Tooth Flank Research Articles

Local considerations and experimental results on the contact behavior of crossed helical gears with general flank geometries

Crossed helical gears belong to gear units with crossed wheel axles and in most applications consist of a steel worm and a plastic wheel. Due to the high transmission ratio in a small installation space, they are used in actuators, auxiliary drives and positioning drives. The research into high-performance polymers is accompanied by increasingly powerful gears, de pending on the properties of the plastic material, to reach the load limits of steel materials. Research on steel/plastic crossed helical gears with geometrically optimized tooth flank geometries offers efficiency improvements and demonstrable efficiency potential, enabling higher overall load capacities and an increase in service life. A more detailed resolution of the contact behavior in the contact area allows friction energies to be considered and provides the basis for local wear and load capacity evaluations. Based on this, new crossed helical gears with general flank geometries can be designed, which have a positive influence on resource conservation and sustainability as a result of the increase in lifetime.

Incident angle optimization with multiple conflicting objectives based on BP-MOPSO in oblique laser interferometry

The oblique incident phase-shifting interferometric measurement method is an effective technique for assessing gear tooth form deviation. In the measurement process, the tooth flank incident angle is a crucial factor determining the quality of interferograms. Addressing the challenge in traditional optical path design, where the selection of the tooth flank incident angle encounters a trade-off among quality features such as measurable tooth area (MTA), interference fringe density (IFD) and interferogram compression ratio (ICR), this paper proposes an optimized method for the tooth flank incident angle. Firstly, a comprehensive evaluation model is established to calculate and analyze the MTA, IFD and ICR of the helical gear. Secondly, by integrating BP neural network and Multi-Objective Particle Swarm Optimization (MOPSO) algorithm, a tooth flank incident angle optimization method is devised to simultaneously optimize the measurement light incident angle γ and the rotation angle of the gear axis β. Finally, simulation analyses and physical experiments are employed to demonstrate the feasibility of the proposed method, compared to before optimization, the pseudocorrelation (PSD) value has increased by an average of 34%, and the residual points have decreased by an average of 80%, confirming its capability to improve quality interferogram and measurement accuracy.

Stiffness Modeling of Tooth Interior Fatigue and Tooth Flank Fracture and Their Fault Characteristics in Electromechanical Coupling Systems

Tooth flank fracture (TFF) and tooth interior fatigue fracture (TIFF) usually occur on case-harden gears in electromechanical coupling systems, both starting from the core caused by metal fatigue. The cracks propagate rapidly compared with the total life of a gear, so that it is necessary to detect and identify the faults in time when they take place in order to avoid danger. In this paper, the time-varying mesh stiffness model of two types of faults is established by the potential energy method and validating by the finite element method. Based on the stiffness model, the influence of faults on the electromechanical system and their fault characteristics are analyzed, which provides a theoretical basis for the health detection of electromechanical coupling systems. The results indicate that in the early stage of the three faults, i.e., tooth root fracture, tooth interior fatigue fracture, and tooth flank fracture, it is hard to discriminate the faults. But after the second stage, the faults can be distinguished by the vibration amplitude, frequency band components, and phase diagrams. The TFF can be discerned into different stages by frequency domains and phase diagrams. When the fracture occurs completely, three faults can be easily distinguished by the time domain and phase diagram. In the frequency domain, the TRF can also be distinguished from the other two faults by referring to the sideband component near the meshing frequency.

Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion.

Before a new type of engine is introduced into civil aviation, it must comply with various safety regulations. These regulations include the analysis of secondary damage caused by the re-ingestion of a tooth fragment. The purpose is to prevent crack propagation through the gear rim, which would lead to catastrophic failure. In this context, identification of the initial crack location is crucial to determine the crack propagation path. Therefore, this paper presents a technique to determine and validate a constitutive material model and fracture locus for case-hardened spur gears. As the modelling of the surface-hardened layer is computationally intensive, it is necessary to homogenise the model. This paper comprehensively reviews and discusses the associated effects and errors. To determine the plastic behaviour of the case-hardened external gear (30CrNiMo8) and the nitrided internal gear (35CrAlNi7-10), the widely acknowledged Johnson-Cook material model is implemented using compression and Vickers indenter tests to define the necessary parameters. The fracture locus implementation is also based on the Johnson-Cook method and an axial shift of the fracture locus based on the hardness profile of the spur gears is determined by quasi-static pulsator tests. For validation, a project-specific gearbox test rig is used, enabling consistent ingestion of defined fragments. In addition, to check the likelihood of a tooth flank crack and to validate the results, a simplified ingestion experiment is performed.

The influence of shot peening on gear teeth micropitting and contact fatigue failure

Case-hardened gears present a high contact fatigue load capacity in a compact and light mechanical transmission systems but sometimes, micropitting appears. This damage can lead to early contact fatigue failure called macropitting (NF ISO 10825-1). A previous study has demonstrated that an appropriate shot peening treatment could reduce the micropitting phenomenon via tests on a twin disc machine.The aim of this paper is to study the influence of shot peening on the micropitting of case-hardened gears tooth flank and its development to macropitting. Experimental tests are carried out using a back-to-back gear test rig, an interrupted test method is defined in order to monitor the micropitting initiation and its propagation on the tooth flank. Two variants of carburized spur gear specimens are tested. The reference specimen has a case-hardened ground tooth flanks which is a typical gear application. The other specimen has a case-hardened ground tooth flanks with a shot peened finishing process. The fatigue tests are run until the appearance of macropitting. The performed inspections of specimens indicate that shot peening modifies the surface roughness, the surface topography and increases the compressive residual stress. The experimental results show that micropitting occurs on both shot-peened and non-shot-peened gears after approximately the same running time. However, a difference is observed in the propagation of micropitting on the tooth flanks. In comparison to reference gears, shot peening has postponed the apparition of macropitting by more than 60%. An analytical study is also conducted to validate the prediction of micropitting using the ISO/TR 6336-22 by comparing the results with the occurrence of micropitting on the tested gears.

Model of the turboprop engine reduction gear tooth harmonic spectral component

The width of spectral components in rotary machines is determined by the frequency modulation of the carrier from the rotor speed deviation in the stationary operation mode. It was shown that, for the tooth spectral component, it is not enough to take into account this factor only. The analysis of publications and the studies performed show that it is also determined by the effect of many other factors: process-related ones (errors in manufacturing and assembly of gear wheels), operation mode parameters (rpm, temperature, transmitted load); design-related factors (flexibility of drive parts; modification of the tooth face), as well as uneven wear of tooth flanks. Using the planetary gearbox of a turboprop engine as an example, the structure of the tooth spectral component width in function of the analyzed influencing factors was considered. Based on the vibration statistics for eighteen gearboxes in overhauled engines, the choice of a ratio for the spectral component width of a frequency modulated process was justified. This choice showed readings closest to the corresponding experimental data. For the vibration of ten gearboxes with different degrees of tooth flank wear, the corresponding dependence of the width on the wear is presented. A mathematical model for the tooth spectral component width in overhauled and newly manufactured gearboxes as the product of the constant coefficient with the deviation dispersion sum from the considered factors was proposed. The same dependence was also given for gearboxes with wear when adding the dispersion from wear to the dispersion sum. It was demonstrated that, for the presented case of the maximum wear, its fraction in the total width was about 50%, whereas the fraction of the frequency modulation from the operating system of adjusting relative rotor speed constancy in the stationary engine operation mode was equal to half of all the other factors.

Origin of non-uniform tooth flank hardening distribution in SCM440 mobile induction heat–treated steel spur gears—a parametrical study with experimental–numerical coupled investigation

Origin of non-uniform tooth flank hardening distribution in SCM440 mobile induction heat–treated steel spur gears—a parametrical study with experimental–numerical coupled investigation

High power pulsed magnetron sputtering tailored low temperature CrAlN + MoWS coatings for dry tribological contacts

Gears are used in a variety of applications, for example, in automotive and aerospace industries. In these applications, gears are exposed to harsh conditions such as high Hertzian pressures. In many cases, lubricants are used to achieve a reduction in the coefficient of friction and, thus, in the wear of the components. Nevertheless, in some applications, the use of a lubricant is difficult, for example, in vacuum environments. One promising approach is the application of solid lubricants by using triboactive elements. The present study shows the potential of a process combining high power pulsed magnetron sputtering (HPPMS) and direct current magnetron sputtering (dcMS) for the deposition of CrAlN + MoWS coatings. In HPPMS/dcMS processes, especially, the share of HPPMS leads to higher ionization of the coating plasma and, therefore, to higher coating thicknesses on the teeth of gears. One major challenge in coating processes is the adjustment of the deposition temperature, since steels used for gear applications are temperature sensitive. Therefore, starting from an established coating process with a high coating temperature, the coating process was adjusted by reducing the number of used cathodes. By reducing the count of used dcMS cathodes, the share of HPPMS cathodes within the coating process was increased. Furthermore, segments of gears were coated in order to determine the coating thickness at different distances from the head of the gear tooth. A sufficient coating thickness distribution on the flank of the gear tooth is crucial for friction reduction and wear protection when used in gearboxes. The reduction of used cathodes led to a decrease in the coating temperature from a maximum coating temperature of Tmax = 281 °C to Tmax = 214 and 197 °C. It was shown by nanoindentation measurements that the effect of soft annealing was eliminated by reducing the coating temperature. At the same time, coatings deposited with increased HPPMS fraction led to a reduced coefficient of friction as well as lower wear volumes for pin-on-disk measurements in a dry tribological contact with an uncoated 100Cr6 counterpart. Moreover, these processes exhibited a good coatability of the gear tooth with a relatively high coating thickness even near the gear tooth root. The present study shows the potential of increasing the share of HPPMS during the deposition of coatings for dry-running applications. By increasing the HPPMS content, the tribological behavior as well as the coating thickness distribution on gears can be significantly improved.

Curvature interference characteristic analysis of offset involute cylindrical worm drive

The theory of calculating the curvature interference limit line of the offset involute cylindrical worm drive based on the singular point condition on the enveloping surface is established. The tooth surface equations and the meshing function of the worm drive are derived. Based on the singular point condition that the normal vector of the enveloping surface is zero, the equation of the curvature interference limit line is obtained. By employing the resultant elimination method and the geometric construction, the existence of the solutions of the curvature interference limit line is determined, and the reasonable initial values for the iteration program are afforded. The numerical outcomes show that there is one meaningful curvature interference limit line on each flank of single tooth of the worm gear, which usually does not enter the worm gear tooth surface. Both flanks of the worm gear are all settled in the side of the limit line, the curvature interference does not happen on the worm gear tooth surface. The undercutting of the cutting engagement process generally does not happen. The results also reveal that the curvature interference limit line is closer to the addendum and heel of the face worm gear on the i flank, which has the greatest potential venture inflict the undercutting.

Revolutionizing gear hobbing machine precision: Innovative thermal error compensation and intelligent error control with enhanced crystal structure algorithm and self-attention bidirectional minimal gated unit network

The thermal error stands as a pivotal determinant, significantly impacting both the precision and its stability of gear hobbing processes. Thus far, conspicuous delays in compensation and insufficiencies in precision have been duly noted. To achieve a proficient and exceedingly precise thermal error compensation, an intricate mathematical correlation is expounded, delineating the connection between the spatial pose error of the hob and the inherent thermal error in the gear hobbing machine. In addressing the thermal error linked to the B-axis, a bidirectional-minimal gated unit network is harnessed to characterize long-term memory attributes. An advanced crystal structure algorithm is introduced, encompassing components such as the population initialization mechanism, the nonlinear convergence factor, the Gaussian perturbation mechanism, and an enhanced optimization equation. The weights of the bidirectional-minimal gated unit network are judiciously assigned via the self-attention mechanism. This innovation, recognized as the improved crystal structure algorithm-self-attention-bidirectional-minimal gated unit network, is introduced for the training of the thermal error model for the B-axis. Subsequently, thermal analysis models are formulated, yielding the thermal errors of the X- and Z- axes. An error control model and an error decoupling model are established, employing the thermal errors of the B-, X-, and Z- axes as their input. Ultimately, an intelligent error control system is crafted, in which the error control model, error decoupling model, and thermal error model are seamlessly integrated. The aim is to mitigate tooth flank errors. With the integration of the intelligent error control system, the levels of precision pertaining to gear helix deviation, maximum deviation of a single pitch, and cumulative total pitch deviation are elevated by one, one, and two levels, respectively. More significantly, the geometric error reduction of the tooth flank achieved by the meticulously designed intelligent error control system surpasses that of traditional pitch compensation by a substantial margin. Furthermore, the execution efficiency of the intelligent error control system, when operating within the machine-edge-fog-cloud framework, exhibits a remarkable improvement of 24.18%, 16.20%, and 57.84% when compared to the intelligent error control system operating within the machine-edge-cloud, machine-fog-cloud, and machine-cloud frameworks, respectively.

Meshing Characteristics of Profile Shifted Cylindrical Quasi-Involute Arc-Tooth-Trace Gears. Part 2. Calculation Results

Abstract Based on the results obtained in the previous research, the values of meshing characteristics of profile shifted quasi-involute arc-tooth-trace gears is calculated. The influence of the values of profile shift coefficient and the angle of tooth trace on meshing characteristic distribution on the tooth flank surface along tooth trace is defined. The results can be used for design of profile shifted quasi-involute arc-tooth-trace gears, cut by Gleason-type cutters with different profile angle value.

An Investigation on the Teeth Crowning Effects on the Transient EHL Performance of Large-Scale Wind Turbine Spur Gears

Crowning is applied to wind turbine gears, including spur gears, to ensure adequate stress distribution and contact localization in wind turbine main gearbox gears to improve the gear performance in the presence of misalignments. Each gear tooth is crowned along the face width using a parabolic curve that graduates from a maximum height at the edges and vanishes at the center of the tooth flank. This crowning transfers the elastohydrodynamic contact problem from a line to a point contact case where the surface curvatures and pressure gradient are considered in both directions of the solution space. A wide range of longitudinal crowning heights is considered in this analysis under heavily loaded teeth for typical large-scale wind turbine gears. Furthermore, the variation in the velocities is considered in the analysis. The full transient elastohydrodynamic point contact solution considers the non-Newtonian oil behavior, where the numerical solution is based on the finite difference method. This work is focused on the evaluation of the effectiveness of teeth’s longitudinal crowning in terms of the consequences on the resulting pressure distribution and the corresponding film thickness. The modification of the tooth flank significantly elevates the film thickness levels over the zones close to the tooth edges without a significant increase in the pressure values. Moreover, the zone close to the tooth edges from both sides, where the pressure is expected to drop to the ambient pressure, is extended as a result of the flank modification.

Detecting Helical Gearbox Defects from Raw Vibration Signal Using Convolutional Neural Networks.

A study on the gearbox (speed reducer) defect detection models built from the raw vibration signal measured by a triaxial accelerometer and based on convolutional neural networks (CNNs) is presented. Gear faults such as localized pitting, localized wear on helical pinion tooth flanks, and lubricant low level are under observation for three rotating velocities of the actuator and three load levels at the reducer output. A deep learning approach, based on 1D-CNN or 2D-CNN, is employed to extract from the vibration image significant signal features that are used further to identify one of the four states (one normal and three defects) of the system, regardless of the selected load level or the speed. The best-performing 1D-CNN-based detection model, with a testing accuracy of 98.91%, was trained on the signals measured on the Y axis along the reducer input shaft direction. The vibration data acquired from the X and Z axes of the accelerometer proved to be less relevant in discriminating the states of the gearbox, the corresponding 1D-CNN-based models achieving 97.15% and 97% testing accuracy. The 2D-CNN-based model, built using the data from all three accelerometer axes, detects the state of the gearbox with an accuracy of 99.63%.

A differential diagnosis approach of localized planet gear fault using overall transmission error

Owing to recent studies on the relationship between the transmission error and the localized gear fault, TE-based differential diagnosis (DD) technology has emerged as a promising approach to identifying the tooth flank spall and the gear fillet crack which have similar signatures but quite different fault mechanisms and prognoses. However, due to complex structural factors, the fault modes can hardly be identified from the calculated overall transmission error (OTE). In light of this, a novel DD framework based on encoder-measured data is proposed in this work. Specifically, the OTE signal calculated from resampled data are filtered by flexible time synchronous average. A reordered singular values decomposition (RSVD) approach guided by the sparse index L2/L1 norm is then developed for fault-dependent residual OTE extraction. Experimental results validate that the faulty events can be accurately identified by the proposed framework without prior information under different speed conditions for planet gear DD.

Consideration of the influences of the driving direction within the calculation of the pitting load-carrying capacity of bevel and hypoid gears

Pitting is, besides scuffing, tooth flank fracture and the phenomenon micropitting, one of the primary failure modes of the flank load-carrying capacity of bevel and hypoid gears. The international standard ISO 10300-2:2014 is widely used for the estimation of the flank load-carrying capacity of bevel and hypoid gears based on operational data and the macrogeometry of the gear set. The calculated safety factors against pitting often show similar values for pinion and wheel. Due to similar safety factors against pitting, the gear is expected to fail as often as the pinion. However, investigations in the field do not confirm this. Initial experimental investigations show an influence of the driven and driving part of the gear set. Within this paper, the phenomenon regarding the driven and driving part of the gear set will be discussed for the first time and the influence parameter will be clarified. Because of the potential for recuperation in electrified agricultural tractors, railroad trains, hybrid and electrical vehicles, this topic is of great importance. In this context an actual calculation approach based on the standard calculation method of the ISO 10300-2:2014 will be presented and verified with test results.

Analytical and Experimental Investigation to Resolve Surface Related Fatigue Failure in Helical Gears

With the improvement of metallurgical process and tools it became possible to modify the material property of the steel to a desired possible level where its torque transmission capability can be enhanced. Case hardening and surface grinding is one such method which is used to leverage the surface durability and core strength of gears. With the enhancement in the torque transmission capability the load per unit area of face width also increased causing huge surface pressure. They are subjected to various conditions of load, speed, temperature, and ambient conditions. Micropitting is one such surface related failure which starts on tooth flank in terms of surface texture change. This may further grow in magnitude and result in catastrophic failure. This research work is performed to compare the results of analytical and experimental investigation for the possible micropitting initiative zone. Analytical approach is carried out by using the KISSsys model and the experimental work is carried out by using a dynamometer test rig to apply the load on the gearbox shaft for a defined load cycle. It was clearly visible that the micropitting has initiated below the pitch line of pinion. Tooth profile is later modified with lead and crown modification. After the application of this modification the tooth profile related failure was not visible for similar load testing cycle.

Influence of axis misalignments in stepped planetary gear stages on the excitation behavior—test rig development and simulative analysis

AbstractOne challenge in the design of automotive gearboxes is the combination of high power density, high efficiency and low noise emission. With the electrification of the powertrain, the requirements in terms of noise emission and efficiency increase additionally. Stepped planetary gear stages are a potential topology to solve the current challenges in gearbox technology. Current research shows the pronounced misalignment behavior of planetary gear stages, especially with manufacturing or assembly deviations. However, the effects of dynamic misalignment behavior on tooth contacts in stepped planetary gear stages have not been adequately investigated. This paper presents a test rig that allows the investigation of the excitation and displacement behavior of stepped planetary gear stages taking into account adjustable axis misalignments. The axis misalignment of the stepped planetary shafts is introduced with eccentric bushings in this test rig concept. To evaluate the excitation and displacement behavior the transmission error and the displacements of different components can be measured. The test rig is modeled in the dynamic multibody simulation. The tooth contact is modeled using the force module GearForce6D. The axis misalignment is varied in the simulation model and the influence on the excitation and displacement behavior is evaluated. The simulation results show that planet pin position errors have the highest influence on the sun trajectory and the load sharing. The misalignments occurring in the tooth contacts due to inclination and skew of the stepped planetary shaft lead to higher tooth flank pressures and an increase in the total transmission error.

Design optical surface as the measurement datum in measuring gear tooth flank by symmetrical laser interferometer

Laser interferometry is a promising method to measure the form deviation of gear tooth flanks. The lack of measurement datum is the bottleneck problem of measuring a gear tooth flank by laser interferometry. Manufacturing a physical reference gear tooth flank as the measurement datum has many drawbacks which restrain the application prospect of measuring gear by laser interferometry. Optical surfaces are more mature to manufacture and have much higher processing accuracy compared with the physical reference tooth flank. Thus, we design and use an optical surface as the measurement datum. First, we invent a symmetrical oblique incidence laser interferometer (SOILI) to reduce the interference fringe’s density and enhance the tractability of interferograms. Second, we propose a design method for calculating the measured tooth flank’s similar optical surface. Lastly, we propose the nonparallel plate model which is a general form of the parallel plate model and can be used to calculate the situations where the normal directions of the measured surface and the reference surface are different. Experimental results verify that an optical surface can be designed and used as the measurement datum. Furthermore, this research provides some references for the measurement datum in the relevant comparative measurements processes by laser interferometry.

Influence of profile modification on the transmission error of spur gears under surface wear

The load distribution, transmission error, and time-varying meshing stiffness of spur gears are all influenced by the teeth dimensions and profiles shape. Any modification on the teeth geometry, as a profile relief frequently used to avoid the mesh-in impact, will affect all these parameters and the entire dynamic behavior of the gearset. In addition, due to the friction between contacting surfaces, wear arises at the teeth flanks. This causes the shape of the meshing profiles to change, which will affect the load distribution and the transmission error for the subsequent meshing cycles. And this new load distribution causes a surfaces wear different form that of the previous meshing cycle. Consequently, the wear depth increase is different at any contact point —because the load and sliding velocity are different— and at any meshing cycle as well —because the load distribution changes with the accumulated wear—. And all the above is also influenced by the profile modification the teeth were manufactured with. In this paper, a simple, analytic model of meshing stiffness, load sharing, and transmission error for spur gears with profile modifications including the influence of surfaces wear is presented. The evolution of the transmission error with the number of wear cycles is studied, and the optimal profile modification for minimizing the dynamic load induced by the transmission error is investigated.

Modeling and compensation of twist error of helical gear with lead modification in continuous generating grinding

A compensating method based on continuously deflecting the dressing wheel is proposed to eliminate the twist error of the lead modification tooth flank. Combining the tooth flank contact trace and the lead modification curve, the mechanism of the twist error is first analyzed. Second, a tooth profile error model is developed at the upper and lower end faces. The flank twist amount is calculated by subtracting the tooth profile error at the upper and lower end faces. Then, the profile slope deviation of the twisted tooth flank is transformed into the pressure angle deviation of the tooth profile, and the method of compensating the pressure angle of the worm wheel is applied to eliminate the pressure angle deviation of the tooth flank caused by the twist error. The grinding partition of the worm wheel is performed according to the diagonal grinding process, and a worm wheel dressing method for continuously deflecting the dressing wheel is provided to compensate for the twist error. Finally, the continuous generating grinding experiment of the lead modification gear verifies the feasibility of the proposed method.