Meshing Zone Research Articles

Innovative insights into nanofluid-enhanced gear lubrication: Computational and experimental analysis of churn mechanisms

This study offers unique insights into the churn lubrication mechanism in gear transmission systems through the utilization of nanofluids for the first time. Various performance parameters of the prepared nanofluid lubrication oil are measured, along with the discussion of suspension stability. Based on the overset mesh method and VOF multiphase flow model, a rotating fluid domain calculation model considering the nanofluid-air two-phase is proposed. The high-speed nanofluid lubrication experiment platform is established to track churn phenomena and identify the oil volume fraction on the gear surface. Comparing simulation results with experimental data confirms the calculation accuracy in depicting oil flow and churn lubrication. Result shows that the interaction between droplets and the gear surface involves splash, rebound, adhesion, and diffusion. The nanofluid exhibits improved adsorption, resulting in a higher oil volume fraction. When the rotation speed is increased, intensified oil spatter and atomization are observed. The ranking of nanofluid lubrication performance is Al2O3, SiO2, Fe3O4, CuO, and TiO2 particles, which are approximately aligned with contact angle magnitudes. For 3 % nanoparticles concentration, less oil is swung off, more is drawn into the gear meshing zone, and subsequently squeezed out. Image recognition results align with numerical simulation, indicating that the oil distribution of nanofluid is better than that of base fluid lubrication. This work serves as a foundational exploration for future nanofluid lubrication and heat dissipation, offering insights into preventing oil film rupture, tooth surface wear, gluing and other failure mechanisms.

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.

A fundamental approach to determine the impact of aramid and carbon fibers on durability and tribological performance of different polymer composites demonstrated in gear transmission process

Abstract When selecting a polymer or a reinforced polymer material for a specific drive technology, it is crucial to have a comprehensive understanding of the component’s operating characteristics, including the mechanics of tribological contact and the fatigue life of the materials used in gears. The choice of material plays a pivotal role in the gear running process, as it induces heat generation in the meshing zone and triggers flank wear progression along the high points of the teeth, which directly impacts the gear’s lifetime. This paper presents the results of durability testing conducted on steel/polymer gear pairs. The tested polymer materials were based on polyacetal and polyamide 66 chemical bases, reinforced with aramid, carbon fibers, and internally lubricated with polytetrafluoroethylene. The aim of the study was to evaluate the durability and thermal response of the materials and determine their correlation with flank wear rate progression. The results indicate that gears produced from polyacetal, and carbon-reinforced polyamide 66 materials exhibit the longest durability. Notably, the generated meshing temperatures are closely connected with flank wear propagation. The lowest wear coefficients were observed in gears produced from polyacetal and polyamide 66 materials reinforced with carbon fibers.

Thermal Elastohydrodynamic Lubrication of Herringbone Gear Considering the Effect of Oil Gas Mixture

AbstractIn order to analyze the dynamic behavior of the oil film in the herringbone gear meshing area under oil injection lubrication conditions more accurately, this paper proposed a thermal elastohydrodynamic lubrication (TEHL) analysis method, by combining the traditional TEHL calculation method with two-phase flow theory. First, ansys/cfx 18.1 was used to determine the air content of the lubricating oil in the meshing zone under the injection condition. Then, considering the influence of air content on the rheological properties of lubricating oil, the traditional TEHL model was improved. On this basis, the influence of injection angle α1 on the oil fraction and the lubrication characteristics of the oil film were analyzed. This research can provide a feasible method for the analysis of the lubrication characteristics of herringbone gear.

CFD Investigation on Oil Injection Lubrication of Meshing Spur Gears via Lattice Boltzmann Method

The meshless Lattice Boltzmann Method (LBM) is introduced and employed to solve the complex two-phase flow problem of jet lubrication of meshing spur gears. Computational fluid dynamics (CFD) simulations based on LBM are carried out using the model of an oil jet impacting rotating gear presented by available experiments, which reveals how the liquid column is broken throughout the tooth tip cutting off the oil jet. Typical oil flow phenomena obtained by simulations are compared with experiments, demonstrating good qualitative agreement, which validates the feasibility of LBM to simulate the air–oil–structure interaction problems involved in the jet lubrication of spur gears. A three-dimensional (3D) simulation model of a spur gear pair lubricated by an oil jet is established, and simulations with different operating conditions are conducted. The evolution process of the oil jet while injecting into the meshing zone is captured, and the effects of jet velocities, jet heights and jet angles on the lubrication performance are investigated.

Meshing theory of offsetting Archimedes cylindrical worm drive

The main purpose of this article is to establish the meshing theory for the offsetting Archimedes cylindrical worm drive, which consists of a cylindrical worm with asymmetric tooth profile and a plane worm gear. The equations of the tooth surfaces, the meshing function, the curvature interference limit function, and the curvature parameters are all obtained for the worm drive. By means of the developed reference-point-based meshing theory, the reference point located strictly on the tooth surfaces of a worm drive is determined via solving the system of nonlinear equations, in which no iteration is needed to perform this process. Based on the location of the reference point, the tooth surface boundaries are ascertained for the plane worm gear. The numerical case is carried out and the conjugate zone, the instantaneous contact lines, and the local meshing property parameters are acquired for the worm drive. The whole thread length of the cylindrical worm can almost be used and the conjugate zone can cover the whole tooth surface of the mating plane worm gear. In the meshing zone, not only the contact stress level between the tooth surfaces is relatively low, but also the lubrication condition is favorable. The comparative study on the meshing properties between the offsetting Archimedes cylindrical worm drive and the Archimedes conical worm drive is carried out.

Modeling the Meshing Procedure of the External Gear Fuel Pump Using a CFD Tool

In modern aircraft engine technology, there is a tendency to replace the mechanical drive of external gear fuel pumps with an electric one. This significantly reduces the integral energy consumption for pumping fuel (kerosene). On the other hand, in order to reduce the dimensions of the structure, it is reasonable to increase the rotation speed of the pumping unit gears. The above considerations make it advisable to study the problems that may arise in the design of pumping units. Analysis of the existing designs of external gear fuel pumps shows that the flow processes in the meshing zone have a significant impact on the pump performance and lifetime. Incorrect truss plate geometry and the compensation system lead to an increase in the velocities when opening and closing the cavity in the meshing zone, which causes intense cavitation. To understand the causes and factors which influence this phenomenon, it is necessary to study the fluid flow behavior in the meshing zone gaps. High-speed cameras are used to experimentally study the flow behavior. However, this approach gives only a qualitative result but does not allow for determining the absolute values of pressure and load in terms of the angle of rotation. Nevertheless, high-speed surveying can be used as a basis for fluid flow model verification. In this paper, the model of the fluid flow in a high-pressure external gear pump was proposed. The verification of the simulation results for HDZ 46 HLP 68 oil operation was carried out according to the results of experimental data visualization. The influence of rotation speed on the position of cavitation zones was revealed and confirmed by operational data. The analysis of the flow process in meshing for kerosene as a working fluid was carried out.

Kinematic-Geometric Lubrication Theory and Its Application to Arc-Toothed Cylindrical Worm Drive

Abstract The kinematic-geometric lubrication theory, which combines the results from the elastohydrodynamic lubrication theory and the meshing theory for gearing, is put forward for a line-conjugate gear drive to investigate its global intrinsic lubricating characteristics to guide its geometric design. The investigation concerning the global lubricating characteristics of the gear drive can be well utilized to seek the lubricating weak zone in the whole meshing zone and to determine the reasonable operating parameters for it. The relationship between the lubricating angle and sliding angle is made clear, and the lubricating angle is recommended to determine the lubricating weak point. The kinematic-geometric coefficient of oil film thickness is proposed to evaluate preliminarily the lubricating characteristics of the gear drive. This theory is applied to the arc-toothed cylindrical worm drive, and it is discovered that there is one path of lubricating weak points on the tooth surfaces. The path is from the worm gear addendum to dedendum and is almost impossible to be eliminated via analysis and research. The path is roughly located in the middle of the worm gear tooth surface, and a lubricating weak zone exists around this path whose area roughly accounts for one-third of the whole meshing zone.

Prediction of tribological and dynamical behaviors of spur gear pair considering tooth root crack

Variations in gear tooth meshing stiffness and tribological characteristics caused by tooth root cracks seriously affect the dynamic performance of gears, limiting the development of durable high strength gears. Therefore, the potential energy method was applied to obtain the time-varying meshing stiffness of the spur gear pair, and the finite element method was applied to verify the calculation results. Secondly, the load distribution of the gear with the cracked tooth root was derived using coordinated deformation conditions, and the effect of the tooth root crack on the tribological characteristics of the tooth surface was obtained based on the elastohydrodynamic lubrication (EHL) model. Finally, the tribo-dynamic behaviors of the gear under the action of the root cracks were investigated. The results indicated that root cracks change the load distribution ratio in the double-tooth meshing zone, which leads to corresponding changes in the tooth surface film thickness and friction coefficient. In addition, when the cracked teeth are engaged in meshing, the reduction in meshing stiffness causes vibration and shock, which causes the appearance of sidebands near the main meshing frequency. The amplitude of the dynamic meshing force increased with the increase in the degree of root cracks.

Thermal Analysis of Herringbone Gears Based on Thermal Elastohydrodynamic Lubrication Considering Surface Roughness

To predict the temperature distribution of the tooth surface of a herringbone gear pair, a numerical method for the determination of frictional heat generation was proposed by establishing a thermal elastohydrodynamic lubrication (TEHL) model in the meshing zone taking surface roughness into account. According to the real micro topography of the tooth surface measured by a non-contact optical system and loaded tooth contact analysis, the friction coefficient was obtained by a TEHL analysis and then the heat generation in the contact zone was determined. With the combination of heat generation and heat dissipation analysis, the single tooth model of the herringbone gear pair due to the finite element method (FEM) was proposed and the steady-state temperature distribution of the tooth surfaces was predicted by FEM simulations. The simulation and the experimental results demonstrated good agreement, which verified the feasibility of the present numerical method.

Optimal analysis of gear modification fitting in alternating time domain aiming at minimizing meshing-in impact of teeth-pair contact interface

In a pair of actual gears alternating meshing process, the transmission system errors and thermal elastic deformation of the gear teeth can cause gears in the meshing zone to form high contact pairs inconsistently mesh-in and mesh-out points to deviate from the theoretical line, which will lead to sudden changes in meshing velocity and an instantaneous meshing effect. Offline meshing impact generates large additional loads, and it increases the vibration and noise of gear transmission system. Further, the gear teeth mesh-in impact is significantly greater than that of gear teeth mesh out. Therefore, to analyze the impact with the minimum value of gear teeth mesh in, the initial mesh-in points need to be determined, and the meshing impact velocity and impact force of teeth meshing-out need to be calculated. The optimized meshing tooth-pair contact interface (CI) anti-impact numerical calculation mode is validated using the loaded teeth contact analysis method.

Meshing Characteristic of Arc-Toothed Cylindrical Worm Pair and Cutting Geometric Condition of Its Worm

Abstract The arc-toothed cylindrical worm has an arc tooth profile in a section, which may be the axial section, the normal section, or an offsetting plane of the worm helical surface. The meshing principle for a gearing containing such a worm is established. The normal vector of instantaneous contact line is determined in the natural frame and the meshing performance parameters are obtained without the help of the curvature parameters of the worm helical surface to ensure the established meshing principle is concise and practical. The numerical results show that the worm working length can be beyond half of the thread length and the meshing zone of the worm pair can cover most of the worm gear tooth surface. The instantaneous contact lines are uniformly distributed and the worm pair forms double-line contact. The numerical outcomes of the induced principal curvature show that the contact stress level between the teeth is higher in the middle of the worm gear tooth surface and near its dedendum. The forming condition of the lubricating oil film is poorer in the middle of the worm gear tooth surface and from addendum to dedendum as demonstrated by the numerical results of the sliding angle. The normal arc-toothed worm lathed by an offsetting cutter is recommended to apply in industry after various researches and analyses. The cutting geometric condition of the worm is investigated quantitatively. It is discovered that the rule of the cutter working relief angle changes along the cutting edge during lathing the worm.

A Transient Mixed Elastohydrodynamic Lubrication Model for Helical Gear Contacts

Abstract In this study, a non-Newtonian, transient, isothermal, mixed elastohydrodynamic lubrication (EHL) model is proposed for helical gear contacts. The model accounts for nonelliptical contacts subject to spatially varying sliding and rolling velocity fields that are not aligned with any principal axis of the contact region, which is the case for helical gear contacts. The time-varying changes pertaining to key contact parameters and relative motion of roughness profiles on mating tooth surfaces are captured simultaneously to follow the contact from the root to the tip of a tooth while accounting for the transient effect due to relative motions of the roughness profiles. Actual tooth load distributions, contact kinematics, and compliances of helical gear contacts are provided to this model by an existing helical gear load distribution model. Measured three-dimensional roughness profiles covering the entire meshing zone are incorporated in the analyses to investigate its impact on the EHL conditions as well as mechanical power loss. Results of a parametric sensitivity study are presented to demonstrate the influence of operating conditions and surface roughness on the EHL behavior and the resultant gear mesh mechanical power loss of an example helical gear pair. The accuracy of the proposed mixed-EHL model is assessed by comparing the mechanical power loss predictions to available experimental results.

Application of polymeric materials for obtaining gears with involute and sinusoidal profile

In the article research related to the increasing in the scope of application of additive technologies in the construction of machines for the production of gears with involute and sinusoidal profile from polymeric materials was presented. The designed original research stand and with its use carried out a series of preliminary fatigue tests of the obtained polymer gears with an involute and sinusoidal profile was show. The tested gears were obtained in the technology of rapid prototyping by the FFF (Fused Filament Fabrication) method from polymer composites obtained in the form of an ABS (acrylonitrile/butadiene/styrene) – based filament. Based on the results obtained, it was noticed that the temperature in the meshing zone of the gears with involute profiles is higher than for sinusoidal profiles, regardless of the type of composite from which the gears were made. It should also be noted that in the range of nominal load, the sound intensity level of the meshing zone is also lower for gears with a sinusoidal profile than for gears with an involute profile. Based on the tests carried out, an increase in sound intensity was noticed in the case of gears obtained from selected composites (Table 2) compared to the gear obtained from unfilled ABS. However, in the case of gears obtained from the tested composite materials, we observe a decrease in the gear operating temperature (Table 2). The most favorable results of these tests were obtained for gears with a sinusoidal profile obtained from ABS + P2 composite, which show the lowest operating temperature of the gear. It should also be mentioned that slightly worse results were obtained for involute gears.

Investigation of gear rattle noise including visualization of vibro-impact regimes

This paper presents an experimental study of gear rattle noise induced by vibroimpacts between gear teeth. A specific experimental set-up is designed to analyse the nonlinear dynamic behaviour of a spur gear submitted to input velocity fluctuation. The drag torque, the mean drive gear rotational speed, the velocity fluctuation amplitude and frequency are controlled during experiment. The dynamic transmission error is measured thanks to high resolution optical encoders. The originality of the experimental set-up consists in using a high-speed camera in order to visualize the contact zone and to identify the occurrence of successive impacts between gear teeth. The rattle threshold is identified as a function of velocity fluctuation amplitude and frequency for various operating drag torques and mean rotational speeds. Experiments show very good agreement with the theoretical master curve. Once impacts occur, stationary nonlinear gear dynamic response and rattle noise radiated by the mechanical system are investigated. Most of the time, an almost periodic response is observed with 2 impacts per period. One impact between the active flanks alternates with one impact between the reverse flanks. A contact phase between gear teeth is observed after each impact instead of an instantaneous rebound. The number of successive tooth pairs crossing the meshing zone without any contact between gear teeth varies according to the ratio of the excitation frequency to the rotation frequency. Analytical and numerical works performed using a gear rattle model show good agreement with experiments. Finally, sound pressure emitted from the gear pair is measured. The acoustic power imputable to gear rattle is found to be proportional to the total kinetic energy transferred per second to the system by the successive impacts.

Contact Fatigue Failure Analysis of Helical Gears with Non-Entire Tooth Meshing Tests

This study presents an experimental approach based on partial tooth meshing contact fatigue with constant amplitude and different lengths of load cycles. To achieve this, 20CrH helical gears were considered, limiting the region of interest to one-third of the tooth to accelerate crack initiation and propagation. Different factors, such as number of fatigue cycles, tooth flank morphology, residual stress, hardness, and microstructure evolution under fatigue, were considered. The ultimate goal was to relate these variations with the observed failure modes. The results showed that with increasing cycle number, the residual stress at the same position in the meshing zone of the tooth flank increased first and then decreased. The residual stress values at the lower position of the pitch circle were larger than that of the addendum and dedendum. After cyclic loading, the content of the twin martensite within the microstructure below the pitch circle decreased and the corresponding hardness value of the tooth flank was reduced. After long-term cyclic loading, the precipitated phases aggregated and grew and the discontinuous distribution hindered the grain boundary slip. The dislocation density increased, and the pile-up of dislocation resulted in stress concentration at the grain boundary and the phase boundary, which induced the initiation of fatigue crack of the tooth flank.

Theory study of a novel planar enveloping internal-meshing worm drive

Some special compact mechanical transmissions with multi-load are required in robot joints, artillery systems, agricultural machinery and multirole shaft-driving devices, but the existing products of mechanical transmissions cannot meet the demand of modern industry, and need some new transmission structure or solution. To this end a novel worm gear named the planar enveloping internal-meshing worm drive is proposed for applications requiring multi-load transmission for the first time. Its meshing functions, including the induced normal curvature, lubrication angle, and relative entrainment velocity, are developed on basis of gear meshing theory. Furthermore, the meshing zone for the worm tooth is analyzed through tooth contact analysis in order to determine the optimal mother plane dip angle β. Moreover, the tooth profile of the worm wheel is optimized and the worm parameters obtained through tooth contact analysis is verified. Finally, the worm gear is manufactured by using the 3D-printing technology to measure the correction for the theory investigation. The presented worm drive exhibits ideal meshing performance, with minor contact stress and high lubrication. This gear set is expected to find applications in such systems as robot joints, artillery systems, and multi-roller shaft-driving devices.

Synthesis of cylindrical gears with optimum rolling fatigue strength

This paper presents a procedure for the geometric synthesis of heavy-duty, cylindrical gear drives. Particularly tooth profile forms were generated here which have almost constant contact stresses along their entire line of engagement. The synthesis is based on analysing the properties of the entire meshing zone in detail. The concept of the synthesis is developed by analysing various methods for increasing the load-carrying capacity of gear drives through optimised gear geometries, by analysing and selecting quality criteria for evaluating gears as well as examining the zone of meshing. Based on the concept of synthesis, a method of interactive synthesis is finally worked out with which especially the geometry of cylindrical gear drives can be optimised with regard to their load-carrying capacity or contact strength. The maximum or rather demanded load-carrying capacity or contact strength are used as reference parameters here.

Study on the Maximum Contact Stress of Involute Gear Pair with a Small Number of Teeth

As the traditional calculation formula for contact strength of involute gear pair is not applicable for the calculation of those with small number of the teeth, some researches on the calculation of contact strength of involute gear pairs have been done. The calculation of the contact ratio of involute gear pair with a small number of teeth can confirm that its end face engagement must be of single-tooth mesh, while the research on the actual contacting lines in the meshing zone can find out the precalculated position, computational formula, and strength condition of the maximum contact stress according with the gear pairs with a small number of teeth.

The Modeling Gear Optimization Design Research Based on Pro-E

With the development of computer technology, gear modeling in industry more and more widely used, the PRO-E tool has good modeling function, on the design of three-dimensional CAD tools has a significant role, the tracing point method, parameter method, plug-in method analysis, optimum gear profile modeling. On the tooth height model modification method, draw gear high maximum model modification, model modification can be assigned in the active or passive gear wheel tooth, but also at the same time in the driving wheel and a driven wheel model modification. Corresponding to a single tooth meshing zone involute not model modification, only to repair the dual meshing zone, reach the gear model optimization objective.