This paper focuses on the study of tool wear and workpiece surface roughness in the process of milling spiral bevel gears. The research starts from the forming theory and meshing principle of spiral bevel gears to establish the tool wear and surface roughness mathematical models. Through simulation analysis of the tool wear form and the change law of the machined workpiece surface strain under different cutting parameters, combined with the cutting experiment to explore the change law of the tool wear form, mechanism and the surface roughness of the workpiece. The minimum tool wear, minimum workpiece surface roughness and maximum processing efficiency are taken as the main evaluation indicators, and the NSGA-II multi-objective optimization algorithm of RBF neural network is used to optimize the cutting parameters, providing certain technical reference for reducing tool wear, improving the surface quality of the workpiece and increasing processing efficiency under high-speed dry cutting conditions.
1. Introduction
1.1 Research Background and Significance
In the mechanical transmission system, gear transmission has high efficiency and large torque. Spiral bevel gears, as a special type of bevel gears, can be divided into two types according to the tooth type: tapered tooth spiral bevel gears and equal-height tooth spiral bevel gears. They have the advantages of large overlap coefficient, smooth transmission and low noise. Compared with belt transmission and chain transmission, spiral bevel gears have the characteristics of high transmission efficiency, strong bearing capacity, good wear resistance and long service life, and are mainly used in the fields of automobiles and aerospace. Figures 1-1 and 1-2 show the transmission system of the helicopter tail wing and the gearbox structure of the Ford car respectively. The position and shape of the tooth surface contact area in the transmission of spiral bevel gears is an important reference basis for evaluating the transmission accuracy and performance of the meshing gear pair, so it is necessary to conduct in-depth research and analysis on the cutting processing of spiral bevel gears.
At present, the traditional single and double-sided inner and outer cutters are mainly used for processing spiral bevel gears in China. Figure 1-3 shows the cutter head for processing spiral bevel gears, and Figure 1-4 shows the cutter bar for processing spiral bevel gears. The tool will gradually wear during the cutting process, which is a common phenomenon. It is mainly related to the mechanical properties of the tool and the workpiece material, cutting parameters, cooling conditions, cutting force and cutting temperature. The combined action of physical impact and chemical reaction is the main reason for tool wear. The selection of cutting parameters in the processing process can affect the surface quality of the actual spiral bevel gear, so it is necessary to study the influence law of cutting parameters on tool wear and the surface roughness of the machined workpiece. With the minimum tool wear and the minimum surface roughness as the main indicators, the cutting parameters are optimized through the RBF neural network algorithm and the NSGA-II optimization genetic algorithm, and the cutting parameters are selected reasonably according to the actual processing requirements.
1.2 Research Status at Home and Abroad
1.2.1 Research Status of Milling Principle of Spiral Bevel Gears at Home and Abroad
The geometric relationship of spiral bevel gear transmission was initially proposed by Wildhaber and Baxter, etc. Later, Baxter analyzed the influence of the installation error of the spiral bevel gear on the gear work. Based on the previous theoretical basis, the Oerlikon company in Switzerland and the Klingelnberg company in Germany also have their own unique technologies for processing spiral bevel gears and have formulated standards. Since the middle of the last century, the Gleason company has gradually formed a set of traditional design schemes and processing technologies for spiral bevel gears. With the improvement of the processing technology of spiral bevel gears, the Gleason company has become the founder of manufacturing spiral bevel gears in the world. There are three typical processing machines for traditional spiral bevel gears, mainly: Gleason, Klingelnberg and Oerlikon machines. Among them, the Gleason company adopts the circular tooth system, and the Oerlikon and Klingelnberg companies adopt the extended cycloidal tooth system. Professor Litvin et al. proposed a local synthesis method independent of the Gleason technology, using the integral of the tooth profile curve, and setting the machine parameters according to the tracking direction of the tooth surface contact point, the change of the transmission ratio, and the length of the instantaneous contact elliptical spindle. Habibi et al. established the mathematical expressions of the cutting edge, rake angle and relief angle of the spiral bevel gear milling cutter, and proposed a new method to improve the tool wear characteristics by reducing the gradient of the rake angle and relief angle of the tool. Alfonso et al. proposed a new method for designing the face milling of spiral bevel gears, by defining the expected topography of the active surface of the pinion, and using the boundary constraint optimization algorithm to reduce the transmission noise and vibration level of the face milling of spiral bevel gears. Mu et al. proposed a tooth surface correction method based on the tool edge shape correction, which can not only effectively avoid the tooth edge contact, but also reduce the maximum contact stress of the tooth surface and reduce the adverse effects of misalignment. Samani et al. proposed a new tooth surface modification method with high-order transmission error, and deeply studied the influence law of nonlinear vibration on the processing error in the process of cutting the spiral bevel gear. Compared with the parabolic transmission error method, the root mean square of the maximum time response of the high-order transmission error method is reduced by 44%, and the peak value of the transmission error is reduced by 35% through the entire frequency range. Wang et al. proposed a new adaptive geometric meshing theory to solve the extreme situation that the geometric meshing theory is not suitable for the case where the calculation points cannot cover the entire tooth surface area. Yavuz et al. proposed a dynamic model including flexible links such as shafts and bearings, and used the multi-harmonic balance method combined with the continuous-time Fourier transform to establish a nonlinear algebraic equation system from the obtained nonlinear motion differential equation, thereby improving the processing accuracy of the spiral bevel gear. Zhao et al. proved that the precision plastic forming technology can manufacture spiral bevel gears, and its numerical analysis model is reliable. Cheng Lin proposed a new global optimization algorithm, namely the real-coded relaxation genetic algorithm (RRGA), to solve the problem that the discrete curves generated by face milling in the current simulation software are often too non-equidistant, and cannot directly generate three-dimensional models and mesh models, and verified the effectiveness of the algorithm through experiments.
Before the 1980s, the Gleason manufacturing technology was used to process spiral bevel gears in China. Due to technical limitations and other factors, the actual meshing performance of the manufactured spiral bevel gears was poor and the processing efficiency was low, which was mainly completed by processing experience. The normal curvature of the gear surface at the reference point is the key and difficulty of the spiral bevel gear technology. In order to solve the above problems, the Wu Danren team of Nankai University and Professor Chen Zhixin of Shanghai Polytechnic University deduced the induced normal curvature formula of the conjugate surface, and this technology still plays an extremely important role in China’s production. Wang Lei et al. conducted research on the tooth surface modification technology based on the processing center of the spiral bevel gear, and the modified spiral bevel gear has better transmission stability and transmission accuracy. Liu Guanglei et al. conducted active design of the meshing trace direction angle of the spiral bevel gear based on the local synthesis method combined with the TCA technology. Deng Jing et al. verified the relationship between the processing residual height of the spiral bevel gear and the cutting parameters through experiments. Cao Xuemei et al. proposed a decomposition algorithm for gear contact analysis, reducing the calculation workload and increasing the application scope of the algorithm.
In summary, many scholars at home and abroad have studied the cutting theory and tool structure optimization of end-milling spiral bevel gears, and discussed and analyzed the meshing theory of spiral bevel gears and the gear forming mathematical model, but there are few studies on the tool wear and the surface roughness of the workpiece in the process of face milling of spiral bevel gears. Therefore, it is necessary to discuss and analyze the tool wear mathematical model and the surface roughness mathematical model.
1.2.2 Research Status of Tool Wear in Spiral Bevel Gear Processing at Home and Abroad
At present, the application of spiral bevel gears and hypoid gears in the fields of automobiles, ships and aerospace is relatively extensive. The tool wear mainly studies the wear mechanism and wear characteristics of single and double-sided milling cutter disks. Stachurski discussed the influence law of the geometric shape of the spiral bevel gear tool and the cutting parameters on the tool wear process and tool life, and stipulated the standard of carbide tool wear and the relevant mathematical relationship of the bevel gear, and concluded that the tool life is related to the surface roughness, microhardness, residual stress size and microcracks and other defects of the workpiece. Bouzakis et al. discussed the cutting process of bevel gears by two-axis milling, and fully considered the cutting conditions of hobbing and the formation of chips in the actual milling experiment process, and further analyzed the cutting performance results of coated tools under different cutting speeds, tool substrates and coating surface mechanical treatments, and analyzed the influence degree of the coating tool surface preparation and geometric shape on the overall tool life. Stadtfeld et al. proposed a double-edge tool TWIN Blade (R) design based on the fully coated rod-shaped blade. The cutting edge of this shape can process the convex and concave sides of the workpiece at the same time. Due to the large tip width of the double-edge (R) tool, the best tool stiffness can always be guaranteed. Compared with the classic fully coated rod-shaped blade, the life of the TWIN Blade (R) tool can be increased by about 30%, which can avoid the situation that the chips are stuck in the edge and side of the blade of the traditional rod-shaped blade, resulting in the failure of the tool. Klocke et al. conducted further research on the processing of spiral bevel gears with traditional carbide tools, determined the correlation between the cutting parameters, cutting materials, tool geometry and tool life, and proposed a new concept of WZL face milling cutter, which is theoretically superior to the most advanced tool system. Liu et al. studied the influence of tool parameters on the cutting force in the dry high-speed cutting process of 20CrMnTi spiral bevel gears and hypoid gears based on the theory of directly evaluating the tool life and the rationality of the cutting parameter setting by the cutting force, and concluded that the three factors of back engagement, cutting speed and rake angle have the most significant influence.
Many domestic scholars mainly focus on the analysis of the cutting temperature, tool geometry and tool wear principle of the processing tools for spiral bevel gears. Wei Wei et al. proposed a tool structure with negative chamfer, which can generate a longer cutting edge, improve the cutting efficiency and significantly increase the tool life. Gao Niping proposed a design method suitable for the cathode tool structure of electrochemical processing, in order to improve the problems of serious tool wear and low processing efficiency in the traditional high-hardness propeller double-sided milling, this method is studied for the 20GrMnTi material. Wen Wu et al. studied the tool wear mechanism of carbide processing 20GrMnTi carburized and hardened steel, and found that the diffusion of Gr, Ti, Fe, Mn and other elements in the workpiece to the tool leads to the decrease of the strength and hardness of the tool, thereby accelerating the failure of the tool. Liao Congjian studied the cutting force of bevel gears, established a cutting force model of a new milling cutter, conducted a cutting simulation of high-speed dry cutting of bevel gears, studied the influence of cutting speed, tool inclination angle, and cutting depth on the cutting force under high-speed cutting conditions, and analyzed the problem of tool wear and the main area of tool wear. The research was compared with the actual cutting situation, and the results showed that the wear of the flank near the cutting edge was more serious.
The above domestic and foreign scholars have conducted a lot of research on the tool wear of processing spiral bevel gears, mainly reflected in the different structures of the tools and the wear forms under the thermal-mechanical coupling conditions in the processing process, but there are relatively few studies on the influence of cutting parameters on tool wear. Therefore, it is necessary to explore the influence law of different cutting parameters on the tool wear form and wear mechanism.
1.2.3 Research Status of Surface Quality in Spiral Bevel Gear Milling at Home and Abroad
The main factors affecting the machined surface quality of spiral bevel gears include cutting force, cutting heat, cutting parameters and residual stress, etc. Due to the interaction of the above factors in the actual processing process, the influence degree of surface roughness can only be obtained by controlling a single factor variable at present. For different mechanical processing processes, scholars at home and abroad established a variety of roughness mathematical models to verify the quantitative relationship between the machined surface roughness and the cutting parameters. Du et al. conducted a cutting simulation analysis based on the forming principle and meshing theory of the spiral bevel gear through a three-dimensional model and finite element simulation software, and adopted CNC milling to process the spiral bevel gear to ensure a high surface processing quality. Deng et al. proposed a face milling processing method with a concave-head disc milling cutter to solve the problems of small cutting band width and poor surface quality commonly occurred in ball-end milling. This method not only improves the surface processing quality of the spiral bevel gear, but also improves the production efficiency. Zheng et al. started from the theory that the tooth surface is formed by the intersection of the tool edge in a specific tool cycle and a specific sequence, and revealed the influence law of the design parameters and process parameters on the surface roughness distribution of the spiral bevel gear through numerical simulation and experimental research. Ghani et al. used coated carbide tools for semi-finishing or finishing hard die steel, and the results showed that a higher cutting speed and a smaller back engagement should be adopted for cutting processing to obtain a smaller surface roughness. Yang Zhenchao et al. analyzed the surface morphology of TC4 at different milling speeds, and found that the machined surface would show a law of first decreasing and then increasing with the increase of the cutting speed. The research showed that the surface quality would rapidly decrease after the tool wear, and the wear was mainly concentrated near the cutting edge. Liu et al. [33] conducted a turning experiment on workpieces with different hardness GCr15 using PCBN tools, and concluded that the lowest surface roughness of the workpiece was around HRC50, and below HRC50, the roughness increased with the increase of hardness.
In summary, at present, scholars at home and abroad mainly study the surface quality of the milling processing of spiral bevel gears from the theoretical model through the cutting force, cutting heat and tool structure, but there are few literatures on the surface quality of the spiral bevel gear processing improved by the parameter optimization algorithm. Therefore, the optimal cutting parameters can be obtained through the optimization algorithm, and the surface roughness can be obtained by using the residual height of the machined workpiece. While optimizing the surface roughness, the production efficiency can also be improved.
1.2.4 Research Status of Cutting Parameter Optimization in Spiral Bevel Gear Milling at Home and Abroad
The selection of cutting parameters in the process of end-milling spiral bevel gears can affect many factors. From the current research, scholars at home and abroad have also done related research, mainly from aspects such as temperature, tool life, cutting force, and surface quality. Foreign scholars Yilmaz et al. proposed the concept of cumulative factor to clarify the change law of the cutting force and the cutting parameters in the cutting process, and obtained the mathematical model of the cutting parameters and the cutting force, and obtained a reasonable cutting force by optimizing the cutting parameters. Tseng et al. [35] used the artificial neural network to establish a burr mathematical model to explore the relationship between the formation mechanism of the machined surface burr and the cutting parameters, and used the neural network of the optimal design method as the cutting parameter optimization tool. The results showed that reasonable cutting parameters can reduce the burr size and improve the surface quality of the machined workpiece. Altan et al. [36] studied the surface roughness of the machined workpiece by changing different spindle speeds, and the results showed that the increase of the cutting speed in the cutting process can improve the surface quality of the machined workpiece. Zerti et al. discussed the wear curves of different wear areas of the tool, and clarified the influence law of the cutting parameters on the tool wear through statistical methods, indicating that the increase of the feed rate will accelerate the wear of the tool. Aramesh et al. [38] studied the average remaining life of the tool after wear under different cutting parameter conditions, developed a proportional model with a Weibull baseline, and verified the accuracy of the model through experimental data. This model can more accurately predict the remaining service life of the tool. Kayabasi et al. [39] used the artificial neural network to determine the prediction model of the surface roughness of the machined workpiece, and obtained the optimal cutting parameters. Domestic scholar Dong Huiting et al. studied the monitoring of the tool wear state based on the problem of the tool temperature, obtained the change law of the cutting temperature under different cutting parameters by establishing different wear tool models for cutting simulation, and further expounded the main wear parts of the tool and the distribution of the tool cutting temperature. Jia Xinjie [41] proposed a roughing cutting parameter optimization scheme based on the harmony search algorithm to improve the service life of the tool. This algorithm can obtain the optimal cutting parameters, which can effectively improve the tool durability and processing efficiency.
In summary, the above domestic and foreign scholars mainly studied the cutting force, temperature, surface quality of the workpiece and remaining life respectively from the cutting parameters. From the current research, most of them are mainly single-factor optimization, but there are few studies on multi-objective optimization of cutting parameters. Therefore, it is very necessary to explore the multi-objective optimization algorithm to calculate the optimal cutting parameters.
1.3 Source and Main Research Contents of the Project
1.3.1 Source of the Project
This project comes from the horizontal project “Harbin University of Science and Technology – Yancheng Hali Power Transmission and Intelligent Equipment Research Project” of the school-enterprise cooperation.
