Gear Surface Research Articles

Influence of the Nitrided Layer Structure on the Micro-Pitting and Wear Behavior of Slow-Running Nitrided External Gears

Nitriding can significantly increase the load carrying properties of gears. While the diffusion layer is primarily responsible for improving the tooth root and flank load carrying capacity, the compound layer mainly determines the tribological properties of the gear surface. In the present work, the influence of the compound layer on the tribological load carrying capacity of nitrided gears in the N/N pairing was investigated. For this purpose, compound layers with different thickness, porosity and phase composition were produced and their micro-pitting and wear behavior were investigated in load stage and speed stage tests. The test results confirm that the properties of the compound layer are decisive for the micro-pitting and wear resistance of nitrided gears. For a high micro-pitting resistance, the presence of pores in the near-surface area of the compound layer is of high importance, since no micro-pitting occurred as long as pores were present. With regard to the wear behavior, no dependence on the compound layer thickness or the porous zone thickness was found while the phase composition of the compound layer shows a decisive influence.

Experimental evaluation of the mesh load factor (Kγ) of a 6MW wind turbine gearbox

The significant increase in rotor diameters seen in modern wind turbines has pushed gearbox manufacturers to introduce technological innovations to increase the torque density of current designs. Driven by the need to lower the cost of energy from wind and size limitations imposed by logistic constraints in onshore wind, a trend has emerged to increase the number of planetary stages and the number of planet gears per stage. One of the main challenges of next-generation gearbox designs is sharing the load evenly between a high number of planets. This paper presents an experimental evaluation of the mesh load factor of a modern 6MW wind turbine gearbox with five planets in the first planetary stage. Results from the traditional method, based on tooth root strain gauges, and from strain measurements in the outer surface of the ring gear are described and assessed. Both experimental approaches have yielded lower mesh load factor values than the default values required in the standard “Design requirements for wind turbine gearboxes” IEC 61400-4. Since the mesh load factor is used for gear rating and sizing, a lower value allows a more optimized gearbox design, which leads to a significant improvement in torque density and cost.

A point-contact conjugate hourglass worm drive based on the meshing theory of conjugate tooth surfaces generated by two generating surfaces

To solve the problems of narrow contact area and small contact ratio of the involute cylindrical worm helical gear drive, this paper proposed a point-contact conjugate hourglass worm drive (PCHW drive) based on the meshing theory of conjugate tooth surfaces generated by two generating surfaces. The hourglass worm and worm gear are generated by the helix surface of an involute helical gear and that of an involute cylindrical worm. A mathematical model of the drive is established and a method for solving contact points based on involute pitch point is given. The instantaneous transmission ratio is proved theoretically to be constant and transmission error is zero. The formation mechanism of the conjugate surfaces of the drive is revealed. The results of the tooth contact analysis for a numerical example show that he contact area of this drive is wider, the contact ratio is slightly increased compared to the involute cylindrical worm helical gear drive. Furthermore, the drive is insensitive to manufacturing and assembly errors. A prototype is manufactured and meshing test is performed to verify the theoretical correctness.

Real-time detection method of gear contact fatigue pitting based on machine vision.

This paper proposes a real-time detection method for gear contact fatigue pitting based on machine vision in order to improve the detection accuracy and detection efficiency of specimen fatigue pitting in gear contact fatigue tests and to realize the visualization, quantification, and real-time detection of gear pitting. Under the principle of gear meshing and the shooting principle of a line-scan camera, a test detection system for gear contact fatigue is established, and the optimal centrifugal shooting distance for the gear tooth surface is obtained by analyzing the gear rotation process. In response to the phenomenon of image overlap caused by the inconsistency between the speed of each point on the gear tooth profile and the line frequency set by the camera, an image correction algorithm of the gear meshing surface has been proposed, which has been proven to have improved the accuracy of the detection results of gear contact fatigue pitting corrosion. The detection accuracy of fatigue pitting corrosion is improved by combining the preliminary detection and the accurate detection of the fatigue features. The depth information of the extracted contour pitting pits is extracted by the sequential forward selection (SFS) algorithm. The experimental results showed that 0.1216mm2 is the average absolute error of pitting corrosion detection, the average relative error is 2.2188%, and the detection accuracy is 97.7812%. The proposed pitting corrosion detection system advances in visualization, quantification, real-time monitoring, and failure judgment with a new, to the best of our knowledge, experimental approach for gear contact fatigue pitting corrosion detection.

Fractal Contact Mechanics Model for the Rough Surface of a Beveloid Gear with Elliptical Asperities

Understanding the contact mechanics of rough tooth surfaces is critical in order to understand phenomena such as tooth surface flash temperature, tooth surface wear, and gear vibration. In this paper, the contact behavior between the meshing tooth surfaces of beveloid gear pairs with elliptical asperities is the focus. The contact area distribution function of the elliptical asperity was proposed for the point contact of curved surfaces by transforming the elastic contact problem between gear meshing surfaces into the contact between elastic curved surfaces with an arbitrary radius of curvature. In addition, a fractal contact mechanics model for the rough surface of a beveloid gear with elliptical asperities was established. The influence of tooth surface topography on the contact load and contact stiffness under different fractal parameters was investigated, and the results demonstrated that the real contact load and the contact stiffness of curved surfaces increase with the increase in the fractal dimension D and the contact coefficient λ. Conversely, the real contact load and normal contact stiffness decrease with the increase in the fractal roughness G and eccentricity e.

Modelling and experiment for grinding forces of gear form grinding considering complete tooth depth engagement

Grinding is an essential gear finishing method. Grinding force analysis and prediction are critical to understand grinding mechanisms. By using a geometry model for gear form grinding and surface grinding mechanisms, a theoretical model was established to calculate the gear form grinding force. By considering the complete tooth depth engagement between tooth grooves and wheel profiles during form grinding, three segments of the involute, transition arc and tooth bottom line, which were included in complete tooth groove profiles, were analysed using the model. Contact relations among the normal grinding depth, wheel equivalent radius, wheel linear velocity and wheel profile were obtained. In addition, grinding experiments were outperformed on the basis of the single tooth, and the unknown coefficients of the form grinding force calculation model were acquired. The effects of the grinding depth, feed speed and grinding speed on grinding force were analysed using the grinding force model. The comparison of the predicted values of the form grinding force model with the experimental results, indicated that the relative errors of tangential and normal grinding forces are within ±10% and ±12%, respectively. The results confirmed the accuracy of gear form grinding force calculation model. These findings play a key role in parameter optimisation during gear form grinding.

Computerized generation and surface deviation correction of face gear drives generated by skiving

This paper presents the computerized generation and surface deviation correction of face gears generated by skiving. Firstly, the mounting relation among the skiving cutter, the virtual shaper, and the being-generated face gear is defined and the velocity relation analyzed. Secondly, the equations for the rake face angle and back flanks of the skiving cutter are defined, and the profile of the cutting blade obtained. Based on the kinematics of the generation movement of the skiving cutter, the surfaces of the face gear teeth are derived. The influence of the parameters of the cutter profile on the face gear surface topology is studied. Thirdly, the correction of the face gear tooth surface deviation has been achieved to some extent by adjusting the cutting depth, the rotation angle of the face gear, and the cutter offset distance during the process of machining. Finally, the simulation of the proposed machining process has been verified with VERICUT. The results show that the deviation of the face gear tooth surface is consistent with that obtained by the computerized generation as proposed in this paper.

Load distribution analysis considering corner contact effects to predict the mechanical efficiency of spur gears

High efficiency is the basic design objective of any gear transmission system. Thus, it is necessary to predict the mechanical efficiency of gear pairs. The purpose of this study was to construct and demonstrate a prediction method based on a frictional loaded tooth contact analysis, which computes the load distribution between tooth surfaces by considering corner contact effects for the mechanical efficiency of spur gears. The load distribution and mechanical efficiency derived by the proposed method were verified against those obtained by using the finite element method. The corner contact effects were found to influence the load distribution and mechanical efficiency. A parametric analysis, to determine the influence of the input angular velocity, load torque, gear surface roughness, and lubricating oil viscosity on the load distribution and mechanical efficiency was performed. The results of the proposed method can be used to effectively improve the prediction accuracy and efficiency of gear transmission system efficiency.

Research on Meshing Gears CIMT Design and Anti-Thermoelastic Scuffing Load-Bearing Characteristics.

In the process of gear meshing, it is an inevitable trend to encounter failure cases such as contact friction thermal behavior and interface thermoelastic scuffing wear. As one of the cores influencing factors, the gear meshing contact interface micro-texture (CIMT) significantly restricts the gear transmission system (GTS) dynamic characteristics. This subject suggests the contact characteristic model and interface friction dynamics coupling model of meshing gear pair with different CIMT. Considering the influence of gear meshing CIMT on distribution type of hydrodynamic lubricating oil film, contact viscous damping and frictional thermal load, the aforementioned models have involved transient meshing stiffness (TMS) and static transmission accumulated error (STAE). Based on the proposed models, an example verification of meshed gear pair (MGP) is analyzed to reveal the influence of CIMT on the dynamic characteristics of GTS under a variety of micro-texture configurations and input branch power and rated speed/shaft torque conditions. Numerical simulation results indicate that the influence of CIMT on gear dynamic response is extremely restricted by the transient contact regularity of the meshing gear surface. Meshing gears’ dynamic characteristics (especially vibration and noise) can be obviously and effectively adjusted by setting a regular MGP with CIMT instead of random gear surfaces.

A novel cyclic-correntropy based indicator for gear wear monitoring

Gearbox is a vulnerable component of a turbine’s drivetrain and plays a vital role in the power transmission in wind turbines. Wind turbines usually operate under harsh working environments, such as in deserts, oceans, and on hills. The adverse operating conditions (such as inevitable fluctuating wind loads and speeds) make the gearbox transmission prone to reliability degradation and premature failure. Gear wear is a common and unavoidable surface degradation phenomenon during the lifespan of the gear transmission system. The gear wear propagation can result in severe failures, such as gear surface spalling, gear root crack, and gear tooth breakage, all of which could lead to the failure of the drivetrain system of wind turbines and bring unexpected economic loss, even serious accidents. Thus, it is crucial to monitor the gear wear propagation progression in order to enable reliable and safe operation. To this end, this paper develops a novel vibration-based health indicator to monitor the gear surface degradation induced by gear wear progression. With the help of the novel indicator developed, the health status of the gearbox can be well evaluated and thus predictive maintenance-based decisions can be made to reduce maintenance costs and minimize gearbox failures in wind turbines. A series of endurance tests under different lubrication conditions and operational conditions are carried out to verify the effectiveness of the gear wear monitoring indicator.

Input torque measurements for wind turbine gearboxes using fiber-optic strain sensors

Abstract. Accurate knowledge of the input torque in wind turbine gearboxes is key to improving their reliability. Traditionally, rotor torque is measured using strain gauges bonded to the shaft. Transferring the resulting signal from the rotating shaft to a stationary data acquisition system while powering the sensing devices is complex and costly. The magnitude of the torques involved in wind turbine gearboxes and the high stiffness of the input shaft pose additional difficulties. This paper presents a new alternative method to measure the input torque in wind turbine gearboxes based on deformation measurements of the static first-stage ring gear. We have measured deformation using fiber-optic strain sensors based on fiber Bragg gratings because of their advantages compared to conventional electrical strain gauges. The present study was conducted on a Siemens Gamesa Renewable Energy gearbox with a rated power of 6 MW, in which a total of 54 fiber-optic strain sensors were installed on the outer surface of the first-stage ring gear. The gear mesh forces between the planets and the ring gear cause measurable deformations on the outer surface of the stationary ring gear. The measured strains exhibit a dynamic behavior. The strain values change depending on the relative position of the strain sensors to the planet gears, the instantaneous variations of the input torque, and the way load is shared between planets. A satisfactory correlation has been found between the strain signals measured on the static ring gear and torque. Two signal processing strategies are presented in this paper. The first procedure is based on the peak-to-peak strain values computed for the gear mesh events, and therefore torque can only be estimated when a gear mesh event is detected. The second signal processing procedure combines the strain signals from different sensors using a Coleman coordinate transformation and tracks the magnitude of the fifth harmonic component. With this second procedure, it is possible to estimate torque whenever strain data of all sensors are available, leading to an improved frequency resolution up to the sampling frequency used to acquire strain data. The method presented in this paper could make measuring gearbox torque more cost-effective, which would facilitate its adoption in serial wind turbines and enable novel data-driven control strategies, as well as a more accurate assessment of the consumed fatigue life of the gearboxes throughout their operation.

Precise Measurement and Visual Expression of Gear Overall Deviation

This paper proposes a non-contact measurement, analysis, and visualization method for the overall deviation of gears based on a laser displacement sensor. We implement error compensation and coordinate transformation on the tooth profile data collected by the laser probe through an algorithm, and fit all the data points to the gear surface using a 3 × 3 degree spline function. According to the established actual surface model of the gear, the tooth profile curve on any section of the gear and its various deviations can be obtained. To find the overall deviation on the tooth profile surface, the deviation data is refined and fitted into a curved surface by the Newton difference method. The overall deviation can be represented on the gear surface in the form of a color map, and then the color map of the overall deviation of the gear can be obtained. In addition, it can intuitively analyze the distribution of the overall deviation on the gear surface, and realize the visual expression of the deviation. Finally, through experimental verification, we prove that this method can quickly and accurately analyze the various deviations of the gears and the distribution of the deviation, and can effectively improve the detection accuracy and efficiency of the gears.

Meshing theory of toroidal surface enveloping cylindrical worm drive with arc-toothed worm

This paper aims to establish a rich and complete meshing theory of the toroidal surface enveloping cylindrical worm drive with arc-toothed worm and obtain the meshing performance of the proposed worm drive. The arc-toothed worm is machined by a disc-shaped grinding wheel whose formulae of the installation position parameters are determined according to differential geometry. The characteristic of the contact line on the worm helicoid during cutting engagement is analyzed by establishing the Frenet frame. Then the relative motion model and some important results of the worm pair are acquired using the meshing theory of gearing. Based on this, the locus features of the knot of meshing are analyzed in different coordinate systems. In addition, the meshing points which determine the conjugated zone and instantaneous contact lines are classified according to their different positions on the tooth surface of the worm gear. Utilizing the methods of eliminating and geometric construction, the nonlinear equations are solved. Finally, a numerical example is implemented and the result shows the proposed worm drive has favorable meshing performance.

Increase wind gearbox power density by means of IGS (Improved Gear Surface)

Increasing gearbox power density is a key factor in reducing the levelized cost of wind energy (LCOE). The tooth root and flank load carrying capacity of gears are strongly affected by surface conditions. Additional finishing methods such as shot peening (SP) and superfinishing (SF) significantly increase the gear load capacity, but these effects have not yet been adequately considered in the current ISO 6336 standard or in any other gear standards.Based on the experimental results, an estimation of the safety margin increase is calculated for a wind gearbox part. Additional fatigue tests are needed to confirm this increase.

Fracture Failure Analysis of Gear Teeth

Gears are important transmission components in the field of aviation industry. Failure cases such as fatigue fracture and fatigue spalling often occur due to poor conditions, and the status of teeth surface is usually one of the important elements for the failure cause analysis, but few have analyzed how the machining status of gear end surface affects the fracture failure. In this paper, one engagement failure of two gears was studied, and the failure phenomenon is as follows: all teeth of the driving gear fractured, two adjacent teeth of the driven gear fractured and several locations of teeth bottom cracked. According to the fracture morphology of the gear, it is judged that the driven gear fatigue-cracked firstly, and the fatigue zone is located at the lower end surface rather than the tooth bottom. Material structure, machining status of gear end surface, and the thickness of nitriding layer were inspected. In addition, the difference of the machining status between the lower and the upper end surface was analyzed. The results show that compared to the upper end surface, the lower end surface is smoother and the grinding amount is relatively larger. The residual stress tested by XRD shows that there is a residual compressive stress of about 84 MPa on the upper end surface and a residual tensile stress of about 238 MPa on the lower end surface. The tensile stress and the working stress cause the local stress level of the lower end surface of the gear to be higher than the fatigue strength, causing fatigue cracking from the lower end surface.

An adhesive wear model of rough gear surface considering modified load distribution factor

The gear wear is closely relative to the rough tooth surface morphology and the load distribution; however, their interactions have been rarely given focus. In this work, an adhesive wear model of rough gear surface is proposed considering modified load distribution factor. The mesh stiffness and load distribution factor are modified by the tooth surface morphology and wear depth. Then, the mean pressure is obtained by Hertzian theory, and the wear depths of the pinion and gear are calculated using Archard model. The wear model is verified by comparing with the pervious works. The effects of surface morphologies, geometric and operating parameters on the wear depth, mesh stiffness, and load distribution factor are investigated. Results indicate that (1) the wear depth is determined by profile error rather than roughness, and the wear depth and the load distribution factor increase with the profile error. (2) The roughness decreases, remains unchanged and then increases with the increment of the mesh cycle. (3) As the module and tooth width decrease or the input torque and mesh cycle increase, the tooth wear depth increases. These findings are significant in reducing tooth wear and improving the service life of gear drive.

Research on quality control of precision machining straight internal gear by abrasive flow based on large eddy simulation

Traditional finishing technology is difficult to realize the precision machining of complex geometric parts. Abrasive flow machining technology solves this problem well. Taking the spur internal gear as the research object, the wall shear force, static pressure, dynamic pressure, and abrasive velocity vector of the internal channel of the straight internal gear under different inlet velocity, abrasive concentration, and abrasive particle size are analyzed by using the large eddy simulation method, and the action law of different parameters on the machining of straight internal gear by solid–liquid two-phase abrasive flow is discussed. At the same time, the orthogonal test was carried out. The results show that the solid–liquid two-phase abrasive flow machining technology can effectively remove the burrs, pits, and bulges on the tooth surface of spur internal gear, reduce the tooth surface roughness, and improve the surface quality. The optimal combination of processing parameters and the primary and secondary order of various factors affecting processing are obtained by range analysis and analysis of variance. The regression equation is constructed by regression analysis to verify the effectiveness and accuracy of the model, which provides theoretical support and data reference for actual processing and production.

Exploratory investigation of chip formation and surface integrity in ultra-high-speed gear hobbing

Gear hobbing is widely employed to manufacture automotive gears, where the productivity depends on the cutting speed. Currently, gear hobbing is performed at ∼300 m/min using high-speed steel hob cutters. In this study, ultra-high-speed gear hobbing was attempted using a large-diameter cemented carbide hob cutter on a gear grinder. This enabled a cutting speed up to 2450 m/min. Many interesting phenomena were acquired in this speed range. Chips were severely oxidized, whereas the gear surface was not affected. Compressive residual stress was generated at the gear surfaces with low surface roughness and high hardness, while the wear of hob cutter was insignificant.

Theoretical model analysis and case simulation of spherical involute surface

The theoretical model of a spherical involute surface is the premise and foundation of the 3D modelling design technology of spiral bevel gear. The forming process of the surface is also the forming process of its mathematical model. Based on the generating principle of spherical involute on cone and surface analysis, the system model is gradually divided into blocks from curve to surface, and the surface of the bevel gear is obtained by parameter coupling. The modelling process of curve, surface or initial spiral can be independently referenced. It can realise the precise modelling of complex spiral profile surfaces such as variable spiral angles. In this paper, the mathematical model of spiral bevel gear was simulated and analysed on the MATLAB2019b platform. The simulation results verified the correctness of the algorithm of the spiral bevel gear model and the practicability of design optimisation.

Optimized design of straight bevel gear tooth root transition surface

Optimized design of straight bevel gear tooth root transition surface