Spur Bevel Gear Research Articles

Transmission performance evaluation of non-circular spur bevel gear based on a novel isochronal measurement method

This paper aims to study the transmission performance evaluation of non-circular spur bevel gear (NCSB-gear) based on a novel isochronal measurement method. Firstly, the mathematical model of NCSB-gear is established. Then a novel isochronal measurement method is proposed, and the actual tooth surfaces are reconstructed by non-uniform rational B-spline interpolation. The advantages of the proposed method are discussed based on the geometric characteristics of tooth surface and measurement fitting error. A pair of forged NCSB-gears is measured through a coordinate measurement machine and the maximum tooth surface fitting error by the proposed method reduces 2μm compared with the traditional method. Moreover, deviation tooth contact analysis (DTCA) and load tooth contact analysis (LTCA) are conducted to evaluate the transmission performance. Finally, the transmission performance of measured NCSB-gear is obtained by a gear rolling tester. By comparing the TCA calculation of different measurement methods, it is found that the relative error of the maximum transmission error based on the isochronal measurement method reduces 4.719% compared with the traditional measurement method, thus verifying the validity of the proposed measurement method.

Precise Shrink Fitting Design of the High Strength Gear Mold for the Precision Forging of Noncircular Spur Bevel Gears

Shrink fitting of forging mold (SFFM) is an effective method for improving mold strength, extending the mold's service life and reducing the manufacturing cost of forging mold. However, due to the asymmetric geometry and complex stress distribution, the precise design of SFFM for the precision forging of noncircular bevel gears is very difficult. In this paper, a new precise design method of SFFM for the precision forging of noncircular bevel gears is proposed, which mainly includes the following five parts. First, a new design method for the mold parting surface-the curved surface parting method-is proposed to design the forging mold of noncircular spur bevel gears. Then, new dimension design methods for the gear mold and shrink rings based on the uniform shrinkage force are proposed. Third, a new design method for the inhomogeneous interference value between shrink rings and the gear mold is developed to provide a precise, uniform shrinkage force. After that, a strength correction method for the shrink-fitted gear mold is proposed to ensure the gear mold and shrink rings have sufficient strength both in the assembly process of the shrink-fitted gear mold and precision in the forging process of noncircular spur bevel gears. Ultimately, finite element simulations and verification experiments are performed to verify the proposed precise design method of SFFM for the precision forging of noncircular bevel gears. The precise design method of SFFM proposed in this paper is not only applicable to the precise design of the high-strength gear mold for noncircular bevel gears, but can also provide a valid reference for the precise design of the high-strength mold for other complicated asymmetric parts.

Simultaneous improvement of microgeometry and surface quality of spur and straight bevel gears by abrasive flow finishing process

This article reports on influence of extrusion pressure, abrasive particle size and volumetric concentration on simultaneous reduction of surface roughness and microgeometry errors of spur and straight bevel gear by abrasive flow finishing (AFF) process. A vertical configured experimental apparatus was developed for two-way AFF and developed fixtures for finishing gears. Experimental investigations were conducted to identify optimum parametric combination, using response surface methodology, based on Box–Behnken design approach. Results revealed that higher values of abrasive particle size and volumetric concentration yield more percentage decrease in surface roughness and microgeometry error. Roughness profile, bearing area curve, microhardness, surface morphology, and wear resistance of the gear having best quality finishing were studied. Surface morphology analysis of the flank regions of the best finished spur and straight bevel gears found them to be smooth and free from cracks and burrs. Reciprocating wear test results revealed higher wear resistance of the AFF finished gears as compared to the unfinished gears. AFF also enhanced microhardness of the finished gears, which would enhance their operating performance and service life. This study shows that AFF is a flexible, economical, productive, easy to operate, and sustainable nontraditional process for precision finishing of gear that can simultaneously improve microgeometry, surface finish, microhardness, surface morphology, wear resistance, and residual stresses of the finished gears. Gear manufacturers and users will be benefited by the outcome of this study. JEL codes: C00, C20

Determination of the parameters of adjusting the gear broaching machine, according to the measurements of the spur bevel gears

The process of adjusting a gear broaching machine is considered, according to the angle of the cone of the depressions and the symmetry of the side profiles of the gear wheel. Standard adjustment methods do not allow measuring the values of the taper angle of the valleys and deviations from the symmetry of the profiles. The article proposes a method for finding the main setting parameters of gear broaching machine, according to the measurement data of spur bevel gears. The measurement method is implemented in the form of a measuring system, including a special control device equipped with inductive probes, and algorithms for processing their readings. The use of the measuring system makes it possible to increase the accuracy of setting up the gear traction machine and to improve the quality of manufacturing of spur bevel gears.

Effect of Heat Treatment Process on Microstructure and Crystallography of 20CrMnTiH Spur Bevel Gear

Obtaining excellent mechanical properties of spur bevel gear has been widely emphasized, owing to its indispensable effect on momentum. However, the conventional long-time and high-temperature heat treatment can cause microstructure coarsening, which dramatically decreases the mechanical properties. Since the normalizing process can significantly modulate the mechanical properties of spur bevel gears by adjusting their microstructure and crystallography behaviors, in the present study, the normalizing before or after carburizing heat treatment processes (NBCP and NACP, respectively) were proposed. The effect of heat treatment processes on the microstructure and crystallography of gear specimens was investigated. The results show that both NBAP and NACP had a strong effect on microstructure refinement and hardness improvement compared to the conventional process. NBCP raised the tendency for AlN precipitation, which could retard the microstructure coarsening during carburizing. Furthermore, NACP directly promoted the precipitation of globular Cr-rich M3C carbides which achieved the strongest pinning effect and brought about extremely fine microstructure. For crystallographic analysis, the 24 martensite variants in all gear specimens held Kurdjumov–Sachs orientation relationship to parent austenite. The orientations of martensite variants in gear specimens applying conventional process and NBCP were distributed regularly. However, the orientations of martensite variants in NACP gear specimen did not follow the strict rule for variant selection inside prior austenite grains owing to the distortive effect of diffuse M3C carbides on the matrix, and the adjacent martensite variants possessed less sharing of {110} habit plane compared to NBCP and conventional process.

Study on the Microstructure and Texture Evolution of Hot Forged 20CrMnTiH Steel Spur Bevel Gear by Simulation and Experiment

Due to the non-uniform dynamic recrystallization (DRX) and deformation behavior during hot forging process, the spur bevel gears tend to receive heterogeneous microstructure which greatly affects their mechanical properties and service life. Therefore, the aim of this study is to investigate the evolution of microstructure and texture of hot forged 20CrMnTiH steel spur bevel gear utilizing both simulation and experiment method. In the present study, a sound finite element model of hot forging of a 20CrMnTiH steel spur bevel gear was developed under the Deform-3D software. The experimental analysis was conducted by employing scanning electron microscope, electron backscatter diffraction and transmission electron microscope. The simulation results indicated that the grain size, effective strain and DRX volume fraction were inhomogeneous from the surface region to the core region of gear tooth. The experimental analysis revealed that the surface region of gear tooth possessed the strongest γ-fiber and lowest dislocation density. However, both subsurface and core regions had a combination of moderate α- and γ-fibers, and large amount of dislocations pinned by precipitates can be observed in these two regions. Furthermore, the microhardness exhibited parabola distribution through the gear tooth, and the subsurface region possessed the largest microhardness value.

Research on Dynamic Model of Double Helical Gear Pair Based on TCA and LTCA

Numerous dynamic models of spur gears, helical gears, bevel gears, and face gears can be found in various studies. However, studies that focus on the dynamic model of a double helical gear pair are quite limited. The author proposed a model of a double helical gear pair by only considering the axial vibration. The author did not consider the friction and multiple backlashes in the proposed model. The friction force of the tooth surface and backlash are important factors that can cause complex non-linear phenomena in gear pairs. Therefore, a dynamic model of a double helical gear pair that takes into consideration the axial vibration, friction and multiple backlashes is proposed. Firstly, based on the tooth contact analysis (TCA) of a double helical gear pair, the path of contact and meshing time from engagement to disengagement are obtained. The formula for determining the sliding friction coefficient is introduced. Based on TCA and the dynamic meshing force provided by the subsequent dynamics model of double helical gear pair, the sliding friction coefficient of the tooth surface is calculated. Secondly, the stiffness excitation, gear-into impact excitation and error excitation (including the axial displacement caused by the errors of manufacture and installation under low speed) are calculated according to the existing research results. Following this, a dynamic model of a double helical gear pair that takes into consideration the axial vibration, friction and multiple backlashes is both built and solved. Finally, an example is presented to verify the corresponding results.

FE prediction method for tooth variation in hot forging of spur bevel gears

Tooth variations in spur bevel gears have significant effects on the transmission performance, noise, and vibration and directly affect the reliability and stationarity of equipment. The hot forging process is the principal method used for the mass production of spur bevel gears owing to its high efficiency and high quality of products. However, hot forging of spur bevel gears is a high-pressure, high-temperature, and instantaneous forming process; hence, the evolution of tooth variations is extremely difficult to predict and measure. An accurate prediction of tooth variations in the hot forging process of spur bevel gears is an important precondition for tooth variation control to improve tooth accuracy. In this study, a new finite element (FE) analysis strategy of tooth variation prediction in the hot forging of spur bevel gears is proposed according to transitive relations of stress, strain, and temperature. Following this new strategy, a series of FE models are developed, so that the positional and shape variations on the tooth surface caused by die shrink-fitting (DSF), die elastic deformation (DED), die thermal expansion (DTE), gear elastic recovery (GER), and nonuniform cooling shrinkage of gear (NCSG) are comprehensively investigated. To verify the reliability of this FE analysis strategy, a hot forging experiment of a spur bevel gear was carried out, and the tooth variations of the tooth die and hot forged gear were measured using a gear-measuring machine. The results show that the factors causing the positional variation in order of importance from highest to lowest are DSF, DED, GER, NCSG, and DTE, and those for shape variation are DSF, DED, GER, DTE, and NCSG. Moreover, the shape variation of the final hot forged gear increases in the tooth profile direction and decreases in the tooth lengthwise direction. Finally, the simulation results closely agree with the experimental results, confirming the reliability of the FE analysis strategy proposed in this study.

Condition monitoring of bevel gear box using Morlet wavelet coefficients and naïve Bayes classifier

A naive Bayes classifier is used for classifying the faults of a gear box. The rotating equipment like gear box has enough scope for condition monitoring its conditions as it plays a significant role as a prime mover in many engineering applications. This paper discusses about the extraction of Morlet wavelet coefficients from the vibration signal for different conditions of the gear box under investigation, and application of naive Bayes classifier for its condition monitoring and diagnostics. In this paper fault diagnostics of spur bevel gear box is treated as a pattern classification problem. The major steps in pattern classification are feature extraction, and classification. This work investigates the usefulness of statistical features of Morlet wavelet coefficients and naive Bayes for classification. The results show that the developed method can reliably diagnose different conditions of the gear box and the algorithm can be applied for online applications of supervised machine learning.

Condition monitoring of bevel gear box using Morlet wavelet coefficients and naïve Bayes classifier

A naïve Bayes classifier is used for classifying the faults of a gear box. The rotating equipment like gear box has enough scope for condition monitoring its conditions as it plays a significant role as a prime mover in many engineering applications. This paper discusses about the extraction of Morlet wavelet coefficients from the vibration signal for different conditions of the gear box under investigation, and application of naïve Bayes classifier for its condition monitoring and diagnostics. In this paper fault diagnostics of spur bevel gear box is treated as a pattern classification problem. The major steps in pattern classification are feature extraction, and classification. This work investigates the usefulness of statistical features of Morlet wavelet coefficients and naïve Bayes for classification. The results show that the developed method can reliably diagnose different conditions of the gear box and the algorithm can be applied for online applications of supervised machine learning.

Social humanoid robot SARA: development of the wrist mechanism

This paper presents the development of a wrist mechanism for humanoid robots. The research was conducted within the project which develops social humanoid robot Sara – a mobile anthropomorphic platform for researching the social behaviour of robots. There are two basic ways for the realization of humanoid wrist. The first one is based on biologically inspired structures that have variable stiffness, and the second one on low backlash mechanisms that have high stiffness. Our solution is low backlash differential mechanism that requires small actuators. Based on the kinematic-dynamic requirements, a dynamic model of the robot wrist is formed. A dynamic simulation for several hand positions was performed and the driving torques of the wrist mechanism were determined. The realized wrist has 2 DOFs and enables movements in the direction of flexion/extension 115°, ulnar/radial deviation ±45° and the combination of these two movements. It consists of a differential mechanism with three spur bevel gears, two of which are driving and identical, while the last one is the driven gear to which the robot hand is attached. Power transmission and motion from the actuator to the input links of the differential mechanism is realized with two parallel placed identical gear mechanisms. The wrist mechanism has high carrying capacity and reliability, high efficiency, a compact design and low backlash that provides high positioning accuracy and repeatability of movements, which is essential for motion control.

Influences of key forging parameters on gear-tooth deviation of cold forged spur bevel gear

An elastic-plastic FE simulation model is proposed to predict the evolution of gear-tooth deviation in cold forging of a spur bevel gear, and the reliability of this FE model is verified by experiment. Then, the influences of the interference value of die shrink fitting, the forming degree of a preformed billet and the friction factor on the tooth thickness error and the shape error of the tooth surface were investigated comprehensively. The results show that, he forming degree of the preformed billet has the most significant influence on the gear-tooth deviation, the interference value of die shrink is secondary, and the impact of friction factor is slight.

Research on the mold release motion for spiral bevel gear forging

At present, spur bevel gears are mainly processed by forging, showing advantages of high processing efficiency, low processing cost and fine microstructure material. Spiral bevel gears, meanwhile, are widely generated by machining, including face-milling, face-hobbing, etc., in spite of the superiority identified of forged spiral bevel gears for years. The major hindrance originally lied in the manufacture of the mold, and along with the development of multi-axial machine tool, it is now no longer a problem. Accurate design of mold release motion (MRM) to avoid interference, however, remains a problem due to the fact that the tooth lengthwise of spiral bevel gear is not straight.To resolve this, this paper, through deriving the equation of the tooth surface, investigating algorithm for mold release motion interference and discussing the motion parameter presetting, proposes first a mold release motion analysis (MRMA) method for forging spiral bevel gear. Subsequently, based on the method, a computerized program is developed, in which the ideal mold release motion can be obtained through adjusting the recommended motion according to the mold release interference analysis.

Design and hot forging manufacturing of non-circular spur bevel gear

Non-circular spur bevel gear (NCSB-gear) is a kind of special spur bevel gear which can perform variable speed ratio transmission. It can achieve several special functions which cannot be realized by circular spur bevel gear (CSB-gear), such as the skid resistance function in automobile differential mechanism. However, NCSB-gear is quite difficult to be designed and manufactured because of its complicated shape and specific transmitting characteristic. In this research, a new design method of NCSB-gear based on vectorial coordinate transmission is proposed to simplify the calculation process of tooth profile, and a NCSB-gear pair which is used in automobile differential is designed. Then, a new hot forging process is proposed to manufacture the driven NCSB-gear, and a pre-forging stage is arranged in this hot forging process so as to pre-allocate the material according to the shape features of the driven NCSB-gear, which is benefit for metal flowing in final forging stage. Several 3D FE simulation models of hot forging process of the driven NCSB-gear with or without pre-forging stage are developed, and the metal flowing, effective strain distribution and temperature distribution are comprehensively investigated and compared. Based on the FE simulation results, several experiments of hot forging process of the driven NCSB-gear are carried out. The results show that, the hot forging process with pre-forging stage can obviously improve the rationality of metal flowing, the homogeneity of the effective strain distribution on NCSB-gear, and the homogeneity of temperature distribution on NCSB-gear and the gear-tooth die. Furthermore, the experiment results are consistent well with the simulation results, and a fully filled NCSB-gear part is obtained by using the hot forging process with pre-forging stage, which confirms that this hot forging process of NCSB-gear is reliable.

Research on process and simulation of the isothermal forging of a spur bevel gear

This paper took the lead in applying isothermal forging technology to form a spur bevel gear in a single operation. According to the isothermal forging process, the forging part drawing of the spur bevel gear was defined. The 20CrMnTi was chosen as the gear materials. A closed-die structure was used in the forging process. Then, the model of the dies and workpiece were built by UG software. After the models was imported into DEFORM-3D, the simulation of the isothermal forging process of the bevel gear was executed. Through simulation, the shape of the gear, the distributions of effective stress and strain, the forming load of the dies, the laws of metal flow and the filling of the metal during the forging process were gained and thoroughly discussed. The results revealed that the full forging process can be divided into four periods and precision spur bevel gear can be obtained without causing under-filling and folding defect by using the isothermal forging with closed-die forging structure, which provides guidance to manufacturing the spur bevel gear.

Differences between traditional cold forging and cold orbital forging of a spur bevel gear

Abstract Cold orbital forging, as an advanced incremental forming process, has been widely researched and used to fabricate the spur bevel gear. However, the mechanism of cold orbital forging is quite different from that of traditional cold forging, which leads to the different forming laws and different properties of forged gear. In this paper, cold orbital forging and traditional cold forging of a spur bevel gear are simulated under the same conditions in the Deform-3D software platform. The filling process, geometric characteristics of forged gear, effective stress distribution, effective strain distribution, gear tooth accuracy are comprehensively clarified and compared. The results show that, comparing with traditional cold forging of a spur bevel gear, cold orbital forging can increase the degree and homogeneity of plastic deformation and improve the gear tooth accuracy.

Vibration signal analysis using histogram features and support vector machine for gear box fault diagnosis

This paper discusses about the extraction of histogram features from the vibration signal of the different conditions of the gear box under investigation, and the application of machine learning method, support vector machine in machine condition monitoring and diagnostics. This paper aims at using classification methods for fault diagnosis of the gear box under investigation. In this paper fault diagnostics of spur bevel gear box is treated as a pattern classification problem. The major steps in pattern classification are feature extraction, and classification. This work investigates the use histogram features and support vector machine for classification. The results show that the developed method can reliably diagnose different conditions of the gear box.

Optimization of the Isothermal Forging Process of a Spur Bevel Gear

In this paper, the optimization of the parameters of the isothermal forging technology to form spur bevel gear was studied. The goal of the optimization is to decrease the forming load during the process. Then, some factors included the ratio of height to diameter of billet, thickness and position of punching recess, deformation temperature and velocity were taken as the optimization values and the orthogonal experimental method was employed to carried out the optimization. After the optimization, a set of optimum technology parameters were obtained. The result demonstrates that the precise spur bevel gear can be formed with less forming load and without causing under-filling and folding defect by using the isothermal forging and choosing suitable parameter, which provides reference to form the spur bevel gear.

Microstructure and Texture Evolution in Cold Rotary Forging of Spur Bevel Gears of 20CrMnTi Alloy Steel

The microstructure of cold rotary forged gears greatly affects their working life. Therefore, the aim of this study is to reveal the evolution of microstructure and texture that occurs during the cold rotary forging of spur bevel gears of 20CrMnTi alloy steel. The evolution of grains of the gear tooth is investigated through optical microscopy. By employing scanning electron microscopy and electron backscatter diffraction, the evolution of the cementite particles and the texture of the gear tooth is also revealed. The results indicate that the grain size distribution is non-uniform from the tooth profile to its center. The cementite particles in the tooth profile are finer and more uniformly distributed than those in the tooth center. After cold rotary forging, the tooth center has a combination of α- and γ-fibers, and the γ-fibers are more developed than the α-fibers, while most of the components in the tooth profile are assembled along the α-fibers.

Effect of key factors on cold orbital forging of a spur bevel gear

Cold orbital forging is an advanced spur bevel gear forming technology. Generally, the spur bevel gear in the cold orbital forging process is formed by two steps: the preforming step and the final step. Due to the great importance of the final step to gear forming and its complication with interactive factors, this work aims at examining the influence of key factors on the final step in cold orbital forging of a spur bevel gear. Using the finite element (FE) method and control variate method, the influence rules of four key factors, rotation velocity of the upper tool, n, feeding velocity of the lower tool, v, tilted angle of the upper tool, γ, friction factor between the tools and the billet, m, on the geometry and the deformation inhomogeneity of the cold orbital forged gear are thoroughly clarified. The research results show that the flash becomes more homogeneous with increasing v, increasing m, decreasing n or decreasing γ. And the deformation of the gear becomes more homogeneous with increasing v, decreasing n or decreasing γ. Finally, a corresponding experiment is conducted, which verifies the accuracy of FE simulation conclusions.