Spiral Bevel Research Articles

Simulation and experimental analysis of traveling wave resonance of flexible spiral bevel gear system

Considering the traveling wave resonance (TWR) phenomenon of the spiral bevel gear system in the aero engine accessory casing, the flexible spiral bevel gear model is established by three-dimensional (3D) shell element and beam element. The dynamic model of flexible bevel gear system considering the change of meshing teeth pairs in the operating process is established by component mode synthesis (CMS) method and rotational modal projection method. The proposed model is verified by finite element (FE) solid model and experiment test results. On this basis, the TWR phenomenon of the bevel gear system is studied in combination with dynamic response and vibration stress experimental test. The results show that the bevel gear system has 3 nodal diameter resonance speeds within the actual operating speed range, which are one 1st nodal diameter resonance of pinion and two 1st nodal diameter resonance of gear. When the bevel gear system operates at TWR state, the amplitude corresponding to fm ± m·fr (fm is meshing frequency, m is nodal diameter number, fr is shaft rotational frequency) is larger than that corresponding to fm in the Fast Fourier transform (FFT) spectrum of the of the gear foundation vibration stress, and the vibration stress cloud map of the gear foundation shows the corresponding nodal diameter vibration shape. The research results provide a theoretical basis for feature recognition and influence law evaluation of TWR of bevel gear system.

Investigation on meshing characteristics of spiral bevel gear under wear fault evolution with assembly errors

Spiral bevel gears have the advantage of transmitting high torque and power comparing to helical gear and straight bevel gear. However, they are susceptible to wear due to factors such as high loads, poor lubrication, and surface imperfections resulting from machining. In this study, we propose an autonomous model for predicting tooth wear and analyze the meshing characteristics of spiral bevel gear (SBG) pairs under different assembly errors. Concurrently, we establish a finite element model to validate the accuracy of our meshing characteristic analyses. We also compare the distribution patterns of wear depth on the tooth surface with existing literature. Our investigation delves into meshing characteristics, encompassing transmission errors and Time-varying mesh stiffness (TVMS), considering wear evolution under assembly errors. The results demonstrate that the fluctuations in TVMS remain consistent across all four types of assembly errors examined. Gear tooth wear leads to an increase in gear backlash and fluctuations in unloaded transmission error. The meshing stiffness fluctuation of the SBG pair enlarges under wear evolution. Assembly errors result in shifts in the initial contact line and contact pattern, subsequently altering the distribution of wear depth. Different forms of assembly errors may cause a similar effect on the distribution of wear depth and meshing characteristics.

Predictive Model for Scuffing Temperature Field Rise of Spiral Bevel Gears under Different Machining Conditions

Spiral bevel gears are extensively employed in mechanical transmissions; however, they are prone to adhesive wear when operating under high-speed and heavy-load conditions. Research indicates that the tooth surface roughness of gears significantly influences the friction and wear of the meshing gears. The present study delves into the origins of tooth surface roughness through the integration of the W-M function and fractal theory. Utilizing an involute helical gear with surface roughness for tooth cutting, a three-dimensional model is established with roughened tooth surfaces. This paper introduces an approach to developing three-dimensional gear models with roughness and applies the finite element method to perform thermodynamic analysis on gears exhibiting diverse levels of surface roughness. The thermal analysis of gears with varying degrees of roughness was conducted using the finite element method. Comparative analysis of the results under specific operating conditions elucidated the impact of roughness on tooth surface temperature rise. In order to validate the simulation model, an experimental test platform for spiral bevel gears of identical size was established. This model integrates tooth surface roughness with thermodynamic analysis, allowing for the rapid assessment of tooth surface temperature rise under different machining conditions, and reducing the cost of validating predicted tooth surface load-carrying capacity.

Mesh characteristic changes of spiral bevel gear pair with assembly errors during tooth crack propagation

Spiral bevel gears (SBGs) are often used because of their strong carrying capacity and lower vibration. However, this heightened load capacity can sometimes result in the development of tooth surface cracks. This study aims to simulate the three-dimensional propagation of cracks in SBGs under various assembly conditions and explore how the presence of cracks affects mesh characteristics. This paper investigates crack propagation in SBGs by applying principles of fracture mechanics. Employing a combination of finite element software ABAQUS and fracture mechanics software FRANC3D, the study conducts a three-dimensional analysis of crack propagation in SBGs. The study analyzes the impact of crack propagation on the lifespan and mesh characteristics of SBGs, including crack propagation morphology, transmission error, time-varying meshing stiffness (TVMS), gear life, and tooth surface force, under various assembly errors.

Implementation of an exact completing method of generation for face-milled spiral bevel gears with uniform depth taper

AbstractThis paper proposes an exact completing method of generation of face-milled spiral bevel gears with uniform depth taper. This method ensures localized bearing contact without kinematic transmission errors in both directions of rotation. Both sides of the tooth are generated simultaneously using the same set of basic machine tool settings. A tip relief on the tooth surfaces is the only required microgeometry modification to achieve a smooth transition of load between consecutive pairs of teeth. An analytical approach to determine the basic machine tool settings and select the grinding cutter parameters has been also developed. The selection of the nominal cutter radius follows the recommendations of Information Sheet AGMA 22849-A12. The basis for alignment error compensation has been also established. Tooth contact and stress analyses demonstrate the advantages and limitations of the proposed method, making it suitable for applications with higher power demands for the drive side than for the coast side.

Full-Scale Gear Tooth Bending Fatigue Tests Obtained Early in the Development of a Rotorcraft Transmission

A new gear testing method is introduced to reduce development cost and time. It allows component-level testing of individual gear meshes and new gear designs. Instrumented gear sets are tested at full load while the rest of gearbox components are still being built. Since the fatigue strength of the gears is determined earlier in the development cycle, design deficiencies are identified and understood earlier. In this new method, an individual gear mesh installed in a stiff facility housing is used to mimic the contact pattern and bending stress demonstrated by the same mesh in an actual aircraft housing. Analytical gear models are used to identify the displacement difference between the stiff test facility and the aircraft housing. The test stand is designed so it can be adjusted accurately to provide gear and pinion positions that are representative of the deflected positions under load in the aircraft housing. A spiral bevel mesh and a split torque double helical reduction stage with multiple meshes are evaluated using the developed method. The contact pattern and strain survey results of the gear meshes are correlated with predicted results.

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.

Analysis and optimization of time-varying meshing parameters of spiral bevel gear with consideration of load sensitivity

Analysis and optimization of time-varying meshing parameters of spiral bevel gear with consideration of load sensitivity

A new multi-DOF envelope forming process for fabricating spiral bevel gears with back taper tooth

Spiral bevel gears are critical transmission components, and are widely used in the aerospace field. This paper proposes a new multi-DOF envelope forming process for fabricating spiral bevel gears. Firstly, the multi-DOF envelope forming principle of spiral bevel gears is proposed. Secondly, the design methods for the envelope tool geometry and movement are proposed based on the envelope geometry and movement relationships. Thirdly, the metal flow and tooth filling laws are revealed through 3D FE simulation of the multi-DOF envelope forming process of a typical spiral bevel gear. Fourthly, a new method for separating the envelope tool and the formed spiral bevel gear with back taper tooth is proposed to avoid their interference. Finally, experiments on multi-DOF envelope forming of this typical spiral bevel gear are conducted using new heavy load multi-DOF envelope forming equipment. The simulation and experimental results show the feasibility of the proposed multi-DOF envelope forming process for fabricating spiral bevel gears with back taper tooth and the corresponding process design methods.

Cutting state recognition of spiral bevel gear face hobbing

Abstract To investigate the issue of chatter vibration during the face hobbing process of spiral bevel gears, this study conducted experiments on the YKA2260 gear hobbing machine, collecting 142 sets of vibration acceleration signals. The optimal combination for wavelet threshold denoising was determined based on the signal-to-noise ratio (SNR), and preprocessing of the raw signals was performed. Utilizing wavelet packet decomposition, the energy entropy of wavelet packet coefficients was extracted as feature values. A recognition model for the cutting state during the face hobbing process of spiral bevel gears was established using a Support Vector Machine, achieving a recognition accuracy of up to 98.0769%. Furthermore, the model’s high recognition accuracy for small training samples in engineering applications was validated.

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.

The Prediction of Stability in the Time-Delayed Milling Process of Spiral Bevel Gears Based on an Improved Full-Discretization Method

Spiral bevel gear drives are widely used in mechanical transmission devices due to their compact structure, smooth transmission, and cost-effectiveness. With the continuous improvement in mechanical product quality, higher and higher requirements are set for the precision, smoothness, and power density of gear transmission devices. Chatter can lead to poor workpiece surface finish on spiral bevel gears, excessive tool wear, and even damage to machine tools. Therefore, the effective prediction of milling chatter during the processing of spiral bevel gears is essential. Regenerative chatter is one of the most fundamental types of vibration in machining processes. This paper presents an improved fully discrete algorithm for predicting the stability of time-delayed cutting in the milling process of spiral bevel gears. The method is validated using single- and double-degree-of-freedom models, demonstrating its accuracy and computational efficiency. The results show that the proposed method improves computational efficiency while ensuring accuracy.

Chatter and Surface Waviness Analysis in Oerlikon Face Hobbing of Spiral Bevel Gears

A vectorized analytical model for the cutting dynamics in the spiral bevel gear face hobbing process has been developed, which is based on machine tool kinematics and vibration vectorization. The structural modal parameters of the cutter head spindle system are obtained through experimental modal analysis with hammer impact testing. The analytical model is utilized to simulate the generation of simulated vibration acceleration signals during spiral bevel gear hobbing. A wavelet threshold denoising method is applied to process the simulated vibration signals of the spiral bevel gear face hobbing with added white noise. Signal processing methods, including short-time Fourier transform are employed for time-domain analysis, frequency-domain analysis, and time–frequency-domain analysis of measured signals and simulated signals, thereby extracting the corresponding statistical features. In addition to the results of the experimental modal analysis, the causes of chatter in spiral bevel gear hobbing are discussed in detail, revealing that the main factor is cutter head vibration in the Y direction of the Hunan ZDCY CNC EQUIPMENT YKA2260 machine tool used in this research. The error in the time-domain characteristic parameters between simulated signals and measured vibration acceleration signals is within 15%, with a difference of 3.5% in spectral peak values. The predicted tooth surface morphology from simulation matches the actual morphology on the workpiece, comprehensively validating the reliability of the cutting dynamics model for the spiral bevel gear face hobbing process. Another conclusion drawn from numerical simulation experiments is that the amount of tooth surface waviness of the spiral bevel gears is the ratio of tool chatter frequency to cutting fundamental frequency.

A method for determining the actual coordinate system of spiral bevel gears by the measured positions of eight tooth surfaces

Abstract The coordinate system for the measurement of spiral bevel gear (SBG) by gear measuring center (GMC) is discussed and the misalignment between the actual coordinate system and the theoretical coordinate system of the SBG is analyzed. The misalignment can cause measurement errors and cannot be neglected in SBG precision measurements. To calculate the misalignment and accurately establish the actual coordinate system, a novel re-fitting method based on the measured positions of eight tooth surfaces is proposed. First, eight sets of gear axis direction vectors and original points can be obtained from the measurement of eight tooth surfaces, by the single tooth surface matching method. Second, the actual axis vector and the original point of the gear can be obtained, by re-fitting those eight sets of gear axis vectors and original points. Then, the actual coordinate system can be established by the actual gear axis direction vector and the original point. The least square method is used to calculate the original point, and a basis vector fitting method is proposed to solve the gear axis direction vector. Finally, two groups of preset coordinate system deviation tests are carried out to verify the accuracy and feasibility of the fitting algorithm. The results show that the fitting error of the original point is far less than 1 × 10 − 1 μ m and the fitting error of the angle is far less than 1 × 10 − 7 degree, which are superior to the design accuracy of the GMC. Therefore, the proposed algorithm can be applied to improve the measurement accuracy of current GMC.

A new method of rolling finishing forming process of spiral bevel gears investigated by numerical simulation and experiment

A new method of rolling finishing forming process of spiral bevel gears investigated by numerical simulation and experiment

Time-varying mesh stiffness calculation and dynamic modeling of spiral bevel gear with spalling defects

Time-varying mesh stiffness calculation and dynamic modeling of spiral bevel gear with spalling defects

Analysis of crack propagation and life estimation of spiral bevel gears with root cracks

Abstract In order to study the effect of tooth root cracks on the fatigue life of spiral bevel gears, a certain spiral bevel gear was taken as the research object, and the mechanism of tooth root fatigue cracks was analyzed based on crack propagation theory; By combining the extended finite element method and the level set method, an initial crack propagation finite element model is established. The crack location of the gear teeth is determined through static analysis of the gear pair, and the influence of alternating loads on the initiation and propagation life of tooth surface cracks is studied. The analysis results indicate that the number of load cycles required for each crack propagation after its first occurrence gradually decreases; The crack propagation path of gear cracks under fatigue load is consistent with the actual tooth surface fracture surface; Realize life estimation from crack propagation to fracture failure.

Loaded tooth contact analysis and meshing stiffness calculation for cracked spiral bevel gears

Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment. In this study, an accurate and efficient loaded tooth contact analysis (LTCA) model is developed to predict the contact behavior and time-varying meshing stiffness (TVMS) of spiral bevel gear pair with cracked tooth. The tooth is sliced, and the contact points on slices are computed using roll angle surfaces. Considering the geometric complexity of crack surface, a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points. According to the positional relationship between contact point and crack path, each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness. Then the compliance model of the cracked tooth is established to perform contact analysis, along with TVMS calculations utilizing three different models. By employing spiral bevel gear pairs with distinct types of cracks as examples, the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis (FEA) outcomes. Furthermore, the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs, including not only cracked tooth pair but also adjacent non-cracked tooth pairs. Hence, the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.

Analysis of scuffing through temperature measurement experiment and numerical simulation for spiral bevel gears

Tooth surface scuffing failure, as one of the primary failure modes of gears, frequently occurs during the operation of gear mechanisms. Scuffing properties of spiral bevel gears were investigated through a numerical analysis and experimental study. A novel temperature model for a single tooth was proposed to predict scuffing temperatures on the tooth surface. The model allows the analysis of variations in tooth surface temperature, considering both operating conditions and tooth contact scenarios. Experiments were carried out to explore tooth surface adhesion of spiral bevel gears under precisely defined operating conditions. Measurement of tooth surface temperatures was conducted by combining non-contact infrared temperature sensors and temperature-measuring cameras. This experiment verifies temperature changes on the tooth surface adhesion of spiral bevel gears. The combination of two temperature measurement methods ensures accurate temperature measurements, with errors below 8%, and facilitates the swift opening of the end cover. Experimental validation of the scuffing prediction model yields a maximum temperature difference of 5.93%. The method establishes a theoretical foundation for evaluating tooth surface adhesion of spiral bevel gears.

Research on the calculation method of grinding temperature field of spiral bevel gear based on generative machining

At present, the process parameter setting of spiral bevel gear grinding is mainly based on an empirical method, and the tooth surface temperature is difficult to estimate effectively during grinding, which may lead to excessive tooth surface temperature and surface burn caused by improper selection of process parameters. Aiming at the above problems, this paper presents a method for calculating the temperature field of spiral bevel gear forming based on a combination of analytical and numerical methods. The motion equation of spiral bevel gear grinding is derived based on the method of tooth surface development. The time-varying heat flow calculation method in tooth surface grinding was developed through the discrete and two-dimensional contact zone. The time-varying temperature field analysis method of spiral bevel gear forming is developed using the time-varying heat flow and finite element calculation method. The related research can realize the temperature prediction of grinding tooth surfaces and provide the basis for improving grinding technology.