Gear Tooth Profile Research Articles

Analysis of Dimensional Variations of Precision Gear Forging Die Geometry Due to Shrink Fit

The usual way to shrink fit design for precision forging dies are made by thick wall cylinder approach; i.e., taking the pitch diameter of the gear as bore diameter of the die insert without considering gear tooth shape. However, the compressive pre-stress due to the shrink fitting causes dimensional variations on the gear profile of the die insert. The dimensional accuracy of the final product is dependent on the accuracy of the gear die. Therefore, the dimensional variations due to shrink fit must be pre-determined and the gear tooth profile on the die insert modified accordingly. In this study, the dimensional variations of the precision spur gear forging die because of shrink fitting are analyzed by finite element method and the results are compared with the experimental ones. The results show that the FE model is successful to simulate the cylindrical die and agree well with thick wall cylinder approach and the experimental measurements. However, both the experimental measurements and the finite element results of gear die predict much higher radial displacements than the results of cylindrical die. Therefore, the determination of shape change of the gear die profile is beyond the capability of the thick wall cylindrical approach.

Geometric design and kinematics analysis of coplanar double internal meshing non-circular planetary gear train

A new type of non-circular planetary gear train is proposed, in which the planetary gear is internally meshed with the sun gear and the ring gear at the same time. The structural form and transmission principle are analyzed, and the design method of non-circular gear pitch curves and related parameters of the gear train are discussed. The input–output relationship under various working conditions of the gear train is deduced. The precise tooth profile of the non-circular gears is obtained by the Boolean operation of MATLAB, then the virtual prototype model of the planetary gear train is established, and the kinematics simulation is carried out in the ADAMS software. The simulation results verify the correctness of the transmission principle and the theoretical analysis of the motion law.

A dynamic model to predict the number of pins to transmit load in a cycloidal reducer with assembling clearance

In the ideal design of a cycloidal reducer, the tooth profile of cycloidal gear can make contact with all pin teeth on the pinwheel, wherein half of the pin teeth participate in load transmission. Meanwhile, the output holes on a cycloidal gear can maintain contact with all pins on the output disc and half of the output pins deliver load. However, under the influence of the assembling clearance caused by tooth modification, manufacturing tolerance, or machining error, the numbers of pins that participate in force transmission on both pinwheel and output disc fails to reach half of the total available. The objective of this research is to present a dynamic model to precisely predict the number of pins used to transmit load in a cycloidal reducer with assembling clearance. The methods for contact detection among the transmitting components are given in detail. In modeling of the contacts, both normal contact, and tangential friction, forces are considered. Finally, a typical cycloidal reducer with a single cycloidal gear is modeled and used as an example to analyze the variation of the number of pins that take part in load-bearing work under the influences of assembling clearance and external torque.

Effect of profile modification on the performance of spur gears in isothermal mixed-EHL regime using load-sharing concept

Spur gears are one of the most important tools for power transmission in the industry and thus can be considered a key mechanical element. As a result of power transmission, gears might fail or experience wear and fatigue. So the improvement in the design and modification of tooth profile of gears can significantly reduce friction loss and wear of the gear teeth and therefore it increases the useful life, improves the quality, and reduces the cost. The purpose of this study is to show the influence of addendum modification on the tribological performance of spur gears which are operating in the mixed elastohydrodynamic lubrication. In this paper, a model based on the load-sharing concept is employed to study the effect of changing addendum modification on the performance of spur gears, the amount of wear rate, and the lubricant film thickness. To this end, a model based on the load-sharing concept is employed which takes the geometry and lubricant properties as input and predicts the friction coefficient, load carried by fluid film and asperities, efficiency, and wear rate as output.

Study of microstructural degradation of a failed pinion gear at a cement plant

Abstract The failed pinion gear assembly of a cement plant was analyzed by visual, residual stress, microstructure and mechanical property examination to determine the root cause of its failure. It is observed that the worn out region contains several surface micro cracks, especially closer to the tip (addendum) as compared to the root (dedendum) of the gear tooth profile. The surface analysis of the worn out regions showed depletion of protective chromium oxide layer at the surface and formation of iron oxide scales due to corrosion attack by lubricants, contaminants resulted in micro pitting and subsequent wear. Residual stress measurements showed tensile residual stresses at the tip (face) of the gear teeth and large compressive stresses at the root (flank) of the gear teeth. The cross-sectional microstructure examination revealed the damages due to rolling contact surface fatigue in the form of subsurface dark etched region bands and coarsened carbides in the surface. Apart from this, the difference in the tempered core microstructure below the case hardened layer between the flank and face regions lead to compressive residual stress in case of soft core and tensile stress in case of harder core respectively. The concentration of tensile residual stresses due to untempered core at the tip aided the micro-pitting and micro-cracking due to the rolling contact surface fatigue was responsible for the initiation of surface cracks and final failure of the gear.

A calculation method of tooth profile modification for tooth contact analysis technology

Tooth contact analysis (TCA) technology is an approach for computerized simulation of meshing of aligned and misaligned gear, which has been widely used in the design of gears. In TCA technology, the gear modification is completed by first modifying the cutter and then using the cutter to cut the gear blank. The obtained results are the modification parameters of cutter rather than those of gear. With the rapid development of numerical control technology, directly modifying tooth profile becomes more convenient than modifying cutter to the complete tooth profile modification. However, at present, there is no bridge between TCA technology and tooth profile direct modification. Therefore, a calculation method of tooth profile modification for TCA technology is proposed in this paper. Firstly, the simulation process of machining gear by standard rack cutter is introduced. The profile equation and coordinates for standard gear tooth profile are given. Secondly, the simulation process of machining gear by modified rack cutter is introduced. The profile equation and coordinates for modified gear tooth profile are derived. Finally, by comparing the standard tooth profile with the modified tooth profile, the modification of tooth profile is calculated. Thus, the modification parameters of rack cutter obtained by TCA technology can be converted into the modification of tooth profile. An experiment which verified the accuracy of method is provided by the comparison between measuring curve of tooth profile of actual modification and theoretical curve of modified tooth profile.

A manufacturing error measurement methodology for a rotary vector reducer cycloidal gear based on a gear measuring center

A manufacturing error of a cycloidal gear is the key factor affecting the transmission accuracy of a robot rotary vector (RV) reducer. A methodology is proposed to realize the digitized measurement and data processing of the cycloidal gear manufacturing error based on the gear measuring center, which can quickly and accurately measure and evaluate the manufacturing error of the cycloidal gear by using both the whole tooth profile measurement and a single tooth profile measurement. By analyzing the particularity of the cycloidal profile and its effect on the actual meshing characteristics of the RV transmission, the cycloid profile measurement strategy is planned, and the theoretical profile model and error measurement model of cycloid-pin gear transmission are established. Through the digital processing technology, the theoretical trajectory of the probe and the normal vector of the measured point are calculated. By means of precision measurement principle and error compensation theory, a mathematical model for the accurate calculation and data processing of manufacturing error is constructed, and the actual manufacturing error of the cycloidal gear is obtained by the optimization iterative solution. Finally, the measurement experiment of the cycloidal gear tooth profile is carried out on the gear measuring center and the HEXAGON coordinate measuring machine, respectively. The measurement results verify the correctness and validity of the measurement theory and method. This methodology will provide the basis for the accurate evaluation and the effective control of manufacturing precision of the cycloidal gear in a robot RV reducer.

Analysis of Spur Gear with Tooth Circular Discontinuity for Weight Reduction

The design of gears and gear drives are becoming challenging in automobile applications in which low contact ratio gears are required to transmit higher loads and be lighter in weight. There are various methods available for optimizing the design. Some researches have been taken place in the areas of gear tooth profile modifications for providing internal stress relief and weight reduction. In most cases, the maximum loads are assumed to be acting on the tip of the tooth. In this study, investigations are carried out on the effect of circular discontinuity on the weight reduction without affecting the root stress. The maximum tangential load is applied on the highest point of single tooth contact. The results show that with the modified gear tooth having a combination of two circular discontinuities of size 0.4 times the module not only provides weight reduction but also gives stress relief at the root.

Formation of Tooth Profiles of Non-Involute Bevel Gears at CNC Machines

В работе рассмотрена цилиндроконическая передача внутреннего зацепления, состоящая из эвольвентного цилиндрического колеса с внутренними зубьями и конической (по форме заготовки) неэвольвентной шестерни, ось которой наклонена к оси колеса. С использованием этих зацеплений могут быть созданы эксцентриковые планетарные передачи с двумя наклонными сателлитами, реализующие большие передаточные отношения и имеющие высокую нагрузочную способность при относительно простой конструкции. По своим характеристикам они сопоставимы с волновыми зубчатыми передачами, но более надежны. Однако зубья неэвольвентной шестерни имеют сложную бочкообразную форму, получение их теоретически точной поверхности затруднено. Нарезание зубьев рассматриваемой шестерни может быть осуществлено в станочном зацеплении заготовки и зуборезной червячной фрезы при ее движении по определенной криволинейной траектории. Получены зависимости для определения траектория движения оси фрезы при нарезании зубьев исследуемой шестерни. Движение фрезы по криволинейной траектории может быть реализовано в зубофрезерных станках с ЧПУ. Результаты исследования использованы при проектировании и изготовлении планетарных редукторов различного назначения.

High Precision Edge Detection Algorithm for Mechanical Parts

Abstract High precision and high efficiency measurement is becoming an imperative requirement for a lot of mechanical parts. So in this study, a subpixel-level edge detection algorithm based on the Gaussian integral model is proposed. For this purpose, the step edge normal section line Gaussian integral model of the backlight image is constructed, combined with the point spread function and the single step model. Then gray value of discrete points on the normal section line of pixel edge is calculated by surface interpolation, and the coordinate as well as gray information affected by noise is fitted in accordance with the Gaussian integral model. Therefore, a precise location of a subpixel edge was determined by searching the mean point. Finally, a gear tooth was measured by M&M3525 gear measurement center to verify the proposed algorithm. The theoretical analysis and experimental results show that the local edge fluctuation is reduced effectively by the proposed method in comparison with the existing subpixel edge detection algorithms. The subpixel edge location accuracy and computation speed are improved. And the maximum error of gear tooth profile total deviation is 1.9 μm compared with measurement result with gear measurement center. It indicates that the method has high reliability to meet the requirement of high precision measurement.

A Method of the High-close-order Gear Construction and Its Characteristics

This paper introduces the piecewise involute method to construct the High-order-close gear tooth profile. Also, parameter equation of the gear profile is obtained. Based on this method, it is proved that the profile curve is fourth-order derivative and continuous at connection points. It indicates that the curvature radius curvature and the Hertz contact stress mutation among the tooth profile won’t occur at the connecting points. The ranges of the initial parameters used to construct the gear are obtained based on the principles of the involute gear parameter standard. At last, a sequence of adequate parameters is selected to complete the solid model construction of the gear which finally achieve the concave-convex meshing form and the gear meshing behavior is analyzed.

Design And FEM Analysis of Helical Gear

In this paper the problem of the failure of gear in speed reduction gearbox developed by Laxmi Hydraulic Pump (LHP) Pvt Ltd, Solapur is resolved by replacing the existing material by a material SAE8620. The Gear and Pinion using AGMA and FEM analysis Method. In the gear design, the bending stress and surface strength of the gear tooth are considered to be one of the main factors to the failure of the gear. In this paper bending and contact stresses are calculated by using analytical method as well as Finite Element Method. To estimate bending stress modified Lewis beam strength method is used as well as AGMA method. Software is used to generate the 3-D solid model of helical gear. Ansys software package is used to analyze the bending stress. Contact stresses are calculated using modified AGMA contact stress method. Ansys software package is used to analyze the contact stress and bending stress. The main objective of this study has to investigate the stresses induced by gear tooth profile. Finally, the results obtained by theoretical analysis and Finite Element Analysis are compared to check the correctness. Estimated stress is used to calculate module of gear which can withstand easily at given loading conditions. A conclusion has arrived on the material which is best suited for helical gear based on the results.

Development of the Involute-Cycloid Composite Tooth Profile Gear Pump to Reduce Driving Noise

Development of the Involute-Cycloid Composite Tooth Profile Gear Pump to Reduce Driving Noise

Effect of Negative Correction Factor in Spur Gear Tooth Profile using FEA

Effect of Negative Correction Factor in Spur Gear Tooth Profile using FEA

Super Finishing of Gear Tooth Profile using Profile Grinding

Super Finishing of Gear Tooth Profile using Profile Grinding

Investigations on microgeometry of meso bevel and meso helical gears manufactured by WEDM process

This article reports about investigations on microgeometry of meso bevel and meso helical gears manufactured by wire electro discharge machining (WEDM) process. Effects of eight WEDM parameters (namely, peak current, pulse-on time, pulse-off time, servo-gap voltage, wire feed rate, wire tension, dielectric pressure and percentage cutting speed) on single pitch error and total pitch error for meso bevel gear and total profile error and total pitch error for meso helical gear were studied. A total of 31 experiments for meso bevel gear and 31 experiments for meso helical gears were conducted using one-factor-at-time approach to identify optimum ranges/values of the eight WEDM parameters for further experiments. It revealed existence of optimum ranges of servo-gap voltage, pulse-on time, pulse-off time, and percentage of the cutting speed to minimize microgeometry errors in meso bevel and helical gears and that use of higher values of peak current, wire feed rate, wire tension, and dielectric pressure yields better quality of meso bevel and helical gears. The best quality meso helical gear has better quality (DIN 6, DIN 6, and DIN 8) than the best quality meso bevel gear (DIN 7, DIN 7, and DIN 10) for single pitch error, total pitch error, and radial runout; whereas for successive pitch error, reverse is true. Meso helical gear has better surface finish (R a 1.1 μm and R max 7.3 μm) than meso bevel gear (R a 1.3 μm and R max 8.0 μm). Examination of tooth profiles of the best quality meso gears by scanning electron microscopy revealed that they have uniform tooth profiles that are free from burrs, nicks, asperities, dimples, undercutting at the root, and sharp edges on both end faces of the gears. It also revealed that tooth flank surfaces are free from micro-cracks, pores, and globules. The present work proves that WEDM has potential to be a better alternative for manufacturing better quality net-shaped meso bevel and helical gears which will not require any further post-manufacturing processing.

The Precise Measurement Technology for Manufacturing Error of Cycloidal Gear Used in RV Reducer

According to problems in manufacturing and measuring process of cycloidal gear used in RV reducer, the profile coordinates of cycloidal gear captured by three coordinates measuring instrument Surveying and mapping do not coincide with the designed tooth profile coordinates in theory, it is difficult to precisely capture the addendum and dedendum of each cycloidal gear teeth, furthermore, the captured addendum and dedendum do not coincide with the actual tooth items. For these problems, this paper introduced a method can accurately calculating the manufacturing error of cycloidal gear.Based on the captured coordinate points of cycloidal gear tooth profile, firstly, find out 39 approximate addendums by calculating and comparing the radial radius of all points, divide the whole scanning points into 39 profile points groups by the 39 approximate addendums, with each group include a whole single tooth profile. Then, in each profile points group, interpolate the spline and precisely calculate the addendums and dedendums by fitting and recalculating radial radius.Set up the coordinate system of surveying and mapping profile by the 39 addendums. calibrate the coordinate system of surveying and mapping profile with the new coordinate system through coordinate transformation, calculate the radial runout error at top and root of tooth profile, pitch error, adjacent pitch error and accumulated pitch error as well as other manufacturing errors of the cycloidial gear at last.Through experiment, this process solve the problem in measuring process of cycloidal gear that the captured point by three coordinates measuring instrument could not be directly used for calculating the errors items.

Diseño de un engranaje con perfil de diente especial bajo criterios geométricos y de resistencia a fatiga

Diseño de un engranaje con perfil de diente especial bajo criterios geométricos y de resistencia a fatiga

Structure design and motion simulation of the pin-cycloid gear planetary reducer with ring-plate-type

The pin-cycloid gear planetary reducer with ring-plate-type is a new type of reducers. It has high transmission ratio range and high efficiency. In this paper the working principle of pin-cycloid gear planetary reducer is discussed, and the structure of the reducer is designed. Especially for the complexity and the difficulty in modelling of the cycloid gear tooth profile, the parametric design module of cycloid gear is developed to solve the cycloid gear modelling problem through the second development of Solid Works. At last, the speed schemes of the input shaft and output shaft of the reducer are obtained by the motion simulation. Through the analysis of the simulation curves, the rationality of the structure design is proved, which provides a theoretical basis for the design and manufacture of the reducer.

Research on cutting vibration characteristics of face-milling involute gear

Abstract Traditional machining methods, such as gear hobbing, gear shaping and gear milling, etc, are commonly used for cutting machining of gear tooth profile, which cannot meet huge machining demand of gears to a certain extent. This article proposes to utilize a face-milling machining method in involute gear machining, which can be used to reduce production cost effectively. Cutting vibration generated during cutting machining has a direct effect on the machining accuracy and machined surface quality of workpiece. Therefore, it is desiderated to perform in-depth research regarding this issue. ADAMS software was used to establish a rigid-flexible coupling virtual prototyping model of face-milling gear milling system and a cutting vibration system model. Cutting vibration analysis was performed for face-milling gear by adopting quick sine frequency sweep method, so that the frequency response characteristics of workpiece in three directions X , Y and Z and space were acquired. The research results will provide reference and theoretical foundation for actual application of face-milling gear machining technology.