Eccentric Gear Research Articles

Dynamic characteristics of gear-rotor system with gear eccentricity and wear fault

Dynamic characteristics of gear-rotor system with gear eccentricity and wear fault

Study on the Vibration Characteristics of the Helical Gear-Rotor-Bearing Coupling System of a Wind Turbine with Composite Faults

As the core component of the wind turbine generation gearbox, the gear-rotor-bearing transmission system typically operates in harsh environments, inevitably leading to the occurrence of composite faults in the system, which exacerbates system vibration. Therefore, it is necessary to study the vibration characteristics of wind turbine helical gear-rotor-bearing transmission systems with composite faults. This paper uses an improved energy method to calculate the theoretical time-varying mesh stiffness of a helical gear with a root crack failure. On the premise of considering the time-varying meshing stiffness of the faulty helical gear, the gear eccentric fault, and the nonlinear support force of the faulty bearing, a multi-degree-of-freedom helical gear-rotor-bearing transmission system with compound faults was established by using the lumped parameter method. The dynamic model of the system was solved based on the Runge–Kutta method, and the vibration response of the system under healthy conditions, single faults with gear eccentricity, single faults with tooth root cracks, and coupled bearing composite faults were simulated and analyzed. The results show that the simulation results based on KISSsoft software 2018 version verify the effectiveness of the improved energy method; the existence of single faults and composite faults will cause the fault characteristics in the time domain and frequency domain responses. In this paper, the influence of a single fault and a complex fault on the time domain and frequency domain of the system is mainly discovered through the fault study of the helical rotor-bearing system, and the influence of the fault degree on the vibration of the gear motion system is discussed. The greater the degree of the fault, the more vibration of the system occurs; accordingly, when the system is under the coupling of tooth root crack and bearing fault, there is a significant difference compared with the healthy system and the single fault system. The system vibration has obvious time domain and frequency domain signal characteristics, including periodic pulse impacts caused by gear faults and time domain impact caused by bearing. The fault characteristic frequencies can also be found in the frequency domain. In this paper, the fault study of a helical gear of wind turbine generation provides a reference for the theoretical analysis of the vibration characteristics of the helical gear-rotor-bearing system under various fault conditions, lays a solid foundation for the simulation and subsequent diagnosis of the composite fault signal of the system, and provides help for the fault diagnosis of wind turbine gearboxes in the future.

Influence of Gear Eccentricity with Non-Parallel Axis on the Dynamic Behaviour of a Gear Unit Using a Gear Slice Model with 26 Degrees of Freedom

Influence of Gear Eccentricity with Non-Parallel Axis on the Dynamic Behaviour of a Gear Unit Using a Gear Slice Model with 26 Degrees of Freedom

Discussion of a variant of eccentric drives utilizing rolling elements

In this paper a variant of eccentric drives will be described, which uses rolling elements instead of an eccentric gear. These rolling elements are constrained by a concentric carrier allowing for radial movement and are moved by an eccentric crank. They mesh with a gear geometry that translates their radial movement into tangential movement and constrains their position. Multiple offset eccentricities may be used with the same gear to reduce occurring forces. Such a drive may prove easier to manufacture than currently used eccentric drives, but the characteristics are not yet fully researched.The components and the working principle of such a drive will be described, and consistent names for the components will be established in this paper. Using these the movement of the rolling elements and the resulting gear geometry will be mathematically described. The forces on a singular rolling element will be derived. An overview of and comparison with related drive mechanisms will be given to aid in the classification of this drive. Different variations of this drive will be discussed, including the choice of rolling elements, whether to use an external or internal gear, and whether a direction-reversing or non-direction-reversing drive is advantageous.

Study on nonlinear vibration and primary resonance characteristics of helicopter face gear-planetary gear coupling transmission system

In order to explore the dynamic response and primary resonance characteristics of the gear transmission system of the helicopter main reducer. The face gear-planetary gear torsion-translation vibration dynamics model is established, and the time-varying meshing stiffness, gear backlashes, gear eccentricity error, and friction are considered. The four-order variable-step Runge–Kutta was used to solve the dynamic response of the system, and the nonlinear dynamic characteristics of the system were described by time domain diagram, phase trajectory plane, Poincaré map, 3D frequency spectrum, and bifurcation diagram. Additionally, using the face gear-spur gear system's transmission as an example, the multi-scale method is used to analyze the face gear-spur gear system's primary resonance characteristics. The influence of load fluctuation amplitude, meshing damping, and meshing stiffness on its amplitude-frequency characteristics is also investigated. It is found that when external load excitation frequency changes, the vibration response of the whole system changes synchronously, which exhibits periodic, multi-periodic, and chaotic motion. In addition, according to the primary resonance analysis, the system's stability will be harmed by increasing the external load fluctuations’ amplitude, lowering the meshing damping, and raising the meshing stiffness.

РАЗРАБОТКА КОМПЬЮТЕРНОЙ МОДЕЛИ ДЛЯ ОЦЕНКИ ОСНОВНЫХ ПОКАЗАТЕЛЕЙ ЭКСЦЕНТРИКОВЫХ ПЕРЕДАЧ С ПАРАЛЛЕЛЬНЫМ РАСПОЛОЖЕНИЕМ ВХОДНОГО И ВЫХОДНОГО ВАЛОВ

The study objective is to develop a computer model of an eccentric gear with a parallel arrangement of input and output shafts, as well as an evaluation of their main performance indicators. 
 The paper presents the basic block diagram of an eccentric gear with parallel arrangement of input and output shafts. A layout variant and a computer model of the gear are developed, its operation is simulated and the results of computer study are obtained. A computer model and a method for evaluating the main performance indicators allow optimizing gear parameters, as well as improving its structure.
 The research methods are based on the tools of the automated design system, which gives the opportunity to simulate mechanisms, including toothed gears. Various kinematics and dynamics analysis tools built into the computer-aided design system allow reading angular velocities and torques. These values serve as the basis for evaluating the efficiency and error of rotation of eccentric gear links.
 The novelty of the work is in the study of a new mechanism that allows the creation of small-sized drive devices with a parallel arrangement of input and output shafts.
 Study results include an evaluation of the efficiency and error of rotation of the the eccentric gear output shaft.

MAIN INDICATORS OF ECCENTRIC TRANSMISSION WITH PARALLEL ARRANGEMENT OF INPUT AND OUTPUT SHAFTS ON THE BASIS OF THE USE OF A MULTI-FLOW LOADING SCHEME

The article considers the main structural diagram of an eccentric transmission with parallel arrangement of the input and output shafts with a multi-threaded loading scheme. A computer model has been developed based on the indicated kinematic scheme with the possibility of its use for studying a single-flow loading scheme. A comparative computer analysis of the main indicators of an eccentric transmission with a parallel arrangement of the input and output shafts of single-flow and multi-flow schemes has been carried out. It is shown that the main indicators of an eccentric gear with a parallel arrangement of the input and output shafts with a multi-flow loading scheme have indicators at the level of known coaxial eccentric gears.

Experimental monitoring of eccentric gears with different mechanical conditions

The use of Condition Monitoring (CM) for engineering design, and industrial gears, has dramatically changed the gear design and manufacturing process in a short space of time. As CM deployment grows rapidly, the feasibility of CM for the diagnosis and prognosis of most common gear failure modes has well been investigated and documented. However, this is not the case for the CM of industrial gear eccentricity. Previous published work, in particular, focused only on the use of simulation models as a basis to investigate the gear eccentricity. Simulations cannot always ease the detection of complex problems and complications that are experienced in real operations. For instance, excessive eccentricity can be considered as one of manufacturing errors that may severely lead to direct effect on the overall dynamic performance of gears. Yet, it produces very high modulated mesh frequency rates; thus, making the detection of faulty machine components very difficult or even impossible. With this in mind, this paper presents the first known attempt at the diagnosis and prognosis of experimental vibration datasets from five different eccentric gear conditions. Datasets were first analysed using Signal Intensity Estimator (SIE) method in time and frequency domains. Then, the data was subjected to additional processing for the classification of gearbox status. Observations from the results showed that the proposed techniques could successfully discriminate the “good” and “bad” gears.

Vibration-based gear continuous generating grinding fault classification and interpretation with deep convolutional neural network

Continuous generating grinding plays an essential role in modern gear manufacturing, while the increasing need for high-quality gear products pushes the quality control of the grinding process. This paper proposed a vibration-based process monitoring method to classify faults generated during grinding processes. Gear grinding measurements have been conducted during experiments with different parameters of the feed rate, infeed, and gear eccentricity. The grinding vibration signals have been gathered to form a dataset with seven gear quality categories. A novel deep learning model is presented in this paper exploiting the power of Wavelet Packet Decomposition (WPD) and Deep Convolutional Neural Network (DCNN). The WPD is adopted to transform the vibration signal into 2D time-frequency representations, used as inputs to the DCNN model for classification. Experimental results show that, the proposed DCNN can achieve a high classification accuracy of 95.83%, demonstrating the methodology's efficiency. In addition, this paper exploits the Gradient-weighted Class Activation Map (Grad-CAM) technique to interpret the deep neural network's decisions in order to facilitate the model deployment in industrial production. The Grad-CAM visualizations are utilized to show the activation regions on the spectrograms, which further indicate that the attentions of the DCNN have a strong correlation with the manufacturing parameters of different grinding passes.

Dynamic characteristics of two-mass impact pipeline robot driven by non-circular gears

Considering small diameter pipes, special pipes conveying corrosive, and flammable medium, a two-mass impact pipeline robot driven by a non-circular gear is proposed to study the walking dynamics of the robot in a dry piping environment. The mechanism principle of the two-mass impact pipeline robot is given to illustrate the walking mechanism of the robot under the combined action of the internal force and the external isotropic coulomb friction force. A dynamic model of a two-mass impact pipeline robot driven by non-circular gear is established. The dynamic response of the robot calculated by the numerical method reveals the walking characteristics of the pipe-impact robot under nonharmonic inertial force. The results show that the moving speed of the robot fluctuating rises with the increase of the input speed. The moving speed of the robot can be effectively improved by increasing the eccentricity of the non-circular gear or setting a certain amount of compression of the spring which is between the internal oscillator and the housing.

Dynamic responses and control of geared transmission system based on multibody modeling methodology

In this study, an innovative modeling approach is put forward to research the effect of eccentricity on the nonlinear dynamical behaviors of geared-bearing system. This refined model contains the rigid body of the rotor-bearing system and separated gear teeth which are considered as individual bodies elastically attached to the gear hub with revolute joints. The internal and external excitations of the proposed model include torsional joint stiffness, roll bearing forces, friction between gear pair, gear eccentricity, and so on. The systematic procedure for the calculation of torsional joint stiffness, bearing forces and friction coefficient considering elastohydrodynamic is also conducted. After that, the influence of eccentricity on nonlinear dynamic characteristics of the geared transmission system is analyzed. To avoid the system moving in the unstable motion state, a dry friction damper controller is designed to control the nonlinear behaviors simulated on the basis of above model. The linear feedback and periodic excitation non-feedback control strategies are, respectively, selected to design the actuator. It is indicated that undesirable behaviors of the geared transmission system can be avoided effectively by applying the proposed control method.

Compound transmission principle analysis of eccentric curve-face gear pair with curvilinear-shaped teeth based on tooth contact analysis

A new type of compound transmission gear pair was put forward, called eccentric curve-face gear pair with curvilinear-shaped teeth. It could realize reciprocating motion of the gear shaft when the intersecting shafts achieve transferring motion and power through its unique tooth profile. The compound transmission principle of this gear pair was fully established based on the profile-closure process of axial direction and meshing process of the end face. The tooth surfaces of the eccentric curve-face gear and non-circular gear were generated. The contact paths of different teeth were obtained, and the compound transmission principle of eccentric curve-face gear pair with curvilinear-shaped teeth was verified by tooth contact analysis. By analyzing the mechanical characteristics of time-varying contact points, the changing rule of contact force was studied, and the compound transmission principle of the gear pair was further revealed from mechanics. Moreover, the experimental platform for transmission of eccentric curve-face gear pair with curvilinear-shaped teeth was set up to measure the motion law and contact area, and the correctness of the analysis results was verified.

Nonlinear Dynamic Analysis of Eccentric Curve-face Gear Transmission System

This paper establishes a dynamic model and a Lagrange bond diagram model for the eccentric curve-face gear transmission system. The dynamic model includes a gear meshing model, a lumped-parameter supporting model, a drive and a load, etc. Considering the impact of cam effect and inertia force caused by gear eccentricity, the dynamic equations are established based on the Lagrange bond diagram model. Moreover, the parameters of the model are analyzed deeply, the effects of gear eccentricity, helical angle, tooth profile of gear pairs, and input velocity on the vibration response in time and frequency domain are studied. It is found that the dynamic response of the eccentric curve-face gear transmission system is a highly nonlinear process. The gear eccentricity can modulate both amplitude and frequency. Introducing a force-locking spring in the eccentric curve-face gear transmission system with helical-teeth will negatively affect the system, resulting in the increase of vibration amplitude. The time-varying helical angle of the eccentric curve-face gear transmission system with circle-arc teeth will also have a negative effect on the dynamic characteristics and cause more small pulses. The axial dynamic response, bending dynamic response, and torsion dynamic response are more sensitive than the radical dynamic response to the change of helical angle. Finally, the correctness of numerical analysis was verified through experimental studies.

MINIMUM DETECTABLE DIFFERENCE OF CT ANGIOGRAPHY SCANS AT VARIOUS CARDIAC BEATS: EVALUATION VIA A CUSTOMIZED OBLIQUE V-SHAPED LINE GAUGE AND PMMA PHANTOM

The minimum detectable difference (MDD) at various beats/min (BPM) of CT angiography (CTA) was evaluated using an oblique V-shape line gauge and poly methyl methacrylate (PMMA) phantom in this study. The customized phantom with the size of [Formula: see text][Formula: see text]cm3 was made from a 1[Formula: see text]cm-thick PMMA. The reciprocating mechanism in the phantom was run by a step motor with an eccentric gear connected to a crank rod to provide a stable harmonic motion, simulating the cardiac beats. The MDD has a unique feature in defining the quality characteristic of CT-scanned images and provides more information than simple line pair/cm in the previous studies. The derived MDD was quantified according to various BPM, and the CTA factor combination was preset following either the conventional recommendation or the optimal one. In doing so, the performance was substantiated by the Taguchi-based signal-to-noise ratio and integrated by another index, namely, figure of merit (FOM). The MDD and corresponding [Formula: see text] (dB) changed from [Formula: see text][Formula: see text]mm to [Formula: see text][Formula: see text]mm and from 16.7[Formula: see text]dB to 14.2[Formula: see text]dB, respectively, for conventional settings; while those obtained for the optimal preset changed from [Formula: see text][Formula: see text]mm to [Formula: see text][Formula: see text]mm and from 12.2 dB to 16.4 dB, respectively of CTA at 0–90 BPM. The integrated FOM values for conventional or optimal cases were 1240 and 1337, respectively. The MDD proved to be a useful technique in justifying the CTA-scanned images. For compliance with previous studies, MDD results can be converted to the line pair/cm results, but it is more informative than the quantized number of line pairs.

Tolerance synthesis for lost motion requirement of planetary gear train based on a mechanism model

In this paper, an original equivalent mechanism with parallel linkages is proposed for lost motion behavior analysis and tolerance synthesis of planetary gear train (PGT). The parallel linkages are equivalent in kinematics of PGT to depict the multiple branches of sun-planet-ring gears with a driving link/sun gear and an output platform/carrier, a slider-block with two strokes in the circle curve guide rail of the platform is introduced in each linkage to intuitively express the lag rotation of output platform driven by the parallel linkages under error condition, and the errors are described by the deviations of link lengths. With the mechanism model, the lost motion expression of PGT is explicitly derived and then the tolerance synthesis method is formulated to allocate the optimum tolerances for satisfying the lost motion requirement with the minimum manufacturing cost. The lost motion behavior of PGT was simulated and the tolerances of errors were allocated involving tooth thickness reduction, planet position errors and gear eccentricity errors. The lost motion tests of two PGTs with the allocated tolerances were conducted. The results well agree with the simulations’, which validated the effectiveness of the developed tolerance synthesis method by the proposed mechanism model.

Justification and selection of design parameters of the eccentric gear mechanism of the piston lubrication and filling unit for the mining machines maintenance

Piston pumps are widely used in the lubrication systems of mining machines. When carrying out technical maintenance (MOT), including lubrication and filling works, at the site of operation of mining machines due to the remoteness from repair shops and warehouses of fuels and lubricants (FAL), mobile repair shops (MRS), maintenance units (MU) and mechanized filling units (MFU) are used. The specificity of carrying out maintenance is to create conditions for the supply of oils, working fluids and lubricants to the corresponding systems of mining machines for their refueling. Existing piston pumps and pumping units, as a rule, are single-flow, and the piston is driven by a crank mechanism driven from the engine through a worm gear. The emergence of unique, hydraulic, low-mobility mining machines in open pit mining required a significant increase in the power of the MU and MFU oil pumping units, primarily for greases. However, the traditional design of the drive design of a crank-type piston pump unit at a power of over 80 kW does not allow achieving the specified operating time, it is accompanied by intensive wear of the drive elements and increased dynamics during operation. In addition, it is necessary to apply various designs of pumping units for the supply of liquid and grease lubricants. Thus, it is necessary to develop new circuit solutions for pumping units of the crank type, to improve mobile refueling facilities with a modernized design of the pump unit drive of the mobile lubrication and filling station MRS.

Modeling and dynamic analysis of spiral bevel gear coupled system of intermediate and tail gearboxes in a helicopter

The coupled dynamic model of the intermediate and tail gearboxes’ spiral bevel gear-oblique tail shaft-laminated membrane coupling was established by employing the hybrid modeling method of finite element and lumped mass. Among them, the dynamic equation of the shaft was constructed by Timoshenko beam; spiral bevel gears were derived theoretically by the lumped-mass method, where the effects of time-varying meshing stiffness, transmission error, external imbalance excitation and the like were considered simultaneously; laminated membrane coupling was simplified to a lumped parameter model, in which the stiffness was obtained by the finite element simulation and experiment. On this basis, the laminated membrane coupling and effects of several important parameters, including the unbalance value, tail rotor excitation, oblique tail shaft’s length and transmission error amplitude, on the system’s dynamic characteristics were discussed. The results showed that the influences of laminated membrane coupling and transmission error amplitude on the coupled system’s vibration response were prominent, which should be taken into consideration in the dynamic model. Due to the bending-torsional coupled effect, the lateral vibration caused by gear eccentricity would enlarge the oblique tail shaft’s torsional vibration; similarly, the tail rotor’s torsional excitation also varies the lateral vibration of the oblique tail shaft. The coupled effect between the eccentricity of gear pairs mainly hit the torsional vibration. Also, as the oblique tail shaft’s length increased, the torsional vibration of the oblique tail shaft tended to diminish while the axis orbit became larger. The research provides theoretical support for the design of the helicopter tail transmission system.

A compensation method for the eccentricity and inclination errors of spiral bevel gear based on improved ICP algorithm

Due to the manufacturing and assembly errors of the spiral bevel gear, the deviations between the measured tooth surface and its theoretical tooth surface will affect the measurement results of the tooth surface. After analyzing the tooth surface deviation of spiral bevel gear, this paper provided a compensation method to compensate the eccentricity and inclination errors by the registration of the theoretical and measured tooth surface. An improved iterative closest point (ICP) algorithm for the registration of the tooth surface was provided. The distance between the point in measured tooth surface and the nearest point in theoretical tooth surface is used to replace the minimum Euclidean distance, and the damping Gauss-Newton method is used to solve the geometric transformation matrix. Simulation experiments were carried out to verify the proposed compensation method. The compensation effect is over 93% for the concave tooth surface and over 89% for the convex tooth surface of the spiral bevel gear. The results also show that the improved ICP algorithm could compensate the eccentricity and inclination errors of the spiral bevel gear more precisely than the basic ICP algorithm.

The Anomalous Sun

Abstract Four clockwork-driven planetary automata built to show the true motion of the planets according to Ptolemaic theory, not just their mean motion, survive from the sixteenth century: one each in Paris, Vienna, Kassel, and Dresden. Close, on-site examination of their mechanisms by a team of historians of science and clockmakers has gone beyond existing accounts and revealed that, though they share a common aim, the machines differ fundamentally in their realization of even the “simplest” of the planetary motions, namely that of the Sun. Indeed, three different ways have been detected for producing the solar anomaly, the Sun’s non-uniform motion along the ecliptic in the course of a year. The oldest of the surviving machines (Paris) uses the uniform motion of an eccentric gear, another (Vienna) adapts what would be a geometrically equivalent epicycle, and the two other machines (Kassel and Dresden) make use of a centered gear with non-uniformly spaced teeth. This paper discusses these findings in detail. It argues that such differing approaches not only reflect varying degrees of collaboration among the actors involved in the construction of these four technical masterpieces – princely commissioners, learned astronomers, and artful craftsmen (with these categories sometimes overlapping) – but also that they offer a further, mechanical contribution to the centuries-old reception and refinement of Ptolemaic planetary theory.

Modal analysis and experimental research on a planetary reducer with small tooth number difference

To comprehensively analyze the modal characteristics of the planetary reducer with small tooth number difference, based on shaft–bearing–gear–shell coupling, a finite element modal analysis model was established in ABAQUS. The teeth meshing sites were constrained by binding, bearings were simulated by spring elements, and then the natural frequencies and corresponding vibration modes of the reducer were obtained by applying the Lanczos method. Further, a hammering modal experiment on the reducer was carried out utilizing LMS Test.Lab. The modal data were analyzed using a modal identification method, and the modal frequencies and damping ratios were achieved, also the experimental modal parameters were validated according to the modal assurance criterion. The research results indicate that the lowest-order natural frequency of the reducer is 148.53 Hz, which is much higher than the rotation frequency of the eccentric shaft, double gear, and output gear. Also, the two-stage gear mesh frequencies are away from the natural frequencies, therefore the reducer under normal operating conditions will not cause coupling resonance. This research provides a theoretical basis and experimental reference for the dynamic structure optimization of the planetary reducer.