Contact Path Research Articles

Tensor based approach for tooth contact analysis of planar and spatial gearing contact

This paper presents a new method for analyzing gear tooth contact, leveraging tensor notation and discrete differential geometry. Existing analytical and numerical methods often face challenges in convergence and computational efficiency. Our proposed approach involves defining a novel tensor notation and applying it to the gear tooth contact kinematics problem. By discretizing the tooth surfaces and using tensor operations, we can accurately determine the kinematics, path of contact, and transmission error of the gear pair. To validate our approach, we compared its results with those obtained from commercial software, KISSsoft and KiMOS. The results demonstrated high accuracy, with mean absolute errors below 0.08 for specific sliding, 0.003 for sliding factor, and 0.1μm for transmission error. Furthermore, we applied our method to analyze non-involute gear types, such as S-gears, pin gearing and cosine gears. Our findings revealed the kinematic performance and contact characteristics of these gear types, providing valuable insights for gear design and optimization. In conclusion, the proposed tensor-based approach offers a promising alternative for gear tooth contact analysis, providing accurate and efficient results for a wide range of gear types.

Modelling Method and Meshing Characteristics of a Novel Curve-Surface Conjugate Internal Gear Drive

Space exploration has become a major focus in the field of technology, with gear transmissions in aerospace equipment playing a crucial role. In the extreme environment of space, gear transmissions face challenges like large temperature differentials, deformation and maintenance difficulties, which will severely impact transmission accuracy and service life. To meet the growing demands for high-performance gear transmissions with high transmission efficiency and error adaptability in the aerospace field, this paper proposes a novel curve-surface conjugate internal gear drive consisting of an involute internal gear and a curve-surface gear. The fundamental theory of curve-surface conjugation is introduced, and the construction method for curve-surface gear based on a selected contact path and meshing tube is presented. The analysis models including induced curvature, sliding ratio and tooth contact analysis with errors (ETCA) are simulated to evaluate the meshing characteristics. Additionally, prototypes are manufactured and experimental setups are established to validate the transmission performance. These results indicate that as the rotational speed increases, the transmission efficiency of the curve-surface conjugate internal gear drive improves, which is contrary to the trend observed in involute gear drives. And the transmission efficiency of the curve-surface conjugate internal gear drive surpasses that of the involute gear drive at higher rotational speeds. Moreover, this novel gear drive exhibits excellent error adaptability, maintaining intact contact paths and high transmission efficiency even in the presence of assembly errors. This study provides new ideas for the design and manufacture of high-performance gear transmissions from the perspective of spatial geometric elements.

Influence of Different Filler Systems on the Thermal Conductivity and Mechanical Properties of Thermosets.

The changing demands in terms of the compactness and performance of electronic devices increase the role of thermal management within this application field. Because polymers and especially thermosets have a low thermal conductivity, filler systems have to be used to improve their performance and make thermosets suitable for applications. So far, several factors influencing thermal conductivity have been defined; however, the combined investigation of mechanical properties as another important value in terms of applications has not been realized. Therefore, this paper analyzes thermal conductivity based on the orientation of fillers and a contact path as well as mechanical properties in different material systems. In addition to the matrix material, the filler type and grade and the geometry and size were varied. It was shown that boron nitride provides the best values in terms of thermal conductivity after orientation along the flow path is realized. An aluminum silicate was defined as the best filler system in terms of mechanical properties. However, the boron nitride was found to reveal the greatest potential in terms of applications, since the mechanical properties are likely to be increased by the usage of finishing additives such as silane.

Tangle- and contact-free path planning for a tethered mobile robot using deep reinforcement learning.

This paper presents a tangle- and contact-free path planning (TCFPP) for a mobile robot attached to a base station with a finite-length cable. This type of robot, called a tethered mobile robot, can endure long-time exploration with a continuous power supply and stable communication via its cable. However, the robot faces potential hazards that endanger its operation such as cable snagging on and cable entanglement with obstacles and the robot. To address these challenges, our approach incorporates homotopy-aware path planning into deep reinforcement learning. The proposed reward design in the learning problem penalizes the cable-obstacle and cable-robot contacts and encourages the robot to follow the homotopy-aware path toward a goal. We consider two distinct scenarios for the initial cable configuration: 1) the robot pulls the cable sequentially from the base while heading for the goal, and 2) the robot moves to the goal starting from a state where the cable has already been partially deployed. The proposed method is compared with naive approaches in terms of contact avoidance and path similarity. Simulation results revealed that the robot can successfully find a contact-minimized path under the guidance of the reference path in both scenarios.

Limit theorems of occupation times of normalized binary contact path processes on lattices

Abstract The binary contact path process (BCPP) introduced in Griffeath (1983) describes the spread of an epidemic on a graph and is an auxiliary model in the study of improving upper bounds of the critical value of the contact process. In this paper, we are concerned with limit theorems of the occupation time of a normalized version of the BCPP (NBCPP) on a lattice. We first show that the law of large numbers of the occupation time process is driven by the identity function when the dimension of the lattice is at least 3 and the infection rate of the model is sufficiently large conditioned on the initial state of the NBCPP being distributed with a particular invariant distribution. Then we show that the centered occupation time process of the NBCPP converges in finite-dimensional distributions to a Brownian motion when the dimension of the lattice and the infection rate of the model are sufficiently large and the initial state of the NBCPP is distributed with the aforementioned invariant distribution.

Computerised design, simulation of meshing and stress analysis of bionic logarithmic spiral spur gear drives

Inspired by the inherent properties of logarithmic spiral in nature, a new cylindrical spur gear drives using logarithmic spiral as a gear tooth profile is proposed. The logarithmic spiral property is explored, and then the equation of meshing, conjugate tooth profile and contact path of the proposed gear pairs are derived. The meshing characteristics of the new pair are investigated, such as pressure angle, contact ratio and sliding ratio. Simulation analysis of the strength, transmission error and transmission efficiency are used to validate the performance of the gear pairs before production of the proposed gear, followed by gluing load capacity and bending fatigue strength testing of the fabricated gear pairs. The results show that the pressure angle at any point of the tooth profile on the proposed gear is constant and equal to the logarithmic spiral strike angle. The contact ratio of the gear decreases with the increase of the strike angle. Compared with that of involute gears, logarithmic spiral gears have better performance in terms of strength, transmission error, transmission efficiency and lifetime.

Optimization of machine tool settings for Spirac hypoid gears by controlling symmetry of contact paths

A novel optimization method to control the symmetry of contact paths on the concave and convex tooth surfaces of the gear then improves the meshing quality was proposed. By modifying the angular setting of the head cutter when cutting the pinion, the direction angles of the two contact paths are equated to estimate their symmetry. The relation between the direction angles is formulated precisely, the influence of the angular setting on the contact paths is investigated, and the equations for obtaining the values of the machine tool settings are derived. The proposed method is applied to a numerical example of a Spirac hypoid gear pair, and the results reveal that the contact paths on the concave and convex tooth surfaces are approximately symmetrical and the transmission errors of both sides are comparable.

Collision-free Tool Motion Planning for 5-Axis CNC Machining with Toroidal Cutters

Collision detection is a crucial part of CNC machining, however, many state-of-the-art algorithms test collisions as a post-process, after the path-planning stage, or use conservative approaches that result in low machining accuracy in the neighborhood of the cutter’s contact paths. We propose a fast collision detection test that does not require a costly construction of the configuration space nor high-resolution sampling of the cutter’s axis and uses the information of the neighboring points to efficiently prune away points of the axis that cannot cause collisions. The proposed collision detection test is incorporated directly as a part of the tool motion-planning stage, enabling design of highly-accurate motions of a toroidal cutting tool along free-form geometries. We validate our algorithm on a variety of benchmark surfaces, showing that our results provide high-quality approximations with provably non-colliding motions.

Linear complementarity formulations for contact analysis and wear prediction in gears

This work presents linear complementarity based formulations for contact analysis and wear prediction in gear trains. Assuming steady motion of gears transmitting constant input torque without transmission errors, three sets of linear complementarity formulations are proposed, first for rigid gear teeth, second for gear teeth with skin compliance, and third for gear teeth with full compliance, the last two being new in linear complementarity literature. The developed formulations are used for contact analysis of two examples of gear trains, a pair of spur gears in mesh, and a planetary gear train. The accuracy of the method is tested by considering various time step sizes and stability of the formulations demonstrated for wide range of time steps. Contact forces between meshing teeth are calculated at a pre-defined set of points on the path of contact, and then wear is calculated on gear tooth flank using Archard’s wear equation. These wear calculations are compared with existing results in literature which demonstrate the applicability of the developed LC formulations. Future work is projected to include more state-of-art friction models and extension to 3D contact analysis in helical gear trains.

Modeling and analysis of elastohydrodynamic lubrication of orthogonal face gear with installation errors

Installation error is one of the most prominent factors affecting the lubrication of face gear. To analyze the lubrication performance of the face gear with installation errors, the installation error model of the orthogonal face gear transmission system is established. Then, the contact path, equivalent curvature radius, load distribution and entrainment velocity are studied using the face gear loaded tooth contact analysis (LTCA). On this basis, the lubrication governing equations of the face gear are established according to the elastohydrodynamic lubrication (EHL) theory. In addition, the oil film thickness, oil film pressure and coefficient of friction in the process of face gear drives are calculated using the method of progressive mesh densification (PMD). Finally, the effects of axis intersection angle error, axis intersection error and axial displacement error on lubrication characteristics are analyzed. The results reveal that when the axial intersection angle error and axial displacement error are negative and the axial intersection error is positive, the minimum oil film thickness of the face gear tooth surface is less than that without error. When the error values are the same, the minimum oil film thickness and coefficient of friction have larger changes with the axial displacement error than with the axis intersection error, and the contact path has a bigger movement range.

Process Optimization of Robotic Grinding to Guarantee Material Removal Accuracy and Surface Quality Simultaneously

Abstract Simultaneously guaranteeing material removal accuracy and surface quality of robotic grinding is crucial. However, existing studies of robotic grinding process optimization have mainly focused on a single indicator that solely considers contour error or surface roughness, while studies that simultaneously investigate the impact of contact force, spindle speed, feed rate, inclination angle, and path space on the material removal profile (MRP) and the surface roughness are lacking. This paper proposes a hybrid optimization method that considers dimensional accuracy and surface quality constraints. First, an MRP model that considers the coupling influence of the contact force, spindle speed, feed rate, and inclination angle is presented. Then, a surface roughness model that considers the inclination angle is established. Finally, the contact force, feed rate, inclination angle, and path space are simultaneously optimized to satisfy the hybrid constraints of MRP accuracy and surface roughness. The proposed method ensures maximum grinding efficiency while satisfying dimensional accuracy and surface quality constraints. The proposed method is verified on an industrial robotics grinding system with a pneumatic force-controlled actuator. The results show that the proposed method has higher profile accuracy and lower surface roughness than traditional methods.

Theoretical and experimental research on tooth root bending stress of face gear

A tooth root bending stress analysis method is proposed to study the tooth surface load distribution and tooth root bending stress during the meshing process of orthogonal face gear. Firstly, the tooth surface equation, transition surface equation and tooth width constraints are derived. Then, Through the tooth contact analysis (TCA), the contact path and spots of the face gear pair are obtained. What’s more, the proposed method based on Load tooth contact analysis (LTCA) is utilized to calculate the tooth surface load distribution and root bending stress of the face gear along the mesh cycle and compared with the finite element method. Meanwhile, root bending stress tests were carried out to verify the proposed method. The comparisons indicate that the proposed method has higher computational efficiency compared with the finite element method (e.g. the finite element method takes about 5 h for a mesh cycle and the proposed method costs 40 s). The results show that the tooth surface load distribution and root bending stress of the proposed method are consistent with those obtained by the finite element method and gear root stress experiment.

Improved joint function when reaching behind the back is associated with patient reported outcomes in individuals with rotator cuff tears following exercise therapy

BackgroundReaching behind the back is painful for individuals with rotator cuff tears. The objectives of the study were to determine changes in glenohumeral kinematics when reaching behind the back, passive range of motion (RoM), patient reported outcomes and the relationships between kinematics and patient reported outcomes following exercise therapy. MethodsEighty-four individuals with symptomatic isolated supraspinatus tears were recruited for this prospective observational study. Glenohumeral kinematics were measured using biplane radiography during a reaching behind the back movement. Passive glenohumeral internal rotation and patient reported outcome measures were collected. Depending on data normality, appropriate tests were utilized to determine changes in variables. Spearman's correlations were utilized for associations, and Stuart-Maxwell tests for changes in distributions. FindingsMaximum active glenohumeral internal rotation increased by 3.2° (P = 0.001), contact path length decreased by 5.5% glenoid size (P = 0.022), passive glenohumeral internal rotation RoM increased by 4.9° (P = 0.001), and Western Ontario Rotator Cuff Index and American Shoulder and Elbow Surgeons scores increased by 29.8 and 21.1 (P = 0.001), respectively. Changes in Western Ontario Rotator Cuff Index scores positively associated with changes in maximum active glenohumeral internal rotation and negatively associated with changes in contact path lengths (P = 0.008 and P = 0.006, respectively). InterpretationThe reaching behind the back movement was useful in elucidating in-vivo mechanistic changes associated with patient reported outcomes. Glenohumeral joint function and patient reported outcomes improved, where changes in Western Ontario Rotator Cuff Index scores were associated with kinematics. These findings inform clinicians of functional changes following exercise therapy and new targetable treatment factors.

Multi-Point Control for Face-Milled Spiral Bevel Gears with a Predesigned Fourth-Order Motion Curve

This paper presents an ultimate motion methodology of a face-milling spiral bevel gear pair to synthesize the mating tooth surfaces with a predesigned fourth-order motion curve. The methodology is to control some contact points along the contact path in the process of tooth contact analysis via application of an extended local synthesis which permits some transmission errors rather than zero at the concerned contact point. The modified offset motion correction is selected to demonstrate the proposed methodology. Applied torque corresponding to an elastic approach of 0.00635 mm at the mean contact point is calculated and the loaded tooth contact analysis is performed. Numerical results show that the extended local synthesis can effectively control the transmission errors on the predesigned fourth-order motion curve at arbitrarily predesigned contact points along the contact path of the spiral bevel gear pair. The tooth contact pattern for the actual tooth pair is scattered into three segments since the rotational motion of the driven gear at any instant angular position is dependent on the tooth pair with the least transmission error among the three adjacent tooth pairs. The actual tooth contact patterns of the spiral bevel gear pair become continuous when meshing tooth surfaces are elastically deformed.

MATHEMATICAL MODEL AND OPTIMIZATION ALGORITHM ACCORDING TO THE CRITERIA OF MINIMUM CONTACT STRESS FOR GEARS WITH CONVEX-CONCAVE CONTACT

Reducing the mass and dimensions of gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with a convex-concave contact of the teeth. The study is devoted to the development of mathematical model and algorithm for the optimal design of cylindrical gears with convex-concave contact of the working surfaces. Optimality criteria: minimum contact stresses taking into account design, geometrical and technological constraints. An objective function is constructed for the case of minimizing contact stresses: contact stresses σH in the mesh must take the minimum possible value when all constraints are met. Variables planning are defined. These are pressure angle at the pole αС, the curvature radius at the upper part of contact path rkh, and the curvature radius at the lower part of contact path rkd. A method for solving the problem of optimal design is chosen – probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The algorithm for optimal design of gear has been developed. They take into account the constructive, technical and technological features. They also allow to reduce the error of the calculations due to the error-control of the calculations. The main stages of the algorithm are as follows: setting input data (numerical constraints on design variables, gear parameters and its load); generation of LPτ-sequence for variables planning with simultaneous consideration of their numerical constraints; checking of functional constraints; additional verification calculations (if necessary) of the gearing contact strength; formation of an array of possible solutions; searching of the best solution variant (the test point corresponding to the minimum value of the objective function) by sorting the array. Keywords: gear, convex-concave contact, optimization, objective function, variables planning, algorithm

Analysis of contact creep behaviour of nanofilled composites

An effective modelling method for analysing the contact creep behaviour of composite materials with different nanofillers was proposed. Considering both the contact and creep material nonlinearities, an augmented Lagrangian algorithm was used to treat the unilateral contact constraints, and a time-hardening creep constitutive equation was adopted to describe the deformation characteristics of the nanocomposites. The constitutive parameters were extracted through a series of linear fittings based on the multiaxial creep theory and creep test curves, and the accuracy of the constitutive equation was validated. The applications of the proposed modelling method were demonstrated using a rope-wheel contact system (RWCS), in which the wheels were made of polystyrene (PS) with carbon black (CB), multi-walled carbon nanotubes (MWCNT), or chemically reduced graphene oxide (CRGO). The results indicated that the addition of nanofillers significantly reduced the creep deformation of the contact zone. The CRGO exhibited a better anti-creep performance than that of CB and MWCNT. Compared with pure PS, the maximum deformation on the contact path of the nanocomposite wheel with 5.0 wt% CRGO sheets at 1500 s and 104 s was reduced by approximately 22 % and 52 %, respectively. The coefficient of friction μ had a strong influence on the contact creep deformation when μ < 0.3. Additionally, the anti-creep capability of the added nanofillers became more evident as the loading time increased. The contact creep deformation of the CRGO composite was less than one-tenth that of the matrix material after 30 d.

A Novel Tooth Modification Methodology for Improving the Load-Bearing Capacity of Non-Orthogonal Helical Face Gears

This study proposes a double-crown tooth surface modification technology that improves the load-carrying capacity of non-orthogonal helical tooth surface gears. The tooth modification is determined by a modified rack-cutter, and its feed motion is related to an intentionally designed transmission error. The novelty of the tooth modification design is that the transmission error can be pre-designed. First, changing the tooth profile of the tool enables preliminary modification along the tooth profile direction; second, by modifying the interaction between the tool and the machined gear, subsequent fine adjustments are made to the contact path. This two-stage tooth modification strategy not only retains the advantages of the traditional method but also significantly improves the balance of the load distribution on the tooth surface through an original contact path modification strategy. Through systematic tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), it was verified that the new method reduces contact stress and tooth root bending stress and improves the gear’s resistance to misalignment errors. This research provides the basis and motivation for further exploring and improving this tooth profile modification technology to solve the challenges faced by more complex gear systems.

Two Contributions to Rolling Contact Fatigue Testing Considering Different Diameters of Rail and Wheel Discs

Scaled rolling contact fatigue tests, used to practically simulate the wear of the wheel and rail material under laboratory conditions, are typically classified into two categories. Tests in the first category use twin-disc stands, while the second group of test rigs use two discs of different diameters considering the rail disc as the larger one. The latter setup is closer to the real situation, but problems can occur with high contact pressures and tractions. The focus of this paper is on two main contributions. Firstly, a case study based on finite element analysis is presented, allowing the optimization of the specimen geometry for high contact pressures. Accumulated plastic deformation caused by cycling is responsible for abrupt lateral deformation, which requires the use of an appropriate cyclic plasticity model in the finite element analysis. In the second part of the study, two laser profilers are used to measure the dimensions of the specimen in real time during the rolling contact fatigue test. The proposed technique allows the changes in the specimen dimensions to be characterized during the test itself, and therefore does not require the test to be interrupted. By using real-time values of the specimen’s dimensional contours, it is possible to calculate an instantaneous value of the slip ratio or the contact path width.

The role of direct contact in forming peace-oriented international relations of a divided country: Focusing on the division of the Korean Peninsula.

The division of the Korean peninsula involved many neighbouring countries in the Korean War. The relations with those countries have since been reorganised due to active exchange. This study examined how the quantity and quality of contact with traditional alliance (US and Japan) and strategic partner (China and Russia) countries affected their national images. To this end, this study analyzed the relation with the national image by measuring the quantity and quality of contact of an individual with each country. The quantity of contact included an evaluation of the individual's subjective amount of contact, contact path, and contact status, and the quality of contact was measured as an evaluation for the pleasure, competitiveness, intimacy, spontaneity, and necessity when contacting each country's culture. A total of 387 participants were divided into two groups based on the presence of direct contact and the quantity and quality of their contact and national images were examined. The participants were followed by a completion of the self-questionnaires including the Culture Experience Questionnaire, National Image Questionnaire, and demographic information questionnaire. The results of this study are as follow: first, regardless of the type of country, the national image was highly correlated with the degree of subjective contact evaluated by individuals, but there was a weak tendency with contact quality. Second, there was no significant interaction between the country type and contact status for national image, however, different national images for each country were detected. In other word, for contact quantity, contact groups showed more positive national images compared to non-contact groups in Russia, but not Japan, China, and the US. For contact quality, the positive contact experience group showed more positive national images compared to the negative contact experience group, but only in traditional alliance countries. This study highlights the importance of implementing different strategies for countries to maintain peaceful international relations.

An ease-off tooth surface redesign for spiral bevel gears considering misalignment under actual working conditions

To improve the loaded performance of spiral bevel gears, a novel tooth surface redesign method considering misalignment is proposed based on ease-off. First, the digital features of the contact pattern were extracted, and the equivalent misalignment was obtained by an optimal method according to the minimum deviation of the contact path. Second, a pinion target surface whose performance under misalignment was consistent with the original gear in standard position was built, and a pinion surface with good meshing performance under misalignment was redesigned with equivalent misalignment. Third, the flank modification was carried out to cut down on the loaded transmission error of gear under misalignment. Through simulations, it is found the transmission error and the contact path of redesign gear considering misalignment were the same as original gear in standard position. The loaded transmission error amplitude of original gear under misalignment was 43.91% higher than original gear in standard position, and the loaded transmission error amplitude of redesign gear after optimization under misalignment was 44.73% lower than original gear in standard position and 61.60% lower than original gear under misalignment. The tooth surface stress of redesigned gear after optimization under misalignment was also significantly improved. This proposed redesign method, which considers misalignment on the basis of ease-off, can greatly improve the loaded meshing quality of gear under actual working conditions.