Meshing Line Research Articles

Computerized design and analysis of a novel high load bearing internal gear drive with curved meshing line

A novel high load bearing internal gear drive with curved meshing line is presented in this paper, and its performance is compared with that of an involute internal gear drive by finite element calculation. First, the novel gears’ meshing line is an S-shaped curve composed of two parabolas. Second, the novel gears’ tooth profiles based on the curved meshing line are designed using differential geometry and gear meshing theory. Third, three-dimensional mesh models of the novel gears are created by procedures, then using finite element calculation to analyze the stress of gear meshing. Finally, numerical examples demonstrate that the novel gears have lower stress and a smoother sliding coefficient than involute gears, implying that the former has a greater benefit in bearing capacity and wear performance. Meanwhile, tooth modifications can improve stress concentration, hence increasing the load-bearing capability of the novel gears.

Research on friction and meshing efficiency of ADC12-POM gear pair considering off-line meshing

Metal-plastic gear pairs, due to their combination of the advantages of both materials, have been widely promoted and applied in many industries. However, research on their transmission performance is not yet complete, especially regarding the tribological properties of metal-plastic gear pairs. The study focus on ADC12-POM gear pairs. Based on the principle of potential energy, the study considers significant elastic deformation during POM meshing, resulting in obvious off-line meshing. Consequently, the study establishes a stiffness model for ADC12-POM gear pairs with off-line meshing. Using this stiffness model and a load distribution model, to calculate the tooth surface load distribution coefficient for the gear pairs. Building upon previous research on friction coefficient models, the study develop a friction coefficient model that accounts for off-line meshing and compare it with the friction coefficient model that does not consider off-line meshing. To validate the accuracy of the friction coefficient model, the study design and create an efficiency test rig for ADC12-POM gear pairs, conducting theoretical and experimental studies on gear mesh efficiency. The study analyzes the distribution of mesh efficiency along the meshing line and its relationship with the friction coefficient. By comparing experimental measurements with theoretical calculations, the study verifies the proposed friction coefficient model, providing a theoretical basis for the study of metal-plastic gears.

Numerical Analysis of Tooth Contact and Wear Characteristics of Internal Cylindrical Gears with Curved Meshing Line

In order to improve the contact strength and reduce the sliding friction of the gear pair, an internal cylindrical gear pair with a curved meshing line is studied in this paper. Firstly, a curved meshing line is designed. The tooth profiles of the internal gear pair with the designed meshing line are calculated by using differential geometry and the gear meshing principle. Secondly, a wear model is established by combining the finite element method and the Archard wear formula. Then, a numerical simulation is conducted; the relative curvature, sliding coefficient, sliding distance, maximum contact pressure, transmission error, and wear depth are calculated. Ultimately, the variation law of tooth surface wear of new gear with and without installation errors is observed under different stress cycles. On this basis, the influence of tooth modification on tooth surface wear is further researched. Through the results, the advantages of the introduced novel internal cylindrical gears in wear resistance are further demonstrated. The study in this paper provides new research ideas and methods for gear wear research and gear design.

A high-speed gear reshaping method for electric vehicles combining the effects of input torque and speed variation.

In this study, we introduce an optimization method for high-speed gear trimming in electric vehicles, focusing on variations in input torque and speed. This approach is designed to aid in vibration suppression in electric vehicle gears. We initially use Tooth Contact Analysis (TCA) and Loaded Tooth Contact Analysis (LTCA) to investigate meshing point localization, considering changes in gear tooth surface and deformations due to load. Based on impact mechanics theory, we then derive a formula for the maximum impact force. A 12-degree-of-freedom bending-torsion-axis coupled dynamic model for the helical gear drive in the gearbox's input stage is developed using the centralized mass method, allowing for an extensive examination of high-speed gear vibration characteristics. Through a genetic algorithm, we optimize the tooth profile and tooth flank parabolic modification coefficients, resulting in optimal vibration-suppressing tooth surfaces. Experimental results under various input torques and speeds demonstrate that the overall vibration amplitude is stable and lower than that of conventional gear shaping methods. Specifically, the root mean square of vibration acceleration along the meshing line under different conditions is 58.02 m/s2 and 20.33 m/s2, respectively. The vibration acceleration in the direction of the meshing line is 20.33 m/s2 and 20.02 m/s2 under varying torques and speeds, with 20.33 m/s2 being the lowest. Furthermore, the average magnitude of the meshing impact force is significantly reduced to 5015.2. This high-speed gear reshaping method not only enhances gear dynamics and reliability by considering changes in input torque and speed but also effectively reduces vibration in electric vehicle gear systems. The study provides valuable insights and methodologies for the design and optimization of electric vehicle gears, focusing on comprehensive improvement in dynamic performance.

Cylindrical gear transmission errors influenced by temperature based on thermal network

Cylindrical gear transmission errors influenced by temperature based on thermal network

Tooth profile design and meshing characteristics analysis of internal meshing gears based on variable center meshing line

A design method of internal meshing gear based on variable center meshing line (VCML) is presented in this paper. The meshing line is an arc line connecting the intersection of the indexing circle connecting the inner and outer gears and the intersection of the tooth top circle, and the center of the line of engagement freely slides on the vertical bisection line of the line connecting the two intersection points. The top tooth profile equation of internal and external gears is derived by rack equation. According to the normal method of gear profile, the equation of gear root meshing line is derived by using the tooth top profile equation of the gear. According to the principle of plane meshing, the root profile equation of gear is derived by using the root meshing line equation of gear. The tooth profile of VCML gear can be deduced quickly by adjusting the center position of the meshing line. The stress, meshing stiffness, transmission error, contact ratio and sliding ratio of the VCML gears are analyzed by finite element method, and the area of significant performance improvement of the meshing line center of the VCML gears is found. The research results show that compared with involute gears, the maximum average stress of VCML gears is reduced by 64.99%, the meshing stiffness is increased by 193.67%, and the transmission error is reduced by 65.95%. This method improves the efficiency of new tooth profile design and transmission performance. By changing the center coordinates of the meshing line, the tooth profile of the VCML gear can be quickly redesigned, which greatly improves the efficiency of the new tooth profile design and transmission performance. This design method provides a new idea for the tooth profile design of internal meshing gear.

Service Performance Optimization and Experimental Study of a New W-W Type Non-circular Planetary Gear Train

To address the vibration problem in traditional W-W-type non-circular planetary gear trains during operation, this study proposes two new combinations of W-W-type non-circular planetary gear trains. The study focuses on analysing the transmission error and improving service performance. By utilizing the conjugate theory and the coordinate transformation theory, an accurate mathematical model for non-circular gears is derived. The transmission error models for the two combination forms of the non-circular planetary gear train are established using the incremental meshing line method. The analysis also examines the influence of eccentricity on the transmission error. Kinematic analysis of the multi-body dynamics model confirms that the new W-W type non-circular planetary gear train, formed by combining non-circular gears and cylindrical gears, exhibits superior transmission performance. Furthermore, a test analysis is conducted on the roller pumping unit test platform and the indicator diagrams of the pumping unit under various working conditions are obtained. The study concludes that the optimal matching mode for the sucker rod counterweight and motor frequency of the reversing device of the pumping unit is 20 kN and 20 Hz, and the dynamic balance of the pumping unit load can be achieved by adjusting the motor frequency.

Study on Heat Transfer Characteristics of High-Speed Herringbone Gear in Meshing Process Under Oil Injection Lubrication

Abstract To quantify the relationship between the total frictional heat and the absorbed heat by the oil film in the herringbone gear transmission, this article investigates the lubrication status and thermal characteristics of the tooth meshing point under the fuel injection condition. First, the contact analysis of the herringbone gears is carried out—studying the variation pattern of the maximum pressure, highest temperature rise, and minimum film thickness of different oil films at various mesh points along the meshing line. Second, the friction coefficient and frictional power for the meshing points on the tooth surface are calculated to determine the ratio of oil film pressure to total pressure distribution. This completes the allocation of frictional power for the meshing points of the driving and driven gears. Finally, by comparing the total heat generated by frictional shear with the heat absorbed by the oil film, the numerical relationship between the two can be quantified.

Machinability and mechanism of abrasive flow machining ultra-precision surface with orientated grinding marks

The loud noise in electric automobile caused by the overlap between orientated grinding marks with meshing line on ground gear tooth surface becomes a big problem for both drivers and manufacturers. Relying on the excellent self-deformation features and trace material removal, the abrasive flow machining (AFM) process exhibited potential machinability for above ultra-precision ground surface. Benefiting by the pseudo network structure, the abrasive media would possess both excellent elasticity and fluid capability, which could be quantitatively reflected by storage modulus, loss modulus and shear thinning nature in rheological properties. Meanwhile, deriving from the CFD simulation, the media exhibited the steady flow velocity and shear stress at the finishing channel, potentially contributing to the finishing uniformity on the target ground channel, which was subsequently confirmed by the change of ground surface morphology and profiles at the initial and finished state. Most convex peaks and concave valleys have been effectively subdued and whittled, leading to a rather smoother surfaces than initial ones. Besides, on account of the different collision position between grains with convex peaks, the finishing mechanism on ground surfaces with orientated marks could be elaborated as the transition effect from directly fractured material removal on convex peak cusp into plastic deformation on residual convex peaks. Combining with the interaction between continuous matrix and discrete grains in flow field, the mechanics on single grain was systematically investigated to establish the material removal theoretical model. Generally, the AFM technique exhibited the stunning machinability on ultra-precision ground surface.

Computerized design, simulation of meshing, and stress analysis of curvilinear cylindrical gears based on the active design of the meshing line function

The computerized design of curvilinear cylindrical gears based on the active design of the meshing line function is presented. The parametric equations of their meshing line functions are based on a parabola to control the curvilinear shape of the teeth along the face width of the gears. Different numbers of control points and different combinations of curves, including parabolic curves, circular arcs, and involutes, smoothly connected with each other at the control points are chosen to form the active tooth profile. The meshing performance, mechanical behavior, and influence of the parameters of combined curves are studied in terms of the contact patterns, variation of the maximum stresses and loaded functions of transmission errors and compared to two types of curvilinear cylindrical gear drives generated by face-milling cutters as a reference. The investigated curvilinear gear drives with five control points show lower maximum contact and bending stresses as well as lower peak-to-peak level of loaded transmission errors compared to other cases of curvilinear gear drives.

Study on the influence of 3D modification on dynamic characteristics of a herringbone gear transmission system

The 3D modification is an advanced technology that comprehensively considers tooth profile modification and axial modification to reduce vibration and noise. Therefore, this paper combines 3D modification technology with contact characteristics and dynamic properties to study the influence of 3D modification on the dynamic performance of a herringbone gear system. This paper employs a parabolic tooth profile instead of the cutter's straight tooth profile to achieve 3D-modified tooth surface and deduces the tooth surface equation. Then, tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) are used to simulate the meshing process of teeth. And the dynamic model of the herringbone gear system under three internal excitations is established. Finally, 3D modification, TCA, LTCA technology, and gear dynamic characteristics are combined to study the influence of 3D modification on the system's dynamic behavior. The results show that, compared with tooth profile modification and axial modification, the 3D modification can effectively compensate for the influence of errors on the gear system and have a very good damping effect. The relative vibration displacements on the left and right meshing lines of the gear pair are reduced by 47.60% and 51.20%, and the root mean square values are decreased by 30.50% and 36.10% before and after modification, respectively.

Study on gear meshing power loss calculation considering the coupling effect of friction and dynamic characteristics

Gear transmission system is widely used in many mechanical equipment to achieve power transmission and rotational speed changes. Meshing power loss is one key index to assess the performance of a gear system, which directly influences heat generation and lubrication, etc. Over the past decades, many computational models of gear meshing power loss have been proposed to support gear design and optimization. However, the coupling effect between the gear friction and dynamic characteristics are usually ignored, including time-varying meshing stiffness (TVMS) and dynamic meshing force (DMF), which are not conducive to accurate calculation and improvement of meshing power loss. Therefore, an improved gear meshing power loss calculation method is proposed to settle this problem in this paper. With the proposed method, the friction calculation model is established considering the effect of DMF and surface roughness based on mixed elastohydrodynamic lubrication (EHL). Then the TVMS is obtained with the friction force along the meshing line and DMF was taken into consideration. On the basis of modelling of friction and TVMS, a six degrees-of-freedom (DOF) gear dynamic model, as well as a power loss iteration calculation process are established and studied. The effects of gear surface manufacturing quality and loads on power loss are analyzed. Furthermore, a gear meshing power loss experimental setup is constructed to verify the effectiveness of the proposed method. The results show that this method is in better agreement with the experimental results than the traditional method which does not consider the coupling effects.

Effect of Machined Tooth Surface Mixed Lubrication Sliding Wear on Gear Dynamic Characteristics

Tooth surface wear causes variation in meshing stiffness and transmission error of the gear system and further causes the fluctuation of dynamic characteristics. In this study, a dynamic behavior prediction model of the gear transmission system was established, which considered the machined tooth surface wear based on the mixed lubrication sliding wear model and the gear tribology-dynamic model. The gear pair wear characteristics along the meshing line were analyzed through simulations, and the impacts of wear conditions, operating torque, and speed on the dynamic characteristics of the gear transmission system with tooth surface wear were discussed. The results demonstrated that the transmission error and the vibration displacement amplitude of the gear system had increased gradually with the increase of the wear degree and that the fluctuation intensified. The fluctuation of gear dynamic characteristics increased with the increase in torque, and the fluctuation of gear dynamic characteristics initially increases and then decreases with the increase in rotating speed.

Design and Application of Non-Circular Gear with Cusp Pitch Curve

To solve the design problem of non-circular gears with cusp pitch curves, this paper proposed a new variable-involute and incomplete variable-cycloid composite tooth profile (VIIVC-CTF), deduced the new VIIVC-CTF mathematical model, and constructed the conjugate gear model based on the envelope method. The design software of the non-circular gear with a cusp pitch curve was developed based on MATLAB. The variation law of rolling radius on an incomplete cycloid profile and its characteristics such as pressure angle and radius of curvature were analyzed. The variation relationship of the rolling radius on the meshing line and the contact ratio of the VIIVC-CTF were studied. The variation relationship of incomplete variable-cycloid profile shape, pressure angle, and curvature radius corresponding to different elliptical eccentricities were analyzed. The meshing analysis of the non-circular gear transmission mechanism was carried out based on virtual software. A comparison of the consistency of the theoretical value and simulation value of the transmission ratio curve verified that the tooth profile design method was feasible, and the VIIVC-CTF was applied to the seedling pick-up mechanism of the non-circular gear planetary gear train. Through the seedling picking experiment of the seedling pick-up mechanism, the feasibility of the application of the VIIVC-CTF was verified.

Computerized design, simulation of meshing and stress analysis of pure rolling internal helical gear drives with combined tooth profiles

The computerized design of non-generated pure rolling internal helical gear drives with combined transverse tooth profiles based on the active design of the meshing line function is presented. The application of different combinations of curves, namely circular arcs and involutes, to form the gear active tooth profiles is discussed. The parametric equations for tooth surfaces and the basic design parameters and equations of geometric sizing are proposed. The meshing performance and mechanical behavior are studied in terms of the contact patterns, maximum contact and bending stresses and peak-to-peak level of loaded transmission errors compared with a design of internal helical gear drive with corrected fillet. The combination of a circular arc and an involute connected at the pitch point to form the active tooth profile for both the pinion and the internal gear shows reduced maximum contact and bending stresses and lower peak-to-peak level of the loaded function of transmission errors. The proposed design of combined tooth profiles will contribute to lower the noise and vibration of the proposed gear drives, increase the endurance and life of the gear drive, and lower the heat generation due to pure rolling conditions of the achieved bearing contact.

Meshing limit line of face worm gear drive with hardened cylindrical worm

This paper systematically establishes the computation method of the meshing limit line for the face worm gear drive with a hardened cylindrical worm. The meshing theory based on the reference point in the tooth surfaces is developed for the face worm gear drive. The reference point is reasonably determined based on the study of the meshing limit line characteristics. The calculation method of the coordinates of the reference point is proposed. The formula for the limit pressure angle at the reference point is obtained. Numerical results show that two meshing limit lines can be obtained on each flank of the worm tooth surface by iteratively solving the system of non-linear equations with four unknowns. These two meshing lines are near the inner end of the worm addendum. When the meshing limit lines are outside the worm tooth surface, the conjugacy of the worm tooth surface is good. Besides, studies of numerical examples find that poorly matched parameters of the face worm gear drive can result in the meshing limit line entering the worm tooth surface first from the inner end of the addendum, which reduces the conjugacy of the worm tooth surface. To avoid this, the conjugacy of the worm tooth surface can be checked by examining the limit pressure angle of the reference point when designing the face worm gear drive.

A New Resultant Vibration Acceleration Model of a Planetary Gear Train and Fault Response Analysis

A new resultant vibration acceleration model is proposed to reveal its signal characteristics more accurately in the healthy and faulty state. First, an analytical lateral-torsional coupled dynamic model is developed with consideration of time-varying mesh stiffness and damping, static transmission error, and gear backlash. Then, the effect of gear backlash and damping on the system is analyzed, and a numerical velocity signal in the healthy and faulty state is carried out. Considering the effects of transmission paths, the resultant acceleration signal along the vertical direction is constructed as the weighted vibration summation. This signal includes a vertical component of the vibration along the meshing lines of both sun-planet and ring-planet pairs. Moreover, it also contains the vertical component of the planet gears, sun gear, and planet carrier acceleration relative to their own supporting bearings. Finally, the simulation results from the resultant signal model are experimentally validated and analyzed in both time and frequency domains.

Study on the Lubrication Characteristics of Spur Gear Pairs With Low Sliding Ratio Under Mixed Elastohydrodynamic Lubrication

Abstract The relative sliding at the meshing point directly affects the contact and lubrication characteristics of the gear pair and is an important factor of gear wear and power loss. In this study, for investigation of a new type of low sliding ratio (LSR) gear pair whose tooth profile is constructed by a cubic function, a three-dimensional (3D) mixed elastohydrodynamic lubrication (EHL) line contact model was established with consideration of the effect of tooth profile geometry, transient motion characteristics, load distribution, and machining roughness. The distribution of the center film thickness of the LSR gear along the meshing line was predicted through an example the result of which was compared with a typical line contact EHL formula to verify the model. In addition, the difference was investigated in film thickness distribution of friction coefficient and temperature rise between LSR spur gears and involute spur gears. Hence, the effect of 3D rough tooth surface on the contact lubrication characteristics of LSR gears was discussed. The results demonstrated that the minimum center film thickness of the LSR gear appeared at the alternating point of the concave and convex tooth surfaces. At the same time, compared with the involute gear, the LSR gear significantly increased the film thickness at the start and ending points of the meshing and reduced the friction coefficient and the flash temperature rise.

Experimental study on transmission error and dynamic backlash of elliptic gear transmission system

The transmission error of the gear transmission system is the main factor affecting its transmission performance. The expansion of special applications of elliptic gear transmission system and the improvement of transmission accuracy requirements put forward higher requirements for its transmission performance. Although many works have been presented to study the transmission error of cylindrical gear transmission system, a few works were focused on the transmission error of elliptic gears for the reason of the inconsistency of the tooth profile of the elliptic gear pair, the difficulty of establishing a transmission error model and obtaining the dynamic backlash. To overcome this problem, the theoretical model of the transmission error and backlash of the elliptic gear pair is proposed and established based on the meshing line incremental method. The ellipse gear transmission test-rig is built and the transmission test is carried out on it. Finally, the correctness of the theoretical model is verified. The results show that the dynamic backlash of the elliptic gear pair can be obtained through the bidirectional transmission error curve. The dynamic transmission error has a negative correlation with the speed and has a positive correlation with the load torque. The dynamic backlash shows an increasing relationship with the increase of speed and load torque. The research results of this article can provide a certain theoretical basis for the anti-backlash control of the elliptic gear transmission system and the improvement of transmission performance.

Computerized design, simulation of meshing and stress analysis of non-generated double circular-arc helical gear drives with different combinations of transverse pressure angle

The computerized design of non-generated double circular-arc helical gear drives with different combinations of transverse pressure angle based on the active design of the meshing line function is presented. The application of different transverse pressure angles for the double circular-arc tooth profiles is discussed and the parametric equations for the driving and driven gear tooth surfaces are derived. The meshing performance and mechanical behavior are studied in terms of the achieved contact patterns and the evolution of the contact and bending stresses for nine cases of design. The results show that one of the cases of design of double circular-arc helical gear drives considering a combination of transverse pressure angles of 25 and 15 degrees for the convex and concave circular-arc profiles of the pinion shows better mechanical performance with respect to the other combinations of different transverse pressure angles. The proposed geometry of non-generated gears is appropriate for manufacturing by injection molding or additive manufacturing for plastic, ceramic, metal as well as nanocomposite gears.