1、05FTM12Modal Failure Analysis of a Gear andDrive Ring Assemblyby: D.D. Behlke, Twin Disc, IncorporatedTECHNICAL PAPERAmerican Gear Manufacturers AssociationModal Failure Analysis of a Gear and Drive RingAssemblyDarwin D. Behlke, Twin Disc, IncorporatedThe statements and opinions contained herein are
2、 those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractAfter years of successful reliable applications, a component failure on a new application cannot be explainedwith static stress analyses, modal failure analyses may
3、 be required. Finite element modal analyses was usedto identify the mode and its frequency that cause a high range gear and drive ring assembly to fail prematurely.A Campbell Diagram was used to identify modes in the operating range of a six-speed transmission that couldcause the drive ring to fail.
4、 Redesigning the assembly to move the critical modes out of the operating range isdescribed.Copyright 2005American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2005ISBN: 1-55589-860-21 Modal Failure Analysis of a Gear and Drive Ring Assembly Darwi
5、n D. Behlke, P.E., Gear Design Specialist Twin Disc, Incorporated, Racine, WI BACKGROUND With the advent of personal computers in the past two decades, modal analysis has become a major technology for determining, improving and optimizing dynamic characteristics of mechanical components. With the re
6、quirements for greater power densities, transmissions are being applied at higher horsepower and lower weight and size. When the vibration of a component is of concern, the challenge lies on better understanding its dynamic properties using analytical means, or experimental, or a combination. In thi
7、s paper, only numerical analysis will be used. To provide background about modal analysis, the following information was paraphrased from He, et al 1. Finite element analysis (FEA) requires rigorous theoretical guidance to ascertain meaningful outcome in the relation to structural dynamics. Modal an
8、alysis (MA) alone cannot determine completely the dynamic behavior of the component, because certain properties such as damping and nonlinearity do not conform to traditional modeling treatment. Also, boundary conditions influence the dynamic analysis and must be applied with great care. Modal analy
9、sis is the process of determining the inherent dynamic characteristics of a component- natural frequencies, damping factors and mode shapes. These characteristics are used to formulate a mathematical model for its dynamic behavior. The formulated mathematical model is referred to as the modal model
10、of the component. The information for the characteristics is known as its modal data. The dynamics of a component are physically decomposed by frequency and position. Modal analysis is based upon the vibration response of the linear time-invariant dynamics system. It can be expressed as the linear c
11、ombination of a set of simple harmonic motions called the natural modes of vibration. This concept is parallel to the use of a Fourier combination of sine and cosine waves to represent a complicated waveform. The natural modes of vibration are determined completely by its physical properties (mass,
12、stiffness, damping) and their spatial distributions. Each mode is described by its mode shape. The mode shape may be real or complex. Each mode corresponds to a natural frequency. The contribution of each natural mode in the overall vibration is determined both by properties of the excitation source
13、(s) and by the mode shapes of the component. The theoretical modal analysis anchors on modeling the physical characteristic of a dynamic system comprising its mass, stiffness and damping properties. These properties may be given in forms of partial differential equations. For example, the wave equat
14、ion of a uniform vibratory string is established from its mass distribution and elasticity properties. The solution of the equation provides the natural frequencies and mode shapes of the string and its forced vibration responses. A more realistic physical model will usually comprise the mass, stiff
15、ness and damping properties in terms of their spatial distributions, namely the mass, stiffness and damping matrices. These matrices are incorporated into a set of normal differential equations of motion. The superposition principle of linear dynamic systems enables us to transform these equations i
16、nto a typical eigenvalue problem. Its solution provides the modal data of the system. Modern FEA empowers the use of almost any linear dynamic structure and has greatly enhanced the capacity and scope of theoretical modal analysis. The resultant finite element model, which is in the form of mass and
17、 stiffness matrices, can be essential for further applications such as sensitivity analysis and prediction due to proposed component changes. Using the modal model of the component, simulation and prediction of “what if” can be conducted. A sensitivity analysis is used to determine the sensitivity o
18、f its modal parameters due to a component physical parameter change. The emphasis here is to identify which physical change is the most effective in making a proposed modal parameter change, such as shifting a natural frequency. Structural modification is guided by variations of modal parameters due
19、 to a selected physical change. 2 For background on gearbox modal analysis, see Drago 2 analysis on the F22 AMAD gearbox. He analyzed all the rotating components with FEA to see if any of them had critical frequencies in the operating range. INTRODUCTION The TD61-1179 transmission (Figure 1.) is use
20、d in a unique application for a haul truck. The engine and transmission were sized for the empty haul truck going up the grade and the fully loaded haul truck coming down the grade. The map with grades of the haul road was used to determine the duty cycle and transmission life. The haul trucks opera
21、te 24 hours a day, 7 days a week and accumulate about 7000 hours per year. The Gear Brown, F.; Sane, A and Stremick, D, “The F-22 AMAD Gear Drive Optimization of Resonance Characteristics by Detuning, Coulomb Damping & Damped Force Response Analyses,” American Gear Manufacturing Association Technical Paper (96FTM6), Cincinnati, OH, 1996 3. Adams, V. and Askenazi, A., Building Better Products with Finite Element Analysis, OnWord Press, Santa Fe, NM, 1999
