Gear Load Research Articles

Multi-objective optimization model of transmission error of nonlinear dynamic load of double helical gears

Abstract In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 107 mm3, and the coincidence degree is 5.9908. After rounding, the design result is m n = 3 , Z 1 = 31 , β = 20 ∘ , Ψ d = 1.2 {m}_{{\rm{n}}}=3,{Z}_{1}=31,\beta ={20}^{\circ },{\Psi }_{{\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.

Static load-carrying behavior and material properties of additively manufactured gears (PBF-LB/M, 16MnCr5)

PurposeNumerous metals can be processed using the additive manufacturing process laser-based powder bed fusion of metals (PBF-LB/M, ISO/ASTM 52900). The main advantages of additive manufacturing technologies are the high degree of design freedom and the cost-effective implementation of lightweight structures. This could be profitable for gears with increased power density, combining reduced mass with considerable material strength. Current research on additively manufactured gears is focused on developing lightweight structures but is seldom accompanied by simulations and even less by mechanical testing. There has been very little research into the mechanical and material properties of additively manufactured gears. The purpose of this study is to investigate the behavior of lightweight structures in additively manufactured gears under static loads.Design/methodology/approachThis research identifies the static load-carrying capacity of helical gears with different lightweight structures produced by PBF-LB/M with the case hardening steel 16MnCr5. A static gear loading test rig with a maximum torque at the pinion of T1 = 1200 Nm is used. Further focus is set on analyzing material properties such as the relative density, microstructure, hardness depth profile and chemical composition.FindingsAll additively manufactured gear variants show no failure or plastic deformation at the maximum test load. The shaft hub connection, the lightweight hub designs and the gearing itself are stable and intact regarding their form and function. The identified material characteristics are comparable to conventionally manufactured gears (wrought and machined), but also some particularities were observed.Originality/valueThis research demonstrates the mechanical strength of lightweight structures in gears. Future research needs to consider the dynamic load-carrying capacity of additively manufactured gears.

Gear mesh stiffness and dynamics: Influence of tooth pair structural stiffness asymmetry

There are certainly a lot of different gear mesh stiffness models in the literature, nonetheless, it is not possible to find comprehensive and in-depth gear parametric studies that sweep the gear geometrical domain. To do so, it is required to have a fast and accurate gear mesh stiffness model, which is precisely one of the main developments of this work. By taking advantage of this new model, a parametric study on the influence of tooth pair structural stiffness asymmetry is conducted. This investigation evaluates how the referred stiffness asymmetry affects the gear mesh stiffness, dynamic displacements and load distribution by performing an extensive number of simulations that cover the entire selected gear geometry spectrum — two randomly generated populations of gears, one for spur and another for helical, are tested with and without the tooth pair structural stiffness asymmetry. It is concluded that tooth pair structural stiffness asymmetry cannot be neglected since it can lead to significant modifications on the frequency content of the gear mesh stiffness signal as well as the dynamic behavior of the geared system.

Optimization of key gear parameters to reduce weight

Problem. The problems of designing, and especially improving, mechanical gears are of key importance in modern mechanical engineering and automotive transport. Gear transmissions are quite widespread relative to other mechanical transmissions because they have a number of crucial advantages. Gear transmissions are widely used in a variety of drives for vehicle components and assemblies, with modern development trends aimed at reducing their weight and size. As the size of the transmission decreases, the dimensions of other parts and assemblies also decrease, and, accordingly, their cost. Therefore, research related to the study of the interdependence of the main parameters of gears for the purpose of their further optimization does not lose its relevance. Goal. The main purpose of this work is to study the dependence of the mass and dimensions of the gears under study on their main parameters. Knowing the influence of various characteristics on the mass, it is possible to provide recommendations for the design of gears to achieve their optimal (smallest) dimensions, which leads to a number of significant advantages. Methodology. First of all, a rather detailed analysis of the scientific literature is performed in order to identify the main statements regarding the influence of certain parameters on the mass and dimensions of the designed gear. The very dependencies of the gear mass on its various characteristics are found by applying a numerical method that is entirely based on the known design dependencies for the design calculation of gears. Also, to compare the results obtained analytically, the method of calculating the mass and dimensions by creating 3D models of gears in the "Autodesk Inventor" environment is used in the work. Results. Based on the results obtained, it can be noted that, ceteris paribus, including gear load, the weight is almost independent of the module and the relative width ratio. At the same time, in some cases, a particular standard value can significantly affect the weight of the gear, i.e., by selecting specific values, it is possible to reduce the weight of the gear by about 15-25%. Originality. Useful results were obtained using a relatively affordable method. The research was conducted both analytically and with the use of modern computer-aided design systems. Practical value. The proposed recommendations for the rational choice of some characteristics of gears will reduce the weight and dimensions of the mechanical drive.

Test method for determining the scuffing capacity of oils with reduced oil volume

Previous studies by several researchers have shown that the aging of the transmission fluid in dual clutch transmissions has a major impact on the wear protection of the highly loaded tribological contacts. Depending on the transmission design, oil sump temperature, transmitted torque, rotational speed and oil volume, the scuffing ability decreases significantly. Since typically only limited quantities of oil from gearbox tests are available to evaluate oil condition with respect to wear protection properties, available analytical standards are currently limited to methods such as viscometry, TAN, elemental analysis, and IR. A test method is presented that can be used to determine the gear scuffing load capacity of transmission fluids with a reduced oil volume. For this purpose, a standard test rig is modified to reduce the test oil volume from 1.25 liters, as specified in the public standards, to 0.5 liters. The applicability of the reduced test oil volume is demonstrated and the remaining scuffing wear protection of several used oil samples from durability testing is presented. A comparison of the tribological results with the chemical oil analysis results shows the advantage of direct testing of the oil's service properties.

Direct Energy Deposition Parametric Simulation Investigation in Gear Repair Applications.

Additive manufacturing technologies have numerous advantages over conventional technologies; nevertheless, their production process can lead to high residual stresses and distortions in the produced parts. The use of numerical simulation models is presented as a solution to predict the deformations and residual stresses resulting from the printing process. This study aimed to predict the tensions and distortions imposed in the gear repair process by directed energy deposition (DED). First, the case study proposed by National Institute of Standards and Technology (NIST) was analyzed to validate the model and the numerically obtained results. Subsequently, a parametric study of the influence of some of the parameters of DED technology was carried out. The results obtained for the validation of the NIST benchmark bridge model were in agreement with the results obtained experimentally. In turn, the results obtained from the parametric study were almost always in line with what is theoretically expected; however, some results were not very clear and consistent. The results obtained help to clarify the influence of certain printing parameters. The proposed model allowed accounting for the effect of residual stresses in calculating the stresses resulting from gear loading, which are essential data for fatigue analysis. Modeling and simulating a deposition process can be challenging due to several factors, including calibrating the model, managing the computational cost, accounting for boundary conditions, and accurately representing material properties. This paper aimed to carefully address these parameters in two case studies, towards reliable simulations.

Rotorcraft Robotic Landing Gear With Locking Mechanisms

Abstract Robotic landing gear (RLG) for rotorcraft improves performance in landing on sloped uneven terrain, unprepared areas, and ship decks. The interaction between the feet of the RLG and the landing surface are pivotal to a successful landing event. Slipping or bouncing of the feet can lead to a failed landing and a catastrophic accident. Proposed herein is the use of locking mechanisms on the RLG feet in order to eliminate landing gear slip and bounce during the landing event. Through the use of a comprehensive multibody dynamic simulation, locking mechanisms on the RLG feet are shown to eliminate landing event failures that can occur with nonlocking landing gear configurations, at the expense of a moderate increase in landing gear loads during a landing event. Results indicate that landing event failures are eliminated even in the situation where some feet-locking mechanisms are inoperable or break away. Furthermore, RLG with feet locking mechanisms permit the reduction or elimination of the need for active control of the RLG legs. The results herein give guidance to the development of integrated RLG with locking mechanisms.

Evaluation of Airport Pavement Base Layer Stiffness Characteristics via Embedded Field Sensors

Real-time stiffness monitoring of unbound aggregate layers using embedded field sensors is crucial for advanced airport pavement design and management. This paper describes research findings on monitoring base layer stiffness characteristics for airport pavements using an embedded bender element (BE) field sensor, inductive coil sensors, and pressure cells. A full-scale pavement test section was constructed at the Federal Aviation Administration (FAA)’s National Airport Pavement Test Facility (NAPTF). A BE field sensor, inductive coil sensor pairs, and pressure cells were installed in the unbound aggregate base to evaluate the layer stiffness, applied load stress, and deformation characteristics. A triple dual tandem gear loading module applied 58,000 lb per wheel to the tested section with a wander pattern consisting of 66 passes arranged in nine lateral wander positions. Dynamic responses of coil sensors and pressure cells were collected during the traffic test, whereas BE signals were collected after completing each wander pattern. Laboratory repeated load triaxial tests with BE instrumentation were also conducted to establish a correlation for converting BE field sensor readings to layer modulus properties. The in situ modulus characteristics of the aggregate base layer were evaluated during full-scale testing using two methods: shear wave velocities from a BE field sensor, and strain and stress measurements from coil sensors and pressure cells. The moduli estimated using both approaches fell into typical ranges of crushed aggregate bases and were highly comparable. The moduli from the dynamic sensor measurements clearly showed the effect of vehicle wander on aggregate base layer measured responses.

Study on gear meshing power loss calculation considering the coupling effect of friction and dynamic characteristics

Gear transmission system is widely used in many mechanical equipment to achieve power transmission and rotational speed changes. Meshing power loss is one key index to assess the performance of a gear system, which directly influences heat generation and lubrication, etc. Over the past decades, many computational models of gear meshing power loss have been proposed to support gear design and optimization. However, the coupling effect between the gear friction and dynamic characteristics are usually ignored, including time-varying meshing stiffness (TVMS) and dynamic meshing force (DMF), which are not conducive to accurate calculation and improvement of meshing power loss. Therefore, an improved gear meshing power loss calculation method is proposed to settle this problem in this paper. With the proposed method, the friction calculation model is established considering the effect of DMF and surface roughness based on mixed elastohydrodynamic lubrication (EHL). Then the TVMS is obtained with the friction force along the meshing line and DMF was taken into consideration. On the basis of modelling of friction and TVMS, a six degrees-of-freedom (DOF) gear dynamic model, as well as a power loss iteration calculation process are established and studied. The effects of gear surface manufacturing quality and loads on power loss are analyzed. Furthermore, a gear meshing power loss experimental setup is constructed to verify the effectiveness of the proposed method. The results show that this method is in better agreement with the experimental results than the traditional method which does not consider the coupling effects.

Investigation on the impact of electrical faults on the loads and exposures of wind turbine gears

For the design of a wind turbine, it is necessary that the design process takes into account the stresses of real operation to a high degree of detail so that targeted dimensioning can be carried out. Depending on its design, the drivetrain of a wind turbine includes a gearbox that connects the rotor to the generator. During operation of a wind turbine, transient load conditions can occur due to loopback from the power grid and faults in the frequency converter. The influence of the resulting stress and possible damage to the gears used in the gearbox is unclear in the design phase. While the stresses on the gears can often be simulated with a high degree of accuracy for constant operating conditions and can thus be integrated into the drivetrain design, this is not the state of the art for dynamic load conditions. The objective of this report is a method for considering dynamic loading events in the design of the cylindrical gear stage used in wind turbine gearboxes using a coupled multi-body simulation and a finite element based tooth contact analysis. Afterwards the method is used to quantify the stress on the tooth flank and tooth root due to special electrical events such as short circuits between the frequency converter and generator or power grid faults for various converter designs. The simulation analyses show that different converter concepts have different effects on the resulting gear load during electrical faults, but are not significantly decisive for the accumulated damage due to elastic material behavior between generator and gear.

Research on Control Method of Dual-Motor Load Simulator

Aiming at the output torque error of a steering gear electric load simulator caused by excess torque and backlash interference, an electric load simulator based on double-motor loading is designed. The double-motor loading mode is adopted in the structure, the mathematical model is established, and the sources of excess torque and backlash interference are analyzed. In the control strategy, firstly, a torque controller is designed as a feedback controller based on the improved error symbol robust integral control method, and then a backlash interference compensator is designed as a feedforward controller based on the drive redundancy strategy. Finally, a dual motor speed synchronization controller is designed based on the improved cross coupling control method to ensure the stable operation of the torque controller and backlash compensator in the dual-motor system. The simulation results show that the compound control method can reduce the tracking error to 1.13%, 4.44% less than the PID control method. The tracking error is only 1.54% in the case of redundant torque, backlash, and different parameters of dual motors. The method proposed in this paper can still output loading torque with high accuracy.

Material influence on mechanical properties of gears with alternative microstructures

AbstractCase hardening represents the most important heat treatment process to increase the load carrying capacity of gear components. Beside predominantly martensitic surface layers with low proportion of retained austenite, there were investigated material structures with differing properties in preceding research work.In a previous publication, the results of three variants made of the material 20MnCr5, which is typically used for gears, were presented. The reference heat treatment was a conventional carburizing with subsequent case hardening. The second variant was also gas carburized, but with a high proportion of retained austenite. The last presented variant had a bainitic structure in the surface layer. The second and the third variant showed a similar tooth root bending strength compared to the reference. The numbers of the pitting resistance were significantly higher than for the reference variant.This paper presents the results of further investigations on the influence of different microstructures on the gear load carrying capacity. For this purpose, gears made of 18CrNiMo7‑6 were tested with regard to their load carrying capacity. 18CrNiMo7‑6 is a case hardening steel like 20MnCr5, too, which is often applied in big gear components. The tooth root bending strength was approximately constant, whereas the pitting resistance decreased compared to the corresponding variants of the material 20MnCr5. In comparison to the carburized 20MnCr5 reference variant, only the 18CrNiMo7‑6 variant with a large proportion of retained austenite showed a higher pitting resistance.The tooth root bending strength investigations took place in the cycle regime of limited life as well in the high cycle fatigue regime. The pitting resistance was only determined in the cycle regime of limited life.

A dynamic gear load distribution model for epicyclic gear sets with a structurally compliant planet carrier

Structural deformations in a planet carrier under operating conditions results in misalignment of planet gears, which can significantly effect the gear mesh load distribution and load sharing of a planetary gear set. Therefore, to capture the influence of structural compliance associated with planet carrier, planet pin, and input/output shaft, a hybrid planetary dynamic load distribution model is developed in this paper. Finite element sub-structuring techniques are employed to ensure that the model is computational efficiency. The proposed model employs a simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation is used to study the effects of planet carrier flexibility on both the quasi-static and dynamic response of planetary gearsets. The discussed results not only illustrate the influence of carrier flexibility on the system response but also highlight the need for such computationally efficient models which could be used as design tools.

Modeling of Crescent‐Type Internal Gear Pumps Considering Gear Radial Micromotion

AbstractThis paper presents a numerical modeling approach for investigating crescent‐type internal gear pumps (CIGPs) considering radial micromotions of both gears. The modeling approach couples a lumped parameter pressure solver on the bulk fluid domain, with a transient computational fluid dynamics film simulator based on transient gap geometries solved from the gear loading forces. Simulation results on a commercial unit shows that for a wide range of operating conditions, the model gives volumetric efficiency predictions with errors less than 2 % comparing to measurements. To highlight the importance of considering radial micromotions, the paper also provides the results achieved assuming nominal position for both gears.

ANALISIS PUTARAN PULI RODA GIGI FLYWHEEL PENGGERAK BEBAN PUTARAN RODA GIGI TRANSMISI OTOMOTIF

The electric power of an ac electric motor of Pin = 310.4 watts produces rotation of the output shaft which is used to drive the flywheel gear pulley to produce a rotational speed of Vrpm(in) = 347.8 rpm with a torque parameter of Tin = 8.53 Nm which is transmitted to each each load rotation of the gear pulley of the forward transmission-1 to the forward transmission-4 and the reverse transmission. The results of the research on the speed of the flywheel gear pulley, the Vrpm(in) parameter of 347.8 rpm, was transmitted to the forward-1 transmission gear load resulting in Vrpm(forward-1) = 89.6 rpm, torque Tout(forward-1) = 33.1 Nm and mechanical power Pout(forward-1) = 191.87 watts. Then it is transmitted to the forward-2 transmission gear load producing Vrpm (forward-2) = 162.7 rpm, Tout (forward-2) = 17.34 Nm and Pout (forward-2) = 100.51 watts. Then transmitted to the gear load of the forward-3 transmission is Vrpm(forward-3) = 248.2 rpm, Tout(forward-3) = 11.36 Nm and Pout(forward-3) = 65.85 watts. Transmitted to the transmission gear load forward-4 produces Vrpm (forward-4) = 347.8 rpm, Tout (forward-4) = 8.11 N and Pout (forward-4) = 47.01 watts. To go to the reverse transmission gear load produces Vrpm (reverse) = 75.4 rpm, Tout (backward) = 37.44 Nm and Pout (reverse) = 217.03watt.

The Effect of Sensor Integration on the Load Carrying Capacity of Gears

Classical machine elements have been around for centuries, even millennia. However, the current advancement in Structural Health Monitoring (SHM), together with Condition Monitoring (CM), requires that machine elements should be upgraded from a not-simple object to an intelligent object, able to provide information about its working conditions to its surroundings, especially its health. However, the integration of electronics in a mechanical component may lead to a reduction in its load capacity since the component may need to be modified in order to accommodate them. This paper describes a case study, where, differently from other cases present in the literature, sensor integration has been developed under the gear teeth of an actual case-hardened helical gear pair to be used within an actual gearbox. This article has two different purposes. On the one hand, it aims to investigate the effect that component-level SHM/CM has on the gear load carrying capacity. On the other hand, it also aims to be of inspiration to the reader who wants to undertake the challenges of designing a sensor-integrated gear.

Six-wheel trolley type landing gear ground load analysis study

为了分析起落架支柱柔性和机身柔性对飞机地面运动载荷的影响, 应用动力学基本原理, 建立了六轮小车式起落架动力学模型及全机模型。对活塞杆与外筒柔性化处理, 并在对称水平着陆、机尾下沉着陆和滚转着陆3种着陆工况下, 分析了小车式起落架的载荷分配情况, 研究了着陆工况及支柱柔度对小车式起落架载荷分配的影响。对机身进行柔性化处理, 分析机身柔性对地面载荷的影响。结果表明: 支柱柔度对起落架航向载荷影响较大, 对垂向载荷影响较小; 考虑机身柔性后, 弹性机身变形吸收能量, 有助于减弱机体振动, 起落架及轮胎上的载荷也明显减小。

Analysis of Planetary Gear Transmission Characteristics Based on ANSYS

Planetary gear transmission is widely used in roadhead, crane and other transmission equipment, its reliability and stability are related to the service life and work efficiency of equipment, but the current research on planetary gear transmission device is not comprehensive, lack of accurate analysis of gear meshing process load. Therefore, in this paper, ANSYS software as a platform, through the construction of dynamics module, to solve the gear teeth surface, gear teeth root and gear teeth tip stress analysis and deformation and displacement, the finite element analysis. The research results provide necessary technical support for the design and production of planetary gear transmission.
 Aims: Through finite element analysis of planetary gear transmission, the dynamic parameters of planetary gear transmission are solved, and the reliability and stability of planetary gear transmission equipment are improved.
 Study Design: By constructing the dynamics module of planetary gear, the stress analysis, deformation and displacement of gear tooth surface, gear tooth root and gear tooth top are solved, and the finite element analysis is carried out.
 Place and Duration of Study: North China University of Water Resources and Electric Power, from March to July 2022.
 Methodology: The finite element analysis was carried out on the model of planetary gear transmission mechanism, and the model was established and simplified by using SolidWorks software. The modal analysis and dynamic analysis were carried out by using ANSYS software, and the meshes were divided and constraints were added. Finally, the parameters such as stress, strain and displacement of the meshing position were solved.
 Results: The result of model meshes is 357575 units and 204871 nodes. The algorithm has 219 iterations and 15 convergence points. The experimental results show that there is a meshing position with the worst contact fatigue strength in the contact area between the outer ring gear and the planetary gear tooth surface. At this position, the contact stress value of the tooth surface is 22626Pa.
 Conclusion: In this paper, the planetary gear device is modeled by SolidWorks software, and the finite element analysis is carried out by ANSYS software to obtain the stress and strain parameters in the transmission process of the device, as well as the worst meshing point of the gear, the most vulnerable point of fatigue and other dangerous points. It lays a certain technical foundation for the optimization and improvement of gear and the design and production of planetary gear transmission device.

Five-state engaging model and dynamics of gear-rotor-bearing system based on time-varying contact analysis considering gear temperature and lubrication

Contact behavior of gear teeth plays a key role in modeling and analysis of geared systems. To reasonably evaluate the time-varying contact characteristics of spur gear systems, a new load-dependent time-varying meshing stiffness model incorporating elastic contact stiffness, temperature stiffness and oil film stiffness is developed. Asperity pressure and lubricant pressure are considered for the oil film stiffness. The engagement of the gear pair is decomposed and classified based on the time-varying contact analysis and then five meshing states are obtained. A novel nonlinear dynamic model of the gear-rotor-bearing system with 5-state mesh including time-varying backlash and time-varying meshing stiffness is established by introducing multiple state sub-functions. The effects of gear temperature and load on the meshing stiffness are analyzed. 5-state meshing behavior is identified and characterized by constructing 5 Poincaré maps. The bifurcation and evolution of 5-state meshing behavior are investigated by changing parameters. Distribution of multi-state meshing behavior in two-parameter planes is analyzed to obtain the correlation between multi-parameter and multi-state behavior. The results demonstrate that temperature and load greatly affect the time-varying meshing stiffness, of which the temperature stiffness contributes the most and the oil film stiffness contributes less. The parameters change the system dynamics by affecting the multi-state meshing behavior. The dynamic behavior is highly dependent on the matching and combination of multiple parameters. Diversity of multi-state meshing behavior is clearly revealed. The presented results provide an understanding of the time-varying engaging characteristics and therefore serve as a useful source of reference for engineering in designing and controlling such gear systems.

Advanced landing gear fibre Bragg grating sensing and monitoring system

In this paper an advanced optical-based landing gear load sensing and monitoring system is presented. The system measures strains using fibre Bragg grating sensor that are converted into loads and torque at the landing gear wheels and provides this data for use by the aircraft systems for integration with aircraft health monitoring, hard landing detection, flight management, flight controls and ground controls. A complete sensing system was developed in the European Union Clean Sky 2 Joint Technology Initiative Advanced Landing Gear Sensing and Monitoring (ALGeSMo), described herein. This involved: the integration of optical fibres into a composite structure, the development of an optical harness (cabling and connectors) meeting aircraft installation requirements, the readout of the optical fibre sensors with state-of-the-art miniature optoelectronics and the processing and communication of the data. Apart from specific tests on the various components, a bespoke test rig was developed to rigorously test the whole sensing and monitoring system on an A320 main landing gear slider tube to validate the performance of the system. The system-level tests performed on the test rig showed a very good correlation with applied actuator loads and additional conventional strain and temperature sensors. It demonstrates that loads along all three axis of the landing gear and the torque about the wheel axle can be accurately measured. Tests performed at cold and elevated temperatures, however, revealed that the generally applied one-dimensional temperature compensation equation is not accurate enough for this application, due to the non-uniform non-stationary temperature field. The ALGeSMo research activities have advanced the state of the art in several key areas for the deployment of optical sensing systems for safety-critical applications, such as integration of optical fibres into composite material, robust optical connections, avionic-compliant optical interrogator and landing gear load measurement up to technology readiness level technology readiness level 5.