scholarly journals The Influences of Gradual Wears and Bearing Clearance of Gear Transmission on Dynamic Responses

Energies ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4731
Author(s):  
Ruiliang Zhang ◽  
Kaida Wang ◽  
Yandong Shi ◽  
Xiuquan Sun ◽  
Fengshou Gu ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Coupled Model ◽  
Nonlinear Dynamic System ◽  
Gear System ◽  
Dynamic Responses ◽  
Tooth Surface ◽  
Wear Depth ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Bearing Clearance

Gears are important components of the transmission system. Tooth wear and bearing clearance are significant factors affecting the dynamics of the gear system. In order to reveal the effects of gradual wears and bearing clearance on the gear system dynamics, a six-degrees-of-freedom bending-torsion coupled model of gear-rotor-bearing which considers surface wear, bearing clearance and backlash is established. The Rung-Kutta method is used to solve the nonlinear dynamic system, and the dynamic responses of the system are obtained. The results show that the time-varying mesh stiffness decreases with the tooth surface from the unworn phase to severe wear phase. At the same time, the change of the mesh stiffness in the double-tooth mesh area and single-tooth area are different. Moreover, the amplitude of the X-displacement, Y-displacement and relative gear mesh displacement will be enlarged slightly with the increase of wear depth or bearing clearance. By analyzing variation tendency in the frequency domain, the different order harmonics show the different change characteristic with the variation of the wear phases or bearing clearances. This study provides a theoretical basis for improving the transmission performance and the selection of the bearing clearances in the gear system.

Dynamic Features of Gear System With Tooth Crack and Tooth Surface Sliding due to Speed Variation

2012 ◽  
Author(s):  
Liming Wang ◽  
Zaigang Chen ◽  
Yimin Shao ◽  
Xi Wang
Keyword(s):  
Degrees Of Freedom ◽  
Surface Friction ◽  
Element Model ◽  
Spur Gear ◽  
Gear System ◽  
Tooth Surface ◽  
Dynamic Features ◽  
Mesh Stiffness ◽  
Speed Variation ◽  
Gear Mesh

It was found that the vibration features resulted from tooth crack and sliding on the contact interfaces due to speed variation are very similar with each other, which is difficult to distinguish. So, it is meaningful to study whether they are the same or not. Firstly, a finite element model of a spur gear pair in mesh with tooth crack at pitch circle is established to calculate the effect of tooth crack on gear mesh stiffness. Then, combined with the tooth crack through mesh stiffness, a spur gear dynamic model with six degrees of freedom (dof) is developed to extract the dynamic features affected by the tooth crack. The tooth surface friction due to different relative velocity is also involved to study its effects on the dynamic characteristics of the gear system. Finally, comparisons are made between the dynamic features of the gear system with tooth crack and the tooth surface sliding to expose their effects to supply some theoretical guidance on fault detection.

Integrated Excitation Models of the Helical Gear System

2007 ◽  
Author(s):  
Takayuki Nishino
Keyword(s):  
Gear Tooth ◽  
Moving Load ◽  
Helical Gear ◽  
Gear System ◽  
Tooth Surface ◽  
Response Analysis ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Face Width ◽  
Single Tooth

The vibration of the helical gear system is generated by three kinds of excitation. The first cause is a displacement excitation due to the tooth surface error. The second is a parametric excitation by the periodical change of the tooth mesh stiffness. The third is a moving load on the tooth surface during the progress of mesh of the teeth. In mesh of a pair of helical gears, the composite load of the distributed load along a contact line moves its operating location from one end of face width to the other end during the process of mesh progress. This moving load causes fluctuation of bearing load that excites the housing. Therefore, it is important to treat gear mesh excitation as a moving load problem. For this purpose, two kinds of mesh models, in which the three different types of excitations above are incorporated, are proposed. In the first model, a pair of gear tooth is represented by the multiple springs and the moving load can be taken into account by the multiple mesh excitation forces that have the phase differences from each other. The second one incorporates the excitation moment into the single tooth spring model. Then, response analysis is done for a simple gear-shaft model. As the result, the moving load causes vibration with non-coupled or independent modes between the drive and driven shaft. Thus, the effectiveness of the proposed method is established.

An Energy-Based Load Distribution Approach for the Application of Gear Mesh Stiffness on Elastic Bodies

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Faysal Andary ◽  
Joerg Berroth ◽  
Georg Jacobs
Keyword(s):  
Degrees Of Freedom ◽  
Design Method ◽  
Mesh Stiffness ◽  
Gear Teeth ◽  
Gear Mesh ◽  
Elastic Bodies ◽  
Single Tooth ◽  
Traditional Approaches ◽  
Energy Based Design ◽  
Gear Mesh Stiffness

This study introduces a new potential energy-based design method for simplifying elastic gear bodies in low- to mid-range frequency applications by bridging over the gear teeth with external stiffness elements. The advantage of the introduced method over more traditional approaches, which are either based on rigid gears or on replacing the teeth, is that the complex gear body and its dynamic behavior are preserved, albeit with fewer degrees of freedom. The method is demonstrated on a gear by replacing a single tooth under load and then validated numerically against a typical flexible gear model. The simulation results show good accuracy within the chosen frequency range and with a clear reduction in calculation time compared to the unreduced model. Furthermore, the extension and optimization potential of the results is discussed.

Torsional Vibrations and Dynamic Loads in a Basic Planetary Gear System

1986 ◽  
Vol 108 (3) ◽  
pp. 348-353 ◽  
Author(s):  
R. August ◽  
R. Kasuba
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Planetary Gear ◽  
Gear System ◽  
Dynamic Loads ◽  
Ring Gear ◽  
Gear Mesh ◽  
Input And Output ◽  
Planetary Gear System ◽  
Three Degrees Of Freedom

An interative method has been developed for analyzing dynamic loads in a light weight basic planetary gear system. The effects of fixed, semi-floating, and fully-floating sun gear conditions have been emphasized. The load dependent variable gear mesh stiffnesses were incorporated into a practical torsional dynamic model of a planetary gear system. The dynamic model consists of input and output units, shafts, and a planetary train. In this model, the sun gear has three degrees of freedom; two transverse and one rotational. The planets, ring gear, and the input and output units have one degree of freedom, (rotation) thus giving a total of nine degrees of freedoms for the basic system. The ring gear has a continuous radial support. The results indicate that the fixed sun gear arrangement with accurate or errorless gearing offers in general better performance than the floating sun gear system.

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 Response Analysis of Wind Turbine Planetary Gear System With Interval Stiffness Parameters

2014 ◽  
Author(s):  
Sha Wei ◽  
Qinkai Han ◽  
Zhipeng Feng ◽  
Yanhua Shen ◽  
Fulei Chu
Keyword(s):  
Wind Turbine ◽  
Planetary Gear ◽  
Transmission Error ◽  
Gear System ◽  
Dynamic Responses ◽  
Lumped Parameter Model ◽  
Response Analysis ◽  
Mesh Stiffness ◽  
Gear Trains ◽  
Planetary Gear System

Planetary gear transmission system is one of the primary parts of the wind turbine drive train. Due to the assembly state, lubrication conditions and wear, the mesh stiffness of the planetary gear system is an uncertain parameter. In this paper, taking the uncertainty of mesh stiffness into account, the dynamic responses of a wind turbine gear system subjected to wind loads and transmission error excitations are studied. Firstly, a lumped-parameter model is extended to include both the planetary and parallel gears. Then the fluctuation ranges of dynamic mesh forces are predicted quantitatively and intuitively based on the combined Chebyshev interval inclusion function and numerical integration method. Finally, examples of gear trains with different interval mesh stiffnesses are simulated and the results show that tooth separations are becoming more obvious at the resonant speed by considering the fluctuating mesh stiffness of the second parallel gear stage. The nonlinear tooth separations are degenerated obviously as the fluctuation error of the mesh stiffness of the second parallel gear set is increased.

Dynamic Analysis of a Geared Rotor-Bearing System with Time-Varying Gear Mesh Stiffness and Pressure Angle

2013 ◽  
Vol 284-287 ◽  
pp. 461-467
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Responses ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Pressure Angle ◽  
Proposed Model ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The dynamic analysis of a geared rotor-bearing system with time-varying gear mesh stiffness and pressure angle is presented in this paper. Although there are analyses for both of the gear and rotor-bearing system dynamics, the coupling effect of the time-varying mesh and geared rotor-bearing system is deficient. Therefore, the pressure angle and contact ratio of the geared rotor-bearing system are treated as time-varying variables in the proposed model while they were considered as constant in previous models. The gear mesh stiffness is varied with different contact ratios of the gear pair in the meshing process. The nonlinear equations of motion for the geared rotor-bearing system are obtained by applying Lagrange’s equation and the dynamic responses are computed by using the Runge-Kutta numerical method. Numerical results of this study indicated that the proposed model provides realistic dynamic response of a geared rotor-bearing system.

scholarly journals Computation Method of Gear Dynamic Response Using Experimental Strain Data and Application in Pitting Fault Analysis

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Yongzhi Qu ◽  
Haoliang Zhang ◽  
Zechao Wang ◽  
Zude Zhou
Keyword(s):  
Dynamic Response ◽  
Gear System ◽  
Dynamic Strain ◽  
Time Varying ◽  
Tooth Root ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Strain Data ◽  
Experimental Strain ◽  
Fbg Sensors

In this paper, A semi-physical method for calculating time varying mesh stiffness and the dynamic response of gear system based on experimental strain data is studied. In a previous work, it was reported that dynamic strain on gear tooth root can be measured under normal operating condition using fiber Bragg Grating (FBG) sensors. This paper aims to compute gear dynamic response using experimental strain data and give an explanation of the fault propagation process. Using the dynamic strain data from FBG sensors, a method for calculating the dynamic response of gear system is proposed. Based on the theory of potential energy and material mechanics, the relationship between the bending strain of the tooth root and the time varying mesh stiffness is established. The time varying mesh stiffness and dynamic response of healthy gear and pitted gear are then calculated respectively. The force transmission during gear mesh under the condition of surface pitting is analyzed. It is concluded that in the case of pitting fault, there will be a significant loss of torque in the power transmission process due to the loss of contact area. It is further inferred that the loss of meshing force andthedecreasing of Hertzian contact stiffness are the major contributing factors for pitting fault. In addition, the semi-analytical method of computing gear dynamic response is validated with experimental study ofacceleration signal in the perspective of dynamic response.  

scholarly journals Experimental and Theoretical Study of Gear Dynamical Transmission Characteristic Considering Measured Manufacturing Errors

2018 ◽  
Vol 2018 ◽  
pp. 1-20 ◽  
Author(s):  
Fang Guo ◽  
Zongde Fang
Keyword(s):  
Transmission Error ◽  
Helical Gear ◽  
Tooth Surface ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Tooth Contact Analysis ◽  
Gear Mesh ◽  
Manufacturing Errors ◽  
Tooth Modification ◽  
Helical Gear Pair

In the research of gear transmission, the vibration and noise problem has received many concerns all the times. Scholars use tooth modification technique to improve the meshing state of gearings in order to reduce the vibration and noise. However, few of researchers consider the influence of measured manufacturing errors when they do the study of tooth modification. In order to investigate the efficiency of the tooth modification in the actual project, this paper proposes a dynamic model of a helical gear pair including tooth modification and measured manufacturing errors to do a deterministic analysis on the dynamical transmission performance. In this analysis, based on the measured tooth deviation, a real tooth surface (including modification and measured tooth profile error) is fitted by a bicubic B-spline. With the tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) on the real tooth surface, the loaded transmission error, tooth surface elastic deformation, and load distribution can be determined. Based on the results, the time-varying mesh stiffness and gear mesh impact are computed. Taking the loaded transmission error, measured cumulative pitch error, eccentricity error, time-varying mesh stiffness, and gear mesh impact as the internal excitations, this paper establishes a 12-degree-of-freedom (DOF) dynamic model of a helical gear pair and uses the Fourier series method to solve it. In two situations of low speed and high speed, the gear system dynamic response is analyzed in the time and frequency domains. In addition, an experiment is performed to validate the simulation results. The study shows that the proposed technique is useful and reliable for predicting the dynamic response of a gear system.

Nonlinear dynamic study and vibration reduction of a power turret gear train with modified design parameters

2014 ◽  
Vol 229 (10) ◽  
pp. 1745-1759 ◽  
Author(s):  
Lijiao Xu ◽  
Nan Chen
Keyword(s):  
Nonlinear Dynamic ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Vibration Reduction ◽  
Numerical Control ◽  
Gear Train ◽  
Design Parameters ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Gear Mesh

This work presents the nonlinear dynamic characteristics and vibration reduction of a numerical control power turret three-stage gear transmission system composed of four spur gears. Considering translational and rotational motions, the nonlinear lumped-parameter and multi-degrees of freedom models of modified and unmodified transmission systems are introduced to study the dynamic behavior while the time-varying mesh stiffness and backlash of gear mesh pairs are involved as internal excitations. For the requirement of high speed and low vibration, high contact ratio by modifying design parameters is suggested in this study. By numerical method, the dynamic vibration responses are calculated. Results in the time and frequency domains show that the vibration amplitudes and mesh forces are efficiently decreased after modification. The influences of key parameters, such as mesh stiffness, damping, backlash, and torque on the dynamic response are also studied here. To demonstrate the effectiveness of the proposed model, the vibration tests are conducted by two physical prototypes of the power turret. The values of vibration acceleration at different tests points and speeds are obtained and analyzed. Experimental results validate that the vibration of turret is decreased by the design improvement of gear system.

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