A Dynamic Model for Double-Planet Planetary Gearsets

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Dylan C. Fyler ◽  
Murat Inalpolat
Keyword(s):  
Dynamic Model ◽  
Forced Vibration ◽  
Transmission Error ◽  
Vibration Response ◽  
Operating Conditions ◽  
Distribution Model ◽  
Design Parameters ◽  
Gear Mesh ◽  
Load Spectra ◽  
Modal Summation

In this study, a two-dimensional (2D), steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of N number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

A Dynamic Model for Double-Planet Planetary Gearsets

2015 ◽  
Author(s):  
Dylan C. Fyler ◽  
Murat Inalpolat
Keyword(s):  
Dynamic Model ◽  
Forced Vibration ◽  
Transmission Error ◽  
Vibration Response ◽  
Operating Conditions ◽  
Distribution Model ◽  
Design Parameters ◽  
Gear Mesh ◽  
Load Spectra ◽  
Modal Summation

In this study, a two-dimensional, steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

A multibody dynamic model for predicting operational load spectra of dual clutch transmissions

2021 ◽  
Vol 263 (2) ◽  
pp. 4132-4143
Author(s):  
Murat Inalpolat ◽  
Enes Timur Ozdemir ◽  
Bahadir Sarikaya ◽  
Hyun Ku Lee
Keyword(s):  
Steady State ◽  
Dynamic Model ◽  
Forced Vibration ◽  
Linear Time ◽  
Vibration Response ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Time Step ◽  
Gear Mesh ◽  
Multibody Dynamic

In this paper, a generalized nonlinear time-varying multibody dynamic model of dual clutch transmissions (DCT) is presented. The model consists of clutches, shafts, gears and synchronizers, and can be used to model any DCT architecture. A nonlinear clutch model is used to determine the transmitted power to the transmission at any speed and clutch temperature. The clutch can be a single- or multi-plate clutch and can operate in a wet or dry-clutch configuration. A combined kinematic and powerflow simulation enables calculation of gear, shaft, bearing and clutch quasi-static loads as well as gear mesh frequencies following a duty cycle as the input. For the corresponding Linear-Time-Invariant (LTI) system model, natural frequencies and mode shapes are obtained by solving the eigenvalue problem. The modal summation technique is used to determine the steady state forced vibration response of the system. For the corresponding NTV system, Newmark's time-step marching based integration is used to determine both the steady state and transient forced vibration response of the system. The DCT model is exercised using a common transmission architecture operating at several different operating conditions. The resulting impact of changing operational conditions on gear and bearing loads as well as dynamic transmission error spectra are demonstrated.

An Analytical and Numerical Investigation of Modulation Sidebands of a Planetary Gear Under Fluctuated External Torque

2018 ◽  
Author(s):  
Yunbo Yuan ◽  
Wei Liu ◽  
Yahui Chen ◽  
Donghua Wang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Operating Conditions ◽  
Radial Acceleration ◽  
External Torque ◽  
Gear Mesh ◽  
Planetary Gear Sets ◽  
Static Transmission Error ◽  
Frequency Modulations ◽  
Mesh Phasing

Certain operating conditions such as fluctuation of the external torque to planetary gear sets can cause additional sidebands. In this paper, a mathematical model is proposed to investigate the modulation mechanisms due to a fluctuated external torque (FET), and the combined influence of such an external torque and manufacturing errors (ME) on modulation sidebands. Gear mesh interface excitations, namely gear static transmission error excitations and time-varying gear mesh stiffness, are defined in Fourier series forms. Amplitude and frequency modulations are demonstrated separately. The predicted dynamic gear mesh force spectra and radial acceleration spectra at a fixed position on ring gear are both shown to exhibit well-defined modulation sidebands. Comparing with sidebands caused by ME, more complex sidebands appear when taking both FET and ME into account. An obvious intermodulation is found around the fundamental gear mesh frequency between the FET and ME in the form of frequency modulations, however, no intermodulation in the form of amplitude modulations. Additionally, the results indicate that some of the sidebands are cancelled out in radial acceleration spectra mainly due to the effect of planet mesh phasing, especially when only amplitude modulations are present.

Development of High-Loaded, Low-Speed Spiroid Gearboxes

2000 ◽  
Author(s):  
V. I. Goldfarb ◽  
V. M. Spiridonov ◽  
N. S. Golubkov
Keyword(s):  
High Reliability ◽  
Operating Conditions ◽  
Design Parameters ◽  
Angular Range ◽  
Operating Modes ◽  
Gear Design ◽  
Gear Mesh ◽  
Numerical Studies ◽  
High Durability ◽  
Spiroid Gear

Abstract Actuator rotation sometimes is required to transmit considerable torques at low speeds in a limited angular range. Such operating conditions are typical, for example, for the rotational drives of gas pipeline stop valves. These conditions are made worse by increased torques requried at the initial instant of motion when the torque is 1.3 to 1.5 times greater than the nominal torque, and by the range of operating temperatures of −60°C to +50°C. A number of gearboxes with a spiroid gear mesh were developed to satisfy these conditions for different torques (i.e. for different standard stop valves), with the steel spiroid pair case-hardened to 60–62 hardness Rc. A set of numerical studies had been conducted in order to choose gear design parameters and other elements of the gearbox. Experimental research performed using special testing rigs for definite operating modes showed high reliability and wear resistance of the drives developed and their high durability compared to known ones which is of great importance for given application domain.

scholarly journals Dynamic Model of Spur Gear Pair with Modulation Internal Excitation

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Wang ◽  
Lei Zhang ◽  
Yuan-Qing Luo ◽  
Chang-Zheng Chen
Keyword(s):  
Dynamic Model ◽  
Transmission Error ◽  
Spur Gear ◽  
Experimental Result ◽  
Time Varying ◽  
Gear Pair ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Modulation Sideband

In the actual measurements, vibration and noise spectrum of gear pair often exhibits sidebands around the gear mesh harmonic orders. In this study, a nonlinear time-varying dynamic model of spur gear pair was established to predict the modulation sidebands caused by the AM-FM modulation internal excitation. Here, backlash, modulation time-varying mesh stiffness, and modulation transmission error are considered. Then the undamped natural mode was studied. Numerical simulation was made to reveal the dynamic characteristic of a spur gear under modulation condition. The internal excitation was shown to exhibit obvious modulation sideband because of the modulation time-varying mesh stiffness and modulation transmission error. The Runge-Kutta method was used to solve the equations for analyzing the dynamic characteristics with the effect of modulation internal excitation. The result revealed that the response under modulation excitation exhibited obvious modulation sideband. The response under nonmodulation condition was also calculated for comparison. In addition, an experiment was done to verify the prediction of the modulation sidebands. The calculated result was consistent with the experimental result.

Frictional dynamic model predictions of FZG-A10 spur gear pairs considering profile errors

2020 ◽  
pp. 135065012096297
Author(s):  
Nabih Feki ◽  
Maroua Hammami ◽  
Olfa Ksentini ◽  
Mohamed Slim Abbes ◽  
Mohamed Haddar
Keyword(s):  
Dynamic Model ◽  
Coefficient Of Friction ◽  
Power Loss ◽  
Spur Gear ◽  
Operating Conditions ◽  
Time Dependent ◽  
Nonlinear Dynamic Model ◽  
Gear Mesh ◽  
Proposed Model ◽  
Profile Errors

In this work, a nonlinear dynamic model of an FZG-A10 spur gear was investigated by taking into account for the actual time-varying gear mesh stiffness and the frictional effects between meshing gear teeth to evaluate the influence of the dynamic effects on frictional gear power loss predictions. The equations of motion of the generalized translational-torsional coupled dynamic system derived from Lagrange principle was extended compared to authors’ previous work in order to account for time dependent coefficient of friction and profile errors. The dynamic response of spur gears, computed by an iterative implicit scheme of Newmark, is changed due to the presence of coefficient of friction and profile errors. A dynamic analysis was performed and the influence of frictional effect including tooth shape deviations, in particular, was scrutinized since a time-dependent coefficient of friction is deeply related to the gear surface roughness and all parameters dependent on gears error profiles are introduced in the proposed model. The predicted meshing gear power losses with constant and local friction coefficient were compared. The influence of constant and variable profile errors considered in the local coefficient of friction formulation was also studied and their corresponding root mean square (RMS) power loss was compared to the experimental results. The results using FZG A10 spur gear pairs running under several operating conditions (different loads and speeds) validate the superiority of the proposed model against previous similar models.

A theoretical study of the overall transmission error in planetary gear sets

2019 ◽  
Vol 233 (21-22) ◽  
pp. 7200-7211 ◽  
Author(s):  
Y Hu ◽  
L Ryali ◽  
D Talbot ◽  
A Kahraman
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Diagnostic Value ◽  
Distribution Model ◽  
Gear Mesh ◽  
Manufacturing Errors ◽  
Time Histories ◽  
Gear Manufacturing ◽  
Planetary Gear Sets ◽  
Error Behavior

In this study, a theoretical investigation on the overall loaded motion transmission error of planetary gear sets is presented. Planetary gear set load distribution model is employed to predict the input-to-output transmission error of planetary gear sets having distinct planet phasing conditions, to establish nominal transmission error behavior. Impact of carrier manufacturing errors resulting in unequal planet-to-planet load sharing on the gear set transmission error is quantified. Gear manufacturing imperfections such as run-out errors at their relative angles are introduced to observe their signatures on the resultant transmission error. Simplified formulations are presented to combine individual gear mesh transmission error functions with required modifications in order to obtain the overall transmission error. The predicted transmission error time histories are examined in the frequency domain to explore their diagnostic value in determining what errors the gear set possesses.

A Transient Mixed Elastohydrodynamic Lubrication Model for Helical Gear Contacts

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
A. S. Chimanpure ◽  
A. Kahraman ◽  
D. Talbot
Keyword(s):  
Power Loss ◽  
Contact Region ◽  
Elastohydrodynamic Lubrication ◽  
Sensitivity Study ◽  
Helical Gear ◽  
Operating Conditions ◽  
Mechanical Power ◽  
Distribution Model ◽  
Rolling Velocity ◽  
Gear Mesh

Abstract In this study, a non-Newtonian, transient, isothermal, mixed elastohydrodynamic lubrication (EHL) model is proposed for helical gear contacts. The model accounts for nonelliptical contacts subject to spatially varying sliding and rolling velocity fields that are not aligned with any principal axis of the contact region, which is the case for helical gear contacts. The time-varying changes pertaining to key contact parameters and relative motion of roughness profiles on mating tooth surfaces are captured simultaneously to follow the contact from the root to the tip of a tooth while accounting for the transient effect due to relative motions of the roughness profiles. Actual tooth load distributions, contact kinematics, and compliances of helical gear contacts are provided to this model by an existing helical gear load distribution model. Measured three-dimensional roughness profiles covering the entire meshing zone are incorporated in the analyses to investigate its impact on the EHL conditions as well as mechanical power loss. Results of a parametric sensitivity study are presented to demonstrate the influence of operating conditions and surface roughness on the EHL behavior and the resultant gear mesh mechanical power loss of an example helical gear pair. The accuracy of the proposed mixed-EHL model is assessed by comparing the mechanical power loss predictions to available experimental results.

Integrated Dynamic Thermo-Mechanical Modeling of High Speed Spindles, Part 1: Model Development

2004 ◽  
Vol 126 (1) ◽  
pp. 148-158 ◽  
Author(s):  
Hongqi Li ◽  
Yung C. Shin
Keyword(s):  
Dynamic Model ◽  
Thermal Model ◽  
High Speed ◽  
Model Development ◽  
Beam Theory ◽  
Operating Conditions ◽  
Design Parameters ◽  
Fully Integrated ◽  
Temperature Distributions ◽  
Coupling Procedure

This paper presents a comprehensive integrated thermo-dynamic model for various high speed spindles. The entire model consists of fully coupled three sub-models: bearing, spindle dynamic and thermal models. Using a finite element approach, a new thermal model has been generated, which can describe complex structures of high-speed motorized spindles, and can predict more accurate temperature distributions. The spindle dynamic model is constructed using finite elements based on Timoshenko beam theory and has been improved by considering shear deformation, material and bearing damping, and the spindle/tool-holder interface. Using the new thermo-dynamic model, more general and detailed bearing configurations can be modeled through a systematic coupling procedure. The thermal expansions of the shaft, housing and bearings are calculated based on predicted temperature distributions and are used to update the bearing preloads depending on the operating conditions, which are again used to update the thermal model. Therefore, the model is fully integrated and can provide solutions in terms of all the design parameters and operating conditions.

scholarly journals Operating Behavior of Sliding Planet Gear Bearings for Wind Turbine Gearbox Applications—Part I: Basic Relations

Lubricants ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 97
Author(s):  
Thomas Hagemann ◽  
Huanhuan Ding ◽  
Esther Radtke ◽  
Hubert Schwarze
Keyword(s):  
Wind Turbine ◽  
Local Maximum ◽  
Axial Direction ◽  
Operating Conditions ◽  
Design Parameters ◽  
Radial Clearance ◽  
Wind Turbine Gearbox ◽  
Local Loads ◽  
Gear Mesh ◽  
Planet Gear

The application of sliding planet gear bearings in wind turbine gearboxes has become more common in recent years. Assuming practically applied helix angles, the gear mesh of the planet stage causes high force and moment loads for these bearings involving high local loads at the bearing edges. Specific operating behavior and suitable design measures to cope with these challenging conditions are studied in detail based on a thermo-hydrodynamic (THD) bearing model. Radial clearance and axial crowning are identified as important design parameters to reduce maximum pressures occurring at the bearing edges. Furthermore, results indicate that a distinct analysis of the gear mesh load distribution is required to characterize bearing operating behavior at part-load. Here, operating conditions as critical as the ones reached at nominal load might occur. Wear phenomena can improve the shape of the gap in the circumferential as well as in axial direction incorporating a significant reduction of local maximum pressures. The complexity of the combination of these aspects and the additionally expected impact of structure deformation gives an insight into the challenges in the design processes of sliding planet gear bearings for wind turbine gearbox applications.

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