Gear Tooth Surface Research Articles

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.

Gear tooth surface modification analysis by support vector machine regression

A modification to the gear tooth surface is crucial for reducing whistling noise generated by gearboxes of electric vehicles. Using the orthogonal test method, this paper studies geometry parameters of gear pair and the effect of load conditions on modification parameters of tooth surface. To achieve this, the paper develops various test models of gear pairs based on MASTA and then corrects the gear profiles according to load distribution state. The influential factors of gear transmission to modification parameters of tooth surface are thereby intuitively analyzed. Finally, a prediction model of the result of gear modification is built, based on test parameters, by method of support regression vector machine, providing a valuable reference to determine the tooth-surface modification parameters of the transmission gear of electric vehicles.

Design, Stress Analysis, and FEA Prediction of Nutation Drive with Face Gear

Background: Nutation face gear transmission is a patent about a new type of transmission based on meshing between two face gears. It replaces spur gear with internal face gear to form a “faceface” meshing gear pair and actualizes its deceleration function by combining the nutation principle, which has the advantages of both face gear and nutation drive. Objective: The purpose of this paper is to study the designing and manufacturing of a nutation face gear reducer to derive the force calculation formulas of the face gear, input shaft and bearings, calculate the contact stress of tooth surface and bending stress of tooth root, determine the basic parameters of the prototype, and analyze the processing points for the core parts of the prototype. Methods: Using the dynamic meshing force analysis method by combining it with modern digital design and manufacturing methods, the designing and manufacturing of a nutation face gear reducer are studied. Results: In the theoretical calculation, the maximum contact stress of the fixed side tooth surface is about 433MPa, and the average contact stress is about 345MPa; the maximum contact stress of the tooth surface on the rotating side is about 579MPa, with an average of about 502MPa; the comparison of which with the finite element analysis results verifies the theoretical calculation results. Conclusion: The dynamic meshing force analysis method of nutation face gear transmission is deduced and given. Based on this, gear tooth surface transient contact stress and tooth root bending stress are calculated.

Dynamic analysis of gear pairs with the effects of stick-slip

The instantaneous dynamic contact state analysis is carried out to reveal the process of scuffing failure of the gear tooth pair. A stick-slip dynamic model of a two-gear set is proposed and the coupling effects of time-varying mesh stiffness, tooth separations, friction between the gear teeth surfaces, and potential stick-slip are considered. Dynamic analysis shows that stick contact is an important source of tooth scuffing failure. Additionally, stick contact dramatically increases the vibration amplitudes and causes chaos. Parametric studies show that heavy load and rough tooth surfaces increase the probability of sticking and increase the time of stick state over a single mesh period. This study provides a design guard for avoiding scuffing failure and improving the reliability of gear transmission.

Modelling method, simulation and experimental verification of hypoid gear involved tooth surface deviation under manufacturing process

Tooth surface errors are inevitable in manufacturing process, and directly affect the meshing performance and NVH properties. In this paper, the tooth profile deviation and midpoint tooth pitch error were considered. Firstly, the theoretical tooth surface model was established by simulating the manufacturing process of face-hobbed hypoid gear. Then, a novel modelling method of tooth surface errors was proposed based on the relationship between discrete tooth surface points and measured error points. A solid model and finite element model by using CAD and CAE technologies were developed to study the effects of tooth surface errors and meshing phase on the contact pattern and transmission error. Results show that the gear tooth surface error was the primary factor while the tooth meshing process contributes the least of total transmission error. The peak-to-peak of the transmission error values of pinion and gear with error was 24.786 times higher than standard. The meshing phase of gear had greater impact on the contact pattern. The range of transmission error fluctuation was 210 μrad within different meshing phases. The tooth surface points measurement and rolling experiment were performed and the fluctuation range was around 233.86 μrad with a 10.2% difference.

Study on the quenching depth and surface hardness of metal materials by laser quenching variable parameters

Laser quenching is one of the most outstanding gear tooth surface quenching methods due to its high efficiency, environmental friendliness, and performance consistency. Since gear tooth surface laser quenching requires repeated scanning, changing the laser scanning velocity and power by program control can meet the needs of variable depth quenching. The effects of laser scanning velocity and output power on the quenching depth and surface Rockwell hardness after quenching were studied and experimentally analyzed. The result shows that by adjusting the parameters, the surface hardness of the specimen changes slightly with the actual received laser energy. However, the quenching depth can be consistent with the laser scanning velocity. The maximum surface Rockwell hardness that a laser quenched material can achieve depends on the material itself, not on the laser power or scanning velocity. Compared with accelerated laser quenching, decelerated laser quenching is more suitable for tooth surface machining due to the cumulative effect of energy within the quenching depth range of metal materials.

A model construction and measurement method for tooth surface deviation of spiral bevel gear based on a one-dimensional probe

The accurate measurement of tooth surface deviation is an important prerequisite for the quality monitoring of high-precision spiral bevel gears. A measurement method for tooth surface deviation of spiral bevel gears is proposed based on a one-dimensional probe, which can accurately measure and evaluate tooth flank. According to the forming principle of the spiral bevel gear tooth surface, the theoretical surface is constructed as the measurement reference flank. A series of measures and methods are adopted to ensure the accuracy and correctness of one-dimensional probe measurement. These effective methods include the construction of a precise positioning model of the gear blank and its surface, the measurement planning of reduction dimension which the gear needs to rotate once the normal angle after each point is measured, and the compensation for the increasing dimension of the one-dimensional probe. In addition, minimization of the normal deviation of the tooth flank is achieved by using the optimum matching technique of the theoretical and the actual surfaces. The deviation degree of the actual surface relative to the theoretical surface can be accurately calculated and evaluated by establishing a deviation model, which ensures the correctness of the evaluation result of the deviation. Finally, the test of tooth surface deviation is carried out on a JD45+ gear measuring center (GMC) using a one-dimensional probe and a Gleason 650GMS GMC using a three-dimensional probe. The measurement results show that the evaluation results of the one-dimensional probe are in good agreement with those of the three-dimensional probe. The proposed theory and method not only expand the measurement range of the GMC using a one-dimensional probe, but also have certain reference significance for the precision measurement of other complex surfaces.

Determination of Undercutting Avoidance for Designing the Production Technology of Worm Gear Drives with a Curved Profile

One of the most difficult production geometry tasks arising in the machining process of the elements of a drive pair is to avoid undercuts. It is a serious technological challenge to determine the production of the elements of worm gear drives avoiding the phenomenon undercut, especially in the case of a pair consisting of a curved profile worm and its mating wheel. The technology of forming the tooth surface requires a separate examination in each case, running the simulation procedure of the tool geometry and the movement conditions when forming different teeth. This article proposes a new concept for determining and then avoiding the positions of undercutting by examining the patented worm with a circular arc profile in axial section, due to its extremely advantageous aspect in terms of production technology. The cutting edge of the hob, formed from the substitutional worm, moves on the tooth surface of the worm, and produces the tooth surface of the conjugate wheel. The gear tooth surface has been determined based on the main law of gearing with the lines consisting of the contact points of the conjugated surfaces. The conditions for the disappearance of the common normal or the relative velocity fitting to the common tangent plane of the contacting points are defined in this paper.

Contact stresses and bending stresses analysis of curvilinear cylindrical gears generated by a face-milling cutter with parabolic profile

Curvilinear cylindrical gear drives are a type of parallel-axis gear set, and the longitudinal geometrical shape of the gear teeth is a part of the circular arc. The main purpose of this paper is to explore the influence of modification amount and assembly error on con-tact stress and bending stress. This study proposes a curvilinear cylindrical gear drive with a parabolic profile. The gear tooth surfaces are generated by a face-milling cutter with a straight-line profile, and the matching gear tooth surfaces are generated by a face-milling cutter with the parabolic profile. Initially, mathematical models of the gear set are described based on the theory of gearing. The finite element method and tooth contact analysis algorithms were applied to contact and bending stress analyses. Finally, four numerical examples are provided to illustrate the mechanical performance of the curvilinear cylindrical gear drive with the parabolic profile. The study results show that curvilinear cylindrical gear drives have superior mechanical performance compared to those with a straight-line profile.

Investigation of influence of grinding wheel and cutting parameters on surface roughness and surface hardening when relieving grinding the gear milling teeth surface based on the Archimedes' spiral

3D surfaces based on the Archimedes' spiral are widely used in mechanical engineering, especially in the manufacturing the gear milling cutters. The machining process to create this type of surface is usually performed in specialized machines. In this study, relieving grinding process was conducted to machine the Archimedes surface of HSS P18 workpiece material using a specialized machine (1Б811) to investigate the influence of the grinding wheel graininess (G), hardness of grinding wheel (Hd), grinding wheel velocity (V), and feedrate (s) on surface quality including surface roughness (Ra) and surface hardening (ΔHRC). The experimental plan with 27 experiments (L27) was designed using the Taguchi method. Applying the analysis of variance (ANOVA), the influence of G, V, s, and Hd on Ra and ΔHRC was investigated. G, V, s, and Hd have different influences on Ra and ΔHRC in the relieving grinding process. V has the greatest influence on Ra and ΔHRC with 40.96% for Ra and 26.43% for ΔHRC. The grinding wheel hardness that has the lowest influence on Ra (0.82%), whereas the feedrate has a negligible effect on ΔHRC (7.01%). The interaction effect of the input parameters on Ra is not significant (2.91%). However, for ΔHRC, the interaction influence degree of these parameters on this criterion is quite high (33.77%). From the experimental data, Ra and ΔHRC were presented as a quadratic function of G, V, s, and Hd with high values of determination coefficient (R2 = 92.75% for Ra and R2 = 92.00% for ΔHRC). In the surveyed range of the input parameters, Ra decreases if G and V increase, and s decreases. Also in this survey range, the hardening increases if the values of the input parameters (G, V, and s) increase. This study also determined that there is no clear rule about the relationship between Ra and ΔHRC. Further studies need to be carried out to find the input optimal values ensuring the quality criteria of the relieving grinding process.

Adaptive grinding method and experimental verification of worm gear tooth surface knife marks

Adaptive grinding method and experimental verification of worm gear tooth surface knife marks

Determination of tooth surface points on bevel gears for checking on a coordinate measuring machine

The use of coordinate measuring machines is an integral part of gear design. In order to this tool to be truly effective, it is necessary to know the surfaces to be measured and to provide comparative values. In the study, the mathematical modelling of the bevel gear tooth surfaces and the exact description of the production are used to produce the theoretical surfaces on which points can be added in any desired arrangement and number. These points form the basis for the evaluation of the measurement by comparison with the measured values.

A Reliability-Enhanced Forming Grinding Method of Cylindrical Involute Gears for Electrical Vehicles

A new form-grinding method of cylindrical involute gears for electrical vehicles (EVs) is proposed to obtain stable contact performance of gear tooth surfaces and improve their reliability based on a predesigned controllable second-order transmission error function. The predesigned second-order transmission error function is assigned to a gear drive based on design specifications of EVs. Mathematical models of modified gear tooth surfaces of the gear pair can be obtained by the predesigned second-order trans-mission error function. Moreover, a section profile of a form-grinding wheel for cylindri-cal involute gears can be determined by a coordinate transformation matrix during form-grinding and settings of computer numerical control form-grinding programs for this active design method. This approach is ultimately conducted on three cylindrical involute gear pairs to demonstrate its feasibility and effectiveness.

Characteristics of internal flow field and convection heat transfer in planetary gear reducer of shield machine

Based on RNG k-ε turbulence model and dynamic grid technology, the internal fluid dynamics model of splash lubrication three stage planetary gear reducer system is established. The distribution of lubricating oil and convective heat transfer characteristic in the system at different input rotational speeds are analyzed. The results show that at high speed condition, the oil gas mixing volume and the degree of atomization of lubricating oil are higher, and the convective heat transfer coefficient of tooth surface is larger, and it takes less time for the convective heat transfer coefficient to reach equilibrium. Meanwhile, the mean convective heat transfer coefficient on the tooth surface of sun gear, planetary gear and ring gear decreases successively.

RELIABILITY ANALYSIS OF PRECISION GEARS WITH MODIFIED INITIAL TOOTH CONTOUR

The article presents the results of a theoretical study that was conducted as part of the search for solutions to the problems of calculating the operational reliability of gears of a new generation that have a significant deviation in the geometry of the profile of the teeth and the entire engagement from the standard initial contour. A method of plotting the wear of the working surfaces of gear teeth has been developed. The essence of the method is that the equation of the worn surface can be obtained by calculating the full variational derivative of the functional of the energy action of wear. Since wear reduces accuracy, the method is used to calculate the probability of failure-free operation of precision gears by the express method. The proposed article is one of the first works on the calculation of the operational reliability of precision gears with teeth profiled by the involute epitrochoid.

Roughness of meshing gear teeth

The article is devoted to the method of calculating some parameters of gear teeth roughness, taking into account the parameters of meshing gears under rolling friction conditions in the presence of relative sliding between the meshing gear teeth. A model for determining the running roughness of the surface of the teeth, which have the form of a truncated cone, based on the roughness model of the spherical form is obtained. The proposed calculation methods allow us to: calculate the depths of penetration of the run-in roughness to the surfaces of the mutually contacting gear teeth; establish the regularities of changes in the roughness parameters of the gear teeth surface depending on the contact parameters of the gear meshing and the load in the meshing. Determined the most probable correlation between the actual and nominal contact area, depending on the degree of relative slip, occurring between the gear teeth, in the zone of the actual contact area of the gear teeth, depending on the engagement module of the contacting gear teeth.

Research on tooth surface design and side milling machining method of ruled line face gear

To solve the problem of generalized design and batch processing of face gear, a method of tooth surface design and side milling of ruled line face gears is proposed in this paper. First of all, the discrete points of the pitch cone surface of the face gear are calculated, and the straight-line cluster and section curve of the tooth surface is constructed to analyze the deviation of the ruled line face gear. Secondly, the tooth surface model of the ruled line face gear is constructed, and the curvature and contact trace are calculated. Thirdly, the curvature and tangent of the ruled line face gear tooth surface are analyzed, the feed plane of the equidistant surface and the guideline are obtained, the torsion angle of the tooth surface and the distribution of the tangent vector along the generatrix are calculated, and the tool axis position based on the two-point offset method is studied. Finally, the side milling processing test of the face gear is carried out, and the tooth surface of the face gear after side milling is measured. The measurement results verify the correctness of the tooth surface design and the side milling processing method of the ruled line face gear.