Cylindrical Gears Research Articles

A fundamental analytical model for micro topography of skived gear surface

Surface topography is important for gear components, as it exerts influence on noise, wear, lubrication, and life expectancy. Different gear finishing processes result in varying micro tooth topographies, which lead to different driving and lubricating performances. The advanced technology of gear skiving, a recent industry application known for its high efficiency and flexibility in both roughing and finishing of cylindrical gears, has become the focus of extensive research. However, investigations into the micro topography of skived tooth flanks have been limited, primarily due to the absence of a highly efficient algorithm, which hinders the prediction and optimization of driving performance. By demonstrating that the skived surface can be obtained through the collection of micro-sections of the cutter trace in a specific order, this paper proposes a comprehensive analytical model for the micro topography of the skived surface. Both numerical and experimental studies reveal the topology texture, surface roughness, and the effects of the cutter and cutting settings. Results indicate that a higher installation angle, feed rate, and cutter tooth number are more effective in reducing roughness.

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.

Geometry strategies for the repair of cylindrical gears teeth using laser-directed energy deposition

Gears are essential components in power transmission systems. The replacement of the transmission of a wind turbine can reach more than $300 000 and face long lead times. Previous studies have shown that laser-directed energy deposition (L-DED) has the potential to be used in the repair of gears. However, there is a lack of understanding of the appropriate toolpath planning strategies and their impact on the performance of the gears repaired by L-DED. In this work, we study several strategies for the repair of cylindrical (straight and helical) gears. The strategies consider several types of gear tooth failures, allowing for the repair of a portion of the tooth and the reconstruction of the whole tooth. The studied strategies encompass planar and nonplanar slicing procedures. We manufactured several gear teeth to demonstrate the geometrical and kinematic feasibility of some strategies. We performed destructive analyses on the manufactured teeth to check for manufacturing faults. We used AISI 316L for these experiments, although we are assessing and testing powdered materials for their potential use in gear repair using L-DED. Future work will be devoted to the evaluation of the mechanical performance (e.g., wear resistance and bending fatigue) of the teeth manufactured with L-DED.

Design of Gearings from Involute-Bevel Gears

The article presents formulas for determining the dimensions of involute-bevel gears and the gearings composed of them. It examines the most general cases of gearings formation, consisting of two involute-bevel gears with crossing axes (hyperboloid gearings), with intersecting axes (bevel gearings), and with parallel axes (cylindrical gearings). Gearings composed of involute-bevel gears have design, technological, and operational advantages compared to gearings composed of conventional cylindrical and bevel gears. The use of involute-bevel gearings with crossing axes allows for achieving the required contact character of the teeth from localized contact to linear contact, reducing sensitivity to manufacturing and assembly errors, and increasing the load capacity of the gearing compared to helical gearings from cylindrical gears. Bevel gearings with involute-bevel gears allow for the creation of gearings with any desired small shaft angles, which is difficult to achieve with conventional bevel gears. The use of internal meshing bevel gearings with modified tooth profiles in planetary reducers allows for gearings comparable to harmonic drives in terms of power and kinematic characteristics, but with a higher operational life. The use of involute-bevel gears in cylindrical gearings improves the smoothness of the mechanism and allows for adjusting the center distance and backlash in the meshing, making them suitable for backlash-free drives. By combining the taper angles of the gears and the inclination of the teeth, it is possible to create a one-way rotation mechanism - a freewheel mechanism. Modern CAD systems do not take into account the geometry features of gearings composed of involute-bevel gears, which limits their application in technology. The article proposes an algorithm for calculating the main geometric parameters of gearings composed of involute-bevel gears with arbitrary axis placement in space. Examples of geometric calculations of various types of gearings based on the proposed algorithm are provided.

Dynamic Characteristics Analysis of the DI-SO Cylindrical Spur Gear System Based on Meshing Conditions

The dual-input single-output (DI-SO) cylindrical spur gear system possesses advantages such as high load-carrying capacity, precise transmission, and low energy loss. It is increasingly becoming a core component of power transmission systems in maritime vessels, aerospace, marine engineering, and construction machinery. In practical operation, the stability of the DI-SO cylindrical spur gear system is influenced by complex excitations. These excitations lead to nonlinear vibration, meshing instability, and noise, which affect the performance and reliability of the entire equipment. Hence, the dynamic performance of the DI-SO cylindrical spur gear system is thoroughly investigated in this research. The impact of excitations and nonlinear factors on the dynamic characteristics was investigated comprehensively. A comparative analysis of the gear system was conducted by establishing a bending–torsional coupling vibration analysis model under synchronous and asynchronous meshing conditions. Nonlinear factors such as periodic time-varying meshing stiffness, meshing damping, friction coefficient, friction arms, load sharing ratio, comprehensive transmission error, and backlash were considered in the proposed model. Then, the effect laws of excitations and nonlinear factors such as meshing frequency, driving load fluctuation, backlash, and comprehensive transmission error were analyzed. The results indicate that the dynamic characteristics exhibited staged stable and unstable states under different meshing frequencies and meshing conditions. At the medium-frequency meshing stage (0.96 × 104~1.78 × 104 Hz), alternating phenomena of multi-periodic, quasi-periodic, and chaotic motion states were observed. Moreover, the root mean square value (RMS) of the dynamic transmission error (DTE) in the asynchronized gear system was generally higher than that in the synchronized gear system. It was found that selecting the appropriate meshing condition could effectively reduce the amplitude of the DTE. Additionally, the dynamic performance could be significantly improved by adjusting control parameters such as driving load fluctuation (0~179 N), backlash (0.8 × 10−4~0.9 × 10−4 m), and comprehensive transmission error (7.9 × 10−4~9.4 × 10−4 m). The research results provide a theoretical guidance for the design and optimization of the DI-SO cylindrical spur gear system.

The reliability function of the case-hardened teeth of wheels of cylindrical gears

BACKGROUND: Methods for calculating the load capacity and reliability of gears, accepted as standardized both at the national and international levels, are based on the laws of distribution of random variables, considered as the only possible ones, which is not entirely true. As a result, the developed gears have either overestimated or underestimated reliability, which leads to their low competitiveness. Therefore, the development of methods for assessing the reliability of the case-hardened gears, taking into account the actual laws of distribution of random variables, remains relevant, as it will make it possible to design competitive transmissions. AIM: Improvement of the current approach to calculating the reliability function of case-hardened gears according to their strength performance criteria. METHODS: The improved approach to calculating the reliability function is based on improved classical methods for testing the load capacity of cylindrical gears for contact and bending stresses (GOST 21354-87 and ISO 6336). The methodology for calculating the reliability function according to the criterion of deep contact durability is based on the Lebedev-Pisarenko criterion, the formulae of which have been modified for application to gears by V.I. Korotkin. The implementation of the proposed methods was carried out in MathCAD software. RESULTS: The methods for calculating the reliability function of the case-hardened gears according to the criteria of contact and bending durability, which take into account the variable value of the misalignment in the gearing caused by the deformation of the shafts, the bearing rings and the housing (force misalignment), are proposed. In addition, the dependence of the calculation results of the reliability function of cylindrical gears on the method of setting the force misalignment in the gearing of teeth (constant or variable value) is shown. Validation of the improved approach was carried out using the data available in the scientific and technical literature on failures of the case-hardened gears. The scientific novelty of the research lies in the proposed method for calculating the reliability function of the case-hardened gears according to the criterion of deep contact durability, which performs the calculation under an unknown law of distribution of effective stresses using the Parzen-Rosenblatt method (the method is also used in methods for contact and bending durability criteria), as well as in taking into account the variable value of the force misalignment in the meshing. CONCLUSION: The practical significance of the research lies in the ability of probabilistic determination of the cause of gear failure according to six criteria (pitting, tooth breakage, tooth interior flank fracture of both the pinion and the wheel), which makes it possible to adjust the design, the manufacturing technology, and the operating requirements in order to ensure the required gear performance during its design.

Dynamic response characteristics of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission system considering wear effect

To illustrate the impact of tooth surface wear on the dynamic response of the cylindrical gear transmission system with variable hyperboloid circular-arc-tooth-trace (VH-CATT), a nonlinear dynamic model of VH-CATT cylindrical gear that considers wear effect was developed in this article. Firstly, according to the analysis conducted through the finite element method, the time-varying meshing stiffness of VH-CATT cylindrical gear is calculated, and the time-varying meshing stiffness considering wear is characterized by introducing wear fault characteristics. Then, the load ratio is introduced to represent the relationship between the error amplitude and the excitation load. By using the error amplitude as the bifurcation parameter, this parameter describes how the excitation load affects the dynamic characteristics of the VH-CATT cylindrical gear. Finally, the bifurcation diagram and maximum Lyapunov exponent of the VH-CATT cylindrical gear transmission system under various wear depths are computed using the fourth-order Runge-Kutta method. At the same time, the response state of the VH-CATT cylindrical gear is verified by phase diagram, Poincaré mapping and time history diagram. The findings indicate that the vibration amplitude of the VH-CATT cylindrical gear system increases as the error amplitude increases. The vibration phenomenon of VH-CATT cylindrical gear transmission system with wear fault is more obvious, and the system enters the bifurcation and chaos effect state in advance. Therefore, the wear of the tooth surface will lead to the decrease of the gear meshing stiffness, which will lead to the increase of the vibration amplitude of the system, resulting in the phenomenon that the dynamic response state of the system is advanced. The research results will provide a theoretical basis for high-quality VH-CATT cylindrical gear transmission and gear nonlinear dynamics research.

Tooth friction in spur gear transmission. From local to mean tooth friction loss

In a gear transmission, power losses come from a variety of sources, classified as load-dependent and no-load-dependent losses. No-load-dependent losses are the ones that remain constant regardless of the applied load, such as losses due to drag in rolling element bearings, seals, churning and/or windage for gears. Load-dependent losses include friction losses due to sliding and rolling between gear teeth. These losses are particularly important in some gear transmissions because of their direct impact on overall efficiency and thermal behaviour. Consequently, knowledge of the friction coefficient associated to this loss is of major interest for optimising gears (geometry, surface finish, lubrication, etc.). In this article, a new method is proposed for predicting the mechanical efficiency losses associated with the mean coefficient of friction for pairs of cylindrical gears. It is based on a model developed previously to estimate the instantaneous tooth friction along the plane of action in gears. This model takes into account the lubricant shear and the friction on contacting asperities. The proposed mean friction coefficient is deduced from the instantaneous friction coefficient using specific calculations, particularly at the pitch point. To verify the method, the estimated results are compared with those in the literature calculated for gears and operating conditions common on FZG test rigs.

Deformation of the Machined Surface and Chip by the Tool in Physical Modeling of the Shaving and Rolling of Cylindrical Gears

Deformation of the Machined Surface and Chip by the Tool in Physical Modeling of the Shaving and Rolling of Cylindrical Gears

Study on the effect of bearing position and stiffness on the dynamic behavior of output stage of CHT system based on the cylindrical gear meshing

The internal and external rotor shafts are important components to transfer power in coaxial helicopters, and bearing supports could affect the dynamic behavior of the transmission system. In order to explore the influence of bearing support structure, bearing position and support stiffness on the dynamic behavior of the output stage of coaxial helicopter transmission (CHT) system based on the cylindrical gear meshing, a rigid-flexible coupled dynamic model is established under cantilever-cantilever support structure and cantilever-simple support structure considering the flexibility of rotor shaft based on Timoshenko beam theory, and time-varying mesh stiffness (TVMS), comprehensive meshing error are also considered. Newmark-beta numerical method was applied to calculate the dynamic response. The result indicates that the load sharing performance of gear pair using cantilever-simple support structure is better than that of cantilever-cantilever structure, but the maximum vibration displacement of bull gears is reduced apparently. Simultaneously, the bearing positions and stiffness can be adjusted to achieve better performance in load distribution and maximum vibration displacement of bull gears.

Gear Hobs-Cutting Tools and Manufacturing Technologies for Spur Gears: The State of the Art.

The present work aims to provide the readers with a bird's-eye view of the general domain of cylindrical gear manufacturing technologies, including the cutting tools used, and related topics. The main scientific sources are explored to collect data about the subject. A systematization of the scientific works is completed, to emphasize the main issues the researchers have focused on in the past years in the domain. Several specific aspects are investigated: chip-forming process, cutting tool lifetime, the materials used to produce gear hobs, temperature and lubrication, the cutting tool geometry, cutting parameters, design methods, and optimization. Some gaps in the research have been identified, which are mainly related to the gear hob's design. These gaps, the organization of knowledge, the current requirements of the industry, and the actual socio-economic priorities form the basis for identifying new scientific research directions for the future in the area of spur gears manufacturing technologies and cutting tools. The main output of this work is a frame to guide the development of scientific research in the domain of spur gear production.

Meshing stiffness characteristics of modified variable hyperbolic circular-arc-tooth-trace cylindrical gears

Abstract. Stiffness excitation is one of the important excitations for the variable hyperbolic circular-arc-tooth-trace (VH-CATT) cylindrical gear system. Accurate calculation of the gear meshing stiffness is of great significance to investigating dynamic characteristics of the VH-CATT cylindrical gear system. Firstly, based on the forming theory of the modified tooth surface, the modified tooth surface equation of the VH-CATT cylindrical gear was deduced, and the 3D reconstruction was realised. Next, the load tooth contact analysis (LTCA) model of the VH-CATT cylindrical gear was developed to calculate the meshing stiffness of the VH-CATT cylindrical gear, and it was verified by the finite-element calculation. Finally, the influence of the load and modification parameters on the VH-CATT cylindrical gear stiffness was investigated. Research shows that the stiffness calculation method of the VH-CATT cylindrical gear based on LTCA is accurate. The meshing stiffness of the VH-CATT cylindrical gear in the double-tooth meshing area is large, and the meshing stiffness of the VH-CATT cylindrical gear in the single-tooth meshing area is small. The stiffness of the VH-CATT cylindrical gear increases with an increase in the load and cutter inclination angle, the stiffness of the VH-CATT cylindrical gear only in the double-tooth meshing area decreases with an increase in the parabolic coefficient, and the stiffness of the VH-CATT cylindrical gear increases with a decrease in the blade parabolic vertex position value. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimising design.

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.

Numerical Analysis of Tooth Contact and Wear Characteristics of Internal Cylindrical Gears with Curved Meshing Line

In order to improve the contact strength and reduce the sliding friction of the gear pair, an internal cylindrical gear pair with a curved meshing line is studied in this paper. Firstly, a curved meshing line is designed. The tooth profiles of the internal gear pair with the designed meshing line are calculated by using differential geometry and the gear meshing principle. Secondly, a wear model is established by combining the finite element method and the Archard wear formula. Then, a numerical simulation is conducted; the relative curvature, sliding coefficient, sliding distance, maximum contact pressure, transmission error, and wear depth are calculated. Ultimately, the variation law of tooth surface wear of new gear with and without installation errors is observed under different stress cycles. On this basis, the influence of tooth modification on tooth surface wear is further researched. Through the results, the advantages of the introduced novel internal cylindrical gears in wear resistance are further demonstrated. The study in this paper provides new research ideas and methods for gear wear research and gear design.

Przykłady Małej Architektury w oparciu o System Arm-Z

Arm-Z is a conceptual hyperredundant robotic manipulator composed on linearly joined number of identical modules. Each of them has one-degree-of-freedom (1-DOF) – the relative twist. Since modules are congruent, Arm-Z presents potential economical advantages and enhanced robustness. The modules can be mass produced and easily replaceable. The control of Arm-Z, however, is difficult and not intuitive. Therefore it most often requires the use of computational intelligence techniques. This article presents selected concepts for kinetic street furniture based on Arm-Z: a helical column of adjustable height, a sun tracking shade or solar energy harvesting device, bio-mimicing sculpture, sprinkler or fountain. All these ideas are based on low-tech approach. For this purpose, the initial unit in the chain is fixed to the solid foundation. For simplicity, the drive is applied directly to the first unit and transferred by the means of internal gears to the following modules. All of them are equipped with a set of cylindrical and bevel gears with straight teeth with involute profile (for connecting the modules).

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.

A comprehensive study on the romax-based comprehensive shaping method for skewed cylindrical gears

Abstract Tooth profile modification is one of the effective ways to solve the vibration and noise problems in gear transmission. This article is based on the dynamic Romax Designer software for simulation and studies the micro modification problem of helical cylindrical gears in a certain reducer. Based on the analysis of the limitations of tooth profile modification and tooth orientation modification methods, a comprehensive tooth profile modification method is proposed. The simulation results show that the transmission error, load distribution, meshing situation, and service life of the gear have improved after adopting the comprehensive modification method, thereby improving the transmission accuracy, reliability, and durability of the gear. This method can provide reference and reference for gear modification of reducers.

Mathematical modelling and cutter design for generating chamfering of transversal profile for cylindrical gears

Mathematical modelling and cutter design for generating chamfering of transversal profile for cylindrical gears

Cylindrical gear transmission errors influenced by temperature based on thermal network

Cylindrical gear transmission errors influenced by temperature based on thermal network

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.