Tooth Contact Research Articles

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.

Loaded tooth contact analysis and meshing stiffness calculation for cracked spiral bevel gears

Tooth cracks may occur in spiral bevel gear transmission system of the aerospace equipment. In this study, an accurate and efficient loaded tooth contact analysis (LTCA) model is developed to predict the contact behavior and time-varying meshing stiffness (TVMS) of spiral bevel gear pair with cracked tooth. The tooth is sliced, and the contact points on slices are computed using roll angle surfaces. Considering the geometric complexity of crack surface, a set of procedures is formulated to generate spatial crack and determine crack parameters for contact points. According to the positional relationship between contact point and crack path, each sliced tooth is modeled as a non-uniform cantilever beam with varying reduced effective load-bearing tooth thickness. Then the compliance model of the cracked tooth is established to perform contact analysis, along with TVMS calculations utilizing three different models. By employing spiral bevel gear pairs with distinct types of cracks as examples, the accuracy and efficiency of the developed approach are validated via comparative analyses with finite element analysis (FEA) outcomes. Furthermore, the investigation on effects of cracks shows that tooth cracks can induce alterations in meshing performance of both entire gear pair and individual tooth pairs, including not only cracked tooth pair but also adjacent non-cracked tooth pairs. Hence, the proposed model can serve as a useful tool for analyzing the variations in contact behavior and meshing stiffness of spiral bevel gears due to different cracks.

The Influence of the external meshing gears’ contact ratio on the contact stress in the transmission system

Abstract Using the Hertz contact theory, the calculation method of tooth contact stresses at different boundary points within the double tooth meshing zone for high contact ratio external meshing gear pair is investigated. The radius of curvature and pressure angle at each boundary point of the external meshing gear with a high contact ratio is given. The boundary point meshing coefficients are introduced to convert the comprehensive radius of curvature at the boundary point into the radius of curvature at the node, to make it in line with the form of calculation of the national standard. The analysis examines how the parameters affect the contact stress at different boundary points of the gear pair with a high contact ratio. When the contact ratio of the gears is 2, there is a sudden change in the contact stress on the tooth surface, and HCR gears have smaller contact stress than LCR gears.

Finite element stress analysis of nano copper-based anti-friction coating for improved threaded connections in petroleum drilling tools

Threaded connections are commonly used in connecting petroleum drilling tools (PDTs). In this study, we use nano copper (NaCU) and epoxy-resin binder to prepare a NaCU-based anti-friction coating (NaCU-AFC). Furthermore, we use finite element analysis (FEA) to validate torque and pressure distribution on the contact tooth surface of threaded joints of PDTs. The results demonstrate that the NaCU-AFC can effectively reduce torque by 35.66%, and significantly improve anti-sticking performance, thereby extending the service life of PDTs. In summary, this study provides valuable insights for practical applications in coating processes for PDTs.

Analysis of scuffing through temperature measurement experiment and numerical simulation for spiral bevel gears

Tooth surface scuffing failure, as one of the primary failure modes of gears, frequently occurs during the operation of gear mechanisms. Scuffing properties of spiral bevel gears were investigated through a numerical analysis and experimental study. A novel temperature model for a single tooth was proposed to predict scuffing temperatures on the tooth surface. The model allows the analysis of variations in tooth surface temperature, considering both operating conditions and tooth contact scenarios. Experiments were carried out to explore tooth surface adhesion of spiral bevel gears under precisely defined operating conditions. Measurement of tooth surface temperatures was conducted by combining non-contact infrared temperature sensors and temperature-measuring cameras. This experiment verifies temperature changes on the tooth surface adhesion of spiral bevel gears. The combination of two temperature measurement methods ensures accurate temperature measurements, with errors below 8%, and facilitates the swift opening of the end cover. Experimental validation of the scuffing prediction model yields a maximum temperature difference of 5.93%. The method establishes a theoretical foundation for evaluating tooth surface adhesion of spiral bevel gears.

Performance reliability evaluation of high‐pressure internal gear pump

AbstractWith the development of the high‐end equipment technology, the performance requirements of the internal gear pump (IGP) under high pressure are also increasing. However, the increase of working pressure will lead to the instability of gear pump performance in terms of volumetric efficiency, noise, reliability and so on, it is necessary to reasonably evaluate the reliability level of high‐pressure IGP. The reliability analysis of the high‐pressure IGP is carried out from the aspects of flow, noise, and gear strength in this paper. First, the output flow rate and far‐field flow‐induced noise of the high‐pressure IGP were obtained through fluid numerical simulation, and experimental verification was conducted. Then, based on the time‐varying meshing stiffness, backlash function and static transmission error of the gear pair, a nonlinear dynamic model of the internal meshing gear pair was established. The time‐varying meshing force was obtained through the dynamic model of the gear pair, and then the tooth contact stress and tooth root bending stress were obtained. Finally, considering the uncertain factors affecting the performance of the high‐pressure IGP, Latin hypercube sampling (LHS) combined with dendrite network (DD) was used for random response modeling. The performance reliability of the high‐pressure IGP, including output flow rate, far‐field flow‐induced noise, and the strength of gear pair, were estimated based on the fourth moment‐based saddlepoint approximation (FMSA). The reliability analysis results can provide a theoretical basis for the structural optimization design of the high‐pressure IGP.

FE-analytical slice model and verification test for load distribution analysis and optimization of planetary gear train in wind turbine

Load distribution behavior of planetary gear train (PGT) is crucial for the contact and bending fatigue failure of wind turbine transmission system. With the increasing power of wind turbines, the load and failure rate of wind turbine become larger, which leads to the demand of accurate and efficient modeling, analysis and optimization for load distribution of PGT. In this paper, a new efficient and accurate FE-analytical slice model for load distribution analysis and optimization of PGT in wind turbine is proposed, which is explicitly formulated by the geometry slice model of external/internal gear contact, original FE-analytical slice model for local contact deformation, and efficient finite element (FE) model for global structural deformation. In the FE-analytical slice model, geometry errors are effectively descripted by discretizing gears into a series of slices, while gear tooth contact elasticity and structural elasticity are addressed by the FE-analytical method accurately and efficiently. Upon the proposed model, the load distribution behaviors of PGT with coupling effects of elasticity and errors are revealed and optimized by tooth modification and in-phase eccentricity arrangement strategy. The load distribution tests of PGT in wind turbine are conducted, verifying the proposed FE-analytical slice model which is significant to improve the load-bearing capacity and avoid the fatigue failure of wind turbine transmission system.

Non-Newtonian thermal elastohydrodynamic mixed lubrication in elliptical contact for nutation-driven double circular-arc spiral bevel gear pair

The new type of nutation reducer with double circular-arc bevel gears as the core is characterized by advantages such as high load-bearing capacity, large transmission ratio, and simple structure. The existing research focuses on the machining methods of gears and the analysis of tooth contact. This article first time establishes an elastohydrodynamic mixed lubrication model for nutation double circular-arc bevel gear. The model's accuracy is verified by comparing it with existing test results. On this basis, combined with the finite element method and tooth contact analysis, the meshing characteristics, tooth contact characteristics, and lubrication characteristics of the double circular-arc bevel gear tooth surface are analyzed. The results show that the entrainment velocity at the contact point of the tooth surface during transmission is much higher than the sliding velocity. Consequently, the meshing motion is close to pure rolling. In constant-speed transmission, the oil film thickness at the engaging-in and exit points near the edge of the tooth surface is smaller than that at other meshing points on the tooth surface. This phenomenon can easily lead to mixed lubrication and lubrication failure, as well as tooth surface wear. During deceleration, i.e., when the speed drops to 50 r/min, the oil film thickness approaches zero, indicating that the gear has entered a mixed lubrication state. The proposed model can be used for lubrication analysis and improving transmission accuracy of nutation double circular-arc bevel gears.

Study on the contact performance of the variable hyperbolic circular arc tooth trace cylindrical gear with installation errors

Abstract. Installation errors are important factor for the contact performance of the variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear; the study of the relationship between installation errors and contact performances is beneficial for gear vibration and noise reduction. Firstly, based on the meshing theory, the tooth surface equation and contact ellipse of the VH-CATT cylindrical gear were deduced, and the tooth surface imprinting experiment was realized. Next, the tooth contact analysis model of the VH-CATT cylindrical gear was developed to investigate the influence of the installation errors on the elliptical contact area. Then, the calculation formulas of the tooth surface gap and contact point flexibility matrix were carried out to develop the load tooth contact analysis model of the VH-CATT cylindrical gear. Finally, the influence of the installation errors on the load distribution was investigated. Research shows that the elliptical contact area of the VH-CATT cylindrical gear is a line contact within a certain range and is located in the middle section of the tooth width. The elliptical contact area of the VH-CATT cylindrical gear increases or decreases rapidly when meshing in and out, and all the installation errors have a certain influence on the elliptical contact area, except for the center distance error. The single-tooth meshing area with the installation errors is greater than that of the ideal gear pair. The load distribution area with the installation errors deviates from the middle section, except for the center distance error. The installation rotation errors around the x and y axis have a certain influence on the maximum load of the single-tooth meshing area. The research results provide a basis for improving the bearing capacity of the VH-CATT cylindrical gear and optimizing the design.

A stiffness model for EHL contact on smooth/rough surfaces and its application in mesh stiffness calculation of the planetary gear set

A method for calculating time-varying mesh stiffness (TVMS) is proposed by developing a stiffness model for elastohydrodynamic lubrication (EHL) contact and integrating it into three-dimensional loaded tooth contact analysis (3D-LTCA). To enhance the accuracy and efficiency of the calculation, three projects have been implemented: Firstly, the contact deformation is modified, and the average slope is employed for calculating contact stiffness. Secondly, the lubricant film and EHL contact deformation are introduced into the deformation compatibility equations. Finally, the polynomial chaos expansion (PCE) surrogate model is employed to enhance computational efficiency. The proposed method is used to calculate TVMS of the planetary gear set, and the influence of speed, torque, and rough surface are analyzed. The results show that the previous method underestimating the TVMS of planet-ring gear pair in double-teeth meshing area under fluid lubrication, while the proposed method effectively addresses the issue. The different effects of the torque and speed on TVMS under mixed and fluid lubrication also have been revealed, emphasizing the significance of surface topography in gear meshing characteristics.

СИСТЕМАТИЧЕСКИЙ ОБЗОР МЕТОДОВ ВОССТАНОВЛЕНИЯ ПРОКСИМАЛЬНЫХ ПОЛОСТЕЙ ЖЕВАТЕЛЬНЫХ ЗУБОВ: СОВРЕМЕННОЕ СОСТОЯНИЕ И ПЕРСПЕКТИВНЫЕ ТЕХНОЛОГИЧЕСКИЕ ДОСТИЖЕНИЯ

Relevance. To maintain dental health and maintain the normal structure of the dental system, a deep understanding of methods for restoring lost dental tissue is necessary. When restoring class II carious lesions, open and closed sandwich techniques were used, as well as various methods of manipulating composite materials. Systematization of existing research will allow the dentist to better navigate the available techniques and provide better treatment to his patients. Aim: To conduct a systematic review of the effectiveness of the method for restoring proximal contacts of posterior teeth. Materials and methods. As part of the study, a systematic analysis of the technique for restoring contact points of teeth was carried out, in compliance with established criteria. Initial data were obtained by searching the Google Scholar, ScienceDirect, PubMed, ResearchGate, CyberLeninka and eLIBRARY.RU databases using the following key terms: «recovery methods», «contact point», «open sandwich», «closed sandwich», «filling technique», «point of contact», «closed centripetal», «open centripetal». Results. To conduct a systematic review, 7 articles were reviewed on the seal quality of restorations made using the open sandwich, closed sandwich, and total bonding methods. In 85% of cases, the open sandwich method was indicated by the authors as the most appropriate for creating sealed class 2 restorations. Conclusions. The best tightness of restorations in in vitro studies in 85% of cases was achieved using the technique of filling an open sandwich. The tightness of the restoration not only affects the choice of material, but also prevents its application. Further comparative in vivo studies on the survival of class 2 restorations made using the open sandwich or total bonding method are needed.

An improved tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors

The contact quality between geometric features significantly affects the assembly accuracy and dynamic performance of mechanical products. However, accurate and efficient contact problem solving is currently a common challenge in the fields of tolerance analysis and tooth contact analysis (TCA). In this paper, a tolerance analysis method for gear mechanisms considering form deviations and elastic-plastic contact behaviors is proposed. Specifically, tolerance modeling of systematic and random deviations on tooth surfaces is represented by skin model shapes (SMS). Elastic-plastic contact behaviors including contact deformation, status, and stress distribution are modeled and calculated by a modified boundary element method (BEM). The accuracy and efficiency of this BEM algorithm are verified by comparing with the finite element method (FEM), indicating that the BEM can greatly improve the computational efficiency while maintaining high solution accuracy. A case study for a pair of spur gears demonstrates the significant effects of contact behaviors on transmission performance. This research provides an effective method to introduce mechanical contact behaviors in tolerance analysis of gear mechanisms. In addition, the contact simulation results can also be adopted in the analysis of vibration, reliability, and other aspects.

Mechanism investigation on gear vibration-cavitation caused by tooth-pair lubricated contact

Elastohydrodynamic contact of gears under the influence of vibration induces cavitation and jet impact. To predict the evolution of cavitation and the degree of cavitation erosion in the gear contact region, the multi-phase flow cavitation model and gear dynamic model are coupled for simulating the cavitation effect in the gear lubrication region and the jet stresses at the tooth boundary under different load torques and rotational speeds. Moreover, the proposed model is confirmed to be valid through comparing to experimental results. The cavitation and jet impact intensity increase and mainly distribute at the outlet of tooth contact under high speed. Load torque mainly affects the cavitation oscillation, but there exists an expectation value that makes both the amplitude and intensity of the cavitation fluctuation and erosion low.

Rear Axle Whine Reduction by Gear Contact Patch Optimization

In-cab whine is a highly annoying phenomena in all the category of vehicles. The in-cab noise of passenger vehicle with Rear Wheel Drive ( RWD) considered for this study consist of axle whine noise. The whine noise is heard at multiple speeds during Wide Open Throttle (WOT) as well as coasting. To resolve the issue of whine noise, series of measurement are carried out to identify the source and transfer path of the whine. The noise measurement revealed that rear axle pinion mesh order is responsible for in-cab whine. It is confirmed through measurement that the whine is structure borne. The order based operational deflections shapes of rear axle show excessive vibration on differential nose in affected speed zones. It is thus learnt that whine is due to poor contact pattern of pinion and crown wheel of the rear axle. The three resonances in operation range amplify this mesh order resulting in whine. It is decided to work on noise source i.e. gear rather than transfer path. The hypoid gear design is optimized through Tooth Contact Analysis (TCA). The lapping and heat treatment processes of gear manufacturing are modified. The contact pattern of optimized gear is identified on gear tester machine. Significant improvement is observed in contact pattern. The in-cab noise measurement is carried out with optimized hypoid gear and it is found that the whine is completely eliminated.
 Keywords: Rear axle, Whine reduction, Gear contact, Patch optimization, Rear Wheel Drive, Whine Source, Vibration on Transfer Paths, Noise Generation, Hypoid Gear, Heat Treatment

Mesh Characteristic Analysis of Spiral Bevel Gear Pairs Considering Assembly Errors and Tooth Tip Chipping Faults

Due to machining errors, location inaccuracies, human error, and various other factors, it is challenging to avoid assembly errors during the production of spiral bevel gears (SBGs). When SBG assembly errors occur, it can cause the appearance of edge contact and may even lead to severe tooth tip chipping. In this study, we propose an improved method based on loaded tooth contact analysis (LTCA) to examine mesh characteristics, including time-varying mesh stiffness (TVMS), unloaded transmission error, and contact stress. Furthermore, we explore the effects of assembly errors and tooth tip chipping. Moreover, it is observed that assembly errors can alter the contact area of SBGs and potentially reduce the peak-to-peak value of TVMS. Additionally, the occurrence of tooth tip chipping decreases TVMS within the chipping region, lowers transmission error, and increases maximum contact stress. Notably, when assembly errors are present, the reduction in TVMS due to tooth tip chipping exceeds that of a properly assembled SBG pair.

Forecasting model for hypoid gear elastohydrodynamic lubrication considering entrainment effect

In full consideration of time-varying meshing performance and oil film characteristics, entrainment effect on elastohydrodynamic lubrication (EHL) is developed for establishing accurate forecasting model of the complex hypoid gears. Firstly, dynamic loaded tooth contact analysis (DLTCA) is employed to determine the meshing interface kinematics, load distribution and entrainment speed under dynamic load condition. Then, entrainment speed is introduced into the EHL governing equation and accurate forecasting model is established. With accurate discretization of EHL governing equation, discrete convolution and fast Fourier transformation (DC-FFT) method is employed to compute the flank elastic deformation. Finally, a hypoid gear set in automotive industrial application is exercised to verify entrainment effect on EHL assessment in the proposed model.

Анализ контакта конических зубьев шестерен на основе машинного обучения

In this paper, we study the analysis of the contact of bevel gear teeth based on machine learning methods. Bevel gear teeth are widely used in various industrial and mechanical systems to transmit rotational motion with high precision and reliability. Traditional methods of gear contact analysis are based on mathematical models and empirical formulas, which may be limited in accuracy and applicability. In recent years, machine learning has become a powerful tool in the field of engineering and mechanics to more accurately model and predict the contact behavior of bevel gear teeth. The paper proposes the use of machine learning methods, such as neural networks or deep learning algorithms, to train models capable of analyzing the contact of bevel gear teeth. Wear, load, and gear geometry data can be used to train models, which can then predict contact parameters and evaluate contact performance.

Flank fractures on spiral bevel gears—transfer of analytical methods for the estimation of residual stresses from cylindrical gears to bevel gears

The classic flank and root load capacity calculation on the component surface forms the basis for the design of power gears today. However, flank fractures also occur in practice, particularly with large-module gears and/or low case-hardening depths. It is a fatigue damage with crack initiation in the tooth interior, its prevention requires the calculation of the stresses below the surface. In addition to understanding the load stresses, the inhomogeneous load bearing capacity and the residual stress profile in case-hardened gears are also of great importance. There are various calculation approaches for this in the area of cylindrical gears, but these have not yet been transferred to the complex geometry of spiral bevel gears. The focus of this publication is on estimating the residual stresses in the tooth volume by generating a three-dimensional residual stress tensor field in the bevel gear tooth based on the two-dimensional calculation approaches used to date on cylindrical gears. In combination with the stress tensor-time curves from a tooth contact simulation with the LTCA tool BECAL, this can be fed into different failure hypotheses, which is illustrated using an example.

Three-dimensional evaluation of interproximal contacts of permanent dentition: a cone beam computed tomography study.

To assess the various patterns of the inter-proximal contact areas of the permanent dentition using the available cone beam computed tomography (CBCT) images. A retrospective cross-sectional study was performed on existing CBCT images from a University hospital and teaching department. Three thousand two hundred and fifty inter-proximal contacts were assessed from 125 existing CBCT scans of patients (age range: 14years 3months-29years 9months) who had matched the eligibility criteria. The types of inter-proximal contacts of the permanent dentition were scored at occlusal, middle, and cervical thirds, according to the OXIS inter-proximal contacts classification. Chi-square test was used to assess the contacts and gender/arches. The most prevalent contact was type I for the posterior teeth contacts, and types S1 and S2 for the anterior teeth contacts. Statistical significance was not observed between the contacts on the left and right sides (P > 0.05), while statistical significance was observed between the inter-proximal contacts of the maxilla and mandible (P < 0.05). The CBCT-based three-dimensional assessment of the inter-proximal contact areas of the permanent dentition is representative of the OXIS classification. The occlusal level contact was predominantly representative of the overall type of the contact.

Factors Related to Masticatory Rhythm in Patients with Oral Tumors.

Background: Older adults who have undergone surgery for oral tumors are at increased risk of impaired masticatory rhythm. This study investigated the correlations between masticatory rhythm, objective masticatory performance, and subjective masticatory performance as well as factors related to masticatory rhythm. Methods: The participants were 44 adults (24 men, 20 women; age range 42~90 years old) who had undergone maxillectomy, mandibulectomy, or glossectomy and were rehabilitated with a maxillofacial prosthesis. The number of functional contact teeth pairs was confirmed by intraoral examination. Chewing rate, cycle duration, coefficient of variation (CV) for cycle duration (reflecting the stability of masticatory rhythm), and mixing ability were measured simultaneously using a mastication movement rhythm tracking device during gum chewing. Maximum occlusal force was measured using the dental prescale system. Patients' perception of chewing ability was rated using a questionnaire. Results: The Spearman's rank correlation test revealed that mixing ability, patient-rated masticatory scores, cycle duration, CV for cycle duration, and maximum occlusal force showed significant correlations with chewing rate. Multiple linear regression analysis identified mixing ability and the CV for cycle duration as significant predictors of masticatory rhythm. Conclusions: Factors associated with a faster chewing rate were higher mixing ability and masticatory scores, greater maximum occlusal force, shorter cycle duration, and smaller CV for cycle duration. Stable masticatory rhythm and mixing ability are significant predictors of chewing rate. Poor masticatory performance and unstable masticatory rhythm can result in slower chewing and thus a higher risk of inadequate dietary intake.