Tooth Contact Research Articles

Study on the dynamic load sharing characteristics of nutation face gear transmission

The nutation face gear transmission is a type of power splitting, and the effects of system parameters such as stiffness and transmission error on load distribution are not yet well understood. The Load Tooth Contact Analysis (LTCA) technique was used to calculate the time-varying meshing stiffness of the conjugate face gear pair. A 22-degree-of-freedom bending-torsional-axial coupled dynamic model of the system was established considering parameters such as support stiffness, time-varying meshing stiffness, meshing error, and installation error. A test bench for nutation face gear transmission system was set up, and experimental results shown that the dynamic model of the nutation face gear system had an accuracy of 2.32%. Based on the solution of the dynamic meshing force of the conjugate face gear pairs, the dynamic load sharing coefficient of the nutation face gear transmission system was defined. Through simulation calculations, the effects of support stiffness, comprehensive meshing error, and torsional stiffness of input shaft on the dynamic load characteristics of the system were analyzed. The research results indicate that the radial support stiffness of each face gear and the coupling stiffness between the oblique axis segment of the input shaft has the greatest impact on the load sharing coefficient. Reducing the radial support stiffness of the left branch, increasing the radial support stiffness of the right branch, and increasing the coupling stiffness between the oblique axis segment of the input shaft can improve the system's load-sharing performance by 76%. The asymmetry of the comprehensive meshing error parameters in the two power transmission branches can increase the system's load-sharing coefficient up to 1.8. These findings provide an important basis for the structural and stiffness parameter design of nutating face gear transmissions.

The effect of eccentricity error on the static load sharing characteristics of PTBTS based on 3D-LTCA method

Eccentricity error represents a common error form in gear transmission systems. Its presence significantly impacts the time-varying meshing stiffness (TVMS) and transmission error among gear pairs, consequently exerting a notable influence on the load sharing coefficient (LSC) of power two branching transmission system (PTBTS). In this paper, the static load sharing model of PTBTS is constructed based on the equilibrium relationships of gear pair with the consideration of position angle, meshing phase, eccentricity error and so on. Additionally, a TVMS model for multi-branching transmission system is established using the three-dimensional load tooth contact analysis (3D-LTCA) method. Finally, the stiffness model and static load sharing model are coupled to achieve precise modeling of the PTBTS static characteristics, and the impact of eccentricity error amplitude and phase on the static load sharing characteristics of PTBTS are studied. The results indicate a substantial influence of eccentricity error and eccentric phase on the load sharing characteristics of the system. As the eccentricity error amplitude increases, the load sharing performance of the system deteriorates. However, it is noteworthy that the static load sharing characteristics of the system can be enhanced by adjusting the eccentricity error phase to an appropriate setting.

Effects of discrete fibre reinforcements on the wear resistance behaviour of polyamide-based spur gears

Abstract In many situations, the polymer gears are the perfect replacement for traditional metal gears. Compared to metal gears, the polymer gears will generate more heat at the gear tooth contact surface and more wear loss. Hence, this study aims to decrease the wear loss and increase the load-carrying capacity of the polymer gears. To achieve this, the reinforcement materials were added to the base polymer gear material. In this study, Nylon-66 was chosen as the polymer matrix material and an isolated glass fibre and steel grid were used as the reinforcement materials. Three different types of polymer spur gears such as Polyamide Gear (Nylon-66), Reinforced Polyamide Gear (Nylon-66+Glass Fibre), and Hybrid Glass Fiber Steel Grid Gear (Nylon-66+Glass Fibre+Steel Grid) named PG, RPG and HGFSGG were fabricated using injection moulding machine and each type of gears were compared for wear loss and specific wear rate under the similar testing conditions. The wear test was performed in the Forschungsstelle fur Zahnrader und Getriebebau (FZG) test rig at 1500 rpm with an applied load of 20 N for 12.5 hours continuously. From the test results, it was identified that HGFSGG polymer spur gears have exhibited a lower surface temperature and better wear properties compared to the other two types of spur gears. From the Scanning Electron Microscope (SEM) analysis, it was noticed that the PG spur gear exhibited deep and uniform wear at the gear tooth surface. In contrast, RPG spur gear exhibited glass fibre distortion and abrasive-type wear. The SEM micrograph of HGFSGG spur gear reveals the presence of very few surface flaws in the gear tooth surface.

Risk factors contributing to interproximal contact loss between an implant crown and a natural tooth.

Interproximal contact loss (ICL) is considered a prevalent complication for a tooth abutting an implant restoration. While numerous potential causes for ICL have been presented, there is no consensus. A review of the current literature with a focus on possible risk factors was performed. A PubMed search using keywords "implant OR dental implants OR implant supported prosthesis AND proximal contact loss OR ICL OR loss of interproximal contact OR open contact OR interproximal open contact OR adjacent natural teeth" resulted in 81 citations, 9 of which were relevant to the focus question. Additional references were culled from the reference lists in the identified articles. Systematic reviews, case series, and case reports were reviewed with a focus on causation, association, or correlation. Eight systematic reviews and 14 case series were reviewed. The prevalence of ICL has been reported to be as low as 16% and as high as 66%. ICL was more common on the mesial side of implants and when a tooth abuts a splinted implant restoration. The absence of a uniform definition to accurately describe an interproximal (IP) contact and an open IP contact is demonstrated in the literature. A lack of standardized measurement strategies that relate to a needed consensus definition further exacerbates the broad range of reported results regarding ICL. The lack of controls for almost all the ICL literature makes it difficult to draw conclusions and comparisons to unrestored, natural tooth IP contacts and the prevalence of ICL in this patient population. As a result, the available studies are inadequate to support a causal theory and the potential risk factors associated with ICL. There is a large range of reported prevalence for IP contact loss. ICL is more common when a natural tooth abutsa splinted implant restoration. ICL is more common on the mesial, as opposed to the distal, of an implant retained restoration. Consensus in the definition and measurement strategies for ICL needs to be established to provide standardized terminology and methodology. Potential risk factors such as occlusion, restorative material, and tooth contact area need to be investigated.

Study on thermal elastohydrodynamic lubrication of face gear pairs with low sliding ratio

The relative sliding interaction between tooth surfaces has a significant effect on the lubrication efficiency. In this study, the non-Newtonian characteristic is taken into consideration when examining the point contact thermal elastohydrodynamic lubrication (TEHL) behavior of a low sliding ratio (LSR) face gear pair. By using the instantaneous rotation axes method, tooth contact analysis (TCA) was carried out. Meanwhile, a combination of the Hertz contact model and finite element analysis (FEA) was adopted in order to conduct load tooth contact analysis (LTCA). Subsequently, a TEHL model for the face gear pair was established, incorporating the non-Newtonian behavior of the lubricant. Multi-grid (M-G) and Gauss-Seidel (G-S) methods were employed to improve the computational efficiency as well as convergence accuracy for relatively dense grids. The lubrication behaviors of LSR face gears and traditional face gears under full film lubrication conditions were compared. Additionally, the lubrication characteristics of face gears with the machined three-dimensional morphology were also clarified. The model and computations were validated through comparison with literature data. The findings reveal that improving contact performance can be achieved by designing gear pairs with low sliding ratios.

Self-reported mandible bracing and teeth clenching are associated with anxiety and depression traits in a group of healthy young individuals.

To assess the correlation between awake bruxism (AB) behaviors and psychological status in a group of healthy young adults. Participants were recruited at the University of Siena, Siena, Italy, by advertising the initiative. The reported frequency of AB behaviors was evaluated through the Oral Behavior Checklist (OBC). The 4-item Patient Health Questionnaire-4 (PHQ-4) was adopted to evaluate the participants' psychological status. Student's t-test was used to detect differences between genders. The Pearson correlation test was performed to assess the correlation between the two questionnaires. Mandible bracing showed the strongest correlation with anxiety and depression traits (r = 0.62), followed by teeth clenching (r = 0.54). Teeth contact (r = 0.33) and teeth grinding (r = 0.32) had the lowest level of correlation. In a sample of healthy young individuals, there is a moderate-to-high correlation between the reported teeth clenching and mandible bracing frequency and the degree of anxiety and depression symptoms. Such findings suggest the importance of the psychological assessment in awake bruxers.

Comparison of meshing characteristics and dynamic behavior of hypoid gear drive under different load conditions

The study of loaded meshing characteristics and dynamic behavior is significant for evaluating the stability of hypoid gear under actual working conditions. Loaded tooth contact analysis (LTCA) of a hypoid gear drive under different loads is carried out. The equivalent meshing force, loaded transmission error (LTE), comprehensive elastic deformation, and time-varying meshing stiffness (TVMS) are investigated. Results show that the LTE and TVMS are sensitive to load, and the LTE and TVMS curves show obvious asymmetric as the load increases. Under low load conditions, the actual contact ratio increases significantly with the increase of load, but tends to be flat when the load reaches a certain range. The obtained TVMS and LTE are fitted by higher Fourier series and introduced into an 8-DOF dynamic model. By comparing the time history diagram, phase diagram, Poincaré section, and spectrum, the dynamic characteristics of the system under different loads are contrasted. On low load condition, the system may exhibit chaotic motion in certain meshing frequency bands and damping ratio intervals. While the tooth backlash increases to a critical value, the system may change to chaotic motion from periodic motion. The results provided a basis for improving the meshing performance of hypoid gear.

The Role of Occlusal Appliances in Reducing Masseter Electromyographic Activity in Bruxism.

Background/Objectives: Bruxism is a masticatory muscle activity, phasic or tonic, with/without teeth contact, that appears in sleep or an awake state. An instrumental technique used to measure the surface electromyographic (sEMG) activity of the masseter muscle is used to diagnose bruxism activity during sleep and while awake. The objective of this study was to compare the variation in bruxism (sleep and awake) indices and masseter activity indices in low sleep bruxism and moderate sleep bruxism before and after wearing an occlusal appliance (OA) for 3 months each night. Methods: A clinical interventional study was designed in which subjects diagnosed with sleep bruxism were randomly selected to be included in the study. After the first sEMG recording, two groups were formed: a low sleep-bruxism group (number of sleep-bruxism events/h between 2 and 4) and a moderate sleep-bruxism group (number of sleep-bruxism events/h equal or higher than 4). All subjects received treatment with a 3D-printed occlusal appliance and wore it each night for 3 months, at which point the second sEMG recording was performed. For each participant of this study, a chart was created that included anamnestic data, clinical data, and sEMG data. The data were statistically analyzed with SPSS, using the Mann-Whitney U and Wilcoxon signed-rank tests. Results: A total of 21 participants were included in the final analysis, 18 women and 3 men, with a mean age of 24.5 ± 2.7 years. The OA lowered all bruxism indices in the whole group, but clusters analysis showed a significant reduction in sleep-bruxism indices in the moderate sleep-bruxism group, while in the low-bruxism group, the sleep and awake indices varied insignificantly, and the number of sleep-bruxism events/h remained constant. Conclusions: The 3D-printed occlusal appliances significantly lowered the sleep-bruxism indices and sleep masseter activity indices recorded with a portable sEMG device in the moderate sleep-bruxism group. The OA lowered the awake-bruxism indices and awake masseter activity indices in the moderate sleep-bruxism group.

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.

A loaded tooth contact analysis (LTCA) model of profile modified gears

A loaded tooth contact analysis (LTCA) model of profile modified gears

Comparison Between Ecological Momentary Assessment and Self-Report of Awake Bruxism Behaviours in a Group of Healthy Young Adults.

The aim of this investigation was to compare the self-reported frequency of awake bruxism (AB) behaviours by means of a validated single-observation point questionnaire (i.e., Oral Behaviour Checklist [OBC]) with the frequency reported in real-time with an Ecological Momentary Assessment (EMA) over 1 week. One hundred healthy young adults took part in the study. The frequency of some activities belonging to the spectrum of AB behaviours (i.e., teeth contact, mandible bracing, teeth clenching, teeth grinding) was evaluated using the EMA approach with smartphone technology support over 1 week. The OBC questionnaire was used to evaluate the self-reported frequency of the same AB behaviours. Spearman's rank correlation coefficient was adopted to test the correlation between the average score of each OBC question considered (i.e., teeth contact, mandible bracing, teeth clenching, teeth grinding) and the average frequency of the corresponding EMA item. Statistical analysis showed a weak-to-moderate level of correlation between the two different AB assessment methods. Mandible bracing showed the highest level of correlation, while teeth grinding had the lowest one. While the OBC represents a valid and easy-to-administer screening tool for evaluating bruxism behaviours, the EMA approach provides a more detailed real-time report on AB behaviours.

Circular Spline Tooth Longitudinal Modification Design and Contact Analysis for Harmonic Drives with Short Flexspline

Harmonic drives (HDs) with short flexspline (FS) always suffer from small meshing areas and severe stress concentration caused by large cone angles when a short FS is assembled and loaded. To address this issue, a tooth longitudinal modification method for the circular spline (CS) with a double circular arc common-tangent tooth profile (DCTP) is proposed. Using neutral layer and envelope conjugation theories, a mathematical model of the conventional straight CS tooth was developed. A shaping cutter for this tooth profile was then designed through coordinate transformation and meshing principles. The proposed longitudinal modification for the CS was achieved by adjusting the cutter’s trajectory. A precise finite element model of the HD was developed, revealing that tooth longitudinal modification can reduce the maximum contact pressure by 69.6% and significantly increase the contact area for HDs with short FS. This work provides valuable technical references for improving the contact state of HDs with short FS.

ASSESSMENT OF ORAL BEHAVIORS AND PSYCHOSOCIAL ASPECTS OF FEDERAL POLICE OFFICERS

Objective: To evaluate the oral behaviors and psychosocial aspects of adults belonging to the Federal Police class. Methods: An observational longitudinal study was conducted with 30 adult individuals from the special group of Federal Police from the city of Curitiba, Paraná. The median age of participants was 39.70 (± 7.35) years. Quality of life, anxiety and perceived stress were assessed using the SF-36, GAD-7 and PSS-14 questionnaires respectively. Awake bruxism was evaluated using the Ecological Momentary Assessment method with the WhatsApp mobile application. Messages were sent 15 times a day, seven days a week, between 9:00 am and 7:00 pm, at random times, to choose one of five oral behaviors: teeth contact, teeth clenching, teeth grinding, mandibular bracing, and relaxed jaw muscles. Cronbach's alpha test, Shapiro-Wilk’s test, Wilcoxon's non-parametric test for paired samples, Friedman's non-parametric test for paired samples, Spearman's non-parametric correlation test, and Kruskal-Wallis non-parametric test, followed by Dunn's 2–2 comparison test were employed. Results: The most frequent oral behaviors during the week were relaxed jaw muscles (49.75 ± 29.28), teeth contact (31.50 ± 24.71), mandibular bracing (10.42± 18.99), teeth clenching (6.82 ± 8.96), and teeth grinding (1.48 ± 3.04). Quality of life was considered excellent, anxiety was low, and there was no stress. There was no correlation between stress, anxiety and quality of life and awake bruxism. Conclusion: The federal police officers evaluated showed a high frequency of awake bruxism, but the psychosocial aspects were considered excellent.

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

This paper presents a new method for analysing 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 analyse 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.

Investigations on mesh stiffness functions in three-dimensional spur and helical gear models. Definitions and numerical simulations

A definition of mesh stiffness as a scalar function connecting spur and helical three-dimensional pinions and gears is presented along with its conceptual limitations. Since it relies on global parameters namely, variations in torque and transmission errors, it can therefore be applied to the vast majority of the models found in the literature. In parallel, a multi-foundation (MF) model of mesh interface is introduced with the objective of being as accurate as three-dimensional finite element (FE) simulations for highly reduced computational costs. Numerous results on mesh stiffness and tooth contact conditions are presented for unmodified spur and helical gears. It is shown that the proposed mesh stiffness functions based on global parameters are sound and that the MF and FE results compare well, particularly when gear body deflections are limited. The contributions of off-line of action contacts, elastic couplings when several tooth pairs are loaded and axial deflections in helical gears are analysed. Finally, the notion of mesh stiffness function representative of the elasticity of a pinion-gear pair for static and dynamic conditions is examined.

Critical Assessment on the Stability and Convergence of the Conventional Gear Tooth Contact Analysis

Mathematical modeling of gear engagement is crucial during design to ensure optimal performance in manufacturing. This study reproduces the conventional tooth contact analysis (TCA) model, highlighting convergence issues in parallel-axis gears and limitations in local synthesis methods. The research critically analyzes the TCA method, which solves five nonlinear equations to assess performance and accuracy. Simulations replicate the conditions of previous studies to ensure valid comparisons. Initial guess values are randomly generated within a specific range to guide the iterative process toward convergence, with this range progressively narrowed to improve computational efficiency and accuracy. Results indicate that the TCA approach is highly sensitive to initial guess values, particularly the starting angular position. Convergence issues arise from the complexity of nonlinear equations and multiple roots. This can lead to divergence or reverting to the initial guess when values deviate significantly from the true solution.

Dynamic Analysis of Helical Gears Considering Friction

The use of high contact ratio (HCR) gears is an effective method to reduce single tooth loads, as well as vibration and noise, making the application of helical gears increasingly widespread. Although the presence of helix angles can cause significant relative sliding, the presence of more teeth in contact makes HCR gears more sensitive to surface quality. The existing literature mainly investigates geometric optimization, load distribution, or efficiency calculation of helical gears. The research on the influence of rough surfaces on the dynamic performance of helical gears is very limited. To this end, a multi degree of freedom mathematical model of static transmission error was established based on the 2-DOF system. The relative sliding friction was studied using different friction coefficients, and the influence of different friction coefficients on the gear system was analyzed in detail. The numerical results indicate that surface roughness has a relatively small impact on the dynamic transmission error of the system, but has a significant impact on the motion and friction in the direction of departure.

Parameters impact analysis on contact characteristics of intersected beveloid gear and involute cylindrical gear

According to gear geometry and tooth contact analysis (TCA) theory, the TCA model of intersected beveloid gear and involute cylindrical gear pair is built. The formulas for calculating curvature and contact ellipse at contact points are derived, and the shape and region of contact ellipse are determined. Then, the impacts of cone angle, helix angle and installation errors on contact characteristics are studied by numerical examples. The finite element model of gear pair is established to carry out the loaded tooth contact analysis (LTCA) and verify the accuracy of theoretical TCA model. The results show that gear pair with small cone angle or big helix angle has wide contact area, large carrying capacity and high transmission quality. The shaft angle error may cause the edge contact of gear pair, while the axial position error has limited effect. The research can provide input parameters for the study of tooth surface wear mechanism and dynamics in the future work.

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.

A novel method to study the long period three-dimensional vibration characteristics of herringbone gear with asymmetry pitch deviation

Most of the existing dynamic models of herringbone gear assume that the three major internal excitations, namely, the comprehensive mesh stiffness (CMS), the comprehensive mesh error (CME), and the meshing impact force (MIF), are the same at each meshing period. However, due to the inevitable asymmetric pitch deviation in the machining and installation process, the three internal excitations are coupled with each other and vary in a long period. In addition, since the driving gear usually adopts an axially floating support, this in turn gives rise to a unique axial displacement (AD) excitation of the herringbone gear. Firstly, an improved loaded tooth contact analysis (LTCA) model of herringbone gear with asymmetric pitch deviation is established, and the coupling relationship between multi-source excitation is explored. Secondly, a nonlinear dynamic model of herringbone gear with asymmetric pitch deviation is proposed, and the above multi-source excitation is introduced into the model to study the effects of load, speed, and asymmetric MIF on the long period three-dimensional (3-D) vibration characteristics of herringbone gear. Finally, the correctness of the theoretical simulation results is verified by experiments. The proposed novel method can predict the 3-D vibration characteristics of herringbone gear more realistically and effectively.