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Author: Junyi Yang Publisher: ISBN: Category : Languages : en Pages : 176
Book Description
This dissertation research focuses on evaluating the nonlinear dynamics of driveline systems employed in motor vehicles with emphasis on characterizing the excitations and response of right-angle, precision hypoid-type geared rotor structure. The main work and contribution of this dissertation is divided into three sections. Firstly, the development of an asymmetric and nonlinear gear mesh coupling model will be discussed. Secondly, the enhancement of the multi-term harmonic balance method (HBM) is presented. Thirdly and as the final topic, the development of new dynamic models capable of evaluating the dynamic coupling characteristics between the gear mesh and other driveline structures will be addressed. A new asymmetric and nonlinear mesh model will be proposed that considers backlash, and the fact that the tooth surfaces of the convex and concave sides are different. The proposed mesh model will then be fed into a dynamic model of the right-angle gear pair to formulate the dimensionless equation of motion of the dynamic model. The multi-term HBM will be enhanced to simulate the right-angle gear dynamics by solving the resultant dimensionless equation of motion. The accuracy of the enhanced HBM solution will be verified by comparison of its results to the more computationally intensive direct numerical integration calculations. The stability of both the primary and sub-harmonic solutions predicted by applying multi-term HBM will be analyzed using the Floquent Theory. In addition, the stability analysis of the multi-term HBM solutions will be proposed as an approximate approach for locating the existence of sub-harmonic and chaotic motions. In this dissertation research, a new methodology to evaluate the dynamic interaction between the nonlinear hypoid gear mesh mechanism and the time-varying characteristics of the rolling element bearings will also be developed. The time-varying mesh parameters will be obtained by synthesizing a 3-dimensional loaded tooth contact analysis (TCA) results. The time-varying stiffness matrix approach will be used to represent the dynamic characteristics of the rolling element bearings. An overall nonlinear dynamic model of the hypoid gear box considering elastic housing structure will be developed as well. A lumped parameter model of the flexible housing will be extracted form an appropriate set of frequency response functions through modal parameter identification method. In order to obtain the rotational coordinates, a rigid body interpolation of the translational responses at the bearing locations on the housing structure will be applied. The reduced model will be then coupled with the hypoid gear-shaft-bearing assembly model by applying a proposed dynamic coupling procedure. Finally, a hypoid geared rotor system model considering the propeller shaft flexibility will be established. The propeller shaft bending flexibility will be modeled as lumped parameter model through using the component mode synthesis (CMS). The torsional flexibility of propeller shaft will be simplified as a torsional spring connecting the inertia of moment of engine and pinion. Physically, the pinion input shaft is driven by the propeller shaft through a universal joint, which will be modeled as a flexible simple supported boundary condition as well as fluctuating rotation speed and torque excitation.
Author: Junyi Yang Publisher: ISBN: Category : Languages : en Pages : 176
Book Description
This dissertation research focuses on evaluating the nonlinear dynamics of driveline systems employed in motor vehicles with emphasis on characterizing the excitations and response of right-angle, precision hypoid-type geared rotor structure. The main work and contribution of this dissertation is divided into three sections. Firstly, the development of an asymmetric and nonlinear gear mesh coupling model will be discussed. Secondly, the enhancement of the multi-term harmonic balance method (HBM) is presented. Thirdly and as the final topic, the development of new dynamic models capable of evaluating the dynamic coupling characteristics between the gear mesh and other driveline structures will be addressed. A new asymmetric and nonlinear mesh model will be proposed that considers backlash, and the fact that the tooth surfaces of the convex and concave sides are different. The proposed mesh model will then be fed into a dynamic model of the right-angle gear pair to formulate the dimensionless equation of motion of the dynamic model. The multi-term HBM will be enhanced to simulate the right-angle gear dynamics by solving the resultant dimensionless equation of motion. The accuracy of the enhanced HBM solution will be verified by comparison of its results to the more computationally intensive direct numerical integration calculations. The stability of both the primary and sub-harmonic solutions predicted by applying multi-term HBM will be analyzed using the Floquent Theory. In addition, the stability analysis of the multi-term HBM solutions will be proposed as an approximate approach for locating the existence of sub-harmonic and chaotic motions. In this dissertation research, a new methodology to evaluate the dynamic interaction between the nonlinear hypoid gear mesh mechanism and the time-varying characteristics of the rolling element bearings will also be developed. The time-varying mesh parameters will be obtained by synthesizing a 3-dimensional loaded tooth contact analysis (TCA) results. The time-varying stiffness matrix approach will be used to represent the dynamic characteristics of the rolling element bearings. An overall nonlinear dynamic model of the hypoid gear box considering elastic housing structure will be developed as well. A lumped parameter model of the flexible housing will be extracted form an appropriate set of frequency response functions through modal parameter identification method. In order to obtain the rotational coordinates, a rigid body interpolation of the translational responses at the bearing locations on the housing structure will be applied. The reduced model will be then coupled with the hypoid gear-shaft-bearing assembly model by applying a proposed dynamic coupling procedure. Finally, a hypoid geared rotor system model considering the propeller shaft flexibility will be established. The propeller shaft bending flexibility will be modeled as lumped parameter model through using the component mode synthesis (CMS). The torsional flexibility of propeller shaft will be simplified as a torsional spring connecting the inertia of moment of engine and pinion. Physically, the pinion input shaft is driven by the propeller shaft through a universal joint, which will be modeled as a flexible simple supported boundary condition as well as fluctuating rotation speed and torque excitation.
Author: Philippe Velex Publisher: Chandos Publishing ISBN: 1782421955 Category : Technology & Engineering Languages : en Pages : 1225
Book Description
This book presents papers from the International Gear Conference 2014, held in Lyon, 26th-28th August 2014. Mechanical transmission components such as gears, rolling element bearings, CVTs, belts and chains are present in every industrial sector and over recent years, increasing competitive pressure and environmental concerns have provided an impetus for cleaner, more efficient and quieter units. Moreover, the emergence of relatively new applications such as wind turbines, hybrid transmissions and jet engines has led to even more severe constraints. The main objective of this conference is to provide a forum for the most recent advances, addressing the challenges in modern mechanical transmissions. The conference proceedings address all aspects of gear and power transmission technology and range of applications (aerospace, automotive, wind turbine, and others) including topical issues such as power losses and efficiency, gear vibrations and noise, lubrication, contact failures, tribo-dynamics and nano transmissions. A truly international contribution with more than 120 papers from all over the world A judicious balance between fundamental research and industrial concerns Participation of the most respected international experts in the field of gearing A wide range of applications in terms of size, power, speed, and industrial sector
Author: Jun Wang Publisher: ISBN: Category : Languages : en Pages : 172
Book Description
Hypoid and bevel gear pairs are high-speed, precision right-angle power transmission devices that are widely used in automotive and aerospace applications. However, their dynamic response due to gear transmission error excitation tends to cause annoying gear whines. The unwanted high frequency whine noise is characteristically tonal and is the result of structural vibration at the gear mesh frequency. This vibratory response is believed to be strongly affected by the nonlinearity and time-variation inherent in the parameters of these types of non-parallel axis gears. To address this problem, the influence of nonlinear time-varying mesh must be understood more clearly. Hence, to address this issue, the goal of this dissertation is to formulate reliable gear dynamic models to analyze the underlying physics controlling the effects of nonlinear and time-varying mesh and dynamic characteristics on gear whine generation and transmissibility phenomena. In order to establish a basis for comparison to results of nonlinear time-varying formulation, a linear time-invariant (LTI) mesh model is formulated first by neglecting gear backlash nonlinearity. This simple form of mesh model is applied to a proposed fourteen degrees-of-freedom lumped parameter dynamic model. The linearized formulation is also employed to study the effects of assembly errors on gear mesh and dynamic responses as well as the effects of key design parameters on the critical out-of-phase gear pair torsion modes. From the parametric study, less sensitive design sets that attempt to achieve a balance between reducing dynamic mesh force and minimizing vibration transmissibility can be identified. To study the true effects of time-varying mesh parameters and backlash nonlinearity, a generalized nonlinear time-varying (NLTV) dynamic model of a bevel or hypoid gear pair is developed. In the proposed formulation, a new exact time-varying mesh model is proposed that can be easily incorporated into the dynamic models. This resulted in NLTV dynamic models of bevel or hypoid gear pair systems with time-dependent nonlinear mesh damping and backlash nonlinearity. The resultant theory is then applied to study the boundary between nonlinear jump phenomena and linear response. Also, the new NLTV dynamic model is further extended to study the effect of mesh stiffness asymmetry on dynamic response. Using this model, numerous single degree-of-freedom NLTV dynamic models with different nonlinearities are analyzed and their results are compared to better understand the primary controlling factors. The single degree-of-freedom NLTV dynamic model is finally extended to a fourteen degrees-of-freedom dynamic representation to investigate the influence of wider range of driveline parameters and system modes.
Author: Gang Liu Publisher: ISBN: Category : Gearing Languages : en Pages : 218
Book Description
Abstract: Multi-mesh gear systems are used in a variety of industrial machinery, where noise, quality, and reliability lie in gear vibration. The dynamic gear mesh forces are the source of vibration and result from parametric excitation and contact nonlinearity. The primary goal of this work is to develop mathematical models for multi-mesh gearsets with nonlinear, time-varying elements, to conduct numerical and analytical studies on nonlinear gear dynamic behaviors, such as parametric instabilities, frequency response, contact loss, and profile modification, and to provide guidelines for practical design and troubleshooting. First, a nonlinear analytical model considering dynamic load distribution between individual gear teeth is proposed, including the influence of variable mesh stiffnesses, profile modifications, and contact loss. This model yields better agreement than two existing models when compared against nonlinear gear dynamics from a finite element benchmark. Perturbation analysis finds approximate frequency response solutions for providing guidance for optimizing system parameters. The closed-form solution is validated by numerical integration. Second, the nonlinear, parametrically excited dynamics of idler and counter-shaft gear systems are examined. The periodic steady state solutions are obtained using analytical and numerical approaches. With proper stipulations, the contact loss function and the variable mesh stiffness are reformulated into a form suitable for perturbation. The closed-form solutions from perturbation analysis expose the impact of key parameters on the nonlinear response. The analysis for this strongly nonlinear system compares well to separate harmonic balance/continuation and numerical integration solutions. Finally, this work studies the influences of tooth friction on parametric instabilities and dynamic response of a single-mesh gear pair. A mechanism whereby tooth friction causes gear tooth bending is shown to significantly impact the dynamic response. A dynamic model is developed to consider this mechanism together with the other contributions of tooth friction and mesh stiffness fluctuation. Perturbation analysis finds approximate solutions that predict and explain the parametric instabilities. The effects of time-varying friction moments about the gear centers and friction-induced tooth bending are critical to parametric instabilities and dynamic response. The impacts of friction coefficient, bending effect, contact ratio, and modal damping on the stability boundaries are revealed.
Author: Yubing Wen Publisher: ISBN: Category : Languages : en Pages :
Book Description
The research investigates the random nonlinear vibration of a spur gear pair subjected to both deterministic and random loads by path integration method. Different models and approaches to apply the path integration method are presented in Chapters 2- 4. Backlash nonlinearity and time-varying mesh stiffness in gear systems are both considered in Chapters 2 and 3. In Chapter 2, the time-varying mesh stiffness is modeled as a constant plus a cosinusoidal component, and the discontinuous backlash nonlinearity is approximated with a cubic polynomial through curve fitting. Then Gaussian closure procedure is employed to obtain the mean and variance of transition probability density function (PDF). In Chapter 3, the time-varying mesh stiffness is approximated with a square wave function. The variance of the responses is calculated and expressed as closed forms for two different cases in gear systems. In Chapter 4, the gear rattling model which only considers backlash is presented. A degenerate Gaussian distribution is employed as transition PDF. The path integration results are compared with deterministic results (Chapters 2 and 3) and Monte Carlo simulation results (Chapters 3 and 4). Good agreement is found between them, which could verify the accuracy of path integration method in the study of random gear dynamics.
Author: Yawen Wang Publisher: ISBN: Category : Languages : en Pages : 64
Book Description
Hypoid and bevel gears are widely used in the rear axles of both on and off-highway vehicles, and are often subjected to harmful dynamic responses which cause gear whine noise and structural fatigue problems. The primary goal of this thesis is therefore to develop a more realistic mesh and dynamic model to predict the vibratory response of hypoid and bevel geared systems, and study the effect of different working conditions, e.g. operating speed, torque load, on the dynamic responses of those systems. First, a multi-point hypoid gear mesh model based on 3-dimensional loaded tooth contact analysis is incorporated into a coupled multi-body dynamic and vibration hypoid gear model to predict more detailed dynamic behavior of each tooth pair. To validate the accuracy of the proposed model, the time-averaged mesh parameters are applied to linear time-invariant (LTI) analysis to calculate the dynamic responses, such as dynamic mesh force and dynamic transmission error, which demonstrates good agreement with those predicted by using single-point mesh model. Furthermore, a nonlinear time-varying (NLTV) dynamic analysis is performed considering the effect of backlash nonlinearity and time-varying mesh parameters, such as time-varying mesh stiffness, transmission error, mesh point and line-of-action. One of the advantages of the multi-point mesh model is that it allows the calculation of dynamic responses for each engaging tooth pair, and simulation results for an example case are given to show the time history of the mesh parameters and dynamic mesh force for each pair of teeth within a full engagement cycle. This capability enables the analysis of durability of the gear tooth pair and more accurate prediction of the system response. Secondly, to have more insights on the load dependent mesh parameters and dynamic responses of the hypoid and spiral bevel geared systems, a load dependent mesh model is developed by using 3-dimensional loaded tooth contact analysis (LTCA). The contact ratio and time-varying mesh parameters including the mesh stiffness, transmission error, mesh point and line-of-action of the mesh force are examined within a wide torque range. Then a nonlinear multi-body dynamic analysis is performed considering the effect of backlash nonlinearity. Simulation results show that the contact ratio and mesh stiffness generally increases as the toque load increases. The effect of torque load on dynamic mesh force is found to be frequency dependent due to the resonance frequency shifts and peak magnitude changes. This study provides an in-depth understanding of the dynamic tooth load sharing and the dynamic behaviors for hypoid and bevel geared systems in terms of change in operating load. Therefore, the proposed model can be employed to assist in gear design optimization.
Author: Dario Di Maio Publisher: Springer ISBN: 3319546481 Category : Technology & Engineering Languages : en Pages : 154
Book Description
Rotating Machinery, Hybrid Testing, Vibro-Acoustics & Laser Vibrometry, Volume 8: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the eighth volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Rotating Machinery, Hybrid Testing, Vibro-Acoustics & Laser Vibrometry, including papers on: Rotating Machinery Vibro-Acoustics Experimental Techniques Advances in Wind Energy Scanning Laser Doppler Vibrometry Methods Hybrid Test Methods
Author: Junyi Yang
Author: Junyi Yang
Author: Philippe Velex
Author: Jun Wang
Author: Gang Liu
Author: Mahdi Mohammadpour
Author: Yubing Wen
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Author: 
Author: Yawen Wang
Author: Dario Di Maio