Gear Mesh Research Articles

Gearbox mixed faults diagnosis under different working conditions based on meshing frequency modulation area

Condition monitoring of gearboxes is mainly based on vibration analysis. Traditionally, spectral lines related to shaft speeds and gear meshing frequency (GMF) are the key components that serve as fault indicators. However, due to the noise level and the dependence of signal energy on operating conditions, this technique can fail. In this article, we present an alternative technique based on the calculation of the area covered by a spectral band around the GMF. This band is observed in the envelope spectrum of the vibration data and covers the modulating components characterizing the appearance of the defects. The experimental results obtained from a gearbox test bench operating under different speeds and load levels show the effectiveness of the proposed fault indicator in the detection of combined faults. Compared to certain other known methods for diagnosing gear faults, the proposed technique shows its superiority in terms of processing time and simplicity of implementation.

Study on Design Constraints of Conjugated Straight-Line Internal Gear Pair

In order to solve the problem that the design constraints of the conjugated straight-line internal gear pair are unclear, the designing and checking of gear pairs requires repeated trial and error. By analogy with the design of the involute gear pair, the basic design parameters of the conjugated straight-line internal gear pair were clarified. Based on the mathematical model of the gear pair, the constraints on basic design parameters were given according to gear engagement theory and the geometrical relations of the tooth profile. The calculation formula and the constraint of the contact ratio were deduced according to the kinematic relations. Based on Litvin’s undercutting theory, the constraints on avoiding undercutting and end cutting were deduced and their correctness was verified by examples. The judgment method of tooth-overlapping interference and its corresponding numerical calculation flow were presented. The constraint on avoiding radial interference was deduced and analyzed. Based on the above content, the influence laws of design parameters on the design constraints were studied. Last, design examples were given and the effective design flow diagram of the conjugated straight-line internal gear pair was summarized. These research results provide a theoretical basis for the parameter design of conjugated straight-line internal gear pairs, provide guidance to avoid the interference of the gear pair, and promote the design system of the gear pair.

Simulation of VERICUT-based Generating Grinding of Involute Beveloid Gears

Based on the principle of generating grinding, VERICUT is used for generating grinding of involute beveloid gears. Firstly, the tooth surface equation of the involute beveloid gears is derived according to the principle of involute beveloid gears forming and gear meshing theory, and the theoretical model of the involute beveloid gear is established; secondly, the CNC conical gear grinding machine model, grinding wheel tool model and tooth blank are built in UG and imported into VERICUT, and the CNC machining program of the generating grinding is written to carry out the generating grinding simulation; finally, the simulated involute beveloid gear is automatically compared with the design model to verify the accuracy of the generating grinding simulation machining method. This study provides theoretical guidance for the practical machining of involute beveloid gears, reduces costs and shortens machining cycles, thus improving the productivity of involute beveloid gears.

Semi-analytical loaded tooth contact analysis method for spiral bevel gears

Loaded tooth contact analysis (LTCA) is an important tool for analyzing the meshing of spiral bevel gears. This paper presents a semi-analytical LTCA method, where the analytical formulas are used to calculate the tooth deformation and contact force, with partial coefficients corrected by finite element analysis (FEA) results. Based on Tredgold's Approximation, the tooth is sliced, of which the flank is determined by simulating the manufacturing process. In order to calculated the potential contact curves of a real gear pair, an optimization model is established to find the points more likely to be in contact within the range of contact curves obtained by the help of roll angle surfaces. The compliance of tooth is modeled as a combination of two contributions, where the deformation of cantilever beam under load is used to determine the global deformation, and the local contact deformation is obtained by Hertz line contact assumption. A contact judgement strategy is proposed to detect the contact of the slices at ends of contact curves, and the correction coefficients are introduced in the tooth deformation to consider the coupling effect among slices. In the end, a numerical instance of LTCA under different load torques is provided, which demonstrates the accuracy and efficiency of the presented LTCA method by comparisons with results of FEA. This method can be easily modified to analyze other gear pairs and has the ability to be extended to simulate the gears with local defects or cracks.

Analytical Model of Gear Thermal Stiffness Based on the Potential Energy Method

Stiffness is the main internal excitation of gear system vibration and is the basis for studying the static and dynamic characteristics of the system. Based on the relationship between thermal stress and strain in plane strain theory and combined with the potential energy method, a novel gear thermal stiffness model is proposed in this paper. The model deduces more general analytical formulas for gear thermal mesh stiffness and time-varying thermal mesh stiffness. The results show that the gear thermal stiffness decreases as a whole compared with the elastic stiffness. The decrease in stiffness is nonuniform along the line of action. The effects of temperatures, temperature distributions and thermal stress on gear thermal stiffness are investigated. The accuracy of the model is verified by comparisons with existing methods and references.

Dynamic characteristics analysis of gear transmission and its support bearings of high-speed train on the curve

The gear transmission in high-speed trains is crucial for transmitting the traction torque. Its dynamic characteristics impact the system's reliability and safety. Additionally, the gear transmission and its support bearings can be affected by wheel-rail interactions, particularly on curves with larger centrifugal forces. To address this, a spatial vehicle-track coupled dynamics model that considers the complete power transmission path and mechanical structure of the gear transmission is proposed. The model considers factors such as time-varying mesh stiffness, dynamic transmission error (DTE), time-varying support stiffness, and internal interactions of the gearcase bearing. Results indicate that when a high-speed train passes through a curve, the derailment coefficient and lateral force of the wheelset are less on the right curve due to the lateral component of the mesh force, but the opposite occurs on the left curve. The centrifugal effect affects the contributions of the lateral and vertical motions of the gear pair, which are balanced by the torsional motions of the components in the power transmission path. Additionally, the internal interactions between the rolling elements and races are intensified due to track irregularity and gear engagement, but the centrifugal effect of the pinion can be ignored.

An improved load distribution model for involute helical gear pairs considering an actual contact ratio

With the increasing requirements of helical gears for high strength and low noise, it is significant to improve the accuracy of the load distribution ratio depending on the minimum elastic potential energy (MEPE) model. In this paper, an improved distribution model is developed to replace the theoretical contact ratio with the actual contact ratio and introduce the potential energy of the fillet foundation for comparison. Then, the operation process of the helical gear is divided into seven cases. Finally, combined with the finite element method, the accuracy of the improved model is confirmed. Results indicate that the load distribution model with fillet foundation energy is only effective under the front or the full tooth meshing. When the gear meshing includes the rear part of a tooth, the inclusion of the actual contact ratio and fillet foundation energy should be considered.

Numerical and experimental study of the dynamic behaviour of a polymer-metal worm drive

Polymer-metal worm drives are common in automotives and mechatronic systems. Despite this, there is a lack of studies on this type of transmission, especially when it comes to their dynamic behaviour. With the modern orientation of Industry 4.0 towards advancing technology in predictive maintenance, it is of a great importance to consider the study of the dynamic behaviour of this mechanism. It is first proposed to introduce an appropriate dynamic model to correctly simulate, by numerical means, the behaviour of a non-defective polymer-metal worm drive. For this purpose, it is necessary to correctly model the Gear Mesh Stiffness (GMS) of the gearing system. The GMS depends on the nature of the worm and worm gear materials. It is assumed that no deformation occurs in the steel worm, in contrast to the polymer worm whose viscoelastic behaviour must be accurately modelled. Generalized Maxwell Model (GMM) is chosen to model this behaviour. Eventually, the vibration signals from the numerical model are compared with those determined by the experimental tests. To obtain more similarities between the numerical and experimental signals, it is proposed to perform an optimisation. The procedure consists in using the Nelder-Mead simplex method to obtain a minimum residual objective function. After optimisation, an accuracy of 94% between the experimental and numerical results is achieved.

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.

К РАСШИРЕНИЮ ЭКСПЛУАТАЦИОННЫХ ХАРАКТЕРИСТИК ЗЕМЛЕРОЙНО-ТРАНСПОРТНЫХ МАШИН

This article presents materials related to the development of a promising dump design for various types of bulldozers used on high-strength soils. The most important parameter of bulldozers is productivity, which depends on the amount of soil moved by the blade in one working cycle, characterized by the volume of the drawing prism. A characteristic sign of overloading of dumps is the slipping of tracks or tractor wheels. This phenomenon significantly affects the reliability of components and parts of bulldozers, reducing their productivity. To eliminate this, rotary dumps can be used, allowing them to be rotated at a certain angle in both directions relative to the longitudinal axis of the machine, but their restructuring is quite time-consuming and not always effective. The analysis of numerous sources made it possible to develop a prom-ising technical solution at the level of inventions, which makes it possible to efficiently perform earthmov-ing operations related to the treatment of high-strength soils. As a result of analytical studies, taking into account the cutting resistance force of 7 kN, the geometric parameters of the gear engagement (gear wheel-rail) were calculated, the engagement module was adopted m = 10 mm. Recommendations are given on the choice of gear wheel and rail material – 45 normalized steel. For angular rotations of the side sections of the blade, it is recommended to use a hydraulic cylinder with a double-sided rod with an internal cylinder diameter of dv = 40 mm and a rod diameter of ds = 20 mm, at a working fluid pressure of p=10 MPa. It is recommended that the blade rods be made of 80x60 Steel 85 pipe, which ensures their stability during the operation of the bulldozer blade.

Vibration Performance of Traction Gearbox of a High-Speed Train: Theoretical Analysis and Experiments

The gearbox is the key component of the traction drive system of a high-speed train. At the same time, the traction gearbox can easily experience a box housing failure due to bearing internal excitation from gear meshing and external excitation from motor torque fluctuation, the wheel polygon, and so on. In order to analyze the vibration and noise of the gearbox, a dynamic model of a high-speed train gear transmission system was established under the conditions of time-varying meshing stiffness and time-varying meshing error. A frequency spectrum analysis of the vibration at the key nodes of the model that changed with the speed was carried out. A test rig for a traction gearbox of a high-speed train was built, and a testing method for the vibration and noise of a high-speed train traction gearbox was put forward. The testing of and research on the traction gearbox under various working conditions were carried out, and the dynamic evaluation indexes of acceleration, vibration intensity, and air noise at different measuring points of the high-speed train traction gearbox were obtained. The study provided a test reference and a basis for the dynamic performance optimization design and fault diagnosis of a high-speed railway traction gearbox system.

Study on nonlinear dynamic characteristics of power six-branch herringbone gear transmission system with 3D modification

The power six-branch herringbone gear transmission system has the advantages of large power transmission and transmission ratio. Because of its multi-way transmission and over-constraint structure, to prevent loaded tooth interference, there are large backlashes between teeth. The system shows complex nonlinear dynamic characteristics under the influence of backlashes, which seriously affects meshing performance. The modification technology can effectively improve gear meshing performance. Hence, on the basis of optimizing meshing performance of the active pair of the six-branch herringbone gear transmission system, this article will combine 3D modification with system nonlinear vibration characteristics and propose an analysis method of the system nonlinear vibration characteristics under 3D modification to reduce vibration and noise. First, the 3D modified tooth surface equation is determined by forming grinding, the loaded transmission error (LTE) of the system's active pair is obtained by tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) technology, and the optimal modification parameters are obtained by Ant Lion Optimizer (ALO) with the minimum error amplitude as optimization objective. Then, the time-varying meshing stiffness of system under the optimal modification is calculated, and the pure torsional nonlinear dynamic model with backlashes, meshing stiffness, and static transmission error (STE) is established. Finally, the global vibration characteristics in parameter field are studied through time domain and bifurcation diagram of system. Results show that the 3D modification can eliminate edge contact of tooth and improve tooth contact performance. With the increase of input power, the root mean square (RMS) values of acceleration increase and the RMS values and jump decrease after 3D modification. With the increase of input speed, the RMS curves appear multiple resonance peaks and jumps at low input speed. After 3D modification, the RMS, jump, and resonance peak values decrease. Compared with level І, the backlashes and STEs of level II and phase difference ϛsII have great influence on system dynamic characteristics and easily make system in chaotic motion, while the 3D modification reduces their influence and makes system motion periodic.

Gear Crack Detection Based on Vibration Analysis Techniques and Statistical Process Control Charts (SPCC)

Vibration condition monitoring is a non-devastating technique that can be performed to detect tooth cracks propagating in gear systems. This paper proposes to apply a new methodology using time-domain analysis, frequency-domain analysis, and statistical process control charts (SPCC) for gear crack detection of a 10 DOF dynamic model of spiral bevel gear system (SBGS). The gear mesh stiffness effect used in the model has been studied analytically for different levels of crack faults. Adding Gaussian white noise is discussed as the first step to simulating the initial modeling signals of real-world conditions. Second, time-domain signal analysis was performed to identify periodic vibration pulses as failure components and calculate the statistical standard deviation (STD) feature as a fault-sensitive feature. Third, a fast Fourier transform (FFT) to time signals of the variable gear mesh stiffness was applied to determine the gear mesh frequency and sidebands to detect tooth cracks. Fourth, the SPCC was designed using the Shewhart X-bar chart and an exponentially weighted moving average (EWMA) chart based on the STD feature of the healthy gears. Finally, in the testing stage, the control charts are carried out with simulation signals under faulty conditions to detect the different levels of cracks. The results showed that the EWMA chart outperformed the time domain analysis, frequency domain analysis, and Shewhart X-bar chart in detecting all levels of cracks at an early stage.

Research on dynamics and failure mechanism of herringbone planetary gearbox in wind turbine under gear surface pitting

In this paper, the herringbone planetary gear system in wind turbine gearbox with tooth surface pitting is modelled, and the time-varying mesh stiffnesses of the gear meshing pairs are calculated. The results show that the aggravation of tooth surface pitting weakened the mesh stiffnesses in different levels based on the pitting condition. Based on the dynamic model of the transmission system, the vibration signal model of the gearbox is established, considering the vibration transmission path and attenuation. The gearbox vibration acceleration signals under tooth surface pitting in different conditions are simulated, the obtained time-domain signals reveal abnormal fluctuations, and the frequency-domain signals illustrate abundant sidebands near harmonics of meshing frequency and low frequency area. For different pitting conditions, the fault frequencies vary, the results provide theoretical basis for the fault analysis and diagnosis of the gearbox. Furthermore, the theoretical analysis results are validated against experimental test results based on the test bench of herringbone planetary gearbox with tooth surface pitting in sun gear.

Analysis of the Dynamic Characteristics of a Gear-Rotor-Bearing System with External Excitation

The dynamic response of the rotor system in a ring die granulator is complex and difficult to solve when it operates under joint external, support and gear mesh forces. To solve this problem, a finite element method and extrusion theory was applied in this study to develop a dynamic coupling model for a hollow overhung rotor with external load excitation. A Newmark-β numerical integration method was used to solve for the dynamic response of the overhung rotor under multiple excitation forces. The results included time-domain response diagrams, frequency-domain response diagrams, phase diagrams, Poincaré section diagrams, and bifurcation diagrams. The model and the method were verified by testing a ring die granulator. On this basis, the dynamic response of the system is predicted according to the influence of different parameters. As the bearing support distance increased, the roller eccentricity decreased, the bearing clearance decreased, the response of the rotor system was significantly optimized, and the system tended to stabilize gradually. Therefore, this paper provides a theoretical basis and experimental verification for the optimization of a pelleting machine transmission structure.

Dynamic Evolution Characteristics of the Gear Meshing Lubrication for Vehicle Transmission System

The transmission in automobiles is the core component to ensure operational stability. Heat accumulation in the meshing process will reduce the transmission efficiency and affect the service life. Here, the essential physical process to improve transmission heat dissipation is the dynamic evolution process and the thermal transfer characteristics of lubricating oil fields during gear meshing. This paper presents a modeling and solving method for gear meshing lubrication and thermal transfer features based on the volume of the fluid model and piecewise linear interface construction (VOF-PLIC). The dynamic mesh technique combines spring smoothing and reconstruction to optimize the numerical solution process. The dynamic evolution law of gear meshing lubrication and thermal transfer is obtained by analyzing the lubrication evolution process under different speed/steering conditions. The results show that the proposed modeling and solving method could well reveal the lubrication and thermal transfer laws of the gear meshing. The temperature of the gear meshing regions was higher than that in the other regions, and the lubrication temperature showed an increasing linear trend with the stirring process. As the gear speed increased, the meshing resistance moment increased, the transmission power loss increased, and the lubrication oil temperature was larger than that of the gearbox. The power loss under the clockwise rotation of the driving gear G4 was higher than that under the counterclockwise rotation of the driving gear. The relevant results can provide theoretical references for the dynamic analysis of automotive transmission lubrication and technical support for gear profile design and lubrication optimization.

Structural health dynamic monitoring for gear transmission based on guided waves

The rotating machinery has a wide range of applications in many fields. The gear transmission system is one of the key structures of rotating machinery. Once the failure occurs to the gear system, it will destroy the equipment itself and lead the whole industrial production to break. Thus, it is necessary to directly monitor the health condition of the gear system under static and running working conditions. Guided waves method is a technology which has been widely used in the field of structural health monitoring. In this paper, guided waves technology is innovatively applied to the condition monitoring of gear system, which realizes the gear structure direct monitoring for low speed rotating machinery. The piezoelectric transducers integrated with the SMART Layer were placed near the gear mesh region for the direct health monitoring. The feasibility was verified by the guided waves monitoring experiments in a fixed-axis spur gear transmission system. The tooth wear and gear crack were monitored by guided waves under a single working condition. In addition, the stability verification experiment of guided waves was also performed under various low-speed working conditions. To characterize the propagation of gear faults, considering the characteristics of guided waves, a modified health indicator extraction methodology is proposed based on permutation entropy. The results indicated that the guided waves technology has fantastic potential applications in gear transmission system dynamic direct health monitoring.

Calculation of the Modulus of Meshing of Spur Gears According to the Wear Resistance of Gear Teeth

Calculation of the Modulus of Meshing of Spur Gears According to the Wear Resistance of Gear Teeth

Extraction and use of frequency-domain relationships between time-varying gear meshing properties and diagnostic measurements

In gears, the key diagnostic information is carried in the gearmesh stiffness and geometric profile errors. These two key gear meshing properties combine nonlinearly with rotations and displacements of the gear shafts to produce a time-varying gearmesh force. This in turn passes through the system dynamic response before finally resulting in actual diagnostic measurements (e.g., vibration or transmission error). The closed form analysis of such transfer paths is rendered impractical by the complexity of the time-varying gearmesh force, and has therefore so far mostly been studied through time-domain simulations. Inspired by a previous linearisation method, this paper develops a matrix-based procedure on a multiple-degree-of-freedom (MDOF) system to linearise the relationship between time-varying gear meshing properties (stiffness and geometric error) and measurements, thus producing frequency response functions (FRFs) between these key diagnostic inputs and the measurements. This FRFs are then used specifically to study the scarcely employed but highly promising diagnostic measurement of transmission error (TE), which is obtained by combining encoder measurements from the two gear shafts. The analysis of TE includes both an application of its experimental measurement for crack diagnostics under different operating conditions, and a discussion of the properties of the TE-FRF that make TE more robust to different operating conditions.

Experimental stress analysis of enhanced sliding contact spur gears using transmission photoelasticity and a numerical approach

Free-Form-Gear (FFG) is a recently published title for a gear that has a curved path of contact and offers contact between a convex addendum and a concave dedendum during the meshing cycle. Based on this method of designing a gear pair, the path of contact can be altered to improve the way the gears mesh and slide against each other by only adjusting the maximum pressure angle and the involute curve parameter. The analytical investigations into this gear pair indicated that, when compared to the standard involute gear pair, the sliding velocity, meshing efficiency, contact, and fillet strengths are improved while the contact ratio is decreased. In this study, experimental stress analysis is conducted on various configurations of the tooth profile and tooth fillet shape for the proposed FFG and the standard involute gear to validate the analytical results. Since it is difficult to measure the contact stress for the gear specimens, the contact stresses at critical points are estimated using an effective computational technique based on photoelastic data and a numerical approach utilizing the nonlinear least squares method. At the fillet zone, isochromatic fringe patterns are used to directly measure the maximum fillet stress. Using addendum modification coefficients, the reduction in contact ratio for the proposed FFG is eliminated, and the results are then verified experimentally. Based on the experimental estimations, the finite element analyses are conducted using ABAQUS to simulate the examined gear specimens. Under the same loading conditions, the experimental, analytical, and numerical results have all been in good agreement.