Contact Analysis Method Research Articles

A novel tooth contact analysis method for conical worm drives: An enhanced ease-off topography-based approach with conforming grid and TE-clearance assessment

This paper focuses on the ease-off based tooth contact analysis (e-TCA) of conical worm gearing with twisted pinion tooth flanks. Existing methods have two significant drawbacks: 1) The calculation of ease-off values employs non-conforming grids, leading to errors, and 2) the determination of contact path boundaries lacks detailed research, resulting in contact patterns that do not reflect variations in the contact ratio. To address the first issue, a conforming discrete grid partitioning method is proposed, which ensures that corresponding nodes lie in the same tangent direction and uses tangent deviation to express ease-off, thereby eliminating errors. To solve the second issue, the TE-clearance formula is introduced, which reflects changes in the contact path length and boundaries under different preset clearance thresholds (PCT), capturing variations in the contact ratio. Additionally, the method for determining the working area has been optimized, making the e-TCA more reliable and enhancing the overall consistency and integrity of the contact curve calculation method. Finally, numerical examples and rolling tests verify the accuracy and advancement of the proposed algorithm, which is expected to replace rolling inspections and finite element analysis.

Robust modification optimization for helical gear mounting errors based on contact ratio

Mounting errors are a disruptive factor in gear utilization. This paper investigates the contribution of mounting error components in helical gears to the helix slope deviation using the involute equations. A model of the helical gear transmission system has been established, by which the impact of mounting errors on the loaded transmission error and contact ratio of the bevel gear transmission was studied using the Loaded Tooth Contact Analysis method. A bench test was then casted as a verification of this model. A methodology was proposed for optimizing the micro modification of helical gear flanks based on contact ratio control. Robust optimization of the mounting error was achieved by reducing the contact ratio under commonly used torques compared to the contact ratio at the local minimum of the loaded peak-to-peak transmission error. This approach has been demonstrated to enhance the robustness of gear transmission against mounting errors and torque fluctuations.

3D dynamic contact analysis of tyre internal deformation using 2D image sensor

Due to the increasing weight of electric vehicles, advanced tyre technology is urgently needed. In particular, there is a need for dynamic contact analysis to determine the energy interaction between tyres and road surfaces. However, the methods developed to date are limited in that they require either numerous contact patches inside the tyre or sensor devices on the ground. In this study, we propose a new method for dynamic tyre-ground contact analysis that overcomes these limitations. By installing a two-dimensional image sensor inside the tyre, deformations can be observed and quantified three-dimensionally during vehicle operation. This method advances tyre engineering through innovative analysis of tyre deformation during operation.

Efficient semi-analytic method for single tooth contact analysis of loaded spiral bevel gears

Accurately and fast calculation of single tooth load contact state of a gear pair is the basis for accurate calculation of multi-tooth load contact analysis. Therefore, this study proposed a semi-analytical quick single tooth load tooth contact analysis (Q-SLTCA) method. First, the ease-off tooth contact analysis (ease-off TCA) method was established, and a numerically stable initial contact stress distribution and contact ellipse analytical model was derived. Then, considering the influence of edge contact, the real-time division method of gear tooth slice was derived. Based on this, the equivalent principle of contact elliptical node and the load correction strategy were innovatively proposed. Then, the calculation method of the meshing characteristics of the tooth slice was established by coupling the boundary element method (BEM) with the equivalent cylindrical Hertz contact theory. The bending deformation, tooth root stress distribution, contact stress, contact deformation and meshing stiffness of the tooth slice were analyzed and calculated, and the instantaneous meshing stiffness of the single tooth was determined by combining the parallel method of the gear tooth stiffness. Finally, a single-tooth finite element method (FEM) meshing model was created for comparison with the method in this study, which verified the calculation accuracy and efficiency of the proposed method. This method can be easily developed into a quick multi-tooth load contact analysis algorithm, which can provide a new method for gear tooth crack and failure analysis.

Numerical modeling and experimental validation of power loss and efficiency in an electric-drive axle system

Power loss and efficiency are pivotal performance metrics significantly impacting the quality of electric-drive axles. This study outlines a numerical method for determining the electric-drive axle system power loss, which includes gear meshing, gear churning, and bearing power losses. Power loss from gear meshing was calculated by analyzing load distribution and friction coefficient. The frictional loaded tooth contact analysis method was employed to ascertain the load distribution during gear meshing. A formula based on a weighting function was utilized to compute the friction coefficient. The finite element method was used to verify the gear load distribution and meshing power loss. Subsequently, empirical formulas were used to calculate the gear churning and bearing power losses. To substantiate the proposed numerical method, an experimental apparatus was employed to measure the power loss and efficiency of an electric-drive axle under various operating conditions. The experimental study demonstrated a strong correlation between the numerical and calculated results. These findings suggest that the proposed method can be an effective tool in predicting the power loss and efficiency of electric-drive axles.

A life-cycle dynamic wear degradation model of planetary gear systems

An accurate prediction model for surface wear in planetary gear systems is essential to decipher wear fault mechanisms and facilitate model-driven failure prognosis. A high-fidelity dynamic wear model relies on the appropriate characterization and updating strategy of the tooth macro-geometry, contact parameters and dynamic load. A geometrically adaptive-loaded tooth contact analysis (GA-LTCA) method is proposed to “bridge” wear morphology and dynamic behaviours. The finite element method and run-to-failure test are adopted to verify the GA-LTCA method and wear prediction model, respectively. Based on the proposed wear model, the life-cycle wear characteristics and the updating strategy of wear geometry are investigated. Owing to the consideration of the micro-cycle of the contact stress and geometrical updating, the predicted wear profile exhibits a desirable agreement with experimental results. The tooth profile deviation vector should be updated more frequently than the finite element model of worn gears. Only the finite element grid of the sun-planet gear pair should be updated because the wear of the sun-planet is much more serious than that of the ring-planet. Numerical results indicate the potential of the proposed high-fidelity model for digital twin-based wear prediction and life cycle failure prognosis.

Wear characteristics analysis of variable hyperbolic circular-arc-tooth-trace cylindrical gear transmission considering assembly error theory

Wear is the main failure form of the gear transmission interface, runs through the whole life cycle of gear service, and the distributed error of the tooth surface due to the introduced assembly error will make the actual meshing state of the tooth surface different from the ideal meshing state, thus affecting the tooth surface wear trajectory and state. Therefore, considering the coupling relationship between assembly error and tooth surface contact analysis, the variation laws of the wear amount of the gear transmission interface of the variable hyperbolic circular-arc-tooth-trace cylindrical gear were studied under the consideration of assembly error in this article. Based on the tooth surface contact analysis method and Hertz contact theory, the transient linear load, the combined radius of curvature, the length axis and short axis of the contact ellipse, and the instantaneous sliding velocity were calculated. Through revising the calculation method of adhesive wear of variable hyperbolic circular-arc-tooth-trace cylindrical gears, the correlations between the tooth surface wear amount and gear parameters of variable hyperbolic circular-arc-tooth-trace cylindrical gears under different assembly errors were analyzed. The results show that the maximum wear occurs at the root of the tooth, and the wear at the indexing circle approaches zero, whether it is standard installation or non-standard installation. The vertical axial error and horizontal axial error have little effect on the wear, while the center distance error will aggravate the wear. The proposed method comprehensively considers the influence of assembly error and gear parameters on tooth surface wear, and this method can provide a theoretical reference for the design and analysis of anti-wear, wear reduction, and life extension of variable hyperbolic circular-arc-tooth-trace cylindrical gear tooth surface.

A multi-perspective method for gear efficiency and contact analysis

Modern gearing applications, in particular electrification, impose new challenges in many different fields of engineering and research. In specific, new demands are imposed on gears, including higher rotational speed, lower noise acceptance, and increased efficiency, as well as increased resistance against pitting and scuffing. To meet these demands, a better understanding of gear contacts is needed. The Eurostars project Effigears proposes a novel multi-perspective methodology for assessment of gear efficiency and contact analysis. The methodology consists of using a novel surface treatment method, Triboconditioning®, implemented in a streamfinishing process, surface measurements using a scattered light method, experimental testing using the standardized FZG test rig, and contact simulations using a novel thermal elasto-hydrodynamic lubrication tool. It is found, in preliminary tests, that enhanced gear performance may be enhanced due to Triboconditioning® surface treatment. Findings also include better understanding of how surface characteristics and lubricants affect scuffing and pitting, and the effect of load distribution on gearset behavior.

Normal contact stress analysis of large-deflection compliant mechanisms using a CPRBM-based method

The contact interaction between compliant mechanisms and external objects is a common occurrence in the field of grasping and manipulation. However, accurately modeling the large deformation and contact force/stress remains a challenging task. This paper presents a contact analysis method to evaluate the deformation and normal contact force/stress of compliant mechanisms with general-shape beams. The general beams are modeled by using the chained pseudo-rigid-body model (CPRBM). On basis of CPRBM framework, linear and distributed contact springs are introduced at the interface to represent the contact force. A numerical method is established to fast calculate the boundary penetrations, and a contact stiffness formulation is proposed based on the theory of elasticity. Then, the effect of contact interaction can be evaluated by the contact potential energy of contact springs, which is part of the system’s total potential energy. By minimizing the potential energy function of the compliant system, the static equilibrium configuration and contact force/stress can be obtained easily. Numerical examples are used to verify the feasibility and accuracy of the proposed method.

Sustainability-oriented dry cutting tool collaborative optimization model for face-hobbing hypoid gears

Dry cutting as an important sustainability manufacturing technology is enhancing ever-higher levels of hypoid gear production. To improve economic and environmental attributes of sustainability manufacturing, a new data-driven dry cutting tool collaborative optimization model considering both geometric accuracy and loaded contact performances is established for face-hobbing hypoid gears. Where, an innovative ease-off tooth contact analysis (e-TCA) method is proposed to establish accurate relations between ease-off flank and loaded contact performance evaluations. Then, for the initial design flank from arc-shaped tool, Top-Rem tool modification is applied to establish the collaborative optimization model. By fine-modifying the ease-off flank relating to Top-Rem tool parameters, the current design flank can get an adaptive approximation to the target flank requiring the loaded contact performance evaluations. Moreover, in addition to the accuracy and efficiency of dry cutting at its own, the cutting gear number of per hour, cutting gear number of per tool and cutting power consumption are used the main assessment items on sustainability. The numerical and experimental examples are provided to verify that the proposed tool collaborative optimization model will significantly improve sustainability in terms of economic and environmental assessments.

Vibration characteristics analysis of flexible helical gear system with multi-tooth spalling fault: Simulation and experimental study

Gear systems operating at high speeds and under heavy loads are susceptible to continuous multiple tooth surface spalling. The time-varying meshing stiffness (TVMS) model of helical gear pair with multi-tooth spalling fault is established by combining image recognition method and loaded tooth contact analysis (LTCA) method to target the actual form of the spalling fault, and its effectiveness was verified through finite element method (FEM). The flexible helical gear dynamic model is established by utilizing 8-node shell model and Timoshenko beam model to simulate the gear foundations and shafts, the TVMS in multi-tooth spalling fault condition is introduced as the excitation. The mapping relationship between the meshing process, TVMS and vibration response under the influence of rotational speed, spalling surface morphology scale, spalling depth and location of spalling occurrence is analyzed by combining simulation and experimental results. As the rotational speed increases, the specific meshing frequency coincides with the natural frequency of the gear system, leading to the phenomenon of superharmonic resonance. Continuous multi-tooth spalling fault results in continuous time-domain shocks and the meshing frequency modulation of the rotational frequency of the gear with spalling fault. In the absence of bottoming out, the increase in spalling surface morphology scale exerts a more pronounced influence on the vibration characteristics of the helical gear system compared to the increase in spalling depth. The research results can provide theoretical basis for gear system fault diagnosis.

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.

Design and Analysis of a Novel Actuator with a Double-Roller Gear Drive

In recent years, with the development of robot transmission technology, the market demand for high-performance actuators, which can be applied to lower limb exoskeleton assist robots, is increasing. These robots help achieve human–robot interaction through rigid and flexible coupling, and they can ensure the flexibility of the elderly or patients in daily walking and rehabilitation training. A novel actuator with a double-roller gear drive structure is proposed with high bearing capability and high transmission efficiency due to multi-tooth rolling contact with small tooth difference such that friction is greatly reduced in the transmission process compared to what occurs in involute planetary transmission. The bearing capacity of the tooth surface was analyzed by using the loaded contact analysis method. Finally, a prototype was manufactured with the 3D printer, and the maximum output torque of the developed actuator was tested with an experimental setup. The results show that this novel actuator, with its double-roller gear drive, has huge potential for use in the hip joint of an exoskeleton robot.

A New Fast Calculating Method for Meshing Stiffness of Faulty Gears Based on Loaded Tooth Contact Analysis

Gear transmission systems are widely used in various fields. The occurrence of gear cracks, tooth pitting, and other faults will lead to the dynamic characteristics deterioration of the transmission system. In order to calculate the meshing stiffness of faulty gear pairs more effectively and precisely, this article improves the loaded tooth contact analysis (LTCA) method by analyzing the influence of different fault types on gear deformation, including bending-shearing deformation and contact deformation, which combines the accuracy of the finite element method (FEM) and the rapidity of the analytical method (AM). The improved LTCA method can model the fault areas accurately and optimize the deformation coordination equation under the actual meshing situation of the faulty gear tooth, making it suitable for calculating the meshing stiffness of faulty gears. Based on the calculation results of the finite element method, the accuracy of the improved meshing stiffness calculation method has been verified, and the sensitivity of different fault type parameters on meshing stiffness has been studied.

Semi-analytical loaded tooth contact analysis method for spiral bevel gears

Loaded tooth contact analysis (LTCA) is an important tool for analyzing the meshing of spiral bevel gears. This paper presents a semi-analytical LTCA method, where the analytical formulas are used to calculate the tooth deformation and contact force, with partial coefficients corrected by finite element analysis (FEA) results. Based on Tredgold's Approximation, the tooth is sliced, of which the flank is determined by simulating the manufacturing process. In order to calculated the potential contact curves of a real gear pair, an optimization model is established to find the points more likely to be in contact within the range of contact curves obtained by the help of roll angle surfaces. The compliance of tooth is modeled as a combination of two contributions, where the deformation of cantilever beam under load is used to determine the global deformation, and the local contact deformation is obtained by Hertz line contact assumption. A contact judgement strategy is proposed to detect the contact of the slices at ends of contact curves, and the correction coefficients are introduced in the tooth deformation to consider the coupling effect among slices. In the end, a numerical instance of LTCA under different load torques is provided, which demonstrates the accuracy and efficiency of the presented LTCA method by comparisons with results of FEA. This method can be easily modified to analyze other gear pairs and has the ability to be extended to simulate the gears with local defects or cracks.

A fully nonlinear three-dimensional dynamic frictional contact analysis method under large deformation with the area regularization

A fully nonlinear three-dimensional dynamic frictional contact analysis method under large deformation with the area regularization

A cell-based smoothed finite element method for multi-body contact analysis within the bi-potential formulation

This paper presents a cell-based smoothed finite element method (CS-FEM) for solving contact problems within the bi-potential formulation. The frictional contact and large deformation are modeled based on the CS-FEM. This method performs based on the generalized smoothed Galerkin weak-form which requires only value of shape functions. Because no isoparametric mapping is needed, the CS-FEM has an advantage when dealing with problems with large deformation which may cause mesh distortion. The contact forces and the relative velocity establish an implicit relationship within the bi-potential formulation in which no user-defined parameter is introduced. Numerical examples show the contact between elastic and hyperelastic bodies calculated by CS-FEM models with different smoothing domains. Compared with FEM, the CS-FEM produces robust and more accurate solutions.

Loaded contact pressure distribution prediction for spiral bevel gear

Contact pressure and load distribution are key indices used in the performance evaluation of spiral bevel gears, and their calculation accuracy and efficiency continue to be the focus of active research. An accurate and efficient numerical approach for predicting the contact pressure and load distribution of a spiral bevel gear is presented based on multi-tooth deformation compatibility. First, an improved discrete tooth surface contact analysis (DTCA) method is developed to obtain the contact characteristics of the gear set under the no-load condition. This method is a geometric approach that avoids numerical instability. A local triangular mesh refinement algorithm is proposed to improve the accuracy and efficiency of the DTCA method. Subsequently, the deformation compatibility relationships of a spiral bevel gear set are derived for single-tooth and multi-tooth meshing. By combining the deformation compatibility relationship and the influence coefficient method, a multi-tooth loaded contact analysis (MLTCA) model of the spiral bevel gear set is established. Moreover, an iterative algorithm based on the conjugate gradient and fast Fourier transform method is proposed to determine the mesh force and contact pressure distribution. Finally, the proposed method is tested using numerical examples to demonstrate its accuracy and efficiency by comparison with finite element simulations and experiment results.

A novel method for longitudinal modification and tooth contact analysis of non-circular cylindrical gears

A novel method for longitudinal modification and tooth contact analysis of non-circular cylindrical gears

Optimal tool path generation and cutter geometry design for five-axis CNC flank milling of spiral bevel gears

Abstract Computer numerical control milling provides greater flexibility and universality for machining complex gears compared to dedicated gear manufacturing. A critical challenge in popularizing the use of five-axis flank milling to spiral bevel gears is to achieve acceptable machining accuracy that ensures the meshing performance of the finished gears. Previous studies, which used approaches such as gear design modification, using multiple tool paths, and end milling, failed to resolve this issue. Thus, this paper proposes a computational scheme to improve the machining accuracy of five-axis flank milling of spiral bevel gears by optimizing the tool path and cutter geometry. The scheme minimizes the geometric deviations between the machined surface and original design using heuristics and optimization algorithms. A simplified tooth contact analysis method was developed to quantitatively evaluate the contact path of the meshing gears. The simulation results of real gears show that the proposed scheme outperforms previous methods in reducing machining errors and further enhance the meshing performance by optimizing the design of form cutters. This work developed an effective approach for flexible and low-cost manufacturing of complex gears.