scholarly journals Gear Defect Modeling of a Multiple-Stage Gear Train

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Andrew Sommer ◽  
Jim Meagher ◽  
Xi Wu
Keyword(s):  
Contact Forces ◽  
Gear Train ◽  
Response Analysis ◽  
Single Pair ◽  
Time Frequency ◽  
Gear Mesh ◽  
Software Model ◽  
Manufacturing Errors ◽  
Tooth Surfaces ◽  
Two Stages

This study demonstrates the transient and steady state dynamic loading on teeth within a two-stage gear transmission arising from backlash and geometric manufacturing errors by utilizing a nonlinear multibody dynamics software model. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. Torsional vibration is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. Vibration and impact force distinctions between backlash and combinations of transmission errors are demonstrated under different initial velocities and load conditions. The backlash and manufacturing errors in the first stage of the gear train are distinct from those of the second stage. By analyzing the signal at a location between the two stages, the mutually affected impact forces are observed from different gear pairs, a phenomenon not observed from single pair of gears. Frequency analysis shows the appearance of side band modulations as well as harmonics of the gear mesh frequency. A joint time-frequency response analysis during startup illustrates the manner in which contact forces increase during acceleration.

scholarly journals The Effects of the Planet–Gear Manufacturing Eccentric Errors on the Dynamic Properties for Herringbone Planetary Gears

2020 ◽  
Vol 10 (3) ◽  
pp. 1060
Author(s):  
Fei Ren ◽  
Ansheng Li ◽  
Guiqin Shi ◽  
Xiaoling Wu ◽  
Ning Wang
Keyword(s):  
Dynamic Properties ◽  
Planetary Gear ◽  
Dynamic Contact ◽  
Contact Forces ◽  
Gear Train ◽  
Parameter Method ◽  
Dynamic Feature ◽  
Actual Structure ◽  
Manufacturing Errors ◽  
Planet Gear

In the presence of manufacturing errors, the dynamic properties of herringbone planetary gear train (HPGT) can be altered from the originally designed properties to have undesired behavior. In this paper, by considering the herringbone gear actual structure characteristics, manufacturing eccentric errors of members (i.e., carrier and gears) and tooth profile errors of gears, time-varying meshing stiffness, bearing deformation, and gyroscopic effect, a novel lateral–torsional–axial coupling dynamic model for the herringbone planetary gear system is formulated by using the lumped-parameter method, which is able to be employed in the dynamic feature analysis of the HPGT with an arbitrary number of planets and different types of manufacturing errors. By applying the variable-step Runge–Kutta algorithm, the dynamic response of a HPGT system is studied for cases with and without planet–gear eccentric error excitations. The dynamic contact forces of gears and bearings are analyzed for the two cases in time and frequency domains, respectively. Moreover, the effect of the planet–gear eccentricity on the vibration accelerations of the HPGT system is also discussed. The obtained results indicate that manufacturing error excitations such as the planet–gear eccentricity have a pronounced influence on the dynamic behavior of the HPGT system.

Dynamic Characteristics of Double Helical Planetary Gear Train With Tooth Friction

2015 ◽  
Author(s):  
Fengxia Lu ◽  
Rupeng Zhu ◽  
Haofei Wang ◽  
Heyun Bao ◽  
Miaomiao Li
Keyword(s):  
Degrees Of Freedom ◽  
Sliding Friction ◽  
Planetary Gear ◽  
Gear Train ◽  
Variable Step Size ◽  
Step Size ◽  
Planetary Gear Train ◽  
Gear Mesh ◽  
Meshing Stiffness ◽  
Nonlinear Dynamics Model

A new nonlinear dynamics model of the double helical planetary gear train with 44 degrees of freedom is developed, and the coupling effects of the sliding friction, time-varying meshing stiffness, gear backlashes, axial stagger as well as gear mesh errors, are taken into consideration. The solution of the differential governing equation of motion is solved by variable step-size Runge-Kutta numerical integration method. The influence of tooth friction on the periodic vibration and nonlinear vibration are investigated. The results show that tooth friction makes the system motion become stable by the effects of the periodic attractor under the specific meshing frequency and leads to the frequency delay for the bifurcation behavior and jump phenomenon in the system.

Dynamic Analysis of a Multi-Mesh Helical Gear Train

1992 ◽  
Author(s):  
Ahmet Kahraman
Keyword(s):  
Loading Condition ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Gear Train ◽  
Loading Conditions ◽  
Gear Mesh ◽  
Natural Modes ◽  
Static Transmission Error

Abstract In this paper, the dynamic behavior of a multi-mesh helical gear train is studied. The gear train consists of three helical gears, with one of the gears in mesh with the other two. An 18-degree-of-freedom dynamic model which includes transverse, torsional, axial and rotational (rocking) motions of the flexibly mounted gears is developed. Two different loading conditions are identified. For case I, the system is driven by the gear in the middle, and for case II, the system is driven by one of the gears at either end of the gear train. Gear mesh phases under each loading condition are determined. The natural modes are predicted, and effects of the helix angle and the loading condition on the natural modes are explained. The forced response, which includes dynamic mesh and bearing forces, due to the static transmission error excitation is found. Effects of loading conditions and asymmetric positioning on the response are also explored. The results suggest that the dynamic forces are lower if the number of teeth of the gear in the middle is (i) an odd number for case I type loading, and (ii) an even number for case II type loading.

A Three-Dimensional Load Sharing Model of Planetary Gear Sets Having Manufacturing Errors

2015 ◽  
Author(s):  
Nicholas D. Leque ◽  
Ahmet Kahraman
Keyword(s):  
Three Dimensional ◽  
Planetary Gear ◽  
Load Sharing ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Proposed Model ◽  
Manufacturing Errors ◽  
Manufacturing Tolerancing ◽  
Planetary Gear Sets

Planet-to-planet load sharing is a major design and manufacturing tolerancing issue in planetary gear sets. Planetary gear sets are advantageous over their countershaft alternatives in many aspects, provided that each planet branch carries a reasonable, preferably equal, share of the torque transmitted. In practice, the load shared among the planets is typically not equal due to the presence of various manufacturing errors. This study aims at enhancing the models for planet load sharing through a three-dimensional formulation of N-planet helical planetary gear sets. Apart from previous models, the proposed model employs a gear mesh load distribution model to capture load and time dependency of the gear meshes iteratively. It includes all three types of manufacturing errors, namely constant errors such as planet pinhole position errors and pinhole diameter errors, constant but assembly dependent errors such as nominal planet tooth thickness errors, planet bore diameter errors, and rotation and assembly dependent errors such as gear eccentricities and run-outs. At the end, the model is used to show combined influence of these errors on planet load sharing to aid designers on how to account for manufacturing tolerances in the design of the gears of a planetary gear set.

Time-frequency equivalence using chirp signals for frequency response analysis

2021 ◽  
Author(s):  
Resmi Suresh ◽  
Raghunathan Rengaswamy
Keyword(s):  
Frequency Response ◽  
Electrochemical Impedance ◽  
Response Analysis ◽  
Chirp Signal ◽  
Simulation Studies ◽  
Frequency Response Analysis ◽  
Time Frequency ◽  
Input Signals ◽  
Chirp Signals ◽  
Potential Impact

Abstract Frequency response analysis (FRA) of systems is a well-researched area. For years, FRA has been performed using input signals, which are a series of sinusoids or a sum of sinusoids. This results in large experimentation time, particularly when the system has to be probed at lower frequencies. In this work, we describe a previously unknown time-frequency duality for linear systems when probed through chirp signals. We show that the entire frequency response can be extracted with a single chirp signal by extending the notion of instantaneous frequency to both the input and output signals. It is surprising that this powerful result had not been uncovered given that FRA has been used in multiple disciplines for more than hundred years. This result has the possibility of completely revolutionizing methods used for frequency response analysis. Simulation studies that support the main result are described. While this result is of relevance in multiple areas, we demonstrate the potential impact of this result in electrochemical impedance spectroscopy.

scholarly journals Modeling and Analysis of Amplitude-Frequency Characteristics of Torsional Vibration for Automotive Powertrain

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Jinli Xu ◽  
Jiwei Zhu ◽  
Feifan Xia
Keyword(s):  
Torsional Vibration ◽  
Transmission Error ◽  
Frequency Characteristics ◽  
Response Analysis ◽  
Lumped Mass ◽  
Modeling And Analysis ◽  
Gear Mesh ◽  
Runge Kutta Method ◽  
Lumped Mass Method ◽  
Automotive Powertrain

In the present paper, the amplitude-frequency characteristics of torsional vibration are discussed theoretically and experimentally for automotive powertrain. A bending-torsional-lateral-rocking coupled dynamic model with time-dependent mesh stiffness, backlash, transmission error etc. is proposed by the lumped-mass method to analysis the amplitude-frequency characteristic of torsional vibration for practical purposes, and equations of motive are derived. The Runge–Kutta method is employed to conduct a sweep frequency response analysis numerically. Furthermore, a torsional experiment is performed and validates the feasibility of the theoretical model. As a result, some torsional characteristics of automotive powertrain are obtained. The first three-order nature torsional frequencies are predicted. Torsional behaviors only affect the vibration characteristics of a complete vehicle at low-speed condition and will be reinforced expectedly while increasing torque fluctuation. Gear mesh excitations have little effects on torsional responses for such components located before mesh point but a lot for ones behind it. In particular, it is noted that the torsional system has a stiffness-softening characteristic with respect to torque fluctuation.

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.

Contact Analysis of Gear Trains Using Linear Complementarity Based Compliant Contact Model

2019 ◽  
Author(s):  
Mangesh Pathak ◽  
Sourav Rakshit
Keyword(s):  
Finite Element ◽  
Computation Time ◽  
Planetary Gear ◽  
Element Model ◽  
Linear Complementarity ◽  
Contact Analysis ◽  
Contact Forces ◽  
Gear Train ◽  
Spur Gears ◽  
Gear Contact

Abstract The current computation models for gear contact analysis and wear prediction are mostly based on finite element analysis which consumes much computation time and effort. In this work, we adopt an alternative approach for gear contact analysis using linear complementarity. This approach was successfully applied to a pair of rigid spur gears and a planetary gear train (gears are considered as rigid bodies) in our previous work. In this paper, we extend our linear complementarity model to consider local deformation caused due to contact between gear teeth in mesh. Thus obtained linear complementarity model is applied to a pair of spur gears and a planetary gear train. A linear complementarity solver computes the contact forces between meshing teeth of gears. From the contact forces, sliding wear in gear teeth is predicted. Archard’s wear model is used for the wear prediction. Using this model, the contact forces are uniquely determined for the examples considered. The results of linear complementarity and finite element model for a pair of spur gears are compared. The linear complementarity model consumes much less computation time than the finite element model.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

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