High Contact Ratio Research Articles

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.

Analysis of the tooth-root stress of external spur gears with high effective contact ratio

For spur gears with contact ratio close to 2, the extension of the contact interval resulting from loaded tooth deflections and local contact deformations may result in an effective contact ratio above 2. In these cases, the load is transmitted by at least two tooth-pairs, the maximum load and tooth-root stress decrease, and therefore the calculation methods of the gear rating Standards ISO and AGMA provide very conservative results. In this work, two models are applied to the calculation of the tooth-root stress of load-induced high contact ratio external gears: (i) an analytic model of load sharing, based on the minimum energy method, and (ii) a finite element model, which validates the results obtained from the previous model. Obtained values of the stress are compared with those provided by ISO and AGMA rating methods, which do not account for the stress reduction due to the higher contact ratio. A new modification coefficient is proposed to correct these conservative values, which allows the AGMA and ISO geometry factors to remain as no load-dependent factors and keep their actual calculation methods and significance.

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.

Thermal contact resistance on cylindrical flux channel with high contact ratio

This paper considers the resistance to the heat flow between two thick solids with a high contact ratio in a vacuum. Based on the least-action principle, we derive closed-form mathematical expressions for the temperature distribution and non-dimensional thermal contact resistance, both expressed as functions of the radii ratio. Furthermore, the thermal contact resistance is investigated as a function of contact pressure and microhardness. A comparison of the conventional and proposed methods reveals that the proposed method is more accurate for calculating the thermal contact resistance with a high contact ratio. In equipment with high contact pressure, such as electromagnetic launch, we compare armature melting models using different calculation methods for contact resistance. Small and all contact models were established based on the traditional and proposed methods, respectively. The melting morphology of the armature obtained from the all contact model is highly consistent with the experimental results. During the experiment, in areas where the armature did not melt, the small contact model incorrectly calculated the melting of the armature. The all contact model can describe the strong cooling effect of the rail on the armature, preventing the armature from melting. The all contact model obtained higher heat sources, contact thermal conductivity, and contact pressure in the melting region. Under the combined effect of the three factors, a deeper and more concentrated melting morphology was obtained. This morphology is more consistent with the experimental results.

Analytical model of meshing stiffness, load sharing, and transmission error for internal spur gears with profile modification

The influence of the teeth geometry on the load distribution, transmission error, and meshing stiffness of internal spur gears is very similar to that of external gears. Therefore, the formulation of the models for strength and dynamic calculations for internal and external gears is also similar. However, the internal gears have usually greater values of the contact ratio, frequently above 1.8, even 1.9. In these cases, the lengthening of the contact interval due to the elastic deflections of the teeth may result in an effective contact ratio greater than 2, with the subsequent changes in the load sharing and transmission error. These changes are not properly described by the theoretical models for high contact ratio spur gears. In this paper, a model of load sharing, quasi-static transmission error, and time-varying meshing stiffness for internal spur gears with profile modification is presented, which has been applied to low contact ratio internal gears which, due to the transmitted load, become high contact ratio internal gears. The influence of the variations of the transmitted load on the load capacity is also studied.

An Analysis of Time-Varying Meshing Stiffness of High Contact Ratio Gears Considering a High-Order Modification Curve

An Analysis of Time-Varying Meshing Stiffness of High Contact Ratio Gears Considering a High-Order Modification Curve

Modelling and dynamic behaviours of a high-contact-ratio spur-gear system considering rough surface

The dynamic characteristics of a high-contact-ratio (HCR) spur-gear system having rough surfaces generated by shot peening (SP) were studied, with specific emphasis on characterisation of the gear-surface topography as well as modelling of the gear backlash and static transmission error. Accordingly, a four-degree-of-freedom dynamic model was established. Simulation experiments were then conducted using surface roughness, rotational velocity, input torque, and shaft-bearing stiffness as the variables. The results show that the dynamic characteristics of the gear system tend toward instability with increasing surface roughness. The models developed in this study outline a method for building indirect relationships between the vibration, dynamics, and tooth-surface microscopic features. This research thus provides a theoretical basis for designing the tooth-surface topography of HCR gears in the future.

Crack detection of a modified high contact ratio gear

For the purpose of vibration-based fault detection and to avoid gear failure consequences it is necessary to investigate the possibility of early fault detection. A reduction in the gear time-varying mesh stiffness (TVMS) due to the existence of a crack can be used to detect and evaluate tooth damage. The reduction in TVMS has an impact on the system’s dynamic response signal, and then the used fault detection indicators are affected. The current article sheds light on the fault detection possibility of high contact ratio (HCR) gears as compared to those standard ones of low contact ratio (LCR). The influence of modifying the gear tooth addendum dimension for obtaining a high contact ratio on the possibility of early fault detection is studied. Twenty different crack cases are examined by using both the LCR and HCR design cases. For every crack case, the mesh stiffness is evaluated and introduced to the used gear dynamic model for obtaining the system’s dynamic response. The TVMS evaluation is presented for both the LCR and HCR gear cases. Four fault detection indicators, namely the RMS, kurtosis, peak value and crest factor are applied as different measures to enhance the research outcome. The results show that the studied indicators will have less increase when the crack size increases in the HCR design than in the LCR one. Therefore, the HCR design will be less sensitive or more difficult to detect from the fault detection perspective. Lowering the amount of signal noise is applied to the HCR case to examine the impact on enhancing the obtained indicators. The four applied indicators show different behaviours with reducing noise.

Stiffness Analysis of High Contact Ratio Spur Gear with Asymmetric Teeth

The demands of high carrying capacity and low vibration of gear transmission systems in aviation, aerospace, and other areas are addressed by high contact ratio gears with asymmetric teeth, which have a wide range of potential applications. The Weber energy technique is utilized to determine the stiffness of high contact ratio spur gears with asymmetric teeth, and the effect law of the stiffness parameters is researched, due to the paucity of study on these gears. The influence of the drive side addendum factor, modulus, and pressure angle on the stiffness of asymmetric high contact ratio spur gears is investigated. The deformation of the gear will be exacerbated by an increase in the addendum factor, and the comprehensive stiffness of the gear will grow as more gear pairs participate in the meshing. The rigidity of gears may be greatly increased without ignoring modulus if the driving side pressure angle is properly increased.

Design of Linear Functional Noncircular Gear with High Contact Ratio Used in Continuously Variable Transmission

Continuously variable transmission (CVT) of noncircular gear has the technical advantages of large bearing capacity and high transmission efficiency. The key technology of CVT with noncircular gear has been broken through some countries, and is in the stage of deep application research. Although the characteristics and design methods of noncircular gear pairs have been continuously studied in China, the noncircular gear CVT is still in the preliminary exploration and research stage. The linear functional noncircular gear pair, whose transmission ratio is a linear function in the working section, to realize continuously variable transmission was the research object in this paper. According to the required transmission ratio in the working section, the transmission ratio function in the non-working section was constructed by using a polynomial. And then the influence of pitch curve parameters in the working section on which in the non-working section was also analyzed to obtain the pitch curve suitable for transmission of this gear pair. In addition, for improving the stability and bearing capacity of gear transmission, the noncircular gear pair transmission with high contact ratio was designed. Furthermore, the accurate value of the contact tooth length was calculated based on the gear principle and the characteristics of the involute tooth profile, from this the contact tooth length error was calculated by comparing the accurate value with its actual value obtained by the rolling experiment. Finally, an indirect method to verify the contact ratio by detecting the contact length error of the tooth profile was proposed.

Research on the Strength Calculation Method and Effects of Gear Parameters for High-Coincidence High-Tooth Gears

This article studies the calculation method for the tooth root bending stress of a high-tooth gear pair with a high contact ratio. The boundary point of the double-tooth meshing zone of the high-tooth gear pair is used as the loading point for the load, and the calculation formula for the bending stress at the dangerous section of the tooth root is obtained. By using ANSYS finite element simulation, the effect of the addendum coefficient, pressure angle, and other gear parameters on the bending stress of the tooth root is studied. The analysis shows that increasing the pressure angle will reduce the bending strength of the tooth root. Increasing the coefficient of a tooth’s top height will lead to an increase in the bending strength of the tooth root. Comparing the finite element analysis (FEA) results with the theoretical calculation results, the analysis shows that under low loads, the maximum error of the theoretical calculation values of the driving toothed gear and driven gear shall not exceed 13.53% and 15.42%, respectively. Under high loads, the maximum theoretical errors of the driving toothed gear and driven gear shall not exceed 8.78% and 10.91%, respectively. This verifies the correctness of the calculation method, which is of great significance for improving the load-bearing capacity of high-tooth gears and for guiding tooth shape design.

Tribological Aspects Affecting Surface durability of Tooth-Sum Altered Spur Gears: A Load Sharing Approach

The performance of tooth-sum altered (ATS) gears is determined by the factors influenced by their profile geometry. This study aims to explore the influence of gear geometry modification on tribological aspects that affect surface wear in ATS spur gears. A computer code is developed to simulate surface wear numerically, using Archard's wear model, Greenwood-Williamson micro-asperity contact model, and Johnson’s load-sharing approach. The outcomes of the study indicate that the low contact ratio ATS gears promote the formation of thick oil film owing to reduced specific sliding and increased speed. However, high contact ratio ATS gears create unfavorable operating conditions resulting in extreme boundary lubrication. The effectiveness of lubricant oil film in reducing wear in ATS gears is associated with its modified profile, sliding velocities, load bearing, operating temperature, and oil viscosity.

A CBCT Evaluation of the Proximity of Mandibular Molar Roots and Lingual Cortical Bone in Various Vertical Facial Patterns and Factors Related to Root-Cortical Bone Contact

The objective of this study was to assess the proximity of the mandibular molar roots and the lingual cortical bone in patients with various vertical facial patterns and determine factors related to root-cortical bone contact. A total of 145 patients (84 males, 61 females, mean age: 22.0 ± 1.76 years) were assigned to hypodivergent (36 patients), normovergent (80 patients) and hyperdivergent (29 patients) groups based on their facial height ratio. Cone-beam computed tomography (CBCT) images were used to measure the distance between the mandibular molar roots and the lingual cortical bone, and any instances of root-cortical bone contact were identified. The study investigated the correlation between the contact of the mandibular molar roots with the lingual cortical bone and several variables, including sex and cephalometric measurements. The distance between the mandibular molar roots and the lingual cortical bone was significantly shorter in the hyperdivergent group than in the hypodivergent group (p < 0.05). Of the total root-cortical bone contact, 87.6% was observed in the mandibular second molars, and the distal roots of the mandibular second molars had the highest contact rate at 43.1% in the hyperdivergent group (p < 0.05). Among the evaluated variables, only the distance between the distal root apex of the mandibular second molar and the mandibular plane was found to be associated with contact of the mandibular molar roots with the lingual cortical bone. An increase of 1 mm in this distance was associated with a 22% decrease in the likelihood of contact between the mandibular second molar roots and lingual cortical bone (p < 0.001). Given the proximity and high contact ratio between the mandibular molar roots and lingual cortical bone, it is recommended that these structures be evaluated using CBCT before planning molar distalization or intrusion in hyperdivergent patients.

Design and simulation of a trenching device for rice straw burial and trenching based on MBD-DEM

Rice straw return is an effective measure to ensure food safety and improve soil fertility. In-depth studies have gradually been conducted on mechanized ditch burying and field returning, but problems in terms of different ditching depths, unstable ditch types and influences on the subsequent operation effects remain. With regard to the problems of different ditching depths and unstable ditch types of a straw ditch burying and field returning machine, a ditching and returning device was designed and optimized in the study presented in this paper, and in-depth analysis was performed on the mechanism of the ditching process. The MBD-DEM coupling method was used to conduct a simulation experiment for the ditching device. The soil particle throwing mechanism in the ditching process was analyzed to explore the influence of the ditching device on the throwing track and falling point of the soil particles. Three stages were clarified in the ditch formation, and the fitting curves and changing trends of the soil particle speeds at different stages were determined. The single-factor simulation tests suggested that the ditch stability decreased with increasing forward speed and horizontal inclination angle and increased with increasing main sprocket speed. The field testing indicated that the actual ditch section had a high contact ratio with the simulated ditch section, which verified the accuracy of the simulation testing. This study can provide ideas for expanding the utilization measures of rice straw return and provide methods for exploring the mechanism of complicated mechanical movement and soil interaction.

Investigation on high contact ratio harmonic two-dimensional tooth profile design based on mid-point meshing method

Investigation on high contact ratio harmonic two-dimensional tooth profile design based on mid-point meshing method

Calculation of line and point contact ratio for orthogonal spur-face gear drive

The contact ratio of face gear drive is hard to calculate precisely because it is point contact adjusted from line contact to avoid jamming. To obtain the calculation methods and improvement measures for the contact ratio of face gear drive, the line contact ratio (LCR) in shaping and the point contact ratio (PCR) in meshing are investigated in this paper. Tooth surface equations of face gear shaping are established based on its generation principle and the contact line midpoint tracks are obtained. Iterative equations to accurately calculate restrictive conditions (undercutting and pointing) for face gear tooth are constructed and verified, their approximate equations are given further. Meshing tracks in face gear drive are obtained by solving the established meshing equations. Calculation methods of the LCR and PCR are elaborated according to their definitions and the fitting equations are given for engineering application. The results show that the PCR is markedly lower than the LCR. The advantage of high contact ratio of face gear drive is significantly affected because it is very sensitive to the realization of point contact. It is acceptable to use the LCR to approximate the PCR when the distribution range of the meshing track on the face gear tooth surface is determined. It provides a theoretical basis for the design and optimization of orthogonal spur-face gear drive.

An investigation of nonlinear flow behaviour along rough-walled fractures considering the effects of fractal dimensions and contact areas

This study focuses on the investigation of the nonlinear flow behaviour along rough-walled fractures with contact areas in the framework of the lattice Boltzmann method. The numerical results indicate that the fracture surface roughness controls both the advective aperture and the eddy aperture in the analysis of pressure, velocity, and vorticity fields. The eddy volume fraction increases from 28% to 40% with the increase in the fractal dimension from D=2.0 to D=2.4. The parametric analysis based on Forchheimer’s equation further demonstrates that the enhancement in the vorticity field contributes to the strengthened nonlinear flow behaviour. The two competing roles of fractal dimension and contact area greatly impact the non-Darcy flow patterns. The fractal dimension is the main factor affecting flow nonlinearity at a low contact ratio, while the contact area dominates the nonlinear flow behaviour at a high contact ratio. The increase in the contact ratio strengthens the boundary effect, and thus greatly increases the volume of the eddy region and enhances the nonlinearity of the flow field. These observations provide a promising pathway to analyse the flow behaviour along the fracture based on vorticity analysis, and enlighten the understanding of the competing mechanism between fractal dimensions and contact areas for the influence of nonlinear flow behaviours.

Load share model based gear loss factor prediction in high contact ratio spur gear drive

Gear loss factor is considered to be a crucial parameter, and is governed by factors like contact load, sliding velocity, contact ratio, etc. Sliding power loss is a function of the gear loss factor and friction coefficient. It depends on the contact tooth load and its contact surfaces. A small decline in the gear loss factor and variation in the friction coefficient reduces the energy consumption which improves gear efficiency significantly. Hence, accurate prediction of the gear loss factor is important. This paper deliberates on measuring the contact load of High Contact Ratio (HCR) non-standard gear drive, using the finite element contact model. The input for the gear loss factor is obtained from a 2D elastic contact model using ANSYS. In the previous works the load is considered as a rigid hypothetical element, but in the real case it is varying at each instantaneous contact point. To address this, a more accurate method of predicting the power loss using the contact load share model is proposed. The effectiveness of this technique, built on the computational data and its accuracy are examined. Based on the accuracy, the load share model was suggested to be the most effective one compared to other techniques. The results show that the proposed model provides an effective tool for making reliability assessments on power loss and efficiency of high contact ratio gear drives under diverse operating conditions.

Taper corrosion in total hip arthroplasty – How to assess and which design features are crucial?

BackgroundIn total hip replacement, wear and corrosion arising from modular taper connections have increasingly become a serious clinical concern. Previous studies led to confounding results regarding the role of specific taper design features, likely due to the application of different analytical approaches. Accordingly, this study has two major objectives: first, to evaluate different analytical approaches to evaluate the fretting-corrosion behavior; and secondly to determine the effect of four specific design variables: the taper engagement situation, the stem taper length and surface topography in terms of roughness and contact ratio. MethodsAn in vitro fretting-corrosion test setup was used including an aggressive solution. Cyclic loading was applied, varying from 300 N to 2500 N at a frequency of 3 Hz. Taper dummies covering different implant designs were tested in seven different test groups.Different quantitative and qualitative analytical test methods such as electrochemical characterization, ion analysis, gravimetry and corrosion scoring were applied in order to quantify the material degradation. ResultsA stepwise linear regression analysis showed that the taper engagement situation is the predominant factor that predicts the metal ion release from the taper connection, followed by the contact ratio of the taper surface and subsequently the taper length. A distal taper engagement situation, as well as a high contact ratio and a short taper length are the relevant parameters that decrease the metal ion release.Hereby, metal ion analysis turned out to be the most precise and reliable method for determining corrosive driven material loss, followed by gravimetry. ConclusionIt was found that the taper engagement length is the major design parameter that influences the total ion release. It further turned out, that the selection of an appropriate analytical approach is essential for the evaluation of the corrosion behavior of taper connections in an experimental setting.

Effect of localised tooth spall defect on dynamic performance of a high-contact-ratio spur gear system

This study considers the tooth spall morphology and establishes a kinetic model of a high contact ratio gear pair system with an ellipsoid tooth spall defect. The mesh stiffness of the spalled gear system is evaluated using the potential energy method. To obtain the accurate dynamic response, the friction force was incorporated into the gear kinetic model. The dynamic transmission error and dynamic meshing force under different rotational speeds are acquired by the proposed model. The dynamics of a healthy gear system and spalled gear system was compared. The results reveal that the presence of the tooth spall defect alters the motion state of the system, making it prone to instability. The study provides a theoretical foundation for future research on spall defect diagnosis of gear transmission devices.