An Improved Nonlinear Dynamic Model of Gear Transmission

2007 ◽  
Author(s):  
Jinyuan Tang ◽  
Siyu Chen ◽  
Changjiang Zhou
Keyword(s):  
Frequency Response ◽  
Dynamic Model ◽  
Friction Force ◽  
Nonlinear Dynamic ◽  
Nonlinear Models ◽  
Harmonic Balance Method ◽  
Gear Transmission ◽  
Force Model ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh

This paper develops a new nonlinear dynamic model of gear transmission on the basis of combining friction, gear mesh stiffness and backlash. In calculating friction force, the dynamic distribution of the load along the actual line of action is taken into consideration. A new period-enlargement method is proposed to set up a friction force model and a gear meshing stiffness model. The non-linear dynamic model is a non-autonomous system. Compared with the former models, the damping coefficient and stiff coefficient in this model developed by the period enlargement method is a periodic function with the same period. Thus it is easier to apply EM (energy method) or other methods for finding the approximate analytical solution of the gear transmission dynamic equations combining with time-varying damping and stiffness. Frequency response function of the nonlinear dynamic model is obtained by using harmonic balance method. Compared the analytic and numerical results of the improved nonlinear model with that of the nonlinear models in the published papers, it is shown that: (a) the former numerical simulation techniques may not work or may result in misleading answers; (b) the coexistence of several different periodic solutions and various impacts are the same with the results in formerly published papers when gear parameters are the same. Finally, the accurate solutions of all three regimes are combined to obtain the overall frequency response of the gear pair.

scholarly journals Rattle dynamics of noncircular face gear under multifrequency parametric excitation

2021 ◽  
Vol 12 (1) ◽  
pp. 361-373
Author(s):  
Dawei Liu ◽  
Zhenzhen Lv ◽  
Guohao Zhao
Keyword(s):  
Dynamic Model ◽  
Parametric Excitation ◽  
Nonlinear Dynamic ◽  
Velocity Ratio ◽  
Harmonic Balance Method ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Discrete Fourier Transformation ◽  
Nonlinear Dynamic Model ◽  
Face Gear

Abstract. A noncircular face gear (NFG) conjugated with a pinion is a new type of face gear which can transmit variable velocity ratio and in which two time-varying excitations exist, namely the meshing stiffness excitation and instantaneous center excitation. Considering the tooth backlash, static transmission error and multifrequency parametric excitation, a nonlinear dynamic model of the NFG pair is presented. Based on the harmonic balance method and discrete Fourier transformation, a semi-analytic approach for the nonlinear dynamic model is given to analyze the dynamic behaviors of the NFG. Results demonstrate that, with increase in the eccentric ratio, input velocity and error amplitude, the NFG will undergo a non-rattle, unilateral rattle and bilateral rattle state in succession, and a jump phenomenon will appear in the dynamic responses when the rattle state of the gears is transformed from unilateral rattle to bilateral rattle.

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

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Zhibo Geng ◽  
Ke Xiao ◽  
Junyang Li ◽  
Jiaxu Wang
Keyword(s):  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Operating Time ◽  
Spur Gear ◽  
Gear Transmission ◽  
Nonlinear Dynamic Model ◽  
Gear Backlash ◽  
Gear Transmission System ◽  
Nonlinear Dynamic Characteristics

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.

Analysis of Postbucking Drillstring Vibrations in Rotary Drilling of Extended-Reach Wells

2009 ◽  
Author(s):  
Vadim S. Tikhonov ◽  
Alexander I. Safronov
Keyword(s):  
Angular Velocity ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Friction Force ◽  
Normal Component ◽  
Method Of Lines ◽  
Force Model ◽  
Nonlinear Dynamic Model ◽  
Rotary Drilling ◽  
Lift Off

One of the most serious concerns of extended-reach drilling is the dynamic behavior of the drillstring and cleaning of well. Good cleaning requires an increased angular speed. However, at higher rotary speeds, the drill string sections lying on the borehole horizontal sections tend to buckle, first, in the form of “snake”, sliding up and down the borehole bottom wall, and then in the form of whirling as the angular velocity increases. This paper presents the 3D nonlinear dynamic model of drillstring in a wellbore of 3D profile. The model suggests the possible contact/lift-off of drill pipes with/from the wellbore wall. The interaction of lateral, torsion and axial vibrations is taken into account. The relation between the normal component of contact force and the deformation of the wellbore wall is taken as quadratic-elastic. The friction force is described based on a hysteretic dynamic model. The friction force model also takes into account the transition from a sliding to a whirling. The equations of the drillstring dynamics are solved numerically using the method of lines. The DYNTUB computer program is developed to analyze the drillstring time-varying processes under different loading. The program is used to study the effects of the angular velocity, compression load, torque, friction factor, well profile, and availability of connectors on the drillstring dynamic behavior.

Analysis of Postbuckling Drillstring Vibrations in Rotary Drilling of Extended-Reach Wells

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Vadim S. Tikhonov ◽  
Alexander I. Safronov
Keyword(s):  
Angular Velocity ◽  
Friction Factor ◽  
Dynamic Model ◽  
Dynamic Behavior ◽  
Friction Force ◽  
Contact Force ◽  
Normal Component ◽  
Method Of Lines ◽  
Force Model ◽  
Nonlinear Dynamic Model

One of the most serious concerns of extended-reach drilling is the dynamic behavior of the drillstring and the cleaning of well. Good cleaning requires an increased angular velocity. This paper presents a 3D nonlinear dynamic model of drillstring in a wellbore of 3D profile. The model suggests possible contact/lift-off of drill pipes with/from the wellbore wall. The interaction of lateral, torsional, and axial vibrations is taken into account. The relation between the normal component of contact force and the deformation of the wellbore wall is taken as quadratic-elastic. The friction force is described based on a hysteretic dynamic model. The friction force model also takes into account, the transition from a sliding to whirling. The equations of drillstring dynamics are solved numerically using the method of lines. The DYNTUB software is developed to analyze the drillstring time-varying processes under different loads. The program is used to study the effects of angular velocity, compression load, torque, friction factor, well profile, and availability of connectors on the drillstring dynamic behavior. From the study follows the key conclusions: (1) The friction factor has a considerable effect on the drillstring rotational behavior in the wellbore; (2) no whirling of drillstring at real value of rolling friction factor in a horizontal well in the discussed examples could be seen at all; (3) when whirling takes place, the contact force shows a dramatic times increase; and (4) snaking can be seen in any wells at moderate compressive load and angular velocity.

Nonlinear Dynamic Modeling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

2003 ◽  
Vol 126 (3) ◽  
pp. 534-541 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dogˇruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Degree Of Freedom ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Gear Mesh

This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine multi harmonic responses of nonlinear multi-degree-of-freedom systems is employed for the solution. The excitations considered in the model are external static torque and internal excitation caused by mesh stiffness variation, gear errors and gear tooth profile modifications. The model suggested and the solution method presented combine the versatility of modeling a shaft-bearing-disk system that can have any configuration without a limitation to the total degree of freedom, with the accuracy of a nonlinear gear mesh interface model that allows to predict jumps and double solutions in frequency response. Thus any single stage gear mesh configuration can be modeled easily and accurately. With the model developed it is possible to calculate dynamic gear loads, dynamic bearing forces, dynamic transmission error and bearing displacements. Theoretical results obtained by using the method suggested are compared with the experimental data available in literature, as well as with the theoretical values calculated by employing a previously developed nonlinear single degree of freedom model.

Nonlinear Dynamic Modelling of Gear-Shaft-Disk-Bearing Systems Using Finite Elements and Describing Functions

2003 ◽  
Author(s):  
Rafiq Maliha ◽  
Can U. Dog˘ruer ◽  
H. Nevzat O¨zgu¨ven
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Dynamic Modelling ◽  
Spur Gear ◽  
Discrete Models ◽  
Nonlinear Dynamic Model ◽  
Disk System ◽  
Describing Functions ◽  
Gear Mesh ◽  
System A

This study presents a new nonlinear dynamic model for a gear-shaft-disk-bearing system. A nonlinear dynamic model of a spur gear pair is coupled with linear finite element models of shafts carrying them, and with discrete models of bearings and disks. The nonlinear elasticity term resulting from backlash is expressed by a describing function, and a method developed in previous studies to determine the harmonic responses of nonlinear multi degree of freedom systems is employed for the solution. The code developed, Nonlinear Geared Rotor Dynamics (NLGRD), combines the versatility of modeling a shaft-bearing-disk system that can have any configuration, with the accuracy of an advanced nonlinear gear mesh interface model. Thus any single stage gear mesh configuration can be modeled easily and accurately. NLGRD is capable of calculating dynamic gear loads, dynamic bearing forces, bearing displacements and making modal analysis of the corresponding linear system. Theoretical results obtained by NLGRD are compared with the experimental data available in literature.

Simulation on Vibration Friction Mechanism of Vibration Pile System

2013 ◽  
Vol 365-366 ◽  
pp. 416-419
Author(s):  
Yun Nan Teng ◽  
Jia Li ◽  
Li Yang Xie ◽  
Bang Chun Wen
Keyword(s):  
Numerical Simulation ◽  
Dynamic Model ◽  
Friction Force ◽  
Nonlinear Dynamic ◽  
Excitation Amplitude ◽  
Nonlinear Dynamic Model ◽  
Friction Mechanism ◽  
Soil System ◽  
Friction Pile

Vibratory pile drivers are widely used in mechanical industry field. In this paper, the nonlinear dynamic model of vibration friction pile-soil system considering the soil friction force is proposed. By numerical simulation, the dynamics characteristics of vibration friction for pile-soil system were obtained. The results showed that with the increasing of excitation amplitude and frequency, the displacement of the pile and frame are both increased.

Analysis of Tourism Ecology Capacity Based on the Nonlinear Dynamic Model

2009 ◽  
Vol 11 (2) ◽  
pp. 163-168
Author(s):  
Long LV ◽  
Zhenfang HUANG ◽  
Jiang WU
Keyword(s):  
Dynamic Model ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Model
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