Gear Tooth Surface Research Articles

Key Parameters and Experimental Study of High-Speed Rotating Meshing Gear Injection Lubrication Based on Moving Particle Semi-Implicit Method

With the rapid development of China’s manufacturing industry, products are changing toward better energy efficiency and precision. Reducing transmission energy waste, enhancing transmission lubrication, and increasing transmission efficiency have all become critical concerns. The moving particle semi-implicit particle approach is utilized in this study to create a high-speed rotating meshing gear lubrication model and conduct a simulation analysis of transmission gears by studying the influence law of sensitive parameter injection diameter on lubrication. The oil distribution state on the gear surface, the gear tooth surface heat dissipation effect, and the degree of gear operating stability are all calculated by computing the gear surface fluid coverage and convective heat transfer coefficient. According to the numerical simulation results, increasing the liquid injection diameter can greatly enhance fluid coverage and convective heat transfer coefficient on the gear surface, hence improving lubrication. However, when the injection diameter reaches a critical value, the contact area between the liquid and the gear is maximized, and additional increases in the injection diameter will not improve the lubricating effect. Experiments have revealed that the liquid injection diameter is the most critical factor influencing gears. The gear torque dramatically increases as the liquid injection diameter increases. According to a rigorous analysis, the gear lubrication effect is optimal when the liquid injection diameter is 2.0 mm. This provides a theoretical foundation for transmission system lubrication design.

A novel design method of low noise spiral bevel gear tooth surface for polynomial ease-off topological modification

In order to reduce the vibration noise of the spiral bevel gear transmission system (SBGTS), a polynomial ease-off topological modification (PETM) method, which combines the load tooth contact analysis (LTCA) and vibration analysis of the spiral bevel gear, is proposed in this paper to minimize the normal dynamic meshing force and normal relative displacement to reduce the vibration noise. Firstly, a new PETM equation is established based on the complete conjugation principle, which is applied to the initial clearance calculation of LTCA and an explicit LTCA calculation method with PETM without requiring inverse processing parameters is constructed. The calculation accuracy is better than that of a general algorithm. Secondly, the dynamic response of an eight-degree-of-freedom dynamic system of spiral bevel gear is calculated according to the loaded transmission error and time-varying meshing stiffness calculated by the explicit LTCA of PETM. Finally, a PETM low-noise tooth surface design method is constructed with the goal of minimizing the normal meshing force and the normal relative displacement and the PETM equation coefficient as the optimization variable. The numerical results show that the new PETM low-noise tooth surface design method can improve the meshing performance and dynamic performance of spiral bevel gears to a greater extent than those before modification and after the second-order topological modification, thus greatly reducing the vibration noise of SBGTS.

Ellipsoid contact analysis and application in the surface conjugate theory of face gears

Abstract. The face gear tooth surface is a high-order variable curvature surface, and the curvature of the surface is complicated, so it is difficult to describe the characteristics of the face gear tooth surface by a specific equation. In this paper, the discrete curvature relation of the surface is used instead of an analytical equation to describe a spatial meshing surface, and the traditional meshing theory is neutralized to analyze the characteristics of the face gear tooth surface. Firstly, according to the structural characteristics of the face gear, the sampling method of the face gear tooth surface is analyzed, and the mathematical model of fitting the tooth surface contact point is established. Then, the discrete asymptotic surface development analysis method is studied, and the ellipsoid contact analysis method of the face gear pair is established by simplifying the conjugate surface and its region. Finally, the contact analysis method of the discrete tooth surface is studied, and the instantaneous contact ellipse of the face gear tooth surface is calculated, which formed a new numerical meshing method of space curved surface.

Three-Dimensional Conjugate Tooth Surface Design and Contact Analysis of Harmonic Drive with Double-Circular-Arc Tooth Profile

A three-dimensional conjugate tooth surface design method for Harmonic Drive with a double-circular-arc tooth profile is proposed. The radial deformation function of the flexspline (FS), obtained through Finite Element (FE) analysis, is incorporated into the kinematics model. By analyzing the FS tooth enveloping process, the optimization of the overlapping conjugate tooth profile is achieved. By utilizing the hobbing process, the three-dimensional machinable tooth surface of FS can be acquired. Utilizing the coning deformation of the FS, simulations are conducted to analyze the multi-section assembly and meshing motion of the machinable tooth surface. The FE method is utilized to analyze and compare the loaded contact characteristics. Results demonstrate that the proposed design method can achieve an internal gear pair consisting of a circular spline with a spur gear tooth surface and the FS with a machinable tooth surface. With the rated torque, approximately 24% of the FS teeth are engaged in meshing, and more than 4/5 of the tooth surface in the axial direction carries the load. The contact patterns, maximum contact pressure, and transmission error of the machinable tooth surface are 227.2%, 40.67%, and 71.24% of those on the spur gear tooth surface, respectively. It clearly demonstrates exceptional transmission performance.

Experimental Investigations to Study the Effectiveness of Cepstral Features to Detect Surface Fatigue Wear Development in a FZG Spur Geared System Subjected to Accelerated Tests

Gears are essential machine elements used to transmit power and motion from one unit to another under desired angular velocity ratio. Various types of gears have been developed to fulfill power transmission requirements in industrial applications. Under normal or fluctuating operating conditions, increase in fatigue load cycles, transition in lubrication regimes, fluctuating loads and speeds, etc., result in various surface fatigue wear modes which affect the performance of geared system. The severity of wear anomalies developed on gear tooth surfaces can be assessed by using vibration signals acquired from the gear box. On the other hand, reliable wear assessment is very important to perform maintenance action which depends on the sensors, data acquisition procedure, vibration signal analysis and interpretation. This paper presents results of the experimental investigations carried out to assess initiation and propagation of surface fatigue failure wear modes developed on gear tooth contact surfaces. A FZG back to back power recirculation type spur gearbox was used to conduct fatigue test experiments on spur gears under accelerated test conditions. Accelerated test conditions resulted in a rapid transition of lubrication regimes, i.e., hydrodynamic lubrication regime to boundary lubrication regime which triggered surface fatigue faults on gear tooth surfaces. A cepstral analysis method was used to assess fault severity in the geared system. The results obtained from the cepstral features were correlated to various surface fatigue faults and reduction in gear tooth stiffness. Results obtained from the experimental investigations highlighted the suitability of cepstral features to assess incipient faults developed on spur gear tooth surfaces.

A cylindrical skiving tool design method based on a conjugate surface for internal gear manufacture

Power skiving is a highly productive method for manufacturing gears, especially internal gears. However, due to the resharpening errors of the conical skiving tool, the insufficient tool life hinders the large-scale applications of power skiving. This work proposes a novel design method of the cylindrical skiving tool based on deriving the mathematical model of two-parameters conjugate tooth surface of an internal gear. The error-free cutting-edge of the skiving tool is obtained from the intersection curve of the conjugate tooth surface and the rake face with an offset along the tool axis. In the present study, a helical internal gear with 97 teeth, module of 1.5875 mm and helix angle of 23.5° is used for the design of a cylindrical skiving tool with 37 teeth. The numerical analysis results show that the tool axial offset zoff, crossed shaft angle Σ and geometric rake angle of tool γ0 result in the asymmetrical tool profile and the uneven clearance angles on both flanks. However, the change of the tool helix angle by 0.7° can obtain an even clearance angles on both flanks when zoff is −30 mm. The noninterference height of the cylindrical tool is 48 % more than the conical tool when machining the same workpiece, which means the cylindrical tool is expected to be a longer tool life. Experiments are conducted on a Profilator Type H skiving machine by using the cylindrical skiving tool by the accuracy of DIN 3. The results show the tool design method is effective and applicable to machine a gear by the accuracy of ISO1328-1 level 7.

An Effective Analytical Approach to Predicting the Surface Contact Temperature of the Face Gear Drives

The anti-scuffing bearing capacity of gears is a significant issue for their service lives, especially for the cases with heavy loads or high speeds. Generally, the anti-scuffing bearing capacity is evaluated according to the surface contact temperature that can be calculated with either analytical methods or finite element analysis (FEA) methods. The analytical methods usually apply the theory of Blok to efficiently obtain the results by simplifying some actual physical conditions, which are well considered in the FEA methods with accurate results but more computation time. Conversely, a new efficient and accurate analytical method is proposed by introducing the actual lubricant film thickness and continuous heat transfer for the theory of Blok. These two physical conditions are the key issues for the calculation of the two parts of surface contact temperature, flash temperature and bulk temperature, respectively. For the calculation of flash temperature, elastohydrodynamic lubrication (EHL) is introduced to consider the lubricant film thickness for the theory of Blok, and the result is obtained by solving the Reynolds equation efficiently with the finite difference method. For the bulk temperature, the result for a contacting point on the gear tooth surface is directly obtained according the theory of Blok, and the continuous heat transfer among the adjacent contacting points is considered with Gaussian heat morphology, which can accurately construct the bulk temperature field distribution in the contact region. The proposed method is validated as in good agreement with the FEA method and with less computation time.

Effect of ground tire rubber media's viscoelasticity and flow passage geometry on the abrasive flow finishing of helical gear

This work aims to elucidate the behavior of viscoelastic ground tire rubber media (GTRM) under abrupt contraction and expansion of the media at the entry and exit of the gear flow channel and its influence on polishing results. Due to the inherent nature of the abrasive flow finishing (AFF) process, the media flow converges at the entrance of the gear tooth as it flows from a larger fixture cross-section to a narrower volumetric space between gear teeth. The material removal and subsequent surface roughness rely heavily on the flow's pressure and velocity. A numerical simulation was performed to obtain the pressure and velocity along the gear flank face width (FFW). To investigate the effect of variation in the media deformation rate along the gear flow channel on AFF results, the material removal height and improvement in average surface roughness at different locations along the tooth flank face width were measured. AFF results reveal that the material removal near the two edges of the gear tooth is higher and has an inferior surface finish compared to the tooth's center. Due to the abrupt compression of the media at the flow channel entrance, the media act elastically dominant, resulting in high pressure and flow velocity near the tooth edge (flow channel's entry). Additionally, the effect of the helix angle on the AFF of various helical gear (HG) was investigated. Among the three HGs chosen, the 30° HG produces the lowest surface roughness under moderate pressure and high velocity. The microhardness and fretting wear analyses further confirm that the AFF polishing increases the microhardness and wear resistance of the gear tooth surface as a result of work hardening and minimizing surface defects.

Dynamic Responses of the Planetary Gear Mechanism Considering Dynamic Wear Effects

Gear wear is unavoidable and results in vibrations and decreased performance in a planetary gear system. In this work, the wear phenomenon of the gear teeth surface and the dynamic responses of the planetary gear mechanism are investigated through a computational methodology. Dynamic responses are presented by considering the dynamic wear effects. First, the model of the planetary gear mechanism dynamics is established by considering the nonlinear stiffness and friction of gear surfaces. The dynamic wear model of the gear is then established based on Archard’s wear model. Further, the coupling between the dynamics and wear characteristics of the planetary gear mechanism is presented by considering the dynamic wear effects. Finally, a numerical investigation is conducted. The simulation results reveal severe wear between the sun and planet gears. The wear depth and meshing vibration responses exhibit prominent nonlinear characteristics. The low-order resonance of the meshing frequency becomes more marked as the mesh times and wear increase.

Control of Tooth Form Deformation in Heat Treatment of Spiral Bevel Gears Based on Reverse Adjustment of Cutting Parameters.

The tooth surface structure of spiral bevel gear is complex and requires high machining accuracy. In order to reduce the tooth form deformation of heat treatment, this paper proposes a reverse adjustment correction model of tooth cutting for heat treatment tooth form deformation of spiral bevel gear. Based on the Levenberg-Marquardat method, a stable and accurate numerical solution for the reverse adjustment amount of the cutting parameters is solved. Firstly, a mathematical model of the tooth surface of spiral bevel gears was established based on the cutting parameters. Secondly, the effect law of each cutting parameter on tooth form was studied by using the method of small variable perturbation. Finally, based on the tooth form error sensitivity coefficient matrix, a reverse adjustment correction model of tooth cutting is established to compensate the heat treatment tooth form deformation by reserving the tooth cutting allowance in the tooth cutting stage. The effectiveness of the reverse adjustment correction model of tooth cutting was verified through experiments on reverse adjustment of tooth cutting processing. The experimental results show that the accumulative tooth form error of the spiral bevel gear after heat treatment is 199.8 μm, which is reduced by 67.71%, and the maximum tooth form error is 8.7 μm, which is reduced by 74.75%, after reverse adjustment of cutting parameters. This research can provide technical support and a theoretical reference for heat treatment tooth form deformation control and high-precision tooth cutting processing of spiral bevel gears.

Residual stress relaxation by bending fatigue in induction-hardened gear studied by neutron Bragg edge transmission imaging and X-ray diffraction

The compressive residual stress on the gear tooth’s surface, a vital parameter to control mechanical properties, such as strength, has a beneficial effect on the component’s fatigue life. A novel procedure, double induction quenching (DIQ), effective for improving the fatigue strength of gear products, has been used for producing gears with steep gradients of compressive residual stress generated in the tooth surface. We performed a Bragg edge imaging experiment at a pulsed neutron source to determine the spatial distribution of the {110} lattice spacing (d110) and the broadening of the {110} Bragg edge (w110) on the DIQ gear product after tooth-bending fatigue tests to which different loading cycles were applied. No significant difference occurred in the d110 and the w110 at Hofer’s critical section (tensile side) of the teeth with different loading conditions within the accuracy of data analysis. However, we detected a decrease in the w110 and changes in the residual lattice strain distribution in the axial direction (through the thickness) along the tooth root directions at the opposite side of Hofer’s critical section for both teeth after 3 × 105 and 8 × 105 cycles, relieving the compressive residual stresses during the fatigue process. The residual stress close to the gear tooth surface determined by X-ray diffraction using sequential polishing showed a slight relaxation and redistribution from the tensile side in the hoop direction, complementary to the neutron Bragg edge imaging information in the axial direction.

Reliability Design of Two-Stage Planetary Gear Wheel Hub Reducer based on Multi-Objective Optimization

The mining dump truck has a large load capacity, low running speed, and the characteristics of low speed and high torque. The planetary wheel reducer can meet this demand, which is widely used in such vehicles. According to the structural characteristics of a 170-ton vehicle two-stage planetary gear reducer, the reliability of planetary gear transmission at all levels was analysed, and the system parameters were optimized on this basis. The multi-objective optimization design method was used to transform the maximum reliability of the system into the maximum reliability of the gears at all levels, and the constraints are established based on the actual processing, operation, installation, assembly and other working conditions. The MATLAB multi-objective optimization module was used to solve the analysis, and the best gear design parameters were obtained after rounding. Under different operating conditions, the planetary reducer before and after optimization was compared and analysed to obtain the reliability and service life of the entire deceleration system after optimization. The analysis results show that: after the parameter optimization of the planetary reducer, the transmission efficiency is 0.946, and the transmission ratio of the system is 30.54, which meets the actual use requirements. The reliability coefficient of the contact strength of the tooth surface of the secondary sun gear is 2.52, the reliability coefficient of the bending fatigue strength of the root of the secondary inner ring gear is 2.59, and the reliability of the secondary gear is 0.989. The reliability is obviously improved. The safety factor of the main parts is high. The service life of each gear of the whole secondary reduction system meets the design requirements. The analysis content and results provide reference for the optimization design and reliability analysis of similar planetary gear systems.

Novel method to establish equation of ZN helicoid and meshing limit line of related worm drive

According to the definition, the straight sided normal profile helicoid is established. It is strictly proved that the normal section of straight sided normal profile helicoid is straight line and the cross-section is extended involute, and the section curve of axial section is obtained. The calculation formula of the guide cylinder radius under different installation modes of ZN-type worm is obtained. The meshing limit line equation of uniform speed vertical staggered shaft drive is derived, make the calculation formula of meshing limit line more simple. The meshing equation and the meshing limit line equation of ZN-type worm drive are derived. Through theoretical calculation, it is verified that the meshing limit line is the inherent characteristic of ZN-type worm pair and cannot be eliminated by modifying parameters. The meshing limit line is solved and some conclusions are drawn. The numerical results show that the meshing limit line exists on the worm tooth surface, which divides the contact area into two parts: effective area and ineffective area. The conjugate line of the meshing limit line is located in the middle of the worm gear tooth surface.

Vibration and control optimization of pressure reducer based on genetic algorithm

Abstract A research challenge of vibration and control optimization of pressurized reducer is solved in this article; a method based on genetic algorithm (GA) is proposed to optimize the vibration and control of reducer. Considering the bending strength of helical gear root and tooth surface contact fatigue strength as constraints, the improved GA is used to solve it, and the optimal parameter combination is obtained. The size of center distance is reduced by 9.59% compared with that before. Based on the optimized results, the vibration becomes weaker with the increase of the load at the output end of the reducer, and its maximum value is only 1/8 of that when the load is 550 N. The experimental results show the optimized surface load distribution of driving gear teeth. The maximum normal load per unit length of the optimized output stage driving gear surface is 521.321 N/mm, which is significantly lower than the 662.455 N/mm before optimization. At the same time, the tooth surface load is evenly distributed. The larger tooth surface load is mainly distributed in the middle of the tooth surface with strong bearing capacity, which effectively solves the problem of unbalanced load before optimization and improves the bearing capacity of gear transmission. It is proved that GA can effectively realize the vibration and control optimization of pressurized reducer.

Effect of grinding conditions of gears made of 20MnCr5 steel after single-piece flow heat treatment on the condition of the surface layer of the tooth working surface

The paper investigated the effect of selected processing conditions during gear grinding on the value and distribution of microhardness and residual stress formed in the technological surface layer of gears after thermochemical treatment (TCT) conducted by a continuous single-piece flow method.The gears were carburised with LPC at 920C, then quenched in a 4D Quenching chamber at 7 bar and tempered at 190C for 3 hours. In the next step, the working surfaces of the gear teeth were ground by supplying grinding fluid (GF) to the grinding zone using the WET method and the MQL method with a minimum amount. Measurements were made on the distribution of microhardness and residual stress formed in the technological surface layer of gears after thermochemical treatment and after the grinding process.The results of the study showed the influence of workpiece speed vw and the method of delivery to the grinding zone GF on selected parameters describing the condition of the technological surface layer of the teeth of gears made of 20MnCr5 steel. The grinding process with a white aluminium oxide grinding wheel causes deterioration in the material's residual stress state. For each of the three analysed workpiece speeds vw, smaller changes in microhardness with respect to the microhardness of the material before grinding occur in the surface layer of samples ground with GF fed with the MQL method. Similarly, residual stress values are in the area of favourable compressive stresses.Environmental considerations and the need to comply with increasingly stringent environmental protection and worker safety regulations are pushing researchers and entrepreneurs to completely eliminate or reduce the consumption of grinding fluids in the grinding process. Based on the research and analysis carried out in this study, it was concluded that applying minimum GF by the MQL method could be an alternative to the conventional WET method.In sustainable manufacturing, it is extremely important to produce high-quality items while reducing the cost of manufacturing and taking care of the environment and workers' health. This includes the manufacture of gears, a basic component used in gear transmissions in the automotive industry, for example. The research has established that it is possible to use the MQL method, which reduces the amount of GF used when grinding the working surfaces of gear teeth, as an alternative to the conventional WET method.The conducted research was the first to determine the most favourable conditions, in terms of the obtained residual stresses and microhardness, for grinding the working surface of gear teeth using the MQL method.

Transmission-error- and vibration-based condition monitoring of gear wear with contaminated lubricant

The presence of contaminant particles in lubricants could cause severe gear wear and damage. Conventional condition monitoring techniques, i.e., gear inspection and oil/wear debris analysis, are often utilised to assess the presence of wear due to contaminants and its severity such as wear depth. However, the traditional approaches require experience or off-line analysis. Although vibration is a non-invasive technique for fault detection and diagnostics, it is less well developed for wear analysis. Recently, an alternative sensor technology, i.e., transmission error (TE), combining angular measurements obtained from the input and output shafts has shown strong potential for wear monitoring. This work aims to investigate the usage of vibration and TE to identify the existence of contaminants and measure the gear wear severity caused by the oil contamination. This is achieved by conducting gear wear tests on a spur gearbox rig, using clean and contaminated lubricants with silica sand. The test in a normal lubrication condition provides a healthy reference of the spur gearbox under a nominal operating condition. In addition to the nominal operating condition, TE and vibration measurements are collected throughout the tests at different operating conditions, together with moulds of the gear tooth surfaces for wear analysis. The results show that the absolute TE can quantitively measure wear depth, and the RMS of vibration can qualitatively correlate with the trend of the average wear depths. The proposed technique extends the field of using TE to diagnose and predict gear wear in contaminated lubricant conditions.

Meshing theory of face worm gear drive with hardened cylindrical worm

This article proposes a novel linear contact face worm gear drive. The novel face worm gear drive consists of a face worm gear and a cylindrical worm enveloped by a tapered surface. The meshing theory for the novel face worm gear drive is systematically built up. The meshing theory on the base of the reference point is further developed aimed at the worm pair where the indexing surfaces are planar and cylindrical. The design methods of the rough size for the face worm gear are introduced. The computing method for the worm limit axial mounting distance is presented by employing the meshing limit line function. The asymmetry of the tooth surfaces for the worm pair is evaluated using the helix angle at the midpoint on the line of section for the worm gear tooth surface and the tooth profile angle for the worm axial section. Numerical results show that the geometric characteristics and the meshing properties for the tooth surface on both flanks of the novel face worm gear drive are asymmetrical. However, the meshing properties for the novel face worm gear drive are satisfactory.

Design and Experiment of Ultrasonic Assistant Grinding Device of Spiral Bevel Gear

The precisely ground tooth surface of the spiral bevel gear still shows the thermal crack, and its micromorphology is the cause of high-frequency noise. The ultrasonic assistant grinding (RUAG) technology has the unique advantage of solving these problems. Therefore, this paper designed the split-type rotary device in which the disc grinder and amplitude horn are core components and bolted together. A deformation coefficient was proposed to calculate the strain stress of the disc grinder. Combined with the stepped horn resonant theory, the theoretical model of a multi-step rotating body can be used to calculate the frequency and amplitude of the grinder and horn. The harmonic response simulation was adopted to verify the theoretical results. The experiment proved that the device’s frequency, node, and amplitude are reasonable. The comparison results showed that the simulated frequency and amplitude were closer to the practical one. Moreover, the difference between them increased with the dimension of the device.

Study on the toroidal helix and manufacturing method of enveloping hourglass worm tooth surface

As a complex space enveloped surface, the tooth surface of dual-lead helical gear enveloping hourglass worm is characteristic with difference tooth profile, unequal pitch and variable tooth thickness. To grasp the geometry characteristics and precision manufacturing method of it, the analytical method for toroidal helix is presented. The mathematical model of toroidal helix is developed, and the geometry characteristics of helix angle, axial tooth thickness, and tooth surface undercutting are analyzed. The helix angle of toroidal helix presents the convex shape, and the undercutting characteristic is affected by the pressure angle, helix angle, transmission ratio, and normal modulus. Based on the toroidal helix of tooth surface, the precision manufacturing method is proposed, and the measuring method is developed. The hourglass worm sample was manufactured and measured, and the transmission accuracy of hourglass worm drive is tested. The results show that the manufacturing and measuring method of toroidal helix is effective and feasible.

Face gear generating grinding residual model based on the normal cutting depth iterative method

The generating grinding method has the characteristics of high machining accuracy and high efficiency. Therefore, it is widely used in the finishing process of the face gear tooth surface. The physical performance of the grinding process is an important factor that influences the machining accuracy of the face gear tooth surface. Therefore, to improve the manufacturing accuracy of the face gear, it is necessary to accurately simulate the grinding process of the face gear. Owing to the influence of the complex spatial geometric characteristics of the face gear tooth surface and the grinding wheel, establishing a surface residual modeling method for the face gear is a key challenge in simulating the generating grinding process. To address the aforementioned issues, this study proposes a normal cutting depth iterative method to calculate the grinding residual in the face gear generating grinding process. This method considers the complex 3D spatial characteristics of the face gear tooth surface and establishes the spatial residual model of each node of the face gear surface in the process of generating grinding. Compared with other residual algorithms based on 2D truncation or Boolean operation of face gears, this algorithm has higher computational accuracy and efficiency. Thus, it lays the foundation for accurately establishing the complex spatial microscopic surface topography in the face gear generating grinding process.