Gear Research Articles

Profile design of grinding wheel and temperature field analysis of internal gear with parabola curve configuration

Profile design of grinding wheel and temperature field analysis of internal gear with parabola curve configuration

Method for Increasing the Energy Efficiency of the Gear Teeth Cutting Process by Smoothing the Cutting Force Variation

The energy efficiency in metal cutting is, sometimes, very low. Recent studies show that the energy consumed for detaching chips represents only about 15% of the total energy involved in material machining. The available solutions for energy optimization in cutting processes mentioned are the improvement of manufacturing equipment, the optimization of processes, and appropriate production scheduling. Already-performed research shows that to increase energy efficiency, the cutting force must be reduced, for example, by reducing the depth of the cut and by increasing the feed rate. However, this is applicable when the cutting force is quasi-constant during the process, which is not the case for gear teeth cutting when the cutting force significantly varies. The present paper proposes a new solution for energy efficiency increase in gear teeth cutting, namely, the smoothing of the cutting force variation during the machining process, by keeping the area of the detached chip section quasi-constant during the cutting process. This can be reached by replacing the constant rolling feed, currently used in gear teeth cutting, with a rolling feed that varies after an appropriate law. An algorithm dedicated to implementing this solution has been developed. It uses graphical modeling in CATIA to find the variation in the detached chip area. Original MatLab R2018a applications were developed (i) to identify the analytical form of the law that approximates this variation and (ii) to find the variation law of the feed during the rolling motion, if imposing a constant area of the detached chip. The algorithm was successfully applied in the cases of toothing with a rack tool (by slotting) and with a pinion cutter (by slotting and turning). A technical solution for method implementation in practice is also presented.

Investigation on meshing characteristics of spiral bevel gear under wear fault evolution with assembly errors

Spiral bevel gears have the advantage of transmitting high torque and power comparing to helical gear and straight bevel gear. However, they are susceptible to wear due to factors such as high loads, poor lubrication, and surface imperfections resulting from machining. In this study, we propose an autonomous model for predicting tooth wear and analyze the meshing characteristics of spiral bevel gear (SBG) pairs under different assembly errors. Concurrently, we establish a finite element model to validate the accuracy of our meshing characteristic analyses. We also compare the distribution patterns of wear depth on the tooth surface with existing literature. Our investigation delves into meshing characteristics, encompassing transmission errors and Time-varying mesh stiffness (TVMS), considering wear evolution under assembly errors. The results demonstrate that the fluctuations in TVMS remain consistent across all four types of assembly errors examined. Gear tooth wear leads to an increase in gear backlash and fluctuations in unloaded transmission error. The meshing stiffness fluctuation of the SBG pair enlarges under wear evolution. Assembly errors result in shifts in the initial contact line and contact pattern, subsequently altering the distribution of wear depth. Different forms of assembly errors may cause a similar effect on the distribution of wear depth and meshing characteristics.

Alumina ceramic insulation layer for strain sensor fabricated by direct laser deposition

ABSTRACT Strain sensors are often used to monitor the use of critical components. The bond strength between the strain sensor and the gear teeth is particularly critical. There is a problem of insufficient bond strength between separated strain sensors and parts. The strain sensor is prone to loosening and flaking in the working environment. Therefore, a method of preparing the ceramic insulation layer of the strain sensor by direct laser deposition (DLD) is proposed. The effects of laser scanning trajectories, laser power, and scanning speed on forming quality were investigated experimentally. In addition, the phase analysis, microstructure characterization, and insulation properties of the insulating layers prepared at different overlap rates were researched. The research shows that the ceramic insulation layer has good insulation properties and hardness. The maximum hardness can reach 2405.74MPa, and the insulation resistance increases with the number of layers. The surface of the ceramic insulation layer is dense and has no cracks.

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

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

Fault Diagnosis Method for Marine Electric Propulsion Systems Based on Zero-Crossing Tacholess Order Tracking

In marine electric propulsion systems (MEPS) driven by variable-frequency drives, motor current signals often exhibit complex modulation components, ambiguous spectra, and severe noise interference, rendering it challenging to extract fault-related modulation components. To address this issue, we propose a zero-crossing tacholess order tracking method based on motor current signals. This method utilizes zero-crossing estimation of the instantaneous frequency to perform angular resampling of stator current signals and demodulates the envelope spectrum to extract fault characteristic spectra, enabling the diagnosis of mechanical faults in MEPS. Given the synchronization of the synchronous motor speed with the inverter fundamental frequency, this method estimates instantaneous frequencies in the time domain without requiring integration or time–frequency representation, which is simple and computationally efficient. Data validation on a small-scale marine electric propulsion test platform demonstrates that the proposed method exhibits good robustness under variable-speed conditions and effectively detects imbalance faults caused by propeller breakages and gear faults resulting from bevel gear tooth defects. Therefore, the proposed method can be applied to diagnose faults in downstream mechanical equipment driven by motors.

Extended influence coefficient method for meshing stiffness evaluation of spur gears considering rotor flexibility

Rotor-supported gears are applied in transmission systems, and the rotor flexiblility leads to the misalignment of the gear pair with multiple degrees of freedom, which ultimately leads to the decrease of meshing stiffness. To evaluate the meshing stiffness of rotor-supported gears, the extended influence coefficient method (EICM) is proposed in this paper. Firstly, the gear contact position adjustment under misalignment condition is carried out. Then, the extended influence coefficients of bending, shearing, axial compression, Hertzian contact and fillet foundation deformation of gears are derived to obtain the extended influence coefficient matrix. Afterward, the load-deformation equations under different contact states are obtained, and the meshing stiffness is calculated. Subsequently, a cantilever rotor-gear coupling dynamic model is established by the rigid body element-extended influence coefficient method (RBE-EICM), and the dynamic meshing stiffness considering rotor flexibility is obtained. The accuracy of EICM and RBE-EICM is verified by comparison with finite element method, literature methods and experimental data, respectively. Finally, the effects of supporting layout, input torque and rotor diameter on the dynamic characteristics of cantilever rotor-supported gears are discussed.

Geometry strategies for the repair of cylindrical gears teeth using laser-directed energy deposition

Gears are essential components in power transmission systems. The replacement of the transmission of a wind turbine can reach more than $300 000 and face long lead times. Previous studies have shown that laser-directed energy deposition (L-DED) has the potential to be used in the repair of gears. However, there is a lack of understanding of the appropriate toolpath planning strategies and their impact on the performance of the gears repaired by L-DED. In this work, we study several strategies for the repair of cylindrical (straight and helical) gears. The strategies consider several types of gear tooth failures, allowing for the repair of a portion of the tooth and the reconstruction of the whole tooth. The studied strategies encompass planar and nonplanar slicing procedures. We manufactured several gear teeth to demonstrate the geometrical and kinematic feasibility of some strategies. We performed destructive analyses on the manufactured teeth to check for manufacturing faults. We used AISI 316L for these experiments, although we are assessing and testing powdered materials for their potential use in gear repair using L-DED. Future work will be devoted to the evaluation of the mechanical performance (e.g., wear resistance and bending fatigue) of the teeth manufactured with L-DED.

Robot Joint Cycloidal Gear Tooth Fault Detection in Robot Working Conditions Based on Piecewise Mean Difference

Robot Joint Cycloidal Gear Tooth Fault Detection in Robot Working Conditions Based on Piecewise Mean Difference

Digital Light Processing Followed by Pressureless Sintering of Metal-Reinforced Ceramics: Adjustment of Process Parameters and Correlation with Composites Properties

AbstractDigital light processing (DLP) belongs to additive manufacturing techniques and is frequently used in shaping ceramics. The paper concerns the adjustment of the DLP method to metal-reinforced ceramics, especially dispersions containing high concentrations of Al2O3 (45 vol%) and molybdenum or nickel particles (0.5 vol%). Different glycol acrylates, deflocculants (polyelectrolytes and diammonium hydrogen citrate), and photoinitiators (Omnirad group) were examined regarding their influence on the rheological properties of the dispersions and the cure depth under the external halide UV lamp and LED projector built into the 3D printer. In the examined systems, the cationic polyelectrolyte KD1 dissolved in 2-butanone allowed to obtain dispersions of the lowest viscosity. Printing parameters (light exposure time, single layer height) were matched, and the properties of the materials were examined. The Vickers hardness of the sintered bodies equalled 19.4 GPa, 14.5 GPa and 17.3 GPa for Al2O3, Al2O3-Ni and Al2O3-Mo samples, respectively. The microstructure was analyzed using SEM, followed by EDS and XRD. The addition of only 0.5 vol% of Ni has improved the fracture toughness of alumina by up to 36–40% (according to Niihara and Anstis equations). The exemplary objects in the form of cog wheels were printed and densified at 1550 °C in a reductive atmosphere of Ar/H2.

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.

Adaptive isogeometric gear contact analysis: Geometry generation, truncated hierarchical B-Spline refinement and validation

Gears are one of the most widely used transmission components. Their operation relies on the contact between mating gear teeth flanks for the transmission of power. Accurate prediction of the contact stresses at these regions, is crucial for the design and dimensioning of these systems. Gear design is centered around highly smooth involute curves that greatly influence their contact behaviour. In this paper, a fully adaptive isogeometric contact modelling scheme, based on hierarchical splines, is presented and applied to the simulation of gear contact problems. In particular, isogeometric simulation is performed for the modelling of mating pair of gear teeth, regarded as linearly elastic bodies. A boundary fitted B-Spline representation of the teeth is automatically generated from engineering design parameters and is used to define the initial discretisation basis. The numerical integration over the contact region is addressed using the so called, Gauss-Point to Surface formulation and a closest point projection procedure. Truncated hierarchical B-Splines are used to capture the highly localised nature of contact, while effectively reducing the number of degrees of freedom. The adaptivity is driven by the strain energy density gradient, which allows to automatically localise the mesh without a priori knowledge of the contact region between the teeth flanks. In our experiments we justify the choices made in different steps of our algorithm and we assess the performance of our adaptive solver with respect to classical tensor product B-Splines.

TVMS calculation model for gear tooth tip chipping failure with EHL

This paper proposes a calculation method for Time-Varying Mesh Stiffness (TVMS) in the presence of tooth tip chipping defects under elastohydrodynamic lubrication (EHL). A contact stiffness model for tooth tip chipping defects under EHL is established, and an analytical equation for the TVMS of chipping defects under EHL is derived. The torsional stiffness at the chipping defect under EHL is introduced, considering the influence of roughness at the chipping defect on the characteristics of the oil film and its stiffness. The effects of chipping defect size, torsional stiffness of the chipping defect under EHL, roughness, and oil film stiffness on TVMS are analyzed, providing methodological support for improving the calculation accuracy of gear TVMS.

Analysis and Simulation of Spur Gear System Considering Geometric Eccentricity

Geometric eccentricity errors inevitably occur in gear systems, resulting in the center of mass and center of rotation not coinciding. During the gear meshing process, the gear center distance and gear tooth meshing condition will change with time. In this paper, a model considering geometric eccentricity is proposed and a finite element model of the gear pair is developed. Finally, the dynamic response under different eccentricity and initial eccentricity angle is discussed. Based on Ansys, the simulation calculation of the gear pair is carried out, and the equivalent force maps of the dangerous areas of the gear tooth flanks are obtained.

Effect of tooth surface pitting on dynamic characteristics under mixed lubrication

The variation of tooth meshing stiffness and frictional characteristics caused by tooth surface pitting increases vibration and noise in the gear transmission system. Assuming a smooth tooth surface and a homogeneous material in studying the gear contact and dynamics is insufficient to reveal the evolution of dynamic contact performance caused by pitting faults. In the present study, we established a coupling analysis model for pitting faults to assess the effect of the tooth surface micro-morphology. The mesh stiffness and static transmission error of gears with randomly distributed pittings were calculated, and the vibration response of gears with different pitting degrees was resolved. Finally, the effectiveness of the applied dynamic response theory analysis was experimentally verified using the constructed pitting fault simulation test bench. The results indicate that pitting failure decreases the effective load-bearing capacity of gear teeth. The mesh stiffness gradually but significantly decreased with the pitting degree, also exhibiting fluctuating values. Pitting faults induced significant periodic features in the vibration response of gear transmission systems, showing complex sidebands around the meshing frequency and its harmonics.

Математическое моделирование бипланетарного механизма для привода смесительных машин

A study on the development of a kinematic scheme of a planetary mechanism with an opening kinematic circuit for driving the working body of mixing machines is presented. The main purpose of the study is to create two kinematic cycles in the planetary mechanism, in which, during one revolution, the satellite drivers consistently perform movements of the epicyclic trajectory of hypocyclic motion. To achieve this goal, braking devices for damping the kinematic energy of satellites and synchronizer devices were used in the transition zones between two segments of different names, for smooth entry of the satellite gear into the gear engagement of these gears. The oscillatory process of the synchronizer at the entrance of the tooth of the satellite gear with the front teeth of the synchronizer is considered. Practical significance includes ensuring the possibility of assembling a planetary mechanism, taking into account the choice of the angle of rotation of the synchronizer around the axis of the support. The discussion makes recommendations for further improvement of the developed biplanetary mechanism for driving mixing machines.

Nonlinear performance of aerospace face gear-planetary gear transmission system under multi-factors including the effect of temperature

Face gear-planetary gear transmission system combines the advantages of both planetary and face gears. And has enormous advantages in the aerospace field. The meshing of gear teeth generates heat through friction, resulting in thermal deformation and affects nonlinear dynamic characteristics. Exploring the temperature effect on the nonlinear dynamics of the transmission system of face gear-planetary gear is of great significance. Considering the temperature variations effect and time-varying meshing stiffness, tooth side clearance as well as meshing error, a nonlinear dynamic model of the face gear-planetary gear system is established. The nonlinear dynamic characteristics of the system were described by maximum Lyapunov exponent diagram, phase diagram, bifurcation diagram et al. The findings indicate that the effect of temperature variations on the gear system is related to the values of the time-varying mesh stiffness coefficient and mesh damping ratio. When the mesh damping ratio is small, the influence of temperature changes on the bifurcation characteristics of the system is more obvious. As the time-varying mesh stiffness value increases, the temperature rise gradually stabilizes in the range of 15°C to 42°C; Under certain temperature changes, as the meshing damping ratio and time-varying meshing stiffness coefficient increase, the face gear planetary gear system gradually tends to stabilize.

The Concept of Technological Support of Operational Properties Based on Stabilization of Mechanical Properties of Gear Materials in a Gas Turbine Engine Drive System

Modern production of gears for gas turbine engines for aviation, marine and land use is inherently related to the calculation of the stress state of the working surfaces of the mating teeth. To create conditions for the operability of the gear train and the drive system as a whole, an engineering analysis of the contact endurance of the mating surfaces is a necessary criterion. The contact strength determines the life of the gear mechanism. The value of the contact strength, taking into account its distribution in the contact zone of the working mating surfaces of the gears, is determined by the processing technology and operation, but the mechanical properties and texture of the material have the greatest influence. This determines the requirements for the stability of the mechanical properties of the materials used for the manufacture of gears, making a topical question on their study. The technology of manufacturing the gears in the gas turbine engine drives forms the layer structure of the toothed crown because of the use of chemical-thermal treatment. The surface hardened layer of the gear tooth after chemical-thermal treatment is saturated with carbon and nitrogen, and as a result of thermal action acquires mechanical properties and structure different from the material in the supply. The paper presents the results of practical research of evolution of mechanical properties of structural steels 20H3MVF-Sh, 18H2N4MA, 16H3NVFM-Sh and 12H2N4A-Sh based on various types of chemical-thermal treatment, as well as microstructure of toughened layer and core of the part. The steel mechanical properties stabilization evaluation in the process of gear technology was performed. The presented results of experimental studies of mechanical properties of the material prove stabilization of mechanical and structural indicators, which are responsible for the contact strength of the mating surfaces of toothed gears.

Simulation and validation of the transmission error, meshing stiffness, and load sharing of planetary spur gear transmissions

Although the load sharing between planets of sequentially phased planetary gear transmissions has been studied in the past, the required solving techniques based on the Finite Element Method result in long time consuming and high computational cost. This limits the possibilities of undertaking extensive studies that take into consideration a high number of cases allowing optimal solutions to be sought or general conclusions drawn. In addition, the determination of the curves of transmission error, time-varying mesh stiffness, and load sharing among tooth pairs in simultaneous contact are also complicated. In this work an analytical model has been developed for the simulation of the time-varying mesh stiffness, quasi-static transmission error, and load sharing ratio between planets and tooth pairs of planetary spur gear transmissions. It is based on similar models for external and internal spur gears previously developed and has been validated by comparison with a hybrid model based on the Finite Element Method and theoretic-experimental correlation.

Spur gear tooth root stress analysis by a 3D flexible multibody approach and a full-FE contact-based formulation

This paper proposes an original method to determine the gear tooth root stresses from a 3D finite element (FE) flexible multibody approach and a full-FE contact-based formulation. The contact problem is dealt with an augmented Lagrangian formulation whereas the analysis is performed by a preconditioned gradient solver (PCG). Tooth flank modifications are directly introduced within the 3D model. This one is thus able to take into account straightforwardly tooth bending and Hertzian-like deformations as well as the micro-geometry effect. Simulations are performed for several mesh periods, without making any assumptions about load distribution, tooth and gear blank flexibilities, and possible premature or delayed contacts between tooth pairs in quasi-static conditions. A precise distribution of tooth root stresses associated with instantaneous contacts conditions is then computed. For this study, a single stage spur gear with micro-geometry modifications corresponding to an arc-shaped profile crowning is modeled. Several output torques are considered. The obtained results are compared to those obtained using a 2D FE ISO-based model, where external forces are applied along the theoretical line of action.