Manufacture Of Spiral Bevel Gears Research Articles

A method to manufacture spiral bevel gears by equivalent completing

As a transmission part for industrial application the manufacture of spiral bevel gear is particularly important. The present machining methods for manufacturing spiral bevel gears, including the so called five-cut method and completing method, have drawbacks such as low processing efficiency, requiring complex calculations and high requirements on the machine-tool performance, respectively. To solve the above problems, an equivalent completing method is proposed to process spiral bevel gear in this paper. Firstly the machine setting parameters by completing were translated from the Cradle-type hypoid generator to Cartesian-type hypoid generator and the workpiece is swing during process. CNC motion axes expression of Cartesian-type hypoid generator were expressed as sixth-order polynomial, the influences of coefficient on the tooth surface topology were researched. Then the method to machine spiral bevel gear was put forward by reducing the swing axis of workpiece, obviously a deviation of tooth surface was caused between theoretical and axis-reduced. As a response, a flank correction model was established and the other polynomial coefficients were adjusted to eliminate the deviation. Finally simulation and cutting experiment were carried out by a numerical example. The experimental results show that the proposed method is effective and feasible. The method proposed in this paper overcome and enrich the disadvantages of existing manufacture methods of spiral bevel gear.

Correction to: Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD‑based model

Correction to: Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD‑based model

Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD-based model

Simulation of spiral bevel gear manufacturing by face hobbing and prediction of the cutting forces using a novel CAD-based model

Loaded contact fatigue-oriented carburizing surface optimization model of spiral bevel gears

In order to improve geometric accuracy and loaded contact fatigue life on tooth surface carburizing, an innovative optimization model is established for spiral bevel gears. First, finite element method (FEM)-based tooth surface carburizing simulation is performed. Where, the output carbon content and hardness gradient are used to determine the S-N curve of the given material 20MnCr5 steel. The output residual stress is integrated into the bending stress solution. The output carburizing surface deformation is introduced into the composite surface geometric accuracy. Second, loaded contact fatigue assessment is performed by FEM-based loaded contact stress and S-N curve. Where, loaded contact stress considering residual stress is determined by simulated loaded tooth contact analysis (SLTCA). Third, loaded contact fatigue life-oriented carburizing surface optimization model is established. In this modeling, the composite surface geometric error including carburizing deformation, loaded contact deformation and the prescribed ease-off is used to reflect manufacturing geometric accuracy. Moreover, the limit fatigue life at dangerous point is used a standard to determine the target surface. A sensitivity analysis strategy-based optimization strategy is developed. The proposed method can effectively improve the process parameter modification strategy by considering the collaborative optimization on geometric accuracy and loaded contact fatigue life. Moreover, it also can provide new technical for the current co-design and manufacture of spiral bevel gears.

Dynamic Simulation and Analysis of Engagement Process for Logarithmic Spiral Bevel Gear Based on Accurate 3D Model

Based on the accurate 3D model of logarithmic spiral bevel gear, the operation of spiral cone gear engagement is analyzed and simulated by ANSYS. Through the nonlinear static contact analysis of different positions, the stress change rule and the maximum contact stress is obtained. Compared with the theoretical contact stress strength rule, this paper also analyzes the dynamic operation situation of the gear pairs, obtains the dynamic contact situation rule at different engagement times and different rotating speeds, the influence of the rotating speed on the gear contact characteristics is compared too. The static, dynamic performance and change rules of the gear engagement is obtained, which lay a solid foundation for the further research, design and manufacture of spiral bevel gears.

A novel CAD-based simulation model for manufacturing of spiral bevel gears by face milling

Bevel gears are employed in the transmission of motion and torque via non-parallel shafts. When higher strength and lower noise is the objective, spiral bevel gears are used because of their higher tooth contact ratio. Face milling and face hobbing are among the most significant operations for the machining of hypoid and spiral bevel gears due to their high productivity. Although the optimization of these processes is crucial for the production of high-quality gears and the minimization of the total manufacturing cost, there are not many studies reported in this research area, owing to the high complexity of process kinematics. Furthermore, several kinematic variations of the two methods are applied in industry and their results depend highly on the cutting tool geometry. A novel simulation model integrated into a commercial CAD platform has been developed. The model achieves the 3D kinematic simulation of both face milling and face hobbing processes, generating the undeformed solid chip geometry as well as the simulated tooth solid geometry of a spiral bevel gear pinion and a spiral bevel gear wheel as an output. The simulation approach has two main purposes. First, is the optimization of the process through the investigation of the effect of cutting parameters on the quality of the obtained solid tooth flank geometry and second, is the calculation of cutting forces with the use of the obtained solid chip geometries. Aiming towards the validation of the model, the resulted tooth flank geometry is compared with the theoretical tooth exported from a well-established commercial gear calculation and design software and it is verified by means of a novel validation algorithm, also developed as part of this study. This paper focuses on the presentation of the kinematic simulation methodology and the simulation results for the face milling process. An insight into the validation model is provided and validation results are also presented. Finally, a sample investigation of the effect of generating feed rate on the produced gear geometry is conducted with the use of both algorithms.

A comprehensive adaptive approach to calculating the envelope surface of the digital models in CNC machining

The digital models are the fundamental elements used in the virtual simulation of CNC machining for process planning, result prediction, analysis, etc. The essential work to build the digital models of machined parts is the calculation of the envelope surface generated by moving a cutter surface relative to workpieces. This calculation is usually complicated, and the requirements in different cases are also varied. Hence, it is very beneficial to develop an effective approach for different requirements. In this work, a comprehensive envelope approach is established, and it adaptively choose 1) the elimination parameter among two cutter surface parameters, 2) the representation form of envelope surface, and 3) the discretization way, so it is robust to satisfy different requirements. The elimination parameter and representation form are adaptively chosen to improve the calculation efficiency by obtaining the closed-form representation of the envelope surface prior to the implicit one. The discretization way is further adaptively chosen to obtain approximately even point distribution to the applications of 3D and FEA modeling. Finally, comprehensive algorithms are proposed to effectively implement this adaptive envelope approach for different applications. The examples are given to the manufacturing of spiral bevel gears and five-axis CNC milling.

Information description and integration of spiral bevel gear manufacturing process under networked manufacturing mode

The continuous maturing and fusion of information and network technologies open a new route for the manufacture of spiral bevel gears. As one of the advanced manufacturing paradigms, networked manufacturing has become an important development direction of spiral bevel gears. Aimed to effectively realize the information description and integration of spiral bevel gear networked manufacturing process, this paper presents a novel information description and integration framework for spiral bevel gear networked manufacturing by combining the information network technologies and spiral bevel gears manufacturing technologies. In this paper, the information flow of spiral bevel gear networked manufacturing process is deeply analyzed, and the information description and integration framework for spiral bevel gear networked manufacturing process are proposed. Furthermore, through developing the prototype of information integration operation management system for spiral bevel gear networked manufacturing, the united description and integration management of spiral bevel gear networked manufacturing process information are realized. Finally, an actual networked manufacturing application experiment of one spiral bevel gear order is provided to demonstrate the feasibility and practicability of the proposed information description and integration framework and its implementation methods.

A novel method to generate the tooth surface model of face-milled generated spiral bevel gears

Tooth surface model is a fundamental element used in the design, analysis, and manufacturing of spiral bevel gears. Based on the face-milled generated process, the tooth surface of spiral bevel gears is mathematically calculated as a complicated representation related to cutter parameters and machine settings. With the representation, the discretized points and curves can be easily obtained from the parameterization of tooth surface. However, the discretized curves for the face-milled generated spiral bevel gears are usually too non-equidistant to directly generate 3D (three dimensional) and mesh models in commercial softwares. This paper presents a novel method to recalculate tooth surface points to generate new approximately equidistant points and curves. The tooth surface representation is introduced at the beginning. Subsequently, a mapping between the isoparametric curve and new approximately equidistant curve is used to recalculate the tooth surface points. To solve the nonlinear equation established from the mapping, a new global optimization algorithm, named real-coded relaxation genetic algorithm (RRGA), is proposed to stably obtain the solutions. Examples are given to validate the proposed method.

Design and manufacturing of spiral bevel gears using CNC milling machines

Gears are some of the most important elements used in machinery. Their purpose is to transmit motion and torque from one shaft to another. When shafts intersect, bevel gears provide the most efficient mean of transmitting power. There are two main forms of bevel gears, straight bevel gears and spiral bevel gears. This paper is the first of a sequence of papers concerning design and manufacturing of spiral bevel gears using computer numerical control (CNC) milling machines. It is an introduction to their designing features, showing the standards that recommend the geometrical dimensions of gear tooth and a theoretical approach to the traditionally used cutting methods of spiral gears, Gleason, Oerlikon and Klingelnberg methods. Finally, it is presented five-axis machining tools that can be used for cutting of spiral bevel gears.

An approach to realize the networked closed-loop manufacturing of spiral bevel gears

Digital closed-loop manufacturing technique, as a significant component of spiral bevel gear manufacturing system, has provided significant guarantee for improving the quantity and efficiency of spiral bevel gear tooth surfaces. The continuous fusion of digital closed-loop manufacturing and network technologies open a new route for the high-efficiency and high-precision manufacturing of spiral bevel gears. In order to realize the integrated operation and the information management in closed-loop manufacturing process of spiral bevel gears, this paper presents a universal networked closed-loop manufacturing model for spiral bevel gears by combining gear digital closed-loop manufacturing technologies and network technologies, which offers better support for the integrated design and machining of spiral bevel gear tooth surfaces. In this paper, the typical digital closed-loop manufacturing process of spiral bevel gears is deeply analyzed, and the framework of networked closed-loop manufacturing model is proposed. Furthermore, the integrated operation mechanism of networked closed-loop manufacturing model is established. On this basis, the key implementation mechanism of networked closed-loop manufacturing model such as the communication network construction, manufacturing information integration mechanism, and networked closed-loop manufacturing integration system development is elaborated respectively. Finally, an actual application experiment of spiral bevel gear pair networked closed-loop manufacturing is provided to demonstrate the feasibility and practicability of the proposed model.

General mathematical model of spiral bevel gears of continuous pure-rolling contact

Sliding contact has negative influence for the performance of gears in most situations, such as frictional loss, pitting, micro-pitting, etc. To avoid sliding contact, this paper discusses the fundamental geometrical characteristics of spiral bevel gears of continuous pure-rolling contact. Differential geometry, gearing kinematics, and conjugate curve meshing method are used to derive the general mathematical model of spiral bevel gears of continuous pure-rolling contact. Simplified equations that continuous pure-rolling contact bevel gears must satisfy are derived. An example is represented to explain and verify this model. The theoretical results benefit further studies on design and manufacturing of spiral bevel gears of heavy loads and high efficiency.

On-Machine Measurement of Tooth Profile Errors of Spiral Bevel Gears and its Simulation

Precise measurement of tooth profile errors is the key technology for realizing close-loop manufacturing of spiral bevel gears. The measuring principle of tooth profile errors and the processing method of measuring datum is the key technology for realizing precise measuring. Based on the generating principle of spiral bevel gears and the model of CNC machine tool, the on-machine measuring principle and the measuring datum processing method were established. In order to verify the correctness of on-machine measuring principle, the on-machine measuring simulation system was established based on AutoCAD development platform. According to the spatial coordinates and normal vector of the discrete points of theoretical tooth profile, the on-machine measurement of tooth profile errors was simulated by intersection Boolean operation and the values of errors were calculated. The correctness of simulation algorithm is validated by comparing simulation result with the practical measuring result.

Parametric Modeling for Spiral Bevel Gear Based on PRO/E

The author describes tooth profile formatting mechanism of spherical involute spiral bevel gear based on Principles of Gear conjugate, establishes the mathematical model of spiral bevel gears. The precise spherical involute of spiral bevel gears is generated with parametric modeling idea and th secondary development method based on PROGRAM of PRO/E software. Finally, a complete spherical three-dimensional modeling of the involute spiral bevel gear is established, which provides a method of parametric design and manufacturing of spiral bevel gears.

Pinion tooth surface generation strategy of spiral bevel gears

Aviation spiral bevel gears are often generated by spiral generated modified (SGM) roll method. In this style, pinion tooth surface modified generation strategy has an important influence on the meshing and contact performances. For the optimal contact pattern and transmission error function, local synthesis is applied to obtain the machine-tool settings of pinion. For digitized machine, four tooth surface generation styles of pinion are proposed. For every style, tooth contact analysis (TCA) is applied to obtain contact pattern and transmission error function. For the difference between TCA transmission error function and design objective curve, the degree of symmetry and agreement are defined and the corresponding sub-objective functions are established. Linear weighted combination method is applied to get an equivalent objective function to evaluate the shape of transmission error function. The computer programs for the process above are developed to analyze the meshing performances of the four pinion tooth surface generation styles for a pair of aviation spiral bevel gears with 38/43 teeth numbers. The four analytical results are compared with each other and show that the incomplete modified roll is optimal for this gear pair. This study is an expansion to generation strategy of spiral bevel gears, and offers new alternatives to computer numerical control (CNC) manufacture of spiral bevel gears.

Twin symmetry roll axial rolling: new method of plastic forming profiles demonstrated using manufacture of spiral bevel gears

When using conventional manufacturing methods for machining gears, the percentage of stock material utilisation in the finished article is low due to the amount of swarf removed during machining. In addition, the machining process itself may result in low tooth strength. Adopting a plastic forming method to produce gear forms can greatly enhance the mechanical properties of the product. The size of the automotive transmission driven by a rear axle spiral bevel gear which is used as a case study in this paper is larger than that usually manufactured by the plastic forming method. Objects of this size require high capacity hot forming equipment, and even then it is difficult to obtain a full profile. In this paper, a new method of plastic forming profiles: twin symmetry roll axial rolling is described using a spiral bevel gear as a case study. The technology was analysed by producing a three‐dimensional model of the spiral bevel gear, and finite element analysis was used to simulate the process. It can be seen that the teeth were completely filled with a well defined outline and only a small amount of horizontal overfilling and vertical flash occurred because there was small contact area between the blank and rolls which minimised the rolling force.

Subdivision surface modeling for spiral bevel gear manufacturing

This paper presents a study on spiral bevel gear (SBGs) manufacturing method based on subdivision surface modeling scheme. The explicit nominal surface descriptions for both gears and pinions have been first developed based on gear generative motions. Then a group of key points on the tooth surface are selected as seed points (starting points) for a subdivision surface. From a given manufacturing precision criteria, a subdivision surface can be generated with a limited number of iterations during a subdivision surface modeling. This new surface modeling technique can be used for manufacturing (SBGs) with a general numerical control machine and a tool cutter in a flexible manufacturing environment. The experimental evaluation has been carried out and indicated that the subdivision surface-based SBG manufacturing method has advantages in high precise SBG manufacturing and precision control.

Advanced Manufacture of Spiral Bevel Gears on CNC Hypoid Generating Machine

An algorithm is developed for the execution of motions on the computer numerical control (CNC) hypoid generating machine using the relations on the cradle-type machine. The algorithm is based on the condition that, since the tool is a rotary surface and the pinion/gear blank is also related to a rotary surface, it is necessary to ensure the same relative position of the head cutter and the pinion on both machines. The algorithm is applied for the execution of motions on the CNC hypoid generator for the manufacture of spiral bevel gears, based on the machine tool setting variation on the cradle-type hypoid generator conducted by optimal polynomial functions up to the fifth-order. By using the corresponding computer program, the motion graphs of the CNC hypoid generator are determined for the manufacture of spiral bevel gears, based on the optimal variation in the velocity ratio in the kinematic scheme and on the variation in the cradle radial setting on a cradle-type generator.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied to conduct the variation in the cradle radial setting and in the cutting ratio in the process for pinion teeth generation. Two cases were investigated: In the first case, the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface; in the second case, the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation in the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation in the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase in transmission errors can be considerably reduced.

Modelling, Implementation, and Manufacturing of Spiral Bevel Gears with Crown

The operational performance of gears in terms of smoothness, quietness, wear and life span is largely affected by how gear and pinion teeth make contact. To enhance the operational performance, a crown is often applied to a standard (nominal) gear tooth surface. Regardless of the presence of a crown, all the gears are machined by special types of machine tools, such as gear hobbers and shapers. This paper develops a tooth surface for a spiral bevel gear with a crown so that it can be machined by numerically controlled machine tools. Specifically, we derived: 1. A bi-parametric tooth surface model for a standard spiral bevel gear. 2. A crown model along the spiral curve direction. 3. A crown model along the involute curve direction. The developed algorithm was tested and implemented in a prototype software system called GearCAM. With the GearCAM system, a set of spiral bevel gear and pinion was machined using a 4-axis CNC milling machine to check the validity and effectiveness of the crowning method. Through various verifications, it is shown that the models developed for the standard and crown gears can be used as a means for design and verification of spiral bevel gears.