Spur Gear System Research Articles

Dynamic characteristic of spur gear system with spalling fault considering tooth pitch error

AbstractThere have been many researches focusing on the dynamic characteristics of gear faults, such as spalling, crack and broken, to improve the accuracy of fault diagnosis methods. However, the tooth pitch error caused by actual gear manufacture precision is usually neglected, which may have a direct influence on the gear vibration response. In order to settle the problem of the underlying vibration mechanism with the combined effect of pitch error and spalling fault, a dynamic modeling method of the spalling gear coupling with pitch error is proposed, in which the relationship between the gear precision level and the pitch error is considered. The changes in both meshing stiffness phase and displacement excitation on the contact line caused by pitch error are analyzed, where the additional effect of spalling fault on stiffness excitation is also taken into consideration. Base on the proposed dynamic model, the dynamic responses and vibration characteristics of spur gear with coupling excitation of pitch error and spalling fault are investigated. The simulation results show that vibration characteristics caused by the early spalling fault are easy to be affected by the pitch error, especially when the gear precision is poor.

Modeling and fault identification of the gear tooth surface wear failure system

Abstract In order to detect the gear tooth surface wear fault, this paper presents a new fault diagnosis method based on Symlets wavelet family multi-structure element difference morphological denoising and frequency slice wavelet transform (FSWT). Besides considering the gear backlash, time-varying mesh stiffness, gear error and bearing longitudinal response, and low frequency excitation caused by the torque fluctuation, random disturbance of damping gear ratio, gear backlash, excitation frequency, and meshing stiffness are also considered. Dynamics equations of a three degrees of freedom spur gear transmission system with tooth surface wear fault are established according to Newton’s laws. The 4–5 order variable step Runge–Kutta method has been used for solving the equations to get the vibration signal of the system. Then, the proposed method is applied to extract the wear fault signal, which verifies the feasibility and effectiveness of the proposed method.

Effects of Tooth Surface Crack Propagation on Meshing Stiffness and Vibration Characteristic of Spur Gear System

Tooth surface cracks are considered as the early stage of the development of tooth surface spalling failure. Understanding the excitation mechanism of surface cracks has a great significance in the early diagnosis of spalling faults. However, there are few studies on the dynamic modelling of surface cracks, and the influence mechanism of surface cracking on the dynamic characteristics of a gear system is also not yet clear during its propagation process. Thus, an analytical calculation model of the meshing stiffness of gear with tooth surface crack is developed. Then, a dynamic model of a spur gear system with six degrees of freedom (DOF) is established based on the proposed surface crack calculation model. The effects of surface crack propagation on the meshing stiffness and dynamic characteristics of gear system are investigated. The results show that the side frequencies of dynamic transmission error (DTE) are more sensitive than those of the acceleration responses during the surface crack propagation, which is more favorable to the surface crack fault diagnosis. Compared to the traditional spalling fault model, the proposed model can accurately characterize the dynamic characteristics of a gear system with the early spalling defect.

Dynamic analysis and chaos control of spur gear transmission system with idler

This study aims to analyze the chaotic dynamics and present a chaos controller for spur gear transmission systems with idler. The chaotic dynamics of the spur gear mechanism has already been investigated. However, the presence of idler gears affects the chaotic behavior and the route to chaos for the nonlinear model of spur gears. This is investigated through the derivation of dimensionless dynamics, defining a Poincare’ section, and extracting the bifurcation diagrams of the system for variations of several parameter models. A nonlinear time-varying dynamic model of a spur gear transmission system with idler is established where backlash, time-varying stiffness, static transmission error, and external excitation are included and a region for the occurrence of chaos is found. The chaotic vibration suppression of the system is done by detecting the unstable periodic orbits embedded in the strange attractors and developing control law by employing sliding mode and adaptive sliding mode control strategy. The controller transmits a chaotic trajectory into the detected unstable periodic orbits. Numerical simulations including phase plane portrait, time histories diagrams, Poincare’ sections, and bifurcation diagrams demonstrate the behavior of the system and confirm the performance of the proposed controller.

Design and stress distribution analysis of composite spur gear

This paper presents the contact stress analysis of the carbon-fiber/epoxy resin composite gear train, where a spur gear models are developed using advanced software for pro-e modelization and torque load application meshed and analyzed using the Abaqus analysis software. The interaction of the tooth in a three-dimensional coordinate of a pair of spur gear systems is analyzed as body touch in this paper. The analysis consists of one loading condition in which, by limiting all degrees of driven gear freedom, the torque load on the driving gear is imposed. The model is mated in such a manner that the fine and coarse components around the gear teeth can be found in other parts of the model. Displacement magnitude and three-dimensional stress are found for both the driven machinery and the moving gear.

Dynamic Response Analysis of Spur Gear System with Backlash

There are few studies on space-driven gear systems in the existing literature. In this paper, a spacedriven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. A nonlinear dynamic response analysis was performed. The backlash was introduced into the dynamic model, and the time-varying stiffness was corrected to make the theoretical model closer to reality. By comparing two kinds of dynamic response curves with and without return difference, it was illustrated that the influence of return difference on dynamic transmission error in a gear system. The results obtained in this paper provide a reference and basis for subsequent research.

Time-varying Response Analysis of Spur Gear System

In this paper, a space-driven two-stage spur gear system is taken as the research object, and a 10 DOF dynamic model is established. Considering the high load characteristics of the space drive system and the time-varying stiffness and tooth clearance of the gear system, a nonlinear dynamic response analysis was performed. The characteristics of the vibration acceleration, shock and transmission error of the gear system are studied in this paper. This paper analyzes the relationship between backlash and return difference, and derives the theoretical formula between the two. The time-varying stiffness was corrected to make the theoretical model closer to reality. The research in this paper enriches the study on space drive systems and high load gear systems.

A new calculation method for tooth fillet foundation stiffness of cracked spur gears

General calculation methods for tooth fillet foundation stiffness will generate significant errors in the rim crack case. In order to solve this problem, a new calculation method is proposed in this paper, which is capable of taking both tooth and rim cracks into account. In the proposed method, the root position of the cracked gear tooth is redefined using the connecting line between the crack vertex and the transition curve endpoint. The tooth fillet foundation stiffness of the cracked gear with different crack parameters can then be calculated. The calculation results using this new method are validated by finite element method (FEM) results. The calculation results of cracked gears based on the proposed method are in good agreement with FEM. The proposed method can meet the calculation of the fillet foundation stiffness for both tooth and rim cracked gears. The new method can be employed to calculate the mesh stiffness of the cracked gear more accurately and further to serve the fault diagnosis process of the spur gear system.

Noise Reduction in Spur Gear Systems.

This article lists some tips for reducing gear case noise. With this aim, a static analysis was carried out in order to describe how stresses resulting from meshing gears affect the acoustic emissions. Different parameters were taken into account, such as the friction, material, and lubrication, in order to validate ideas from the literature and to make several comparisons. Furthermore, a coupled Eulerian–Lagrangian (CEL) analysis was performed, which was an innovative way of evaluating the sound pressure level of the aforementioned gears. Different parameters were considered again, such as the friction, lubrication, material, and rotational speed, in order to make different research comparisons. The analytical results agreed with those in the literature, both for the static analysis and CEL analysis—for example, it was shown that changing the material from steel to ductile iron improved the gear noise, while increasing the rotational speed or the friction increased the acoustic emissions. Regarding the CEL analysis, air was considered a perfect gas, but its viscosity or another state equation could have also been taken into account. Therefore, the above allowed us to state that research into these scientific fields will bring about reliable results.

Bifurcation and chaos analysis of a spur gear pair system with fractal gear backlash

The dynamic characteristics of a spur gear pair system with two kinds of gear backlash are studied, in which the modeling of gear backlash is emphasized. Meanwhile, the sliding friction force is derived. On this basis, a torsional dynamic model is established. Some simulation experiments are conducted using rotational velocity and initial gear backlash as variables. And the bifurcation and chaos of the system with fixed backlash and fractal backlash are compared. The results show that both two conditions exhibit a common pattern in motion state evolution, but the system with fractal backlash enters chaos at a higher rotational speed and a larger initial gear backlash. The system with fixed backlash exhibits more rich nonlinear dynamic behaviors. The dynamic model with fractal backlash deduced in this paper outlines a method of establishing an indirect relationship between bifurcation, chaos, and tooth surface microscopic features. The results provide fundamental support for designing and manufacturing the spur gear in the future.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

Abstract In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

Effects of random interval parameters on spur gear vibration

Gear driving devices are commonly used in mechanical transmission systems. Due to the inevitable random errors in manufacturing, installation, and operation, the dynamics of a gear transmission system will fluctuate randomly. To reveal the dynamic characteristics, an interval parameters dynamic model of a single-stage spur gear pair is established, in which the uncertainties of displacement excitation, load excitation, and stiffness excitation are included, and their formulations are derived in detail by using interval mathematics. The established interval parameters dynamic model is solved by combining the Chebyshev inclusion function method and the Runge–Kutta method. Finally, the influence of the random interval parameters of meshing stiffness, input torque, and transmission error as well as backlash on the vibration velocity interval and transmission reliability of the gear transmission system are studied. The analysis results show that the three types of excitations have different effects on the dynamic characteristics. To be specific, the effects of uncertain parameters on the dynamic characteristics can be ordered as meshing stiffness, input torque, backlash, and transmission error in sequence from the strongest to the weakest. The present study may serve as a sound theoretical basis and can provide references for the design and vibration control of spur gear transmission systems.

Dynamic analysis of uncertain spur gear systems

Gear transmission systems are widely used in mechanical equipment. Due to manufacturing and processing errors, material defects, wear and external environments, there are uncertain parameters such as mass, mesh stiffness and support stiffness. Parametric uncertainty plays an important role in response predictions of the gear transmission systems. In order to evaluate reasonably the dynamic characteristics of the gear transmission systems, a dynamic model of an uncertain single-stage gear system is established. The dynamic responses of the bounded uncertain gear transmission system are investigated by an interval analysis method based on the Chebyshev inclusion function. A matrix form of the least square method is applied to improve the calculation efficiency of the interval approach. The investigation reveals the effects of different uncertain parameters on amplitude-frequency responses of the gear system. It is the first time to design and to implement a test rig of an uncertain single-stage spur gear transmission system. The experimental results verify the accuracy and the effectiveness of the theoretical analysis results. The results demonstrate that the parametric uncertainty may propagate in the gear transmission system and the propagation results in significant variations of the dynamic responses.

Nonlinear dynamic analysis of spur gear system based on fractional-order calculus

In this paper, nonlinear dynamic model of spur gear pairs with fractional-order damping under the condition of time-varying stiffness, backlash and static transmission error is established. The general formula of fractional-order damping term is derived by using the incremental harmonic balance method (IHBM), and the approximate analytical solution of the system is obtained by use of the iterative formula. The correctness of the results is verified by comparing with the numerical solutions in the existing literature. The effects of mesh stiffness, internal excitation amplitude and fractional order on the dynamic behavior of the system are analyzed. The results show that changing the fractional order can effectively control the resonance position and amplitude in the meshing process. Both the mesh stiffness and internal excitation can control the collision state and the stability.

Lubrication reliability analysis of spur gear systems based on random dynamics

An approach for lubrication reliability analysis of spur gear systems considering the randomness of external load and surface roughness is presented. The instantaneous failure probability of gear lubrication is captured by a gear stochastic dynamics model and a reliability model of elastohydrodynamic lubrication (EHL). The stochastic dynamics model is adopted to obtain the numerical characteristics of meshing force. The reliability model is established based on a mixed EHL line contact film thickness formula. The first-order second-moment method is employed for predicting failure probability of lubrication. The lubrication reliability of a gear pair excited by different intensity random load is studied. The results show that the lubrication failure probability in dedendum and single meshing region are higher than addendum.

Study of Mesh Stiffness of Spur Gear Tooth by Considering Pitting Defect under Dynamic Load Conditions

Gear drives are one of the most essential mechanism of power transmission systems in numerous industrial applications such as automobiles, aerospace and wind turbines, etc. As the speed of gear transmission increases, the study of the dynamic behavior of the gears are more important in the gear design. Gear mesh stiffness plays an eminent role in gear dynamics and it varies in the existence of gear fault such as pitting, spalling and crack. The dynamic performance of the gears are affected by module, contact ratio, pressure angle and transmission error, etc. In order to understand the dynamic properties of spur gear system, it is necessary to calculate the mesh stiffness of the gear tooth pair effectively. In this paper, a comparative study has been carried out using FEM between healthy gear and fault gear by considering pitting defect. Gear mesh stiffness of healthy and fault gear has been compared under dynamic load distribution in gear tooth contacts.

Bending Fatigue Life Prediction of Spur Gear in Axial Misalignment Condition

Misalignment between pinions to wheel gears induces bending stresses continued influences the fatigue life of the spur gear system. Lack of research projected to the issues causes uncertain in their useful lifetime estimation. In this paper, the bending fatigue life of the spur gear in axial misalignments condition was predicted. A three teeth FEM model of spur gear with the same geometrical profiles was constructed according to ISO 6336-1:2006. The gear was subjected with five misalignment from 0.1mm to 0. 5mm at different torque loadings from 50Nm to 300 Nm. Exerted with quasi-static approach; the stress variant was analysed to stress life model as well as the damage accumulation model for fatigue life prediction in ANSYS V19. Results showed that the application of axial misalignment had a small impact significantly reduce the life of the gear, in percentage difference between 0.1 - 2%. This suggested that the bending fatigue life did not reflect to the existence of axial misalignments as the effect is very small that it is possible to be neglected.

Linear Feedback Control of Chaotic Motion in Gear Transmission System

Considering the internal and external excitations such as backlash, time-varying mesh stiffness (TVMS), transmission error and friction force, a lumped mass model of the spur gear system is established. On this basis, the influences of the support stiffness on dynamic response including bifurcation diagrams, time response diagrams, amplitude-frequency spectrums, phase plane diagrams, Poincaré maps are examined by using numerical method. To avoid the system moving in the unstable region, a linear feedback control method (LFCM) in the gear system is realized. Numerical simulations show that the LFCM is effective and feasible, hence the gear system can be controlled from chaotic motion to stable periodic orbits by using the appropriate control parameter.

Dynamic Modeling and Analysis of Involute Spur Gear Transmission System Considering Friction and Multi-State Meshing Conditions

A dynamic model for an involute spur gear system involving multi-state mesh and friction is formulated to analyze the dynamic response and meshing state property under different lubrication conditions, such as an elastohydrodynamic and mixed lubrications as well as dry friction. The dynamic equations of the system under teeth separation, drive-side and back-side tooth meshes are derived respectively based on the meshing principle of the gear transmission and the force analysis acting on teeth. The effects of the different lubrication schemes on the dynamic meshing force and motion orbit of the system are studied. Results show that the lubrication scheme greatly affects the amplitude of dynamic meshing force. However, the influence of the lubrication scheme on the motion orbit depends mainly on the meshing state. It means that the system motion orbit is largely affected by the lubrication scheme without drive-side and back-side tooth impacts, while the orbit is slightly affected by the lubrication scheme when drive-side and back-side impacts occur. Additionally, the dynamic response and meshing property are investigated with the decrease in load by defining three different Poincaré mappings. The system performs a drive-side meshing state as the load is large. The teeth separation is observed periodically with the decrease in load. While, both teeth separation and back-side mesh are observed under small load, which strengthens the impact vibration between the meshing teeth.

Dynamic Modeling of Gear System Based on 3D Finite Element Model and Its Application in Spalling Fault Analysis

A reduced-order dynamic model, based on three-dimensional (3D) finite element model (FEM) and component modal synthesis technique (CMS), was presented for simulating the dynamic behavior of the spur gear system. The gear shaft and gear body were established via 3D elements to simulate bending and torsion of the gear system. The CMS technique was used to generate a reduced-order model of a spur gear system. A pair of mating teeth was assimilated to two different foundations (one for the pinion tooth and the other one for the gear tooth) linked in series by some independent springs, which was used to simulate the contact stiffness. The validity of the proposed model was verified by static analysis, dynamic analysis, and experimental analysis. The results show that the proposed model is an effective model. In addition, the proposed model has also been applied to analyze spur gear spalling faults. The results show that the dynamic response of the gear system is periodic vibration shock response due to the alternate meshing of single and double teeth. When the spalling fault occurs, some shock responses with significantly enhanced amplitude will be generated as the result of contact loss.