Tooth Surface Of Spiral Bevel Gear Research Articles

Sensitivity analysis and compensation for tooth surface deviation of spiral bevel gear machine tool

To analyze the quantitative mapping relationship between the geometric errors of the five-axis CNC machine tool and the tooth surface deviation of spiral bevel gears, and identify the key geometric errors that affect the machining deviation of the spiral bevel gear tooth surface, a sensitivity analysis method for tooth surface machining deviation of spiral bevel gear based on screw theory and EFAST method is proposed. Firstly, the machining model of the spiral bevel gear tooth surface based on the five-axis CNC machine tool is established. Then, the geometric error transfer model of the machine tool is established based on the screw theory. Combined with the EFAST global sensitivity analysis method, the key geometric errors that affect tooth surface deviation are identified. Finally, the reliability and effectiveness tests are performed by comparing the results to the local sensitivity analysis method and simulating compensation for the key geometric errors. The result of compensation shows that the tooth surface deviation is reduced significantly according to global sensitivity analysis. The feasibility of applying sensitivity analysis to control the tooth surface deviation of spiral bevel gears has been demonstrated.

Compensation method of the spiral bevel gear tooth surface error based on eight tooth-surface fitting

Abstract The misalignment error between the gear theoretical coordinate system and actual gear coordinate system is illustrated, as well as its influence on the measurement of tooth surface deviation is discussed. On the analysis of the tooth convex and concave surface error measurement process, the measured points in the theoretical coordinate system are transformed from the actual measured points in the actual coordinate system. Then, an eight tooth-surface fitting method is utilized to calculate the misalignment error and the compensation method is given. Finally, actual measurements of three different spiral bevel gears are analyzed, and the misalignment error are calculated. Using the proposed compensation method, both the eccentricity and tilt are compensated to some extent. And the machining suggestions of each spiral bevel gear are also given according to its compensated tooth surface error distribution.

A novel design method of low noise spiral bevel gear tooth surface for polynomial ease-off topological modification

In order to reduce the vibration noise of the spiral bevel gear transmission system (SBGTS), a polynomial ease-off topological modification (PETM) method, which combines the load tooth contact analysis (LTCA) and vibration analysis of the spiral bevel gear, is proposed in this paper to minimize the normal dynamic meshing force and normal relative displacement to reduce the vibration noise. Firstly, a new PETM equation is established based on the complete conjugation principle, which is applied to the initial clearance calculation of LTCA and an explicit LTCA calculation method with PETM without requiring inverse processing parameters is constructed. The calculation accuracy is better than that of a general algorithm. Secondly, the dynamic response of an eight-degree-of-freedom dynamic system of spiral bevel gear is calculated according to the loaded transmission error and time-varying meshing stiffness calculated by the explicit LTCA of PETM. Finally, a PETM low-noise tooth surface design method is constructed with the goal of minimizing the normal meshing force and the normal relative displacement and the PETM equation coefficient as the optimization variable. The numerical results show that the new PETM low-noise tooth surface design method can improve the meshing performance and dynamic performance of spiral bevel gears to a greater extent than those before modification and after the second-order topological modification, thus greatly reducing the vibration noise of SBGTS.

A model construction and measurement method for tooth surface deviation of spiral bevel gear based on a one-dimensional probe

The accurate measurement of tooth surface deviation is an important prerequisite for the quality monitoring of high-precision spiral bevel gears. A measurement method for tooth surface deviation of spiral bevel gears is proposed based on a one-dimensional probe, which can accurately measure and evaluate tooth flank. According to the forming principle of the spiral bevel gear tooth surface, the theoretical surface is constructed as the measurement reference flank. A series of measures and methods are adopted to ensure the accuracy and correctness of one-dimensional probe measurement. These effective methods include the construction of a precise positioning model of the gear blank and its surface, the measurement planning of reduction dimension which the gear needs to rotate once the normal angle after each point is measured, and the compensation for the increasing dimension of the one-dimensional probe. In addition, minimization of the normal deviation of the tooth flank is achieved by using the optimum matching technique of the theoretical and the actual surfaces. The deviation degree of the actual surface relative to the theoretical surface can be accurately calculated and evaluated by establishing a deviation model, which ensures the correctness of the evaluation result of the deviation. Finally, the test of tooth surface deviation is carried out on a JD45+ gear measuring center (GMC) using a one-dimensional probe and a Gleason 650GMS GMC using a three-dimensional probe. The measurement results show that the evaluation results of the one-dimensional probe are in good agreement with those of the three-dimensional probe. The proposed theory and method not only expand the measurement range of the GMC using a one-dimensional probe, but also have certain reference significance for the precision measurement of other complex surfaces.

A direct preset method for solving ease-off tooth surface of spiral bevel gear

In order to realize the global integrated control of spiral bevel gear tooth surface, this paper presents a direct preset method for solving ease-off tooth surface of spiral bevel gear. This method integrates the preset contact path (CP), geometric transmission error (TE) and curvature of difference curve at the contact point (CDC), which is called CPTE-CDC. Based on the relationship between ease-off and tooth surface planning grid, CPTE-CDC is used to establish a nonlinear overdetermined equations to solve ease-off surface equation. According to the ease-off surface obtained from the solution, the ease-off target tooth surface of pinion related to cuttting parameters is established, and its optimal machining parameters are solved based on Levenberg–Marquardt (LM) algorithm. Finally, a numerical example is created using TCA and LTCA techniques. The results show that the tooth surface obtained by CPTE-CDC method not only meets the preset contact characteristics, but also meets the design requirements, which proves the correctness of the proposed method. CPTE-CDC method can be used as a theoretical basis for improving the global control of spiral bevel gear tooth surface.

Optimization of high-efficiency tooth surface accuracy of spiral bevel gears considering machine-tool motion errors

With the continuous improvement of the requirements of spiral bevel gear transmission for low noise and high precision, the optimization of high-efficiency tooth surface accuracy considering the motion axis error of machining machine tool has become a key point in the process of designing and manufacturing spiral bevel gear. Based on the theory of the multi-body dynamics system and the principle of gear meshing, a new tooth surface error model of spiral bevel gear considering the error of machine-tool moving axis is proposed and optimized, so as to obtain higher tooth surface accuracy and meshing efficiency. Firstly, according to the motion and machining principle of spiral bevel gear NC grinding machine, the corresponding relationship between the motion error of each axis of the NC gear grinding machine and the variation of cutting parameters of spiral bevel gear is analyzed, and the geometric motion error model of spiral bevel gear grinding machine is given; secondly, the tooth surface equation of the spiral bevel gear considering the machine-tool motion axis error is established; then, in view of Powell's dog leg optimization algorithm, the tooth surface considering the motion axis error of the machine tool is optimized, and the optimal cutting parameters of spiral bevel gear tooth surface machining are obtained. Finally, the simulation results show that the difference between the peak and peak values of transmission error and the maximum contact stress of the tooth surface is reduced by 72.6% and 1.62%, respectively, and the meshing efficiency is improved from 0.9798 to 0.9803 after optimization; by comparing the rolling experiment and simulation results, the maximum error between the quantitative parameters of the two groups of tooth surface contact marks is no more than 9%, which verifies the effectiveness and feasibility of this method, and provides a certain theoretical basis for practical production and processing.

Numerical study on mixed thermal-elastohydrodynamic lubrication of grease lubricating lubricated spiral bevel gear for heavy-duty unmanned aerial vehicle

Aiming to solve the problem of the gear lubrication of unmanned aerial vehicles (UVAs), a grease mixed Thermal-elastohydrodynamic lubrication (TEHL) model is established, and the lubrication state of the gearbox of oil-powered heavy-duty UAVs is numerically analyzed. In this study, grease is regarded as a non-Newtonian fluid whose properties change nonlinearly with respect to pressure, temperature, and other conditions. The complex meshing state of a spiral bevel gear tooth surface is analyzed using the loaded tooth contact analysis (LTCA) method, and three points on the tooth surface are selected as samples to describe the lubrication state of the entire tooth surface. The thickness of grease film and the temperature rise of the tooth surface are studied in detail, considering the natural roughness of the tooth surface and influence of different greases. The results show that the established model agrees with results from the literature. The dangerous point of tooth surface lubrication is at the meshing midpoint. Under cruise conditions, the lubricating grease viscosity significantly influences the temperature rise of the tooth surface.

An alignment angle error compensation method of spiral bevel gear tooth surface measurement based on tooth surface matching

In the precision measurement of spiral bevel gears (SBGs) by gear measuring center (GMC), as the manufacturing and assembly error of the GMC exists, there is an alignment angle error between the upper and lower centers. The tooth surface error caused by this alignment angle error is analyzed. A method of accurate registration between the measured tooth surface and the theoretical tooth surface is proposed to calculate the tooth surface deviation variables. And a matching point search method is proposed to solve the corresponding relationship between the measured tooth surface and the theoretical tooth surface of SBG. Then, cubic B-spline interpolation and spiral interpolation are combined to interpolate the points around the theoretical points. Finally, experimental results show that the tilt angles and eccentricities are calculated precisely, which verifies the accuracy and feasibility of the registration algorithm proposed in this paper. After compensation, the alignment angle error of the gear axis that is included in the measurement results of the SBG tooth surface deviation reduces remarkably, and this method can improve the measurement accuracy of the gear measuring machine significantly when measuring the tooth surface deviation.

Compensation Method for Inclination Errors in Measurement Results of Tooth Surface of Spiral Bevel Gear

The manufacturing error of spiral bevel gear tooth surface has a great influence on transmission efficiency and gear life. The error of the gear tooth surface needs to be measured accurately and fed back to the machine tool to adjust the parameters. When measuring the spiral bevel gear using a gear measuring machine, combined with the measurement theory of the tooth flank of spiral bevel gear, this paper proposed a method to compensate the inclination error in the measurement result precisely. Based on the iterative search method, a precision matching method for the theoretical and the measured tooth surface of the spiral bevel gear was designed to calculate the compensation results. The experimental results show that the inclination errors included in tooth surface measurement results reduced from more than 3 μm to less than 0.5 μm, and more than 70% of the errors are compensated by the proposed method. The accuracy of the measurement results improved significantly after compensation, and furthermore, it can provide a more accurate basis for the adjustment of machine tool parameters in the manufacturing process.

Application of the Bilateral Filter for the Reconstruction of Spiral Bevel Gear Tooth Surfaces From Point Clouds

Abstract Reconstruction of gear tooth surfaces from point clouds obtained by noncontact metrology machines constitutes a promising step forward not only for a fast gear inspection but also for reverse engineering and virtual testing and analysis of gear drives. In this article, a new methodology to reconstruct spiral bevel gear tooth surfaces from point clouds obtained by noncontact metrology machines is proposed. The need of application of a filtering process to the point clouds before the process of reconstruction of the gear tooth surfaces has been revealed. Hence, the bilateral filter commonly used for 3D object recognition has been applied and integrated in the proposed methodology. The shape of the contact patterns and the level of the unloaded functions of transmission errors are considered as the criteria to select the appropriate settings of the bilateral filter. The results of the tooth contact analysis of the reconstructed gear tooth surfaces show a good agreement with the design ones. However, stress analyses performed with reconstructed gear tooth surfaces reveal that the maximum level of contact pressures is overestimated. A numerical example based on a spiral bevel gear drive is presented.

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.

Spiral Bevel Gear B-Spline Tooth Surface Reconstruction Algorithm and Precision Analysis

To increase the utility rate of machine, the sculptured surface machining method was researched to use in the spiral bevel gear tooth surface manufacturing with the industrial CNC milling machine. The three dimentional tooth surface points are required to design tool path planning in the SSM method. For obtaining the arbitrary point of tooth surface, the uniform bicubic B-spline tooth surface was reconstructed by cutting simulation and fitting programs. The discrepancies between fitted and theoretical points of tooth surface were provided with CAD/CAM platform. According to the results, the tool path planning of sculptured tooth surface machining can be designed and realized further.

Surface Quality and Accuracy Characteristics of Spiral Bevel Gear by Electrochemical Mechanical Finishing

Spiral bevel gears (SBG) are the core transmission elements for realizing intersection shaft driving. Owing to the outstanding advantages of finishing efficiency and capability, electrochemicalmechanical finishing (ECMF) is used to finish the tooth surfaces of SBG for improving surface quality and accuracy.The forming ECMFmethod is put forward, the influence of processing parameters on the surface roughness is studied, and the influence of the forming ECMF method on the accuracy of SBG’s tooth profile is studied experimentally. The results indicate that the surface roughness R a is reduced from 1.6 μm to 0.05 μm. After finishing, the dimensional accuracy between teeth can be enhanced by 1∼2 grades compared with the technical specifications before finishing and the accuracy of gear teeth profile are also improved.

Digital Conjugate of Tooth Surface of Logarithmic Spiral Bevel Gear

Based on the surface of the envelope principle and the digital conjugate surface theory, The taper logarithm helical gear meshing theory further perfect. According to the mathematical model of logarithmic spiral bevel gear tooth surface meshing, using MATLAB powerful scientific analysis and calculation visual features and functions for the conjugate tooth surface equation to get the enveloping surface discrete conjugate points and draw out the conjugate tooth surface. Again through the optimization of surface get rid of the noise, end up with conjugate tooth surface precision, and can B spline fitting. Said for further analysis of spiral bevel gear drive are very valuable.

Face-milling spiral bevel gear tooth surfaces by application of 5-axis CNC machine tool

In order to solve some common problems of CNC-machined spiral bevel gears such as small cutting strip width and poor surface quality, while milled by the ball-end, a machining method of face milling using a disk cutter with a concave end is presented. The research theories are based on the foundation of spiral bevel gears’ geometry structure. Firstly, a bigger diameter disk cutter with a concave end is selected. Then, change the setting order of cutter orientation angles. The functions of cutter tilt and yaw angle are separated, and tooth surfaces machined with big cutting strip width and no bottom land gouge can be expected. Since the cutter yaw angle, determined firstly by cutting contact point, positions in the tooth surface machine, the bottom land gouge interference can be avoided effectively. Then, the tilt angles of the gear pair, both side tooth surfaces, are determined by the theory of sculptured surfaces machined by the flat-end cutter, respectively. As a result, the improved cutting strip width and machining efficiency can be realized. Finally, feasibility of this method is verified through machining experiment and measurement of a spiral bevel gear pair.

Designing and Manufacturing Spiral Bevel Gears Using 5-Axis Computer Numerical Control (CNC) Milling Machines

The design of spiral bevel gears remains complex since tooth geometry and the resulting kinematic performance stem directly from the manufacturing process. Spiral bevel gear cutting up to now has relied on the works of several manufacturers. Recent advances in milling machine technology and computer aided manufacturing (CAM) now make it possible to manufacture good quality spiral bevel gears on a standard 5-axis milling machine. This paper describes the computer aided design (CAD) definition and manufacturing of spiral bevel gear tooth surfaces. Process performance is assessed by comparing the resulting surfaces after machining with the predefined CAD surfaces. This manufacturing process makes it possible to obtain geometry analytically, making design easier than with standard spiral bevel gears.

Parametric Modeling of the Tooth-Surface of Spiral Bevel Gears with Spherical Involute

Based on the the principle of generating line of spiral bevel gears, a new modeling method about spiral bevel gears is proposed. Mathematical pattern of spiral bevel gears with spherical involute is developed about two parameters. A kind of simulation modeling software of spiral bevel gears with spherical involute is developed in matlab-guide environment. The data of tooth-surface are collected and calculated in the simulation system according to the machining parameters of a pair of gears which are established. It is convenient to establish accurate solid models of spiral bevel gear by obtained data points. Thus it can provide a feasible and effective way for CAD/CAE modeling and is modeled perfectly in computer so as to simulate the platform of virtual manufacture and meshing analysis.

Computerized Modeling and CNC Machining Simulation of Spiral Bevel Gear

Based on the theory of gearing and differential geometry, a CNC hypoid generator mathematical model for spiral bevel has been developed. A mathematical model of a spiral bevel gear-tooth surface based on the CNC Gleason hypoid gear generator mechanism is proposed in the paper. The simulation of the spiral bevel gear is presented according to the developed machining mathematical model. A numerical example is provided to illustrate the implementation of the developed mathematic models.

Research on Spiral Bevel Gear Tooth Surface Reconstruction Based on NURBS

The tooth surface shape of spiral bevel gear is complex. In the detection process of errors tooth surface model is constructed based on coordinate data of limited the actual tooth surface sampling points. The model is used to analysis and manufacture of gear to meet the processing requirements. NURBS (non-uniform rational B-Spline) method is the most effective reconstruction method for geometry there are both freedom and analytic curves and surfaces. NURBS method is used to calculate non-uniform knot vector, NURBS control points and B-Spline inverse and reconstruct tooth surface. Reconstructionof spiral bevel gears in using NURBS is achieved and the tooth surface reconstruction is drawn out in Open GL in VC environment. And then reconstruction error on the tooth surface is analyzed. It proves that using the method of NURBS to reconstruct spiral bevel gear tooth surface is correct and feasible.

Research on Curvature of Tooth Flank of Gleason Spiral Bevel Gears

According to spiral bevel gear machining process, use the method of computer simulation to get the discrete points’ three-dimensional coordinates of Gleason spiral bevel gear tooth surface, and then solve the tooth surfaces’ NURBS surface as the unified mathematical model. On this basis, research the curvature of tooth surfaces of various types of Gleason spiral bevel gear, draw the mean curvature diagram, and study the link between the adjustment of processing parameters and the change of tooth surfaces’ mean curvature. Establish a theoretical foundation for the processing error adjustment based on tooth surface’s curvature diagram.