Gear Profile Research Articles

A revised elastic-plastic contact model of cycloidal pinwheel based on length scale

This study explores the relationship between surface roughness and characteristic scale through theoretical analyses and experimental data. Considering the concavity and convexity of cycloidal gear tooth profile curvatures, a curved surface contact coefficient model suitable for both inner and outer contacts, with either equal or unequal curvatures, has been developed. Moreover, a fractal contact model is constructed for cycloidal pinwheels. This model considers scale correlation and analyzes the influence of microscopic parameters on the elastic-plastic critical grade and the behavior of the contact area. Additionally, the influence of the micro-convex body frequency index on surface contact performance is explored to provide theoretical insights for improving the elastic contact ratio and reducing wear on contact surfaces.

Numerical method for dynamic prediction of temperature field in aviation gear profile grinding

Numerical method for dynamic prediction of temperature field in aviation gear profile grinding

Geometric synthesis in the profile of the involute tooth for improving the performance of bending in the material of the spur gear

Abstract Transferring power from one rotational axis to another in numbers of axes requires portable equipment such as gear. In operation, involuted teeth were reported as bending and pitting failures. Bending fatigue causes gear tooth cracks at the root, and pitting causes more wear. This bending failure was reduced with the help of material selection, geometric modifications like changes in profile shape, transmission error, module, tip relief, pressure angles, and the application of forces. A normal force acting on a gear tooth gets resolved into three components, like tangential, radial, and axial. When it comes to enhancing bending strength, the geometric forms of profiles have a significant impact. A variety of tools and techniques, including hobbing, shaping, grinding, etc., are available at the fingertips for altering gearing tooth. Changing the borders of gear tooth profiles with hobbing tools is becoming more popular among the authors as a means for altering gear tooth. There are four distinct geometric profiles that may be used to change gear geometries and enhance bending strength by reducing stress on the tooth. These profiles include trochoidal, circular, bezier, and cubic spines, and they are implemented using a hob cutter. It is noteworthy to note that these designs boost strength by integrating the shape of number of teeth on the spur gear. This study compares the number of teeth on the gear’s pinion with other geometric characteristics, including pressure angle, module, etc., in order to discover the optimal way for modifying the involute tooth of the gear in order to increase the bending resistance effectively of the spur gear. For the purpose of boosting the strength of gear material, a number of research endeavours have utilized circular profiles; nonetheless, this profile is older than the Bezier curve profile. Here, Bezier curves with a three-and five-point profile give better results than other profiles with significant reductions in bending stress for the same quantity of tooth on the gear.

Development of a new gear profile measuring machine with five-link closed-loop mechanism

Development of a new gear profile measuring machine with five-link closed-loop mechanism

Mathematical model and generation analysis for crossed helical gear system

Purpose Crossed helical gears have point contact and their surfaces are subject to high surface stress. Contact stress and root tooth stress are the most common sources of failure in crossed helical gear. This paper aims to study the load-carrying capacity and performance of crossed helical gear teeth with different gear tooth profiles. To overcome defects and reduce the sensitivity to small shaft angle changes. The combined tooth profile is designed to reduce the bending stresses, contact stresses and tooth deflection, and prevent pinion failure in the gearbox. Design/methodology/approach The principle of the method is a line contact is introduced instead of a point contact between two teeth in mesh with each other. The tooth surface of the helical gear is designed and cut by a modified tool. Higher normal pressure angles like 25° and 35° are used. The modified involute is accomplished to eliminate interference between the teeth. Engineering software packages have been applied to generate all crossed helical gears gear profiles. The modification is compounding curves consisting of an epicycloid-involute-hypocycloid gear teeth profile generated by the cutter modified. Findings The stresses in the crossed helical gear teeth profile were reduced by increasing the normal pressure angle values. Using a 35° pressure angle the enhancement percentage in contact stress and teeth fillet region will be about 29.345% and 15.421%, respectively. The best enhancement in a gear’s resistance is the epicycloid-involute-hypocycloid gear teeth profile. The enhancement was 32.610% and 18.588%. The skew in line of action in skewed helical gear will be sensitive when the crossing angles are small. Their teeth surface tends to be easily worn out; however, the wearing process will be reduced by using a proposed gear teeth profile. Practical implications The gear teeth to be modified are cut by a shaper process. The modifying rack cutter of this study can be used as a reference for creating a different helical gears sample. The helical teeth surface is modified to become an envelope of the other. This makes an original point contact change into a line contact. The epicycloid-involute-hypocycloid gear teeth profile is preferred for a higher contact ratio and a large load capacity. This work explicitly introduces a new method of kinematic consideration to improve the load capacity of crossed helical gear. Originality/value This paper showed some novel results by the unique shape of the rack-cutter designed to generate different helical angles and different gear positions. In the future, it will make valuable contributions to the further development of the dynamic performance of a crossed helical gear system through the study in the field of using asymmetric teeth profiles of helical gears with tip relief as the manner to enhance the crossed helical gear performance. Investigation of crossed helical gear by applying a predesigned parabolic function of transmission error enables the absorption of linear discontinuous functions caused by misalignment.

The Use of Heuristic Optimization Techniques on RV Cycloid Reducer Design: A Comparative Study

In this study, heuristic optimization algorithms such as particle swarm optimization (PSO) and quantum particle swarm optimization (QPSO) have been used to optimize the weight of the cycloid reducer based on the values of some parameters. The algorithms were applied separately to the design problem, and their performances were compared. Initially, a basic design was performed using conventional approaches. Constraint conditions have been defined based on geometric features and the essential component of the reducer, the cycloidal gear, and then the existing basic design has been optimized in terms of size and weight. Finally, finite element analysis was conducted to validate the obtained parameter values and control the stresses in the contact areas of the cycloid gear profile. It has been determined that PSO reduced the weight of the basic design by 33.3 %, whereas QPSO reduced it by 33.8 %. Moreover, the results of the finite element analysis showed that the design obtained according to both optimization methods was safe in terms of the resulting stresses. Consequently, it has been demonstrated that the selected design parameters and constraint equations have been sufficient and that the basic designs could be enhanced using intuitive optimization methods.

Analysis of the effect of circular spline tooth profile parameters on flexspline gear stress based on response surface methodology

Abstract This study presents a simulation model for the wave generator and flexspline assembly, examining the relationship between radial and main section deformations. Adjusting the wall thickness enables interference-free meshing of various sections. A response surface model for the effect of circular spline profile parameters on flexspline stress has been established. To assess how various parameters of the involute gear profile affect the meshing stress of flexspline. Thus providing a theoretical basis for optimizing gear profile modifications.

Automation of control of geometrical characteristics of worm and bevel gears by means of coordinate measuring

The article contains the results of research on the automation of control of the geometric characteristics of gears. The use of coordinate measuring machines can significantly improve the productivity and accuracy of measurements. However, their use for testing gears requires the use of special programs for carrying out and processing the results of measurements of products with complex surface shapes. The use of software for metrological control of the geometric characteristics of worm and bevel gears makes it possible to achieve high accuracy of control and measurement work. To automate the control of geometric characteristics of worm and bevel gears, an additional module has been created for the standard program. With its help, all points of the measured curved surface of gears, obtained by contact method according to a standard measurement program, are structured into a single data array with a measurement protocol. Based on these data, the module generates a profile of the measured surface of a wheel tooth and builds a geometric contour of the profile of the measured tooth. The result of the module's operation is the formation of a general profile of the entire gear and its comparison with the original (theoretical) profile of the gear as a whole. The control process itself is carried out in a short time interval, which makes it possible to use the proposed approach to automating the control of gear profiles in small-scale production.

Calculation and Analysis of TVMS Considering Profile Shifts and Surface Wear Evolution Process of Spur Gear

Profile shift is a highly effective technique for optimizing the performance of spur gear transmission systems. However, tooth surface wear is inevitable during gear meshing due to inadequate lubrication and long-term operation. Both profile shift and tooth surface wear (TSW) can impact the meshing characteristics by altering the involute tooth profile. In this study, a tooth stiffness model of spur gears that incorporates profile shift, TSW, tooth deformation, tooth contact deformation, fillet-foundation deformation, and gear body structure coupling is established. This model efficiently and accurately determines the time-varying mesh stiffness (TVMS). Additionally, an improved wear depth prediction method for spur gears is developed, which takes into consideration the mutually prime teeth numbers and more accurately reflects actual gear meshing conditions. Results show that consideration of the mutual prime of teeth numbers will have a certain impact on the TSW process. Furthermore, the finite element method (FEM) is employed to accurately verify the values of TVMS and load sharing ratio (LSR) of profile-shifted gears and worn gears. This study quantitatively analyzes the effect of profile shift on the surface wear process, which suggests that gear profile shift can partially alleviate the negative effects of TSW. The contribution of this study provides valuable insights into the design and maintenance of spur gear systems.

Optimizing Structural Steel Spur Gear Design for Reduced Stress Concentrations in Industry 4.0 Using Finite Element Analysis

Abstract: The advent of Industry 4.0 has highlighted the importance of spur gears in power transmission across the automotive, aerospace, and marine industries. However, these gears are susceptible to failure due to bending and contact stresses from fatigue. Designing an involute gear profile presents challenges, particularly in managing tooth root stresses and avoiding interference. This study tackles these issues through comprehensive stress analysis, using modeling and FEM assessment. The focus is on evaluating bending stresses at critical locations and identifying strategies to reduce stress concentrations at the gear tooth root. By enhancing gear robustness, this research could contribute to potential patents in gear technology. Background: Spur gears are crucial for power transmission but often fail due to fatigue-induced stresses and design challenges at the tooth root. Objective: This study aims to address spur gear design challenges through comprehensive stress analysis, using modeling and FEM to assess bending stresses and explore strategies to reduce stress concentrations at the tooth root. Methods: The research uses SolidWorks and ANSYS for FEM analysis, focusing on bending stresses and exploring modifications in gear design using various materials for optimization. Results: The analysis shows strategic modifications to the gear's fillet radius and addendum can reduce stress at the tooth root by 38.26%, with stainless steel being the optimal material for enhanced gear strength. Conclusion: The study emphasizes strategic adjustments in fillet radius and addendum to reduce stress in spur gears, highlighting stainless steel's superior performance for optimized design and enhanced strength.

Rapid and high-precision measurement method for fine pitch gears without high-precision installation

To address the measurement issues posed by fine pitch gears, due to the characteristics such as low stiffness and narrow tooth space, this paper proposes a rapid and high-precision measurement method which does not require precise installation by combining optical and visual principles. A calibrated artifact, featuring cylindrical and flat surfaces, was designed to accurately determine the relative positions of the line laser sensor, camera, and rotary table. An experimental setup was constructed, and measurement experiments were conducted on two types of cylindrical gears. To validate the precision of the measurement system, gear profile deviation, helix deviation and pitch deviation were evaluated according to ISO 1328-1:2013. The results were compared with the reference evaluations from Klingelnberg Gear Measuring Center P26, with difference less than 2.4µm. Eight repeatability experiments were conducted, demonstrating that the method proposed satisfies the measurement requirements for fine pitch gears with an accuracy of class 6.

Research on the surface modification and microstructure evolution during gear profile grinding based on cellular automaton

The matrix structure of high-strength gears mainly comprises martensite with high stacking fault energy. The dominant mechanism of microstructure evolution in the surface layer during profile grinding is continuous dynamic recrystallization. However, the understanding of continuous dynamic recrystallization structure evolution during gear profile grinding remains limited. In this study, a predictive model based on cellular automaton for martensite structure evolution during gear profile grinding is proposed. Coupled with the finite element method, the microstructure evolution prediction of high-strength steel gears in profile grinding is conducted. The proposed model demonstrates good consistency with experimental data in calculating the proportion of low angle grain boundaries during grinding process. By combining experimental and theoretical prediction results, the mechanism of the influence of grinding depth on grain refinement in surface layer during gear profile grinding is elucidated. The dislocation density increases with the increase of grinding depth, leading to the generation and transformation of more subgrains. By analyzing the grain size and the proportion of subgrain boundaries, an optimal grinding depth threshold under dry grinding conditions is determined. This study provides valuable insights into the continuous dynamic recrystallization structure evolution during gear profile grinding process.

Computerised design, simulation of meshing and stress analysis of bionic logarithmic spiral spur gear drives

Inspired by the inherent properties of logarithmic spiral in nature, a new cylindrical spur gear drives using logarithmic spiral as a gear tooth profile is proposed. The logarithmic spiral property is explored, and then the equation of meshing, conjugate tooth profile and contact path of the proposed gear pairs are derived. The meshing characteristics of the new pair are investigated, such as pressure angle, contact ratio and sliding ratio. Simulation analysis of the strength, transmission error and transmission efficiency are used to validate the performance of the gear pairs before production of the proposed gear, followed by gluing load capacity and bending fatigue strength testing of the fabricated gear pairs. The results show that the pressure angle at any point of the tooth profile on the proposed gear is constant and equal to the logarithmic spiral strike angle. The contact ratio of the gear decreases with the increase of the strike angle. Compared with that of involute gears, logarithmic spiral gears have better performance in terms of strength, transmission error, transmission efficiency and lifetime.

Method for a Comprehensive Analytical Study of Contact Pressures, Wear, and Durability of Metal-Polymer Helical and Spur Gears with Steel Pinion and Polyamide Gear

An analytical complex study of metal-polymer (MP) helical and spur gears by a new author's analytical method was carried out. The influence of the helix angle on the contact pressures in the engagement, the teeth wear, and the durability of the MP gears of different polymers has been established. MP gears with a pinion made of carbon steel (0.45% C) and gear made of basic polyamides PA6, PA66, and their composites with the following fillers: fiberglass (PA6+30GF), carbon fiber (PA6+30CF), molybdenum disulfide (PA6+MoS2), and oil filled cast polyamide (PA6+Oil) are studied. According to the developed procedure for determination of the angles of engagement parity change, it is shown that there is two-one-two-pair or three-two-three-pair engagement depending on the helix angle. Quantitative and qualitative regularities of changes in the initial maximum contact pressures and their reduction due to tooth wear over the time from the moment of the entrance of teeth to engagement up to their exit from it are established. In particular, at a helix angle of β = 10°, the contact pressures reduce to 33% compared to spur gears. The linear wear of the gear polymer tooth profile at selected points of engagement and different helix angles has been investigated, and the influence of the pressure angle on it is shown. It is established that its regularities of change during the engagement phase are the same for all polymeric materials studied. The durability of transmissions is calculated, and its comparative evaluation is given. At the helix angle β = 5°, a slight increase in durability is achieved compared to spur gears, and at β = 10° the durability of MP gears increases by about 1.5 times for all polymeric materials studied.

Study on the Parameter Influences of Gear Tooth Profile Modification and Transmission Error Analysis

Gear transmission systems are widely used to transfer energy and motion and to guarantee the accuracy of the entire machine system. The modification technique is a common method that improves the gear profile and reduces the transmission error. Based on the parametric model, a modified gear can be established for the evaluation of static and dynamic characteristics. The influences of profile modification parameters and gear parameters are investigated while changing the rules of different kinds of factors. Based on sensitive parameters, a two-stage profile modification curve is proposed to improve the performance of gear pairs. Thus, considering the time-varying mesh stiffness and backlash, a novel, dynamic modified gear model is established to analyze the dynamic performance, such as the dynamic transmission error. Based on the proposed curve, the range and amplitude of the transmission error can be decreased. Additionally, the vibration displacement and noise can be reduced to improve the running characteristics.

Dynamic Simulation Analysis of Aviation Gear Transmission Based on Rough Tooth Surface

In order to explore the influence of tooth surface microstructure on the dynamics of aviation gear transmission, this paper describes the profile of aviation gear considering rough surface based on fractal theory. With the help of the established gear fractal contact model, the dynamic parameters such as time-varying friction coefficient, time-varying meshing stiffness and transmission error of rough tooth surface are characterized. The nonlinear dynamic model of aviation gear is established to solve the dynamic response of smooth and rough tooth surface. The dynamic meshing force, dynamic friction force, vibration time domain and frequency domain diagram are obtained, and the corresponding experiments are carried out. The simulation and experimental results show that the fluctuation range of the dynamic simulation results of aviation gear transmission based on rough tooth surface will be larger, and it has a certain degree of disorder, which is closer to the experimental results.

A novel harmonic movable tooth drive with almost surface contact conjugate tooth profiles: Parametric design, modification and analysis

This paper focuses on a novel harmonic movable tooth drive as an alternative of currently used harmonic gear drives. Different from the harmonic gear drives, the novel drive removes small module teeth from thin-walled flexible rim, instead, adopts several rigid movable teeth with logarithmic spiral tooth profile. Such tooth geometry makes almost surface contact possible under load condition, in comparison with the conventional involute tooth profile creating a linear contact. Aiming at the issue of cusp meshing between movable tooth and ring gear during the meshing process, this paper proposes a modification design method for the conjugate tooth profiles. First, the radial motion law of movable tooth is modified, in order to avoid rigid impacts at the exchange point of the rise travel and return travel. Then, the tooth profile of ring gear is generated by the envelope of the modified profile of movable tooth. Based on the formulated modification scheme, the equations of the conjugate tooth profiles are derived, and the influences of spiral angle and modification parameters on the meshing characteristics are systematically investigated. Finally, the wave generator cam profile and pivoted segment profile are established considering the strength consistency. The outcomes can provide significance guidance for the parametric design and optimization of this novel drive.

Tooth profile design and meshing characteristics analysis of internal meshing gears based on variable center meshing line

A design method of internal meshing gear based on variable center meshing line (VCML) is presented in this paper. The meshing line is an arc line connecting the intersection of the indexing circle connecting the inner and outer gears and the intersection of the tooth top circle, and the center of the line of engagement freely slides on the vertical bisection line of the line connecting the two intersection points. The top tooth profile equation of internal and external gears is derived by rack equation. According to the normal method of gear profile, the equation of gear root meshing line is derived by using the tooth top profile equation of the gear. According to the principle of plane meshing, the root profile equation of gear is derived by using the root meshing line equation of gear. The tooth profile of VCML gear can be deduced quickly by adjusting the center position of the meshing line. The stress, meshing stiffness, transmission error, contact ratio and sliding ratio of the VCML gears are analyzed by finite element method, and the area of significant performance improvement of the meshing line center of the VCML gears is found. The research results show that compared with involute gears, the maximum average stress of VCML gears is reduced by 64.99%, the meshing stiffness is increased by 193.67%, and the transmission error is reduced by 65.95%. This method improves the efficiency of new tooth profile design and transmission performance. By changing the center coordinates of the meshing line, the tooth profile of the VCML gear can be quickly redesigned, which greatly improves the efficiency of the new tooth profile design and transmission performance. This design method provides a new idea for the tooth profile design of internal meshing gear.

Research on gear profile deviation detection method based on linear structured light

Research on gear profile deviation detection method based on linear structured light

Features of using the power skiving method for multi-pass cutting of internal gears

The paper presents the results of a simulation on a 3D model of undeformed chips and cutting forces during three-pass gear cutting using the power skiving method. At the level of individual blades and teeth in successive angular cutting positions, the main component of the cutting force and the tangential force on the cutter axis are shown. The analysis of the forces acting on a single gear tooth and the continuous cutting forces allowed the development of a methodology for the selection of rational cutting modes – the value of the axial feed, the number of passes with different cutting depths in order to ensure the minimum time consumption and to achieve the required accuracy of the gears in terms of the parameter of the permissible angular deviation of the profile of the cut gear. It is shown that, provided the required machining accuracy is ensured, higher productivity is achieved by increasing the axial feed at a lower depth of cut and increasing the number of passes, rather than by reducing the feed and increasing the depth of cut.