Bevel Gear Tooth Research Articles

Fault Diagnosis Method for Marine Electric Propulsion Systems Based on Zero-Crossing Tacholess Order Tracking

In marine electric propulsion systems (MEPS) driven by variable-frequency drives, motor current signals often exhibit complex modulation components, ambiguous spectra, and severe noise interference, rendering it challenging to extract fault-related modulation components. To address this issue, we propose a zero-crossing tacholess order tracking method based on motor current signals. This method utilizes zero-crossing estimation of the instantaneous frequency to perform angular resampling of stator current signals and demodulates the envelope spectrum to extract fault characteristic spectra, enabling the diagnosis of mechanical faults in MEPS. Given the synchronization of the synchronous motor speed with the inverter fundamental frequency, this method estimates instantaneous frequencies in the time domain without requiring integration or time–frequency representation, which is simple and computationally efficient. Data validation on a small-scale marine electric propulsion test platform demonstrates that the proposed method exhibits good robustness under variable-speed conditions and effectively detects imbalance faults caused by propeller breakages and gear faults resulting from bevel gear tooth defects. Therefore, the proposed method can be applied to diagnose faults in downstream mechanical equipment driven by motors.

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.

Non-Newtonian thermal elastohydrodynamic mixed lubrication in elliptical contact for nutation-driven double circular-arc spiral bevel gear pair

The new type of nutation reducer with double circular-arc bevel gears as the core is characterized by advantages such as high load-bearing capacity, large transmission ratio, and simple structure. The existing research focuses on the machining methods of gears and the analysis of tooth contact. This article first time establishes an elastohydrodynamic mixed lubrication model for nutation double circular-arc bevel gear. The model's accuracy is verified by comparing it with existing test results. On this basis, combined with the finite element method and tooth contact analysis, the meshing characteristics, tooth contact characteristics, and lubrication characteristics of the double circular-arc bevel gear tooth surface are analyzed. The results show that the entrainment velocity at the contact point of the tooth surface during transmission is much higher than the sliding velocity. Consequently, the meshing motion is close to pure rolling. In constant-speed transmission, the oil film thickness at the engaging-in and exit points near the edge of the tooth surface is smaller than that at other meshing points on the tooth surface. This phenomenon can easily lead to mixed lubrication and lubrication failure, as well as tooth surface wear. During deceleration, i.e., when the speed drops to 50 r/min, the oil film thickness approaches zero, indicating that the gear has entered a mixed lubrication state. The proposed model can be used for lubrication analysis and improving transmission accuracy of nutation double circular-arc bevel gears.

Анализ контакта конических зубьев шестерен на основе машинного обучения

In this paper, we study the analysis of the contact of bevel gear teeth based on machine learning methods. Bevel gear teeth are widely used in various industrial and mechanical systems to transmit rotational motion with high precision and reliability. Traditional methods of gear contact analysis are based on mathematical models and empirical formulas, which may be limited in accuracy and applicability. In recent years, machine learning has become a powerful tool in the field of engineering and mechanics to more accurately model and predict the contact behavior of bevel gear teeth. The paper proposes the use of machine learning methods, such as neural networks or deep learning algorithms, to train models capable of analyzing the contact of bevel gear teeth. Wear, load, and gear geometry data can be used to train models, which can then predict contact parameters and evaluate contact performance.

Flank fractures on spiral bevel gears—transfer of analytical methods for the estimation of residual stresses from cylindrical gears to bevel gears

The classic flank and root load capacity calculation on the component surface forms the basis for the design of power gears today. However, flank fractures also occur in practice, particularly with large-module gears and/or low case-hardening depths. It is a fatigue damage with crack initiation in the tooth interior, its prevention requires the calculation of the stresses below the surface. In addition to understanding the load stresses, the inhomogeneous load bearing capacity and the residual stress profile in case-hardened gears are also of great importance. There are various calculation approaches for this in the area of cylindrical gears, but these have not yet been transferred to the complex geometry of spiral bevel gears. The focus of this publication is on estimating the residual stresses in the tooth volume by generating a three-dimensional residual stress tensor field in the bevel gear tooth based on the two-dimensional calculation approaches used to date on cylindrical gears. In combination with the stress tensor-time curves from a tooth contact simulation with the LTCA tool BECAL, this can be fed into different failure hypotheses, which is illustrated using an example.

A study on the thermodynamic characteristics of a mechanical A/C swing angle milling head

Several studies have evaluated the thermal error modeling and structural characteristics of the swing angle milling head; however, few studies have reported the thermodynamic characteristics of the swing angle milling head. Therefore, based on the thermodynamic theory, the thermodynamic characteristics of the mechanical A/C swing angle milling head of the five axis CNC gantry milling machine are evaluated, and the relevant heating calculation results are obtained. The temperature field distribution and thermodynamic characteristics of the swing angle milling head were simulated and analyzed by using ANSYS Workbench finite element software. In addition, the accuracy and rationality of the finite element simulation results of this study are verified based on the experimental conclusions of other relevant scholars that the maximum temperature of the gear is also mainly distributed near the pitch line of the tooth surface. The research results indicate that the maximum heat generation area inside the swing angle milling head is mainly concentrated on the pitch line of the bevel gear tooth surface of the main spindle execution component, with a maximum temperature of 43.559°C. The maximum thermal deformation is located at the tip of the swing angle milling head, with a maximum thermal deformation of 1.8353 × 10−5 m, this study can provide important theoretical reference and data support for the structural optimization and thermal deformation control of subsequent swing angle milling heads.

Multi-time scale thermal tribological dynamics coupling model of the helicopter intermediate reducer under severe loss of lubrication

There is no lubrication in the contact area, which leads to a significant influence of the thermal characteristics on the friction dynamics and life of the helicopter intermediate reducer because the helicopter experiences severe loss of lubrication. In this study, for evaluating the non-linear friction dynamics and transient thermal network models of the intermediate gearbox, a multi-time scale coupling method was proposed to establish a proportional allocation method between the oil film region and the rough peak contact region of the tooth surface by considering the effect of temperature and to study the adsorption film under the condition of severe lubrication loss. The coupled thermal and kinetic characteristics of the severe lubrication loss condition were obtained by calculating the friction coefficients in the lubricated and dry-friction regions. The results showed that the friction coefficient of the bevel gear tooth surface fluctuated between 0.1 and 0.6, and the degree of the gear axis trajectory shift was more evident owing to the increase in the friction force excitation caused by the increase in the friction coefficient.

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.

Finite element analysis of bevel gear tooth side clearance and fatigue characteristics under alternating torque

In this paper, the effect of different tooth side clearances on the fatigue characteristics of bevel gears under alternating torque is investigated using finite element analysis technology. The article first determines the structure form and main parameters of the bevel gear and completes the establishment of the three-dimensional model of bevel gear transmission. Then, based on the principle of finite element analysis, the fatigue characteristics of the bevel gear under different tooth side clearances are simulated by ANSYS workbench software. Next, according to the simulation results, the changes in service life and safety coefficient of bevel gear with tooth side clearances are analyzed, and the relevant conclusions are drawn. Finally, combined with the finite element analysis results, the axial adjustment amount of the bevel gear assembly of this project is guided, and the actual use effect is verified. The results show that when the tooth side clearance jn is taken in the range of 0.04·m∼0.08·m, the fatigue safety coefficient and service life of bevel gear gradually decrease with the increase of tooth side clearance jn.

Determination of the Accuracy of the Straight Bevel Gear Profiles by a Novel Optical Coaxial Multi-Ring Measurement Method.

Straight bevel gears are widely used in mining equipment, ships, heavy industrial equipment, and other fields due to their high capacity and robust transmission. Accurate measurements are essential in order to determine the quality of bevel gears. We propose a method for measuring the accuracy of the top surface profile of the straight bevel gear teeth based on binocular visual technology, computer graphics, error theory, and statistical calculations. In our method, multiple measurement circles are established at equal intervals from the small end of the top surface of the gear tooth to the large end, and the coordinates of the intersection points of these circles with the tooth top edge lines of the gear teeth are extracted. The coordinates of these intersections are fitted to the top surface of the tooth based on NURBS surface theory. The surface profile error between the fitted top surface of the tooth and the designed surface is measured and determined based on the product use requirements, and if this is less than a given threshold, the product is acceptable. With a module of 5 and an eight-level precision, such as the straight bevel gear, the minimum surface profile error measured was -0.0026 mm. These results demonstrate that our method can be used to measure surface profile errors in the straight bevel gears, which will broaden the field of in-depth measurements for the straight bevel gears.

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.

Modal Analysis of Aeronautic Spiral Bevel Gear in the Temperature Field

The temperature of the bevel gear tooth surface will increase greatly because of its special structure. Modal is the characteristic of reaction structure. In order to design and manufacture higher quality aerial bevel gears, it is necessary to study the modal of aerial bevel gears under the action of the temperature field. Firstly, a temperature field calculation model is established according to heat transfer theory. Then, based on the traditional linear modal theory, the modal analysis model under the influence of temperature was established considering the influence of rotational speed and temperature field on the stiffness. Based on the model, modal analysis of the driven gear of a certain aviation bevel gear is carried out. It can be seen from the analysis results that the speed has a great influence on the gear stiffness, and the positive and negative effects are related to the direction of the centrifugal force. Secondly, the inhomogeneity of temperature field distribution also affects the natural frequency and then the gear stiffness. When the speed field and temperature field work together, the pitch shape changes the most, so it is necessary to consider temperature as an influencing factor in the design of aerial bevel gears.

Mathematical Modeling and Machining of the Internal Double-Arc Spiral Bevel Gear by Finger Milling Cutters for the Nutation Drive Mechanism

A method of machining the internal double-arc spiral bevel gear with a finger milling cutter was presented. The mathematical model of the internal spiral bevel gear tooth profile was established considering the principle of machining a spiral bevel gear by the generating method, and a three-dimensional (3D) tooth profile graph was developed. Subsequently, by applying the gear meshing theory, the 3D model of the tooth alignment curve for the finger milling cutter was established. Based on the tooth surface equation of crown gear, the cutter intercept equation was derived. The cutter was divided into four finger milling cutters considering the design difficulty of the cutter, which is used to manufacture different arc segments of the double-arc tooth profile, respectively. The special machining tool model of the internal spiral bevel gear was further developed by using SolidCam, and the simulation experiment was carried out. The simulated gear model was compared with the theoretical gear model and the error of the simulation experiment was estimated. Actual machining on the machine tool and the internal spiral bevel gear were inspected. The maximum error is 0.035 mm, and the minimum error is 0.005 mm. The machining accuracy meets the requirements. The feasibility of machining the internal double-arc spiral bevel gear with a finger milling cutter was verified.

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.

Optimized design of straight bevel gear tooth root transition surface

Optimized design of straight bevel gear tooth root transition 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.