Abstract:
Gear hobbing is highly valued in gear manufacturing due to its high productivity and versatility. However, the complexity and uniqueness of the hobbing process necessitate the establishment of simulation models and methodologies to aid in its analysis. This paper discusses the application of CAD geometric simulation and finite element simulation in gear hobbing, elucidating research methods and achievements in chip formation, cutting forces, cutting temperatures, and tool wear. It also analyzes existing research gaps, summarizes findings, and provides outlooks, offering valuable references for process optimization, tool life enhancement, and workpiece surface quality improvement in gear hobbing.
1. Introduction
In current gear manufacturing methods, gear hobbing occupies a dominant position due to its high cutting speed and long service life. However, the complexity and specificity of the hobbing process make it difficult to analyze specifically, requiring the integration of simulation to visually represent the hobbing cutting process. Finite element simulation discretizes continua to analyze continuum mechanical and thermal issues, while CAD-based solid modeling technology for geometric simulation also holds broad application prospects. The simulation of gear hobbing provides a reference for optimizing cutting conditions, improving cutting tool life, and enhancing workpiece surface quality. Combining precise predictions from gear hobbing simulations with actual production processing can reduce costs and enhance productivity.
This paper mainly reviews gear hobbing based on CAD geometric simulation and finite element simulation (chip morphology, cutting forces, cutting temperatures, and tool wear), expounds on simulation analysis methods and research achievements in gear hobbing, and presents initial outlooks for gear hobbing simulations. It provides a reasonable reference for optimizing gear hobbing processes, improving cutting tool life, and enhancing workpiece surface quality.
2. Basic Content of Gear Hobbing Simulation
2.1 Methods for Constructing Gear Hobbing Simulation Models
Finite element cutting simulations for gear hobbing generally consist of three stages: data modeling, finite element environment simulation, and post-processing. The specific steps are shown in Figure 1. The steps for geometric simulation based on CAD secondary development are shown in Figure 2.
2.2 Comparative Analysis of Commonly Used Simulation Software for Gear Hobbing
Most commercial finite element analysis software can simulate metal cutting processes, such as Abaqus, ANSYS, Hyperworks, Advantedge, and Deform-3D. For gear hobbing, commonly used finite element simulation software includes ANSYS, Abaqus, and Deform-3D. Some CAD software can also perform geometric simulation analysis after calculating the cutting path using secondary development methods, such as NX, SolidWorks, Catia, Pro/E, and AutoCAD. Scholars have also developed software like HobSim and HOB3D to simulate undeformed chips generated in gear hobbing and predict cutting forces and wear.
3. CAD-Based Geometric Simulation for Gear Hobbing
CAD-based geometric simulation for gear hobbing can quickly and accurately simulate the cutting process, obtain gear profile geometric accuracy, simulate undercut phenomena, calculate the maximum thickness and width of undeformed chips generated by the tooth profile path trajectory during gear hobbing, and thus study the total cutting forces and cutting components. Simulating the gear hobbing process through CAD geometric simulation can save design and development time and increase benefits.
3.1 Modeling Gear Motion Based on CAD Secondary Development
Based on the principle of gear hobbing, CAD secondary development is used to model the profiles of hobs and gears, laying the foundation for subsequent generation of undeformed chips and prediction of cutting forces. Michalski J et al. proposed a cylindrical gear modeling method that can precisely define geometric shapes and surface morphologies, capturing gear profiles of any complexity.
3.2 Chip Formation Process Based on CAD Geometric Simulation
After obtaining the models of the hob and gear and their relative motion relationships, the CAD geometric simulation process for gear hobbing is studied. This primarily involves studying undeformed chips, chip thickness, tooth profiles, etc., to analyze the path trajectory of the machined tooth shape, cutting forces, and tool wear.
Khurana P et al. developed the HobSim gear hobbing simulation program to perform geometric simulations of the gear hobbing process and predict cutting forces in combination with experiments, analyzing part deflection relationships and the resulting profile deviations. Zhou Li simulated the morphology of undeformed chips using Mathematics and CAD 3D modeling software, comparing and analyzing them with finite element simulations and actual processed chips. It was found that the deformation of chips during high-speed dry hobbing has periodicity, but the study did not combine undeformed chips with experiments to predict cutting forces. Zhang Rongchuang et al. performed simulations of undeformed chips through the UG secondary development platform, obtaining the thickness and basic morphology of undeformed chips. Geometric simulations of the gear hobbing process were conducted on CWE, and the cutting thicknesses of the hob’s straight and arcuate edges were calculated, paving the way for predicting dynamic hobbing forces.
3.3 Prediction of Cutting Forces and Tool Wear Based on CAD Geometric Simulation
Data generated from 3D geometric modeling and simulation can also be effectively used for optimizing gear hobbing methods, predicting cutting forces, tool stresses, and wear during the gear hobbing process. Naoual S et al. determined the variation in the thickness of undeformed chips generated during the cutting process of each hob tooth through CAD geometric simulation and predicted the distribution of cutting forces using the simulation model. Dimitriou V et al. addressed the shortcomings of 2D simulations by developing the HOB3D software module based on commercial CAD software. By establishing spatial surface trajectories, the kinematics of gear hobbing were directly applied to individual teeth, but in-depth research on cutting forces was not conducted. Klocke F et al. developed the SPARTApro software, which simulates the geometric shape of undeformed chips during gear finishing processes, identifies critical cutting edges, and predicts tool wear. Kaan E et al. used dexter geometric modeling to predict the engagement and processing performance of tools and workpieces, with simulation results aligning well with measurements. This research has now been extended to areas such as the forming, elastic deformation, and vibration prediction of helical gears and hardened gears.
4. Finite Element Simulation Research in Gear Hobbing
Although CAD-based gear hobbing simulation research can simulate undeformed chips, tooth profile generation, and predict cutting forces and tool wear, saving considerable time, it also has its limitations. For example, analyzing structural displacements, velocity fields, temperature fields, and electric potential fields is difficult to achieve accurately with CAD software. However, using the finite element method to discretize the established model and obtain the corresponding model for solution can enable these analysis processes. Therefore, it is necessary to explore the current status of finite element simulations of chips, cutting forces, cutting temperatures, and tool wear, analyze the achievements and areas for improvement in current finite element simulation research, and propose preliminary outlooks.
4.1 Chip Simulation in Gear Hobbing
During gear hobbing, chip deformation has a significant impact on the compressive damage, wear, and failure of hob teeth. The deformation of chips during the flow process can also lead to reduced workpiece surface quality. By improving finite element analysis criteria, a more comprehensive set of criteria can be obtained to make cutting simulation models closer to actual conditions.
Ceretti E et al. used the DEFORM finite element program to study plane strain cutting processes and simulated chip formation using an improved program. Zhang LC et al. took the chip failure stress separation criterion as the default criterion and conducted simulation analyses based on different criteria, concluding that using normal failure stress as the default value yields more reliable results for effective plastic strain calculations.
During the cutting process, studying chip flow to simulate chip deformation patterns enables the development of programs to simulate chip geometry, investigating its impact on workpiece surface quality and cutting temperatures. Bouzakis KD et al. visualized chip formation and chip flow processes in gear hobbing through the FEM program, using the computer program FRS/MAT to calculate isothermal and isostress curves on the chip and workpiece surfaces, comparing them with corresponding real chips. The results showed that the material flow stress law has a certain influence on the simulation results. Fritz K et al. conducted finite element simulations of cutting models from aspects such as chip deformation, wear characteristics, and tool design features, analyzing the influence of chip geometry on wear behavior and chip flow, and assessing the impact of different cutting parameters and chip flow conditions on cutting forces and temperatures. During gear hobbing, when chips are squeezed between the hob cutting edge and the machined gear tooth surface, damage often occurs to the hob cutting edge and the machined surface.
Li Benjie et al. analyzed the high-speed dry hobbing process through chip numerical simulation and metal cutting finite element simulation, studying chip deformation patterns and flow characteristics and discussing the causes of hob tooth fracture. Li Guolong et al. used Abaqus software to obtain the maximum chip thickness that the hob top edge can cut, combining experiments to determine chatter frequencies, which can be used for chatter prediction in gear hobbing processes and provide certain reference value for process optimization in gear hobbing.
Studying the compression and failure process of gear hobbing chips lays the foundation for optimizing tool wear and workpiece surface accuracy. By analyzing the deformation patterns of gear hobbing chips, methods such as optimizing processing parameters and hob structures can be adopted to effectively control the flow and compressive failure of gear hobbing chips, thereby improving the surface quality of the processed workpiece and tool life.
4.2 Cutting Forces and Cutting Temperatures
In gear hobbing processes, cutting forces and cutting temperatures are crucial factors that significantly impact the quality of the workpiece, tool wear, and overall process efficiency. This section discusses the simulation and analysis of these two aspects using finite element methods.
4.2.1 Simulation of Cutting Forces in Gear Hobbing
With the continuous improvement of finite element theory in the field of metal cutting, scholars at home and abroad have studied the influence of different parameters on hobs and workpieces through the combination of finite element simulation and experiments.
Finite element simulation software, such as ANSYS and Abaqus, is employed to simulate the metal cutting deformation process and analyze the variation of cutting forces during the initial stage of cutting. These simulations help predict dynamic cutting forces, providing valuable insights for selecting appropriate cutting parameters.
For instance, Bouzakis K.D. et al. applied the finite element method to the gear hobbing process, determining the cutting forces that occur at various generation and rotational positions during chip formation. They verified the consistency of these forces with calculated values using the FRS/DYNA program. Similarly, Feng D. et al. reconstructed a geometric error model of the machine tool due to rolling cutting forces through ANSYS simulation, exploring the influence of machine tool geometric errors on gear accuracy and proposing error compensation methods to enhance the quality of gear hobbing.
Furthermore, research has been conducted on the fracture process of cutting edges. By adopting the maximum principal stress criterion as the fracture criterion, simulations have been performed to study the crack propagation in the top and side edges of hobs. The results indicate that cracks in positive-angle side edges are more prone to propagation than those in negative-angle side edges.
However, it should be noted that although finite element simulations can predict cutting force values, there is still a gap between these predicted values and actual measurements. This discrepancy is primarily caused by the complex geometry of three-dimensional hob teeth and gear clearances. Therefore, finite element methods for calculating gear hobbing cutting forces need to be adapted based on actual processing conditions, with appropriate modifications to the models.
4.2.2 Simulation of Cutting Temperatures in Gear Hobbing
Cutting temperatures during metal cutting processes can affect tool wear, the formation of built-up edges, and the accuracy of the processed surface, leading to residual stresses and other surface defects. In high-speed dry gear hobbing, the high cutting speeds and the absence of cutting oil and cooling lubrication result in elevated temperatures of both the hob and the workpiece, significantly impacting the surface accuracy of the processed workpiece.
Finite element simulations provide an effective solution to address the difficulty of directly measuring gear hobbing cutting temperatures. By simulating the three-dimensional cutting temperature field of the hob teeth, the variation of cutting temperatures with cutting parameters can be obtained.
For example, Zhou P.J. used ANSYS to simulate the three-dimensional cutting temperature field of the hob teeth, revealing the variation of high-speed dry gear hobbing cutting temperatures with cutting parameters. Stark S. et al. focused on thermal deviations in gear hobbing, employing a two-step simulation process using Deform-3D. The first step assessed the heat generated during chip formation, while the second step used this heat for thermal flow simulation. The results demonstrated good consistency between the measured and simulated temperature fields during chip formation and thermal flow processes.
In addition, Grzesik W. et al. simulated the temperature distribution at different sampling points in the tool-chip contact area and hob coating materials, finding that changes in temperature distribution were primarily caused by alterations in heat transfer conditions. Sibylle S. et al. predicted thermal deviations in tooth profiles by improving the flying cutter test for numerical simulation, using the finite element method to calculate and measure the measuring device, numerical simulation device, forces, and temperatures. This method is applicable to the flying cutter test and some analogous tests of workpieces.
In summary, finite element simulations play a pivotal role in understanding and optimizing cutting forces and temperatures in gear hobbing processes. By accurately predicting these parameters, the quality of the processed workpieces, tool life, and overall process efficiency can be significantly improved.