Geared Shaft System Research Articles

Designing Comprehensive Shifting Control Strategy of Hydro-Mechanical Continuously Variable Transmission

The shift quality is one of the most important criteria for evaluating the operation and transportation of a hydro-mechanical continuously variable transmission (HMCVT) tractor. In this study, a comprehensive shifting control strategy of a hydro-mechanical continuously variable transmission in a high horsepower tractor is investigated for enhancing shift quality. The detailed mathematical model of the transmission assembly components, such as the pump-motor system, the clutch system and the equivalent gear shaft system of the hydro-mechanical continuously variable transmission, are established to analyze the exact shifting process. For different transmission systems, two different control methods are proposed to achieve precise control of the transmission. The double-loop control (PID-Model Predictive Control) is used for the pump-motor hydraulic system, which not only ensures the anti-interference of the control signal when the displacement is a fixed value but also improves the response characteristics and stability of the control output when the displacement ratio is variable. The PID control is used for oil pressure control of the clutch system, and experimental results reveal that a simple method can obtain better control performance. Finally, a comprehensive control strategy in the process of shifting is proposed, and the optimal control strategy is obtained by comprehensively adjusting the pump-motor hydraulic system and the clutch system at the shifting point. The results show that the shift acceleration under the optimal control strategy is 64.4% lower than that without control. The proposed control strategy can effectively reduce shift shock and Improve shift smoothness.

Defect Diagnosis of Gear-Shaft Bearing System Based on the OWF-TSCNN Composed of Wavelet Time-Frequency Map and FFT Spectrum 1

In the defect diagnosis of the gear-shaft-bearing system with compound defects, the generated vibration signals are complicated. In addition, the information acquired by a single sensor is easily affected by uncertain factors, and low diagnostic accuracy is caused when traditional defect diagnosis methods are used, which cannot meet the high-precision diagnosis requirements. Therefore, a method is developed to identify the defect types and defect degrees of the gear-shaft-bearing system efficiently. In this method, the vibration signals are collected using multiple sensors, the dual-tree complex wavelet and the optimal weighting factor (OWF) methods are used for the data layer fusion, and the preprocessing is realized through wavelet transform and FFT. A learning model based on two-stream CNN composed of 1D-CNN and 2D-CNN is established, and the obtained wavelet time-frequency map and FFT spectrum are used as the input. Then, the trained features from the output of the connected layer are classified by the SVM. Compared with the OWF-1DCNN and OWF-2DCNN models, the time consumption of the OWF-TSCNN model is increased by 14.5%–26.6%, and the convergence speed of the network is decreased. However, its accuracy reaches 100% and 99.83% in the training set and test set, and the loss entropy and over-fitting rate are also greatly reduced. The feature extraction ability and generalization ability of the OWF-TSCNN model are increased, reaching 100% diagnosis accuracy on different defect types and defect degrees, which is more suitable for defect diagnosis of the gear-shaft-bearing system.

Analysis and Prediction of Reliability for Motion Error of Polish Mechanisms for Composite Box Based on Monte-carlo Method

The polish mechanisms for composite material box is produced for polishing box within demanding error range, it is made up of gear system, shaft systems and other transmission parts, the clearance and eccentric in the assembly lead to motion error in the polish mechanism; hence, the error reliability of polish mechanisms should be investigated. The error distributions follow normal distribution, the parameter are defined according to the multi-object software ADAMS simulation experiments results. The position accuracy reliability analysis bases on the Monte-carol method to estimate reliability of the polish equipment. Error distribution parameters are calculated with ADAMS simulation experiments instead of the real experiment, which can spare the experimental cost and time and makes it easy to predict reliability with little consumption. The error analysis focuses on the gear system and shaft system mainly, the other factor from other parts are neglected due to their little influence on the error, the reduced analysis benefits to the rapid obtaining reliability results.

An efficient multibody dynamic model of three-dimensional meshing contacts in helical gear-shaft system and its solution

The dynamics of helical gear-shaft systems are characterized by three-dimensional (3D) meshing contacts that have significant variations in the location and size of the contact area, resulting in noise that is unavoidably transmitted to the gearbox through the shaft. Accurate and efficient predictions of the dynamic behaviors of helical gear and shaft are indispensable in reliable and cost-effective gearbox design. Available analytical methods, though computationally feasible, cannot consider multi-point contacts and uneven tooth-load distribution. In contrast, the finite element (FE) method provides a high-fidelity approach to compute the dynamic behaviors of a general gear-shaft system at high expenses of computation. This paper aims to establish a high-efficiency multibody dynamic model for 3D contacts in helical gear-shaft systems, in which the helical gear is pertinently represented under the framework of Arbitrary Lagrangian Eulerian formulation and the shaft is discretized by 3D Timoshenko beam elements. The computational efficiency is greatly improved through the following four steps. First, the low-frequency approximation technique is adopted to reduce the degrees of freedom (DOFs) resulting from the fixed boundary normal modes. Second, under the framework of ALE formulation, only the FE nodes of three meshing tooth-faces are defined as boundary nodes. Then, the dynamic equations and Jacobian matrix are simplified by ignoring the inertial forces associated with deformation. Finally, a two-step algorithm is adopted to accelerate the contact detection process. The accuracy and efficiency of the proposed method are demonstrated through five numerical tests with correlation to commercial nonlinear finite element software.

Vibration of high speed helical geared shaft systems mounted on rigid bearings

Analytical model for linear vibration analysis of a pair of meshing helical gears mounted on compliant spinning parallel shafts is developed. The gears are modeled as rigid disks while the shafts are modeled as flexible rotating cantilever beams. The rotational speed is high such that the gyroscopic effect is non-negligible. Hamilton’s principle is used to obtain the non-dimensional governing equations. Longitudinal and rotational mesh stiffnesses and corresponding elastic energies are incorporated in the total strain energy formulation. Extended operator formulation is used to express the system equations in a consolidated form and later, discretized using Galerkin method. Gyroscopic system structure is apparent in the system equations. Natural frequency sensitivity to various system parameters such as the rotational speed and mesh stiffnesses is determined. Response to loaded static transmission error at the mesh is obtained by performing modal analysis after reducing the system to a first order form. The study shows that gyroscopic effect is present even for short lengths of the shafts. Natural frequency veering between flexural frequencies is present at low speeds and rare at high speeds. For coupled frequencies, response of the system is found to be approximated by modal superposition of smaller number of modes.

Optimal Bayesian control policy for gear shaft fault detection using hidden semi-Markov model

Abstract A new optimal Bayesian control approach is presented to predict early fault of a partially observable gear shaft system subject to deterioration and random failure. The gear shaft system deterioration process is modeled as a three-state continuous time hidden semi-Markov process. States 0 and 1 are unobservable and represent the good and warning system states, respectively. Only state 2 is assumed to be observable and represents the failure state. The general Erlang distribution is considered for modeling the sojourn time in each of the hidden states, which is closer to the actual deterioration process modeling of the gear shaft system than the exponential sojourn time distribution assumed in a hidden Markov model (HMM). The optimal maintenance policy represented by a multivariate Bayesian control scheme based on a hidden semi-Markov model (HSMM) is developed. The objective is to maximize the long-run expected average availability per unit time. An effective computational algorithm is designed in the semi-Markov decision process (SMDP) framework to obtain the optimal control limit and the optimal average availability. Using multidimensional data obtained from condition monitoring, the proposed approach can not only predict early fault occurrence of the gear shaft, but also update the remaining useful life (RUL) at each sampling epoch. A comparison with other maintenance policies is given, which illustrates the effectiveness of the proposed approach.

Study on the running torque of angular contact ball bearings subjected to angular misalignment

Angular misalignment is unavoidable in most applications of rolling-element bearings. The goal of this study is to examine the effects of angular misalignment on the running torque of angular contact ball bearings. A computational method to calculate the running torque of misaligned angular contact ball bearings was introduced. Then, the effects of angular misalignment, along with radial and axial loading, on the running torque of angular contact ball bearings were investigated for two representative preloading methods: constant-force preload and constant-displacement preload. The simulation results showed that (1) the angular misalignment, irrespective of bearing loading, significantly increases the angular contact ball bearing running torque when the constant-displacement preload method was implemented, and (2) the angular misalignment has an insignificant effect on the angular contact ball bearing running torque when the constant-force preload method was adopted. Furthermore, an extensive simulation was performed to examine the effect of load-induced angular misalignment on the running torque of angular contact ball bearings implemented in a geared shaft system. The simulation results showed that the radial load-induced angular misalignment requires additional running torque to the actual rotor-bearing systems, especially when using the constant-displacement preload.

Dynamics of low speed geared shaft systems mounted on rigid bearings

Analytical model for the linear vibration analysis of a pair of coupled spur geared shaft system is developed. The model is a hybrid discrete-continuous one in which the gears are modeled as rigid disks mounted on the elastic shafts having transverse as well as torsional flexibilities and supported by rigid bearings. The non-dimensional governing equations along with the natural boundary conditions are developed using the Hamilton’s principle. An extended operator formulation is employed to simplify the system to a compact analytical form and demonstrate that the system is self-adjoint. The natural frequencies and vibration modes are determined by discretizing the system using the assumed modes method, where the critical feature is the use of Lagrange multipliers to enforce the matching boundary conditions at the disk-shaft interfaces. The sensitivities of the natural frequencies to various system parameters are examined and correlated with the modal energy distribution. Response due to the loaded static transmission error at the gear mesh is presented.

Optimal Bayesian estimation and control scheme for gear shaft fault detection

Fault detection and diagnosis of gear transmission systems have attracted a lot of attention in recent years, but there are very few papers dealing with the early detection of shaft cracks. In this paper, a new methodology for predicting failures of a gear shaft system is presented. The time synchronous averaging (TSA) method is applied to the gear shaft vibration data, and the wavelet transform technique is then used to obtain quantitative indicators of gear shaft deterioration. System deterioration is modeled as a hidden, 3-state continuous-time homogeneous Markov process. States 0 and 1, which are not observable, represent healthy and unhealthy system conditions, respectively. Only the failure state 2 is assumed to be observable. The computed quantities, which are stochastically related to the system state, are chosen as the observation process in the hidden Markov modeling framework. The objective is to develop a method for optimally predicting impending system failures, which maximizes the long-run expected average system availability per unit time. Model parameters are estimated using the EM algorithm and an optimal Bayesian fault prediction scheme is proposed. The entire procedure is illustrated using real gear shaft vibration data.

Coupled torsional–lateral vibration analysis of geared shaft systems using mode synthesis

Coupled torsional–lateral vibration analysis of geared shaft systems using mode synthesis

Vibration Analysis of Helical Gear System Including a Gearbox. Study on Analysis Method.

Two methods of analyzing vibratory response of helical gear system including gearbox are proposed. In the first method, gear shaft system and gearbox system are assembled to one FE-model and response analysis is done to mesh exciting force. In the second method, response analysis of gear shaft system is done separated from gearbox system and dynamic bearing forces are evaluated. Next, dynamic bearing forces are given to gearbox and response analysis of the gearbox is done. These two analysis methods are applied to single stage gearbox that a pair of helical gears with tooth surface modification is built in. The analytical and experiment results show that these methods are effective.

Development of resin gear balance shaft system for 2AZ-FE engine

In-line 4 engines have many merits when compared to engines with more cylinders, such as low cost, excellent gas mileage, low weight and compactness. However, one disadvantage is a vibration at 2nd order frequency. This vibration can be canceled by applying a 2nd order balance shaft. For the 2AZ-FE engine, a world class balance shaft system was achieved using resin gears for the first time ever. Reliability was achieved by developing a high-strength resin optimal impact absorption characteristics. Cost, friction and weight of the balance shaft system were lowered 50% when compared to the Toyota 5S-FE engine.

Coupled torsional-lateral-axial vibration analysis of a geared shaft system using substructure synthesis

A general model of multistage and multimesh geared shaft systems is proposed which takes into account the coupling effects between torsional, lateral and axial vibrations. The system can be divided into several substructures which are dynamically analysed using a finite element method. The boundary conditions at the nodes which are related to the engagement between a pair of gears are used to synthesise all of the substructures so that the first few eigenproperties of the global system can be obtained.

Dynamic Analysis of Geared Shaft Systems By Using a Continuous System Model

In this study dynamic mesh forces and dynamic factors in a geared shaft system are studied by using a continuous system model. The system consists of a gear pair, two shafts carrying gears, and two inertias representing drive and load in the system. A continuous system model is used to include the shaft inertias, which are usually disregarded even in most of the sophisticated models. The primary aim of this work is to provide a tool for studying the effect of shaft inertia in gear dynamics, and to present some case studies. The results of the continuous system model are compared with those of a discrete system model in which the shaft inertias are neglected, and with the results of previous studies. Typically, the dynamic factors obtained by using the discrete system model are found to be greater than those obtained from the continuous system model, especially when shaft masses are large. It is concluded that the computation of dynamic factors by using the continuous system model suggested in this study in order to include the effects of shaft masses is a very good alternative to finite element models which are much more expensive to use.

Derivatives of Eigenvalues for Torsional Vibration of Geared Shaft Systems

Design sensitivity analysis of natural frequency for geared shaft systems is of practical importance in the optimal design of these systems. This note provides a simple and easily implemented method to calculate the eigenvalue derivatives of a geared shaft system with respect to a design parameter ν, including gear inertia J, shaft stiffness K, and transmission ratio Q, when the eigensolution is known. An example is given to illustrate the method.

Modal simulation of gear box vibration with experimental correlation

A newly developed global dynamic model was used to simulate the dynamics of a gear noise rig at NASA Lewis Research Center. Experimental results from the test rig were used to verify the analytical model. In this global dynamic model, the number of degrees of freedom of the system are reduced by transforming the system equations of motion into modal coordinates. The vibration of the individual gear-shaft system are coupled through the gear mesh forces. A three-dimensional, axial-lateral coupled, bearing model was used to couple the casing structural vibration to the gear-rotor dynamics. The coupled system of modal equations is solved to predict the resulting vibration at several locations on the test rig. Experimental vibration data was compared to the predicitions of the global dynamic model. There is excellent agreement between the vibration results from analysis and experiment.

On the Dynamic Response of a Helical Geared System Subjected to a Static Transmission Error in the Form of Deterministic and Filtered White Noise Inputs

The vibration of a helical geared shaft system is studied, considering the coupling between the torsional, flexural, rotational (about the diametral axis), and axial motions of the gear carrying shafts. The effects of the nonlinear backlash function and time varying tooth stiffness are also considered. The excitation to the geared shaft system is in the form of a static transmission error which has deterministic and filtered white noise components. The equations of motion are formulated in state space form and solved using matrix exponential approach. Piecewise linearization is used in the simulation and results for the mean and variance of the dynamic response are presented.

A Note on the Calculation of Torsional Natural Frequencies of Branch Systems

An adoption of matrix techniques is proposed as a method for the solution of torsional natural frequencies in a branch or geared shaft system. Both fundamental and higher mode shapes and frequencies are produced by a comparatively rapid and straightforward technique. The method is illustrated by a numerical example of a coupled turbine and reciprocating engine system driving a common propeller.

Critical Speeds of Torsional Oscillation of Geared-Shaft Systems Due to the Presence of Displacement Excitation

The system investigated in this paper incorporates a gear-pair which has a velocity ratio which is nominally n: 1 but which in fact varies periodically with rotation, performing p cycles of its variation per revolution of the input shaft. In this analysis, n and p are arbitrary and so the results presented here are effectively a generalization of those previously obtained for a Hooke’s joint system for which n = 1 and p = 2.

A Note on the Calculation of Torsional Natural Frequencies of Branch Systems

An Adoption of matrix techniques is proposed as a method for the solution of torsional natural frequencies in a branch or geared shaft system. Both fundamental and higher mode shapes and frequencies are produced by a comparatively rapid and straightforward technique. The method is illustrated by a numerical example of a coupled turbine and reciprocating engine system driving a common propeller.