scholarly journals Effect of the variable gear mesh model in dynamic simulation of a drive train in the wind turbine

2021 ◽  
Vol 41 (2) ◽  
Author(s):  
Yonghui Park ◽  
Wei Shi ◽  
Hyunchul Park
Keyword(s):  
Fourier Series ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Drive Train ◽  
Contact Forces ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Mesh Model ◽  
Constrained Equation ◽  
The Fourier Transform

To acquire transient response of a drive train, we consider more detailed mathematical model including variable gear mesh. The gear mesh is represented by the Fourier series. In transient analysis, gear’s angular velocity is considered as constant. It makes sense when we consider steady-state. However, the gear mesh is the only part which vary according to angular displacement. It should be considered not only by the Fourier series model but also as a modified system displacement. To establish the gear mesh model, we use a curve fitting theorem. Equations of motion are derived by the Lagrange’s equation, constrained equation and gear relation. The equations are solved by numerical integration method, the Newmark method. Through these processes, we get dynamic results including angular displacement, velocity, acceleration, gear mesh contact forces. Also, the Fourier transform is used to see signals more detailed. At last, we compared the variable gear mesh and constant gear mesh, gave physical meaning, and analyzed cause of the phenomenon.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

Dynamic Analysis of a Nonlinear Torsional Flexible Coupling With Elastic Links

2003 ◽  
Vol 125 (3) ◽  
pp. 509-517 ◽  
Author(s):  
Charles W. Bert ◽  
Shiyuan Wu
Keyword(s):  
Dynamic Analysis ◽  
System Performance ◽  
Power Transmission ◽  
Angular Displacement ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Flexible Coupling ◽  
Elastic Links ◽  
Lagrange’S Equation ◽  
Power Transmission Systems

Torsional oscillations in mechanical power transmission systems are a significant source of dynamic loads which are harmful to the system performance. The effects can cause a drive shaft to become unstable and self-destructive at critical speeds. This research focuses on dynamic analysis of a nonlinear torsional flexible coupling with elastic links. The equations of motion are derived by means of Lagrange’s equation. These equations are used to obtain the quasi-static performance of torque vs. angular displacement at constant rotational velocity. An exact solution is also found for the phase-plane representation for free oscillation torque. The fluctuation ratios of input velocity vs. output velocity of the system are obtained for determining the system performance. The results of the analyses of steady running and transient oscillation performance are applied to the determination of optimum proportions of the couplings. Results are compared with those of rigid-link couplings to show the influence of elasticity of the link on dynamic behavior of the system.

scholarly journals A new pendulum motion with a suspended point near infinity

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
A. I. Ismail
Keyword(s):  
Degrees Of Freedom ◽  
Angular Displacement ◽  
Equations Of Motion ◽  
Circular Path ◽  
Large Parameter ◽  
Pendulum Motion ◽  
Third Order ◽  
The Third ◽  
Lagrange’S Equation ◽  
Pendulum Model

AbstractIn this paper, a pendulum model is represented by a mechanical system that consists of a simple pendulum suspended on a spring, which is permitted oscillations in a plane. The point of suspension moves in a circular path of the radius (a) which is sufficiently large. There are two degrees of freedom for describing the motion named; the angular displacement of the pendulum and the extension of the spring. The equations of motion in terms of the generalized coordinates $$\varphi$$ φ and $$\xi$$ ξ are obtained using Lagrange’s equation. The approximated solutions of these equations are achieved up to the third order of approximation in terms of a large parameter $$\varepsilon$$ ε will be defined instead of a small one in previous studies. The influences of parameters of the system on the motion are obtained using a computerized program. The computerized studies obtained show the accuracy of the used methods through graphical representations.

Dynamic Model Development of Wind Turbine Drivetrains by Using Sensor Measurements

2021 ◽  
Author(s):  
Diederik van Binsbergen ◽  
Amir R. Nejad ◽  
Jan Helsen
Keyword(s):  
Wind Turbine ◽  
Angular Displacement ◽  
Model Development ◽  
Rotational Frequency ◽  
Sensor Data ◽  
Gear Mesh ◽  
Modal Properties ◽  
Vibration Sensors ◽  
Displacement Sensors ◽  
Simulation Based

Abstract This paper aims to analyze the feasibility of establishing a dynamic drivetrain model from condition monitoring measurements. In this study SCADA data and further sensor data is analyzed from a 1.5MW wind turbine, provided by the National Renewable Energy Laboratory. A multibody model of the drivetrain is made and simulation based sensors are placed on bearings to look at the possibility to obtain geometrical and modal properties from simulation based vibration sensors. Results show that the axial proxy sensor did not provide any usable system information due to its application purpose. SCADA data did not meet the Nyquist frequency and cannot be used to determine geometrical or modal properties. Strain gauges on the shaft can provide the shaft rotational frequency, while torque and angular displacement sensors can provide the torsional eigenfrequency of the system. Simulation based vibration sensors are able to capture gear mesh frequencies, harmonics, sideband frequencies and shaft rotational frequencies.

The Influence of Tank Orientation Angle on a 2D Structure-Tuned Liquid Damper System

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
J. S. Love ◽  
M. J. Tait
Keyword(s):  
Mechanical Model ◽  
Vibrational Energy ◽  
Equations Of Motion ◽  
Orientation Angle ◽  
Structural Response ◽  
Tuned Liquid Damper ◽  
Lagrange’S Equation ◽  
Equivalent Mechanical Model ◽  
Principal Axes ◽  
2D Structure

Tuned liquid dampers (TLDs) utilize sloshing fluid to absorb and dissipate structural vibrational energy, thereby reducing wind induced dynamic motion. By selecting the appropriate tank length, width, and fluid depth, a rectangular TLD can control two structural sway modes simultaneously if the TLD tank is aligned with the principal axes of the structure. This study considers the influence of the TLD tank orientation on the behavior of a 2D structure-TLD system. The sloshing fluid is represented using a linearized equivalent mechanical model. The mechanical model is coupled to a 2D structure at an angle with respect to the principal axes of the structure. Equations of motion for the system are developed using Lagrange’s equation. If the TLD and structure are not aligned, the system responds as a coupled four degree of freedom system. The proposed model is validated by conducting structure-TLD system tests. The predicted and experimental structural displacements and fluid response are in agreement. An approximate method is developed to provide an initial estimate of the structural response based on an effective mass ratio. The results of this study show that for small TLD orientation angles, the performance of the TLD is insensitive to TLD orientation.

Fourier Series and the Fourier Transform

2013 ◽  
pp. 535-638
Author(s):  
Boris Makarov ◽  
Anatolii Podkorytov
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
The Fourier Transform

Dynamic Analysis of Ball Bearings Due to Clearance Effect

2009 ◽  
Author(s):  
S. H. Upadhyay ◽  
S. C. Jain ◽  
S. P. Harsha
Keyword(s):  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Peak Frequency ◽  
System Response ◽  
Ball Bearings ◽  
Outer Race ◽  
Lagrange’S Equation ◽  
Rolling Elements ◽  
Machine Systems ◽  
The Individual

In this paper, the nonlinear dynamic behavior of ball bearings due to radial internal clearance and rotor speed has been analyzed. The approach presented in this paper accounts for the contact between rolling elements and inner/outer races. The equations of motion of a ball bearing are formulated in generalized coordinates, using Lagrange’s equation considering the vibration characteristics of the individual constitute such as inner race, outer race, rolling elements. The effects of speed of rotor in which rolling element bearings shows periodic, quasi-periodic and chaotic behavior are analyzed. The results also show the intermittent chaotic behavior in the dynamic response is seen to be strongly dependent on the speed of the rotor. The results are obtained in the form of frequency responses. The validity of the proposed model verified by comparison of frequency components of the system response with those obtained from experiments. The peak-to-peak frequency response of the system for each speed is obtained. The current study provides a powerful tool design and health monitoring of machine systems.

Railway Truck Response to Random Rail Irregularities

1975 ◽  
Vol 97 (3) ◽  
pp. 957-964 ◽  
Author(s):  
Neil K. Cooperrider
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Tangential Force ◽  
Contact Forces ◽  
Guidance Force ◽  
Power Spectral ◽  
Power Spectral Densities ◽  
Rail Irregularities ◽  
Frequency Domain Techniques

This paper discusses the random response of a seven degree of freedom, passenger truck model to lateral rail irregularities. Power spectral densities and root mean square levels of component displacements and contact forces are reported. The truck model used in the study allows lateral and yaw degrees of freedom for each wheelset, and lateral, yaw and roll freedoms for the truck frame. Linear creep relations are utilized for the rail-wheel contact forces. The lateral rail irregularities enter the analysis through the creep expressions. The results described in the paper were obtained using frequency domain techniques to solve the equations of motion. The reported results demonstrate that the guidance force needed when traveling over irregular rail at high speed utilizes a significant portion of the total available tangential force between wheel and rail.

Evaluation of Mechanical and Thermal Stresses in Polymer Gear Teeth through Simulation Approach

2013 ◽  
Vol 302 ◽  
pp. 468-473 ◽  
Author(s):  
Per Lindholm ◽  
Jian Qin
Keyword(s):  
Thermal Properties ◽  
Thermal Stresses ◽  
Material Selection ◽  
Gear Tooth ◽  
Gear Wheel ◽  
Spur Gear ◽  
Contact Forces ◽  
Mechanical And Thermal Properties ◽  
Gear Mesh ◽  
Tensional Stress

One way to achieve lightweight and lubricant-free drive train is, among others, to convert conventional steel to polymer composite materials. This paper describes a part of this endeavor by taking a spur gear pair as a study object. One of the steel gear wheel is replaced with three different materials including Victrex PEEK 650G, Victrex PEEK 650CA30 and Luvocom PEEK 1105-8165 while keeping the gear geometry unchanged. Mechanical stresses and thermal properties are two major criteria for material selection at this stage. Therefore carbon fiber filled PEEK (Victrex PEEK 650CA30) and PEEK filled with thermal conductive minerals (Luvocom 1105-8165) are chosen to benchmark each of the criterion. The evaluation is done by modeling the gear mesh and analyzing the contact forces and heat generated in the gear tooth. The results show surface temperature on the tooth flanks, root tensional stress and contact pressure during the tooth mesh. The work suggests a guideline of materials selection. Depending on actual application a compromisation between mechanical and thermal properties often needs to be considered within the tolerance boundary in order to obtain optimized results. This work only deals with material selection. Gear design such as optimization of tooth geometry for polymer gears is out of the scope of this study and will not be discussed.

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