ding et al. experimentally studied the residual stress in cold-rolled involute splines. Their results showed that residual stress increases with surface depth along the tooth profile, with the minimum stress occurring at the spline tooth surface. Additionally, die feed speed and rotation speed significantly impact residual stress at the tooth profile and tooth root, while their effect on residual stress at the tooth tip and pitch is less pronounced. Die feed speed increases the depth of the residual stress layer, whereas rotation speed has the opposite effect.
2.2 Research Status of Induction Heating Technology
2.2.1 Basic Principles of Electromagnetic Induction Heating
Electromagnetic induction occurs when an alternating current passes through a heating coil, generating a changing magnetic field around the element. This induces a flowing current within the element, with electrons colliding with thermal atoms during their directed movement, converting energy into heat. The thermal effect of electric current can be quantitatively described using Joule’s Law.
When a direct current passes through a conductor, the current density is uniformly distributed across the conductor’s cross-section. In contrast, when an alternating current passes, the current density distribution is non-uniform, gradually weakening from the outer surface to the center. This phenomenon is known as skin effect and can be quantitatively expressed using the formula:
i_I = i_0 e^{-\frac{r}{\delta}} \] where: – \( i_I \) is the current intensity at a distance \( r \) from the surface; – \( i_0 \) is the surface current intensity; – \( \delta \) is the current penetration depth; – \( \rho \) is the resistivity; – \( \mu_r \) is the relative magnetic permeability; – \( f \) is the current frequency. From the formula, it can be observed that the current penetration depth is related to the current frequency \( f\delta = \sqrt{\frac{2\rho}{\omega\mu}} \] where \( \delta \) represents the skin depth, \( \rho \) is the resistivity of the material, \( \omega \) is the angular frequency of the alternating current, and \( \mu \) is the permeability of the material. The skin effect explains why the heating effect is more concentrated near the surface of the conductor when using alternating current.
2.2.2 Advancements in Induction Heating Technology
Induction heating technology has seen significant advancements in recent years, driven by improvements in power electronics, control systems, and materials science. These advancements have led to higher efficiency, better temperature control, and increased versatility in applications. One key development is the use of solid-state power supplies, such as inverters, which convert direct current (DC) to alternating current (AC) at high frequencies. These power supplies enable precise control over the heating process and allow for rapid changes in power output, improving the overall efficiency and responsiveness of induction heating systems. Another important advancement is the implementation of closed-loop temperature control systems. By continuously monitoring the temperature of the workpiece and adjusting the power output accordingly, these systems ensure more accurate and uniform heating, reducing the risk of overheating or underheating. Additionally, advancements in coil design and materials have improved the effectiveness and efficiency of induction heating. Customized coils can be designed to optimize the heating pattern for specific applications, while the use of high-performance materials, such as copper alloys with low resistivity and high thermal conductivity, enhances the coil’s ability to transfer energy to the workpiece.
2.2.3 Applications of Induction Heating
Induction heating technology is widely used in various industries due to its numerous advantages, including fast heating rates, precise temperature control, and energy efficiency. Some of the primary applications include: – **Metal Heat Treatment**: Induction heating is used for processes such as annealing, quenching, and tempering, providing rapid and uniform heating of metal parts. – **Melting and Holding of Metals**: Induction furnaces are employed for melting and holding various metals, offering precise temperature control and reduced energy consumption. – **Welding and Brazing**: Induction heating can be used for welding and brazing applications, particularly in situations where precise control over the heating process is required. – **Heating of Plastics and Composites**: Induction heating is employed in the plastics and composites industry for processes such as curing and molding. – **Food Processing**: Induction heating is used in food processing for tasks such as pasteurization and sterilization, providing rapid and uniform heating without directly contacting the food product. Overall, the research status of induction heating technology continues to evolve, with ongoing advancements in power electronics, control systems, and coil design driving improvements in efficiency, precision, and versatility. As this technology continues to mature, it is expected to find even wider applications in various industries.