Gear Pair Research Articles

Effects of periodic long-wave deviations on the dynamic behaviors of spur gear systems

Noise reduction plays a major role in the drive train of motor vehicles operating at higher speeds. Long-wave deviations of gear systems related to manufacturing and assembly errors, such as tooth pitch deviation and geometric eccentricity, exhibit circumferential variations and have been demonstrated to be significant contributors to noise generation. However, a comprehensive and effective model that considers multiple long-wave deviations simultaneously has seldom been studied. To fill this gap, a new numerical model of spur gear systems with long-wave deviations is established, in which the coupling effects of both tooth pitch deviation and geometric eccentricity are taken into consideration. A time-varying mesh stiffness (TVMS) analytical model for spur gear pairs is established, which considers the relationship of errors between pitch deviation and eccentricity. The time-varying contact state of the gear pair under periodic long-wave deviations is also analyzed. A translation-torsion coupled dynamic model is established to investigate the excitation behavior of gear pairs with periodic long-wave deviations. The accuracy of the TVMS and the dynamic model is verified through comparisons with reference and experimental results. Results show that gear pairs with long-wave deviations exhibit periodic fluctuations in TVMS compared to ideal gear pairs, accompanied by phase differences. The mesh stiffness impact phenomenon becomes less pronounced for higher gear precision under lower-load conditions. Conversely, the periodic vibration characteristics induced by eccentricity become less prominent for the lower gear precision level. The excitation behavior of the gear pair with pitch deviation is masked by eccentricity at lower rotational orders, but it still dominates at higher rotational orders. This method can predict the dynamic characteristics of gear transmission systems with periodic long-wave deviations, providing theoretical guidance for reducing the vibration and noise levels.

Tensor based approach for tooth contact analysis of planar and spatial gearing contact

This paper presents a new method for analyzing gear tooth contact, leveraging tensor notation and discrete differential geometry. Existing analytical and numerical methods often face challenges in convergence and computational efficiency. Our proposed approach involves defining a novel tensor notation and applying it to the gear tooth contact kinematics problem. By discretizing the tooth surfaces and using tensor operations, we can accurately determine the kinematics, path of contact, and transmission error of the gear pair. To validate our approach, we compared its results with those obtained from commercial software, KISSsoft and KiMOS. The results demonstrated high accuracy, with mean absolute errors below 0.08 for specific sliding, 0.003 for sliding factor, and 0.1μm for transmission error. Furthermore, we applied our method to analyze non-involute gear types, such as S-gears, pin gearing and cosine gears. Our findings revealed the kinematic performance and contact characteristics of these gear types, providing valuable insights for gear design and optimization. In conclusion, the proposed tensor-based approach offers a promising alternative for gear tooth contact analysis, providing accurate and efficient results for a wide range of gear types.

RATIONAL SHIFTS OF THE BASIC RACK’S PROFILE FOR WHEELS OF A CYLINDRICAL SPUR GEAR PAIR TO DECREASE TEETH WEAR

Purpose. It is to create a method for determination of such shift coefficients of the basic rack’s profile for driving and driven wheels of a cylindrical spur gear pair, that during gear pair operation time the wear rate of a surface layer on the most wearing sections of the teeth’ involute surfaces will be minimal. Research methods are based on integrated application of the involute gear pair theory and tribological laws. The golden section method is used to minimize the function. Results. We have obtained a dimensionless quantity, which is a function of shift coefficients of the basic rack’s profile for driving and driven wheels of a cylindrical spur gear pair. Values of this function are proportional to the greatest wear rate in the neighborhood of characteristic points on teeth’ involute profiles of these wheels. The method is created for determination of rational shift coefficients of the basic rack’s profile, which minimize the obtained dimensionless function, and which maximize the service life of the spur gear pair until the greatest worn-layer thickness on the teeth’ active surfaces reaches limiting permissible value. Scientific novelty. It is proved, that increasing of the worn-layer thickness during spur gear pair operation time will be occurring most rapidly in the neighborhood of certain characteristic points on teeth’ involute profiles of the wheels. Calculation model is elaborated for determination of the worn-layer thicknesses in the neighborhood of extreme active points on teeth’ profiles of the cylindrical spur gear pair and in the neighborhood of the lowest and the highest bounding points of single-pair contact. This model takes into account the influence of specific slides and numbers of wheels’ teeth as well as hardness values of teeth’ surface layer on the wear rates at characteristic points of teeth’ profiles. In addition, the model takes into account sharing of total force of the wheels interaction between two teeth pairs in double-pair contact and also a change of force transmitted by single pair of teeth when it comes into or go out of engagement. Practical value. Application of the created method for determination of shift coefficients of the basic rack’s profile is expedient in design of cylindrical spur gear pairs for machines and equipment, which operate in conditions when ingress of abrasive particles in the teeth engagement region is possible. An example of application of this method in design calculation of the cylindrical spur gear pair is given.

Study on meshing and dynamic characteristics of herringbone gear pair considering tooth surface wear and modification

Due to errors and tooth surface wear of herringbone gear is inevitable. And tooth surface modification is the key technology to improve gear performance. Therefore, this paper studies the influence of tooth surface uneven wear and modification on herringbone gear pair's meshing and dynamic characteristics with errors. Firstly, herringbone gear pair meshing characteristic analysis model based on discrete tooth surface is established. Secondly, herringbone gear pair bending-torsion coupling dynamic characteristic analysis model considering friction is established, and the dynamic frictional force analysis process is given. Thirdly, combined with Archard's wear theory, the tooth surface uneven wear amount is obtained. The tooth surface uneven wear amount is substituted into meshing matrix as a tooth surface deviation. Finally, the meshing and dynamic characteristics of herringbone gear pair considering tooth surface wear and modification are studied by using the established analysis model of meshing characteristics and dynamic characteristics. The calculation results show that without tooth surface modification, tooth surface wear will deteriorate the meshing and dynamic characteristics rapidly. However, reasonable tooth surface modification can effectively improve meshing and dynamic characteristics of gear pair, so that the gear pair can still maintain stable transmission under wear condition.

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.

Parameters impact analysis on contact characteristics of intersected beveloid gear and involute cylindrical gear

According to gear geometry and tooth contact analysis (TCA) theory, the TCA model of intersected beveloid gear and involute cylindrical gear pair is built. The formulas for calculating curvature and contact ellipse at contact points are derived, and the shape and region of contact ellipse are determined. Then, the impacts of cone angle, helix angle and installation errors on contact characteristics are studied by numerical examples. The finite element model of gear pair is established to carry out the loaded tooth contact analysis (LTCA) and verify the accuracy of theoretical TCA model. The results show that gear pair with small cone angle or big helix angle has wide contact area, large carrying capacity and high transmission quality. The shaft angle error may cause the edge contact of gear pair, while the axial position error has limited effect. The research can provide input parameters for the study of tooth surface wear mechanism and dynamics in the future work.

Extended influence coefficient method for meshing stiffness evaluation of spur gears considering rotor flexibility

Rotor-supported gears are applied in transmission systems, and the rotor flexiblility leads to the misalignment of the gear pair with multiple degrees of freedom, which ultimately leads to the decrease of meshing stiffness. To evaluate the meshing stiffness of rotor-supported gears, the extended influence coefficient method (EICM) is proposed in this paper. Firstly, the gear contact position adjustment under misalignment condition is carried out. Then, the extended influence coefficients of bending, shearing, axial compression, Hertzian contact and fillet foundation deformation of gears are derived to obtain the extended influence coefficient matrix. Afterward, the load-deformation equations under different contact states are obtained, and the meshing stiffness is calculated. Subsequently, a cantilever rotor-gear coupling dynamic model is established by the rigid body element-extended influence coefficient method (RBE-EICM), and the dynamic meshing stiffness considering rotor flexibility is obtained. The accuracy of EICM and RBE-EICM is verified by comparison with finite element method, literature methods and experimental data, respectively. Finally, the effects of supporting layout, input torque and rotor diameter on the dynamic characteristics of cantilever rotor-supported gears are discussed.

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.

Analysis and Simulation of Spur Gear System Considering Geometric Eccentricity

Geometric eccentricity errors inevitably occur in gear systems, resulting in the center of mass and center of rotation not coinciding. During the gear meshing process, the gear center distance and gear tooth meshing condition will change with time. In this paper, a model considering geometric eccentricity is proposed and a finite element model of the gear pair is developed. Finally, the dynamic response under different eccentricity and initial eccentricity angle is discussed. Based on Ansys, the simulation calculation of the gear pair is carried out, and the equivalent force maps of the dangerous areas of the gear tooth flanks are obtained.

Capabilities of Software Package Gearacl for Design Gearings and Transmission Elements

Creation of a mathematical model of gearing operation belongs to one of the most knowledge-intensive fields of knowledge. Interdisciplinary research is being conducted to develop the model. For practical use, the results of this work are embodied in strength analysis standards. Due to the complexity of the processes occurring in gearings, performing analysis of one pair of gears today requires not only significant time costs from the engineer, but also a deep understanding of hundreds of pages of calculation techniques described by groups of interrelated standards. The calculation formulae include clarifying coefficients, the contribution and values of which are determined by a group of specialists developing the standard, based on research of analysis result coordination, experimental data and calculations performed using the finite element method. To perform the analysis, the designer needs knowledge about the principles of choosing coefficient values and their meaning. Performing the analysis of gearings according to the standard is a time-consuming process that can be correctly performed only by an engineer with experience in designing gearings. To facilitate the work of the engineer, software products both domestic and foreign were created. However, the trends of recent years require replacement of foreign software products. In 2022, the specialists of the Central Institute of Aviation Motors developed the Gearacl software package, which allows replacing foreign products in the volume required by the aviation industry enterprises in the field of cylindrical gearings, shafts and bearings analysis. Modern analysis methods have been introduced into the software package. This article is devoted to the capabilities of the Gearacl software package.

Design and Stress Analysis of Bevel Line Gears with Vertical Flank Suitable for Micro Machining

The line gear (LG) exhibits promising applications in micromachinery owing to its simple structure and minimal teeth count. This paper aims to advance the meshing theory of LG and introduce a conical LG tooth configuration specifically tailored for micro-machining that is capable of driving with high performance. Based on the meshing principle of LG, a conical line gear pair with vertical flank (VFLG) of the driving gear was designed. Subsequently, adhering to the curvature non-interference principle that no local interference occurs in the meshing process and the specified range of fitting error in one direction, the design parameters for LG were determined. A comparison of the contact stress between two sets of different contact line types revealed the distinct advantage of VFLG with parameters identical to those of traditional LG. The experimental results conclusively demonstrate a transmission ratio error of 0.004, affirming the feasibility of the design. The curvature non-interference design formula proposed in this paper refines the LG design theory, and the novel LG design method presented holds significant implications for subsequent micromachining.

Multi-objective optimization of helical gear transmission geometric parameters using MOPSO

Abstract Helical gears are widely used in mechanical devices, but insufficient tooth strength can easily lead to premature failure, which is an urgent problem to be solved. To overcome this challenge, this paper introduces a multi-objective particle swarm optimization algorithm, which comprehensively considers the comprehensive effects of modification coefficient, number of teeth, and modulus on the performance of helical gears. By constructing a mathematical model with the geometric parameters of helical gears as the core design variables, aiming to minimize the difference between the maximum bending stress of helical gear roots and the contact stress on the tooth surface, we have achieved optimization of gear performance. Using MATLAB for algorithm programming, the established model was efficiently optimized and solved. After optimization, the bending strength difference and tooth surface bearing capacity of the gear pair have been significantly improved, ensuring the stability and reliability of the operation of the high-pressure sleeve disassembly transmission device.

Effect of meshing-induced deformation on lubrication for journal planet gear bearings

To increase the power density and reliability of wind turbine gearboxes (WTGs), journal planet gear bearings (JPGBs) are increasingly employed in their low-speed planet stages. Except for the pressure- and temperature-induced deformations, the JPGB is also structurally deformed by the gear pair meshing in this application, complicating the lubrication and deformation characteristics. Considering the above meshing-induced deformation, a thermo-elasto-hydrodynamic (TEHD) model is proposed for the JPGB, whose deformation is predicted using a self-programmed procedure based on the finite element method (FEM). Besides, this model is verified through a lubrication experiment of the JPGB in the WTG. It is found that the appropriate meshing-induced deformation, varying periodically in the meshing process, can improve the TEHD and misalignment behaviors of the JPGB due to the load-carrying region expansion or twice hydrodynamic action. This phenomenon becomes increasingly obvious with increasing the WTG's input power and the planet's inner radius.

Structural design and dynamic analysis of a metal rubber composite gear pair

This paper introduces a metal rubber composite gear for gear vibration reduction. A comprehensive structural design calculation program is developed for the metal rubber composite gear pair. The design incorporates a gap between the tooth ring and the hub to accommodate thermal expansion and contraction, ensuring smooth transmission without jamming or seizing. The design process takes into consideration the compression and damping properties of the metal rubber material. A significant variable in the design process is the relative density of the metal rubber material. It is utilized to calculate the torsional stiffness, starting friction torque, and dynamic performance of the composite gear pair. To guide and optimize the design process, a nine-degree-of-freedom dynamic model is employed for dynamic analysis. The vibration reduction effect of the metal rubber composite gear is validated through numerical simulations and experimental testing. The results confirm the efficacy of the gear in reducing vibrations. This paper provides valuable insights and guidance for future designs focused on gear vibration reduction, paving the way for further advancements in this field.

Solving time-varying mesh stiffness of spur gears based on improved potential energy method

Meshing stiffness is an important factor in gear dynamics analysis. At present, there are many ways to calculate the meshing stiffness of gears, and we usually use the potential energy method to solve and calculate the meshing stiffness of healthy (faulty) gears. In this paper, the potential energy method, the improved potential energy method and the theoretical calculation method are used to solve the time-varying stiffness of the healthy spur gear pair, and the solution results are compared, which verifies the feasibility of the improved potential energy method to solve the gear meshing stiffness.

Computerized generation, deviation correction and rapid tooth contact analysis of helical face gear

This paper delves into the generation of helical face gears using a grinding worm. It investigates the computerized generation process and explores the inherent geometric constraints associated with the application of a grinding worm for helical face gears. An approximate grinding method, tailored for helical face gears featuring large helix angles, is proposed, with an evaluation of the resulting theoretical deviations. Furthermore, a novel rapid computational approach for determining the bearing contact of helical face gear pairs is introduced and validated through Finite Element Analysis (FEA). The subsequent analysis comprehensively examines the effects of the machine tool positioning errors on tooth flank deviations, bearing contact, and transmission errors. A sensitivity matrix is developed to elucidate the relationship between machine tool positioning errors and the tooth flank deviations, leading to the proposition of a correction method for theoretical generating deviations. Finally, the paper introduces a tooth flank modification method for helical face gears and the meshing performance is highly improved.

A comprehensive analysis on coast side contact behaviour of thermoplastic gears against steel gear: a FEA approach

PurposeThe research paper comprehensively investigates the gear tooth deflection of standard thermoplastic gears with steel gear as the driver and driven companions. An accurate mapping of characteristic contact regions between the meshing gears was done, and the behaviour of the gear tooth in the premature and prolonged contact zones was studied.Design/methodology/approachThe study employs the finite element method to conduct a quasi-static 2D analysis of meshing gear teeth. The finite element model was created in AutoCAD and analysed using the ANSYS 19.1 simulation package.FindingsIn the polymer-polymer gear combinations, premature and prolonged contact primarily occurs along the addendum radii of meshing gears, whereas a novel contact phenomenon was observed in the coast side for polymer-metal and metal-polymer combinations, exhibiting a path perpendicular to the standard drive side contact. As well, the deflection of the tooth alters the load distribution across the interlocking gears, leading to a decrement in the root stresses.Originality/valueThe Lewis bending equation demonstrates that bending stresses depend solely on the applied load and the geometry of the tooth. It does not consider the effects of deflection. However, the computational results showed that the gear tooth deflection caused by different gear pair combinations also affects the bending stresses. The contact stresses observed in the polymer-polymer gear combination were observed to be within the material’s proportional limit. However, when a steel gear is paired with a polymer gear, the contact stresses exceed the proportional limit due to coast side contact.

Study on Temperature Field Distribution of a High-Speed Double-Helical Gear Pair with Oil Injection Lubrication

The temperature field distribution of high-speed double-helical gears under oil injection lubrication is investigated by obtaining heat flux density and convective heat transfer coefficients through theoretical calculations and CFD (computational fluid dynamics) simulations. Based on the CFD method, fluid simulations are performed to obtain the distribution of lubricating oil on the surface of the double-helical gears, the velocity streamline diagram of the lubricating oil, and the convective heat transfer coefficients of different surfaces of the gears. The friction heat flux density is calculated using Hertzian contact theory and theoretical formula of heat generation. The double-helical gears’ steady-state temperature field simulation uses this heat flux density as a boundary condition. The correctness of the calculation method is verified through experiments. The study shows that increasing the jet velocity allows the jet to reach the tooth surface more effectively, improving the cooling effect and reducing the maximum gear temperature. However, the relationship between the jet velocity and the minimum gear temperature is non-linear. Within a certain range, increasing the jet diameter makes the jet wider, and the area covered by the lubricating oil becomes larger as the jet spreads around the gear teeth, enhancing the cooling effect. An increase in gear speed leads to an increase in frictional heat flux density; moreover, the high-velocity airflow generated by the increased speed reduces the amount of lubricant entering the mesh zone, which in turn causes the maximum temperature of the gears to continue to rise.

Design and Analysis of a Robotic Gripper Mechanism for Fruit Picking

A gripper is the critical component of the robot end effector for the automatic harvesting of fruit, which determines whether the fruit can be harvested intact or undamaged. In this paper, a robotic gripper mechanism based on three-finger and variable-angle design is designed and analyzed for spherical or cylindrical fruit picking. Among the three fingers of the mechanical gripper, two fingers are rotatable through a pair of synchronous gears to ensure enough contact area for the grasping surfaces, which adapt to fruits of different sizes, such as cherry, loquat, zucchini, and so on. Furthermore, the mathematical relationship between gripper driving force and finger gripping force is obtained by the kinematic analysis of the gripper to realize stable grasping, and a grasping index is employed for the structural parameter optimization of our gripper. The grasping motion is analyzed, and the kinematic simulations are carried out, when the driving speeds of the gripper are 5 mm/s, 10 mm/s, and 15 mm/s, respectively. The system transfer function related to driving speed is obtained by curve fitting. Then, the grasping experiments are conducted with various spherical and cylindrical fruit, of which the weights are between 8 and 300 g and the diameters are from 9 to 122 mm. The experimental results demonstrate that our gripper has good kinematic performance and fruit adaptability. At the same time, the grasping is stable and reliable while no obvious damage appears on the fruit surface.

A novel forward performance-driven design method for gear parameters

Gear is one of the most crucial components of the transmission system, and the performance of gear directly affects the efficiency and reliability of the transmission system. Conventional methods for designing gear parameters involve several time-consuming and complex steps, which may not guarantee optimal performance. Therefore, we propose a new method for designing gear parameters that aims to improve efficiency and accuracy. First, the tooth surface equations of spur and helical involute gears suitable for symmetric and asymmetric teeth are deduced based on the gear-forming machining principle. Second, the performance evaluation models for load capacity, dynamic performance, efficiency, and power density of the gears are established based on the precise gear surface. The design objectives are standardized and evaluated comprehensively using a linear weighting method. Finally, a forward performance-driven design method of gear parameters is established. The proposed method is applied to a helical gear pair design case, and the results show that 90.7% of the individuals in the Pareto optimal front are asymmetric gears, with 9.3% being symmetric gears. This suggests that asymmetric gears have more opportunities to be optimal than symmetric gears. The highest-ranked gear designed using the proposed method is superior to the gear designed using conventional methods.