Tooth Friction Research Articles

Tribo-dynamics model of a spur gear pair with gyroscopic effect and flexible shaft

This study proposes a tribo-dynamic model of a spur gear by coupling an elastic dynamic model and an isothermal elastohydrodynamic lubrication (EHL) model. In this model, the gear shafts are modelled as flexible bodies by the resultant elements of Timoshenko beam and bar elements, and the gyroscopic effect of gear rotors and shafts is also included. The transient and non-Newtonian effects are considered in the EHL model to predict tooth friction forces and moments. Then, an example is provided to analyze the interaction between gear tribology and dynamic behavior. Results indicate that the fluctuations of mesh force and surface tangential velocity caused by gear vibration considerably affect the pressure and thickness of the lubricant film. The gyroscopic effect exerts a significant influence on the dynamic and tribology properties of the gear drive at high speed. The proposed model has important guidance for the design of lubrication systems and dynamic properties in gear drives.

Tooth friction force and transmission error of spur gears due to sliding friction

This study investigated the tooth friction force and transmission error (TE) of spur gears due to sliding friction under quasi-static condition. The sliding velocity and friction force of spur gears and mesh compliance during meshing were calculated. The load–deformation relations between the tooth normal load, tooth errors, and mesh compliance, and moment equilibrium equation, including friction force, were derived. The friction force, tooth load, and TE of unmodified and linear tip-relief modified spur gears were analyzed by using the derived equations. Results indicated that the friction force, tooth load, and TE increased during approach and decreased in recess regardless of tooth modification, particularly in the single-mesh region. Friction caused larger peak-to-peak change of TE than that without friction. Xu’s friction coefficient generated smooth TE and tooth load transitions near the pitch point, and BK’s friction coefficient remained approximately constant, except for the sharp increase in tooth load and TE near the pitch point.

Impact of backlash, manufacturing deviations and friction on the load sharing factor of planetary gear systems

Techniques and software tools, which were recently introduced by the authors, allowed for effi-cient automatic generation of 3D gear flanks and selective meshing of the gears of a simple planetary gear system with backlash and manufacturing imperfections. Friction of the meshing gear flanks was neglected. First results were promising and showed that even in geometrically perfect planetary gear systems the torque distribution is not uniform. It was further verified that pitch errors have a strong impact on the load distri-bution and that a self-aligning sun gear significantly enhances the torque distribution among the planets. In the current study, the procedure mentioned above is enhanced in several aspects. First, the tooth friction is considered. The friction coefficient is assumed constant along the path of contact; however different values for the sun-planet and planet-ring gear mesh may be given to account for the different contact conditions. Second, deviations are generated between given limits in a stochastic way. This feature significantly reduces the time needed to setup a model. Third, the entire analysis procedure is further automated by extensively employing Python scripting, enabling the solution of successive snapshots in much shorter time. Besides the torque distribution among the planets, the mesh load factor Kγ and the deformation of the teeth, the planet bearing load is also shown.

Shakedown analysis of a wind turbine gear considering strain-hardening and the initial residual stress

Under some heavy-duty conditions, the shakedown state may occur on gears such as those used in a megawatt wind turbine gearbox. The plastic deformation and the residual stress formed within the shakedown process further influence the contact behavior and the service life of the gear. The initial residual stress caused by the heat treatment of the case-hardening gear, together with the strain-hardening constitutive behavior of the material, have a combined effect on the shakedown state. A two-dimensional elastic-plastic contact numerical model was developed for a case-hardened wind turbine gear to study effects of the initial residual stress and the strain-hardening properties. Plastic strain and residual stress are calculated at each loading cycle without the consideration of the tooth friction. The initial yield limit and the hardening modulus of the material were obtained through a tension test on a universal tensile test machine. The initial residual stress distribution was measured with the X ray diffraction method and then embedded in the finite element model. The results show that strain-hardening behavior can significantly improve the shakedown performance, and the larger the hardening modulus is, the less the maximum plastic strain is at the final shakedown state. Initial residual compressive stress is helpful to improve the shakedown performance, while initial residual tensile stress has negative influence on the shakedown performance. As the normal load increases, the influence of the initial residual stress on the shakedown state becomes weakened.

Study of Dynamic Model of Helical/Herringbone Planetary Gear System With Friction Excitation

Tooth friction is unavoidable and changes periodically in gear engagement. Friction excitation is an important excitation source of a gear transmission system. They are different than the friction coefficients of any two points on the same contact line of a helical/herringbone gear. In order to obtain the influence of the friction excitation on the dynamic response of a helical/herringbone planetary gear system, a method that uses piecewise solution and then summing them to analyze the friction force and frictional torque of tooth surfaces is proposed. Then, the friction coefficient is obtained based on the mixed elastohydrodynamic lubrication (EHL) theory. A dynamic model of a herringbone planetary gear system is established considering the friction, mesh stiffness, and meshing error excitation by the node finite element method. The influence of friction excitation on the dynamic response of the herringbone planetary gear is studied under different working conditions. The results show that friction excitation has a great influence on the vibration acceleration of the sun and planetary gear. However, the effect on the radial and tangential vibration acceleration of a planetary gear is the opposite. In addition, the friction excitation has a slight effect on the meshing force.

Effect of friction in a single-tooth fatigue test

The primary objective of the single tooth fatigue test is to generate gear-tooth bending fatigue data at a comparatively low price. Assuming a negligible influence on fatigue data, the effect of friction is not evaluated. The aim of this study is to evaluate the effect of tooth friction on tooth bending fatigue life and on the location of the crack initiation site in a single-tooth fatigue test of case carburized steel spur gear. By using Neuber’s rule, tooth root stresses predicted by means of two-dimensional elastic finite element analysis are translated into estimates of elastic-plastic stress and strain behaviour. The fatigue life and location of crack initiation site are predicted on the basis of the strain-life approach with consideration of mean stress, surface finish and residual stress effects. Two load models are considered. In the first load model, which represents the operating principle commonly used in practice, the test tooth is loaded through the actuating arm. In the second one, which is proposed in this study, the test tooth supports the reaction through the fixed anvil. In both load models, the test tooth is contacted at the highest point of single tooth contact, while the other one is contacted at a lower position along the tooth profile. The computational model is validated against experimental crack initiation lives from literature. The study revealed that friction has a more significant impact on tooth bending fatigue life and location of the crack initiation for the first load model as opposed to the second one.

Influence of the Operating Conditions of Two-Degree-of-Freedom Planetary Gear Trains on Tooth Friction Losses

In a planetary gear train (PGT), the power loss by tooth friction is a function of the potential power developed within the gear train elements rather than that being transmitted through it. In the present work, we focus on the operating conditions of two-degree-of-freedom (two-DOF) PGTs. Any operating condition induces its own internal power flow pattern; this implies that tooth friction loss depends on the mechanism of power loss developed in the gearing that differs from one case to another over the entire range of operating conditions. The approach adopted in this paper stems from a unification of the kinematics and tooth friction losses of PGTs and is based on potential powers and power ratios. The range of applicability of the power relations is investigated and clearly defined, and tooth friction loss formulas obtained by their use are tabulated. A short comparison with formulas currently available in the literature is also made. The simplicity of the proposed method for analyzing two-input or two-output planetary gear trains is helpful in the design, optimization, and control of hybrid transmissions. It assists particularly in choosing correctly the appropriate operating conditions to the involved application.

Tribological behavior of coated spur gear pairs with tooth surface roughness

Coating is an effective way to reduce friction and wear and to improve the contact-fatigue lives of gear components, which further guarantees a longer service life and better reliability of industrial machinery. The fact that the influence coefficient linking the tractions and stress components could not be expressed explicitly increases the difficulty of coated solids contact analysis. The complicated tribological behavior between tooth surfaces influenced by lubrication and surface roughness further adds difficulty to the coated gear pair contact problems. A numerical elastohydrodynamic lubricated (EHL) contact model of a coated gear pair is proposed by considering the coupled effects of gear kinematics, coating properties, lubrication, and surface roughness. The frequency response function and the discrete convolute, fast Fourier transformation (DC-FFT) method are combined to calculate the surface deformation and the subsurface stress fields at each meshing position along the line of action (LOA). The Ree-Eyring fluid is assumed to incorporate the non-Newtonian effect, which is represented in the generalized Reynolds equation. Influences of the ratio between the Young’s modulus of the coating and the substrate on the contact performance, such as pressure, film thickness, tooth friction coefficient, and subsurface stress field, are studied. The effect of the root mean square (RMS) value of the tooth surface roughness is studied by introducing the roughness data, deterministically measured by an optical profiler.

Helical gear wear monitoring: Modelling and experimental validation

Gear tooth surface wear is a common failure mode. It occurs over relatively long periods of service nonetheless, it degrades operating efficiency and leads to other major failures such as excessive tooth removal and catastrophic breakage. To develop accurate wear detection and diagnosis approaches at the early phase of the wear, this paper examines the gear dynamic responses from both experimental and numerical studies with increasing extents of wear on tooth contact surfaces. An experimental test facility comprising of a back-to-back two-stage helical gearbox arrangement was used in a run-to-failure test, in which variable sinusoidal and step increment loads along with variable speeds were applied and gear wear was allowed to progress naturally. A comprehensive dynamic model was also developed to study the influence of surface wear on gear dynamic response, with the inclusion of time-varying stiffness and tooth friction based on elasto-hydrodynamic lubrication (EHL) principles. The model consists of an 18 degree of freedom (DOF) vibration system, which includes the effects of the supporting bearings, driving motor and loading system. It also couples the transverse and torsional motions resulting from time-varying friction forces, time varying mesh stiffness and the excitation of different wear severities. Vibration signatures due to tooth wear severity and frictional excitations were acquired for the parameter determination and the validation of the model with the experimental results. The experimental test and numerical model results show clearly correlated behaviour, over different gear sizes and geometries. The spectral peaks at the meshing frequency components along with their sidebands were used to examine the response patterns due to wear. The paper concludes that the mesh vibration amplitudes of the second and third harmonics as well as the sideband components increase considerably with the extent of wear and hence these can be used as effective features for fault detection and diagnosis.

Comparison of excursive occlusal force parameters in post-orthodontic and non-orthodontic subjects using T-Scan® III

Objective: Published studies indicate that orthodontically treated patients demonstrate increased posterior occlusal friction contributing to temporomandibular disorder (TMD) symptoms. This study investigated measured excursive movement occlusal contact parameters and their association with TMD symptoms between non- and post-orthodontic subjects.Methods: Twenty-five post-orthodontic and 25 non-orthodontic subjects underwent T-Scan® computerized occlusal analysis to determine their disclusion time (DT), the excursive frictional contacts, and occlusal scheme. Each subject answered a TMD questionnaire to determine the presence or absence of TMD symptoms. Statistical analysis compared the within group and between group differences (p < 0.05).Results: Statistically significant differences were observed in the disclusion time: DT = 2.69 s in the post-orthodontic and 1.36 s in the non-orthodontic group. In the non-orthodontic group, 72.7% working and 27.3% non-working side contacts were seen, while in the post-orthodontic group, (near equal) 54.7% working and 45.3% non-working side contacts were seen. Presence of canine guidance was seen in 60% of the non-orthodontic group and 24% in the post-orthodontic group. Seventy-two percent of the post orthodontics subjects presented with one or more TMD symptoms.Conclusion: Significantly longer disclusion time, higher posterior frictional contacts, and more TMD symptoms were observed in the post-orthodontic group, suggesting that orthodontic treatment increases posterior tooth friction. Computerized occlusal analysis is an objective diagnostic tool determining the quality of excursive movements following orthodontic treatment.

Influence of Rolling Element Bearing Modeling on the Predicted Thermal Behavior of the FZG Test Rig

ABSTRACTA thermomechanical model of the FZG test rig is presented. The numerical model is based on the thermal network method and takes into account power losses due to tooth friction, rolling element bearings (REBs), oil churning, and shaft seals. Some measurements underline that REB rings run at different temperatures. To investigate this difference, several REB models are proposed and compared to measurements. Their influence on the global thermal behavior of the gear unit is discussed and analyzed.

Modelling of damping in lubricated line contacts – Applications to spur gear dynamic simulations

The various damping mechanisms in elasto-hydrodynamic lubrication contacts are investigated with the objective of deriving damping models representative of the lubricant contributions which can readily be used in gear dynamic simulations. Several simplified models are proposed which make it possible to simulate the damping caused by tooth friction and lubricant squeezing by the teeth with and without momentary contact losses and impacts. A one-degree-of-freedom gear dynamic model is set up which combines these lubricant damping sources along with structural damping. A number of comparisons with benchmark experimental evidence are presented for a range of operating conditions and gear geometries which prove that the proposed approach is sound in the case of spur gears. It is shown that the damping associated with lubricant squeezing contributes for the most part when contact losses and shocks between the teeth occur at critical speeds. For permanent contact conditions, however, structural damping appears as the major contributor to the overall system damping.

A quantitative calculation approach research of tooth surface friction characteristic parameters

A new calculation approach of tooth surface friction characteristic parameters is raised in this paper, the caclulation approach is based on gear drive test experience and finite element multi field coupling analysis method and technology.In the process of solution, friction characteristic concept of engineering oriented complex gear drive is raised, “experiment-calculation composite model” is built, tooth surface friction characteristic parameters(friction coefficients) are inversely analyzed by the composite model under different lubrication conditions. The problem of complicated tooth friction coefficients is solved. The calculation method is a new idea on solving friction characteristic parameters under complex lubrication conditions, it unites theoretical research, system modeling, numerical simulation and experimental test, so its solution is more reasonable. Exactly research friction coefficients can help to search gear friction principle and to upgrade the level of decrease noise and vibration of gear.

Wear load capacity of crossed helical gears with wheel made from sintered steel

Crossed helical gears have an important position in power transmission. Important advantages of the crossed helical gears are the small design, the realization of high ratios in one stage, and the low noise characteristics. The paper presents a theoretical and experimental research of mesh efficiency, tooth friction coefficient and wear for a wheel of crossed helical gears made of Fe1.5Cr0.2Mo sintered steel with sinter-hardening treatment and without additional treatment. The calculation method is also given for the determination of wear load capacity of the worm with a helical gear made of Fe1.5Cr0.2Mo sintered steel with sinter-hardening treatment. These results provide product developers with the first important clues for indicators for calculation of the worm with a helical gear.

A simplified multi-objective analysis of optimum profile modifications in spur and helical gears

A simplified analysis is presented in order to evaluate the influence of the profile modifications minimising transmission error time-variations on some other key design criteria such as mesh forces, stresses and tooth friction losses. A unique equation for the set of profile modification rendering transmission error nearly constant is presented and a number of original stress and loss factor closed-form formulae are derived whose results compare very well with those obtained by numerical simulations. Some general results are then deduced about the evolutions of the design criteria with regard to optimum relief parameters which are believed to be useful at the early stage of profile modification design.

&lt;b&gt;Evaluation of palatal rugoscopy in dentulous and edentulous cases for human identification in forensic dentistry &lt;/b&gt;

The search for identity is based on a set of characteristics, which defines the uniqueness of a person. Principles such as classificability, immutability, persistence, practicability and uniqueness must be considered when applying an identification technique. This study aimed to evaluate the use of palatal rugoscopy in dentulous and edentulous volunteers, with or without upper removable denture, for purposes of human identification. In this study 60 subjects were asked to give dental casts and photography of the upper dental arch, defined in the following groups: Group A (n = 30, edentulous patients with full upper removable dentures) and Group B (n = 30, dentulous without upper removable partial denture). The rugoscopy analysis method used was Martins-dos-Santos classification, for checking the applicability and success in human identification. It was found that it is possible to use this technique and it has an application of 40% in the group A and 86.66% in the group B. In conclusion, the identification method by palatal rugoscopy is satisfactory for dentulous patients, however in cases of tooth loss and friction cases generated by prosthetic devices, the region of the palate lose its characteristics, but even then it is still possible to be applied.

Excitation prediction by dynamic transmission error under sliding friction in helical gear system

Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.

Tooth friction losses in internal gears: Analytical formulation and applications to planetary gears

An original formulation for tooth friction power losses in internal gears including the influence of tooth profile modifications is presented. For unmodified gears, the results agree well with the classic formulae in the literature thus validating the proposed approach. The contributions of profile modifications on internal gear efficiency are compared to that on external gears and the formulation is extended to planetary gears. Finally, the role of profile relief on planetary gear efficiency is pointed out and commented upon.

Analysis of Tooth Surface Temperature Field and the Influencing Factors of Face Gear Driven

According to the theory of heat transfer, it analyzed the calculating method of tooth friction heating in the process of face gear tooth meshing. It emulational analyzes the thermal coupling of the face gear with ANSYS/LS-DYNA, and extracts the state of each engaged positions in the meshing process, emulate the temperature distribution &amp; temperature changing trends in the process of face gear tooth meshing. Through the temperature measurement experiment the face gear contact, it verifies the correctness of the emulation results. Simultaneously, it also analyzes the influence to the surface temperature of face gear of rotation and load, In the case of other conditions remain unchanged, low-speed is an effective way to prevent instantaneous temperature rise.

Tribological Investigation of K Type Worm Gear Drives

This paper presents a calculation method to determine the locally changing tooth friction coefficient along each contact line based on the TEHD lubrication theory for worm gear drives operating in mixed lubrication conditions. This also involves a detailed presentation of a procedure to specify the proportions of boundary lubrication and hydrodynamic lubrication as well as temperature states in contact. By comparing the calculated tooth friction coefficients with experimental test results, it can be stated that the calculated results properly approximate the measurement results.