Tooth Surface Contact Stress Research Articles

Research on the correlation between roughness parameters and contact stress on tooth surfaces and its dominant characteristics

The contact performance of the tooth surface is a crucial factor affecting the operational lifespan of gears. There is a significant correlation between tooth surface topography and contact stress, as well as fatigue performance. To investigate the influence of different topography parameters on tooth surface contact stress, this paper performs analytical calculations on asperity contacts of rough tooth surfaces based on reconstruction modeling. Through efficient calculations, sufficient correlation analysis data is obtained. The neural network analysis method is used to measure the degree of influence of roughness parameters on tooth surface contact performance. Research on the correlation between micro-topography parameters and maximum contact stress on tooth surfaces, as well as regression analysis, is conducted. The results show that: (1) Considering rough surfaces, the tooth surface contact stress field exhibits two stress peaks in the near-surface layer and sub-surface layer, with a maximum Mises stress increase of up to 30 % compared to a smoother surface. (2) In the case of low roughness (Sa < 0.2 μm), the amplitude of the maximum Mises stress peak in the near-surface layer is close to that in the sub-surface layer. However, as the roughness amplitude increases, the amplitude of the near-surface stress peak increases sharply. (3) Ranking the roughness parameters based on their influence on contact stress, the main parameters characterizing contact performance are identified as Spk, Vmp, and Sq. The peak characteristics of the surface are the decisive factors affecting fatigue extremes, which are stronger than the traditional surface roughness parameter Sq. This paper establishes a direct correlation model between tooth surface topography parameters and contact stress, providing a foundation for simplifying stress calculations considering complex topographies and offering new insights for fatigue-resistant design of tooth surfaces.

The Design, Analysis, and Optimization of a New Pitch Mechanism for Small Wind Turbines

This article proposes and designs a novel variable pitch adjustment device for small wind turbines. The generator spindle is designed to be hollow so that the drive rod passes through it and connects the pitch drive mechanism to the pitch actuator. The article introduces the basic structure and working principle of the pitch mechanism and verifies the feasibility of the pitch device by using 3D printing technology to produce a small-scale model. The stress analysis of the wind turbine was carried out using the unidirectional fluid–structure coupling method. The results show that the maximum equivalent stress of the pitch mechanism is 27.42 MPa, the maximum tooth surface contact stress of the gear is 38.40 MPa, and the maximum tooth root bending stress is 18.13 MPa. The rack synchronous disk, blade handle, and gear rack mechanism were designed with light weight using various optimization schemes. The results of the optimization showed that the overall mass of the pitch mechanism was reduced by 33.2%, improving the applicability of the new pitch mechanism.

Calculation and influence analysis of tooth surface friction coefficient of planetary gear system in mixed lubrication condition

Based on the gearing theory, the calculation formulas of comprehensive curvature radius, relative sliding speed and tooth surface contact stress of internal and external meshing gear pair of the planetary gear system are deduced in this paper. Combined with load sharing theory and thermal elastohydrodynamic lubrication analysis method, the oil film thickness, film bearing ratio and friction coefficient are solved and the effects of roughness and input power on the friction coefficient are studied. The results show that with the increase of tooth surface roughness, the film bearing ratio decreases and friction coefficient increases; As the input power increases, the film temperature increases, the oil viscosity and film thickness decreases, which causes the tooth surface friction coefficient increases.

Design methods and stress analysis of asymmetric offset face-gear transmission

The paper proposed a new asymmetrical offset face-gear transmission, applied meshing theory to derive the tooth surface mathematical model, and used discrete numerical methods to obtain the tooth model. Subsequently, the limitation of pointing and undercutting on effective tooth width of asymmetric offset face-gear were studied, and the influence of the eccentricity on the effective tooth width was analyzed. Finally, the finite element method was used to analyze the tooth surface contact stress of four groups of asymmetric offset gear pairs with different working pressure angles. The conclusion shows that the tooth surface contact stress takes the minimum value when the working side pressure angle is 30°, and the contact stress significantly reduced compared to the face-gear pair that does not adopt an asymmetric structure. The research provides a reference to the design of asymmetric offset face-gear.

Investigation of Load Capacity of High-Contact-Ratio Internal Spur Gear Drive with Arc Path of Contact

Tooth root bending stress and surface contact stress are two major determinants of the load carrying capacity of gear drives. Generally, a high contact ratio has the potential to enhance the gear strength. In this paper, the basic procedures and methods for constructing a high-contact-ratio (HCR) internal spur gear pair with the arc path of the contact are presented. The effects of design and modification parameters such as deflection angle, modification angle, and addendum coefficient on gear drive are analyzed in detail based on 2D finite-element models (FEMs). A comparison of experimental and finite-element analyses (FEA) of the bending stress, contact stress, and contact ratio between HCR and involute internal spur gear drives was conducted to demonstrate the advantages of the HCR gear drive in terms of load capacity. The results show that appropriately increasing the deflection angle and addendum coefficient is beneficial for reducing bending and contact stresses. It was also observed that the bending and contact stresses of a HCR pinion are lower than those of an involute one. Moreover, the contact ratio increases with input torque.

Calculating the Load Distribution and Contact Stress of the Disposable Harmonic Drive under Full Load

Mechanical equipment that will not be reused is defined as disposable machinery. Disposable harmonic drives (HDs) are commonly used in the field of aerospace and are sensitive to payloads. Reasonable calculation of the gear strength is essential for structural design. A method of calculating the contact characteristics of HDs under full load by combining a surface contact model with a three-dimensional finite element model (FEM) is proposed in this work. The mathematical model was established for calculating the no-load backlash of conventional and disposable harmonic gears after assembly. Afterward, the tooth load distribution and surface contact stress were determined using the Hertz contact theory. Finally, ABAQUS software was used to establish the FEM of the disposable HD, and the results were compared with those obtained from the theoretical model. The results revealed that the disposable harmonic gear can realize short-term transmission under full load.

Optimization of Topological Modification Parameters for Heavy-Duty Helical Gears

To improve the meshing state of gear pairs, the abrasion of tooth surfaces must be reduced and on the other hand, the functional requirement of transmission stability for different conditions of heavy-duty helical gears must be increased. To do this requires a topological modification of the tooth profile and tooth alignment. The topological modification parameter optimization model is established based on Hertz theory, which takes the functional requirement as a goal, and the tooth surface topological modification parameters as the design variables. The constraint condition equations in the tooth contact analysis process are derived, and the improved genetic algorithm is used to solve the numerical conditions of the tooth surface microgeometry parameter optimization model. Then, the modification parameters optimized by different modification schemes are obtained. The loaded transmission errors, the mesh misalignment movements, and the distribution characteristics of the tooth surface contact stress are studied. The parameter optimization model of the tooth surface topological modification for the functional requirements is established. With different modification parameters heavy-duty helical gear pairs under various loads, the research results provide a theoretical basis for tooth surface micro design of heavy-duty helical gears in practical application and in determining the reasonable modification parameters.

Analysis of Tooth Surface Contact Stress of Involute Spur Gear

Through the establishment of a pair of spur gear contact models, based on Hertz contact theory, the tooth surface contact stress is calculated; then the Ansys finite element analysis software is used to simulate and analyse the stress distribution. Through the analysis and comparison of the two results, it is proved that the contact stress calculated by Hertz theory is relatively small, which is close to the results of the finite element simulation analysis. Theoretical calculation can verify the accuracy of the finite element simulation analysis model, and the finite element simulation analysis provides an effective way to accurately calculate the contact stress of the tooth surface.

Analysis and Optimization of Tooth Surface Contact Stress of Gears with Tooth Profile Deviations, Meshing Errors and Lead Crowning Modifications Based on Finite Element Method and Taguchi Method

Based on the three-dimensional (3D) finite element method (FEM) and Taguchi method (TM), this paper analyzes the tooth surface contact stress (TSCS) of spur gears with three different influence factors: tooth profile deviations (TPD), meshing errors (ME) and lead crowning modifications (LCM), especially researching and analyzing the interactions between TPD, ME and LCM and their degree of influence on the TSCS. In this paper, firstly, a 3D FEM model of one pair of engaged teeth is modeled and the mesh of the contact area is refined by FEM software. In the model, the refined area mesh and the non-refined area mesh are connected by multi-point constraint (MPC); at the same time, in order to save the time of the FEM solution on the premise of ensuring the solution’s accuracy, the reasonable size of the refined area is studied and confirmed. Secondly, the TSCS analyses of gears with one single influence factor (other factors are all ideal) are carried out. By inputting the values of different levels of one single factor into the FEM model, especially using the real measurement data of TPD, and conducting the TSCS analysis under different torques, the influence degree of one single factor on TSCS is discussed by comparing the ideal model, and it is found that when the influence factors exist alone, each factor has a great influence on the TSCS. Finally, through TM, an orthogonal test is designed for the three influence factors. According to the test results, the interactions between the influence factors and the influence degree of the factors on the TSCS are analyzed when the three factors exist on the gear at the same time, and it is found that the TPD has the greatest influence on the TSCS, followed by the lead crowning modified quantity. The ME is relatively much small, and there is obvious interaction between ME and LCM. In addition, the optimal combination of factor levels is determined, and compared with the original combination of a gear factory, we see that the contact fatigue performance of the gear with the optimal combination is much better. The research of this paper has a certain reference significance for the control of TPD, ME and LCM when machining and assembling the gears.

Analytical Calculation of the Tooth Surface Contact Stress of Cylindrical Gear with Variable Hyperbolic Circular-Arc-Tooth-Trace

In order to theoretically research the tooth surface maximum contact stress of a Cylindrical Gear with Variable Hyperbolic Circular-Arc-Tooth-Trace (VH-CATT), the computing formula of maximum contact stress of VH-CATT cylindrical gear is investigated according to Hertz formula in this paper. Insufficient contact fatigue strength will lead to pitting corrosion, plastic deformation of tooth surface and other damages. Therefore, the maximum contact stress of tooth surface must be carried out. The contact stress calculation formula is particularly considering the effect of normal force, total carrying length, synthetical curvature radius, and position angle. The present work establishes analytical solutions to research the effect of different parameters for the contact stress of VH-CATT cylindrical gear incorporating elastic deformation on the tooth surface, and which have shown that the different module, transmission ratio, pressure angle, tooth width, and the cutter head radius have a crucial effect on the contact stress and contact ellipse of VH-CATT cylindrical gear along the tooth width direction. Moreover, a finite element analysis is carried out to verify the correctness of the theoretical computing formula of contact stress of VH-CATT cylindrical gear. By contrast with the theoretical calculated value and the stress value of finite element analysis, its error is very small. It is indicated that the derived formula of contact fatigue strength of VH-CATT cylindrical gear has high accuracy and can accurately reflect the real contact stress value of tooth surface, which is beneficial for research on tooth break reduction, pitting, wear resistance and fatigue life improvement of the VH-CATT cylindrical gear. The study results also have a certain reference value for the design and check calculation of the VH-CATT cylindrical gear.

Analytical calculation of the tooth surface contact stress of spur gear pairs with misalignment errors in multiple degrees of freedom

Misalignment errors (MEs) in multiple degrees of freedom (multi-DOFs) along gear pair axis are unavoidable under actual working conditions. These MEs lead to changes in tooth surface contact stress (TSCS) and make its accurate calculation complicated and difficult. Unlike the traditional methods of obtaining TSCS with MEs in multi-DOFs via experimental tests, finite element methods (FEMs) or coefficient methods following international standards, a new analytical calculation model is proposed in this paper. The profile equation of a gear pair with MEs in multi-DOFs is first established. Then, a new profile equation for meshing pairs of gear and pinion slices with non-standard shapes that are coplanar with the line of action of the meshing force is obtained. On this basis, the correctness of meshing force transmission, as well as the accuracy and speed of calculation, can be guaranteed with the contact analysis of gear pairs. Finally, the magnitude and distribution of the TSCS of a gear pair with MEs in multi-DOFs are obtained. Compared with the results of a FEM model, the new model can accurately and rapidly calculate the TSCS of a gear pair with MEs in multi-DOFs.

Accurate numerical computation of loaded tooth surface contact pressure and stress distributions for spiral bevel gears by considering time-varying meshing characteristics

In order to meet the high strength demand from gear transmission in industrial applications, identification of loaded tooth contact performance using loaded tooth contact analysis (LTCA) has become an increasing important design stage for spiral bevel gears. To distinguish with the conventional simulated loaded tooth contact analysis (SLTCA) applying commercial finite element software, a numerical loaded tooth contact analysis (NLTCA) method is proposed to determine the loaded contact pressure and stress. In particular, focusing on the time-varying meshing characteristics of loaded tooth contact, the loaded contact pressure and stress distributions on both instantaneous and whole contact ellipses of tooth surface are determined by the proposed NLTCA, respectively. First, the universal mathematical tooth surface mode is established by applying machine settings satisfying the universal motion concept (UMC). Moreover, the curvature analysis of the contact points is performed to determine the loaded tooth surface contact pattern as the input for the proposed numerical analytical calculation method. In the identifications of loaded contact pressure and stress, their distributions having the different directions in both the instantaneous contact ellipse and the whole loaded contact pattern are taken into account. Finally, the numerical instances are given to verify the proposed methodology.

An analytical method for calculating the tooth surface contact stress of spur gears with tip relief

Spur gears with tip relief can effectively improve transmission performance, and accurate determination of their tooth surface contact stress (TSCS) can provide guidance for structure optimization and performance evaluation. However, since the tip-relieved gear profile has not been accurately approximated with a quadratic parabola, the TSCS cannot be calculated using the cylindrical contact model of the Hertzian contact theory (Hertz model). Therefore, a new more accurate analytical model for calculating the non-Hertzian TSCS of tip-relieved gears is proposed in this paper. This model is established based on the accurate tooth profile equations represented by the parameter equations (new model). The solution of the model with an implicit function and a singular integral is also studied. Finally, the TSCS of two gear pairs with and without tip relief are compared for different parameters under different loads according to the new model, the finite element method (FEM model) and Hertz model. The results show that the tip relief will affect the maximum TSCS, location and size of the contact area, whereas the Hertz model cannot quantify these effects. However, the new model, which is validated using the FEM model, can provide accurate and reliable results.

Study on the Influence of Gear Rattling on Pitting Fatigue Failure

The pitting fatigue failure is one of the main gear failure modes, and it has extremely important significance in studying on the influence of dynamic characteristics on pitting fatigue failure. The article has set up increasing-speed test-bed, using photoelectric encoder and NI DAS to measure and collect rotational-speed pulse of driving wheel and driven wheel. Arc-length difference and rotational-speed difference of driving wheel and driven wheel are analyzed to verify gear rattling phenomenon under increasing-speed transmission. And then gear surfaces under certain cycles are observed and analyzed utilizing surface mapping microscope to explore the influence of gear rattling on pitting fatigue failure under increasing-speed transmission. It is shown that there is rotational-speed difference between driving wheel and driven wheel, which indicates that gear rattling phenomenon appears in the meshing process, or more precisely, gear rattling phenomenon appears on both surfaces of the tooth because rotational-speed difference fluctuates bilaterally. In addition, tooth surface contact stress is 221.3Mpa, in theory, if actual contact stress is less than fatigue limit, pitting fatigue failure should not occur. However, through gear surface observation, pitting phenomenon authentically appears with the tendency from micro pitting to destructive pitting. In a word, gear pitting fatigue failure is induced by gear rattling to a certain extent.

Thermal-Mechanical Coupling Analysis of Power Spilt Device Gear Train

Power Spilt Device (PSD) is the key power component of Hybrid Electric Vehicle (HEV). It is very important to simulate and analyze the temperature field and stress field of PSD gear train. The thermal-mechanical coupling analysis is difficult, as it involves the interaction between temperature field and stress field. This paper presents the process of the thermal-mechanical coupling simulation in ABAQUS, and tooth surface temperature and contact stress are obtained and analyzed.

Finite Element Analysis for Gear Contact Based on UG and ABAQUS

According to the cutting theory of involute tooth profile, established an exact three-dimensional parametric model by UG. Used ABAQUS to crate finite element model for gear meshing. After simulated the meshing process, discussed the periodicity of the tooth surface contact stress. Based on the result of finite element analysis, made a comparison of the maximum contact stress between finite element solution and Hertz theoretical solution, analyzed the contact stress distribution on tooth width, and researched the effect of friction factor on contact stress. All that provided some theoretical basis for gear contact strength design.

Precise modeling of arc tooth face-gear with transition curve

A fabrication method is adopted for which an imaginary gear simultaneously realizes conjugated meshing with an arc tooth cylindrical gear and an arc tooth face-gear. The cutter fillet and tooth crest edge form the tooth root fillet of the gear, and the linear tooth surface equation of the imaginary gear and the position vector of the curvature center of the cutter fillet are constructed with certain cutter inclination to deduce a working arc tooth surface equation. The tooth root fillet equation of the arc tooth face-gear is derived from the meshing geometry and kinematics. A numerically controlled machining model of the arc tooth face-gear is established through the transformation of adjustment parameters from the cutter-tilt milling machine to a common multi-axis NC machine. Motion parameters of each movement axis of the NC machine are acquired. A processing example is presented to verify the precision of the fabrication method in processing the arc tooth face-gear. The method provides a theoretical and tentative basis for the analysis of tooth surface contact stress, tooth root bending stress and dynamics. A hobbing test is conducted to demonstrate the good meshing condition of the arc tooth face-gear pair.

Analysis of Helicopter Main Reducer Planetary Gear Contact Strength

Theoretical method and the finite element method for a helicopter main reduction gear of the planetary gear train are done this article. The contrast drawn: the reliability and accuracy of the finite element simulation method used in the calculation of tooth surface contact stress. Provides an effective approach for accurate analysis of helicopter main reduction planetary gear contact stress.

Meshing Performance Analysis of New Non-Zero-Positive Modification Spiral Bevel Gear

For non-zero-modification spiral bevel gear, its machining parameters could be designed with big contact ratio by Local Synthesis. This design method could make up the shortage of low coincidence degree resulted by increasing mesh angle in the non-zero-positive transmission designing. Taking an example, according to comparing the new with conventional design simulation results, the max root tensile stress of pinion was reduced by 28.36%, and the max root compressive stress was reduced by 23.31%, and the max tooth surface contact stress was reduced by3.5%, and the root stress of gear was a bit decreased under the same load conditions. The conclusions showed that the pinion bending strength was improved obviously, and new tooth profile design and its machining parameters made gear pair possess higher life and reliability.

Finite Element (FE) Analysis of Meshing Performance of a Theoretical Assembling Symmetrical Bevel Gear Differential

The aim in this paper is to analyze tooth surface contact stress and transmission errors, verify existence of tooth end effect and discuss symmetry of symmetrical bevel gear differential (SBGD), etc. With this aim, a 3D elastic FE model of SBGD is established under the ANSYS software environment and its meshing characteristic is determined. Starting from here, by analyzing stress and circumferential displacement of tooth, the phenomena of stress concentration is acquired; the distribution of tooth surface contact stress is studied; tooth end effect is confirmed; transmission error is assessed. The analysis is ended by assessing the symmetry of SBGD. Research results provide valuable guidelines for the design of SBGD. The developing model method proposed in this paper makes it possible to study other complex gear mechanisms such as planetary gear system.