A parameterized numerical model for the evaluation of gear mesh stiffness variation of a helical gear pair

2008 ◽  
Vol 222 (7) ◽  
pp. 1321-1327 ◽  
Author(s):  
J Hedlund ◽  
A Lehtovaara
Keyword(s):  
Numerical Model ◽  
Transmission Error ◽  
Helical Gear ◽  
Hertzian Contact ◽  
Mesh Stiffness ◽  
Fe Method ◽  
Gear Design ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

One of the most common challenges in gear drive design is to determine the best combination of gear geometry parameters. These parameters should be capable of being varied effectively and related to gear mesh stiffness variation in advanced excitation and vibration analysis. Accurate prediction of gear mesh stiffness and transmission error requires an efficient numerical method. The parameterized numerical model was developed for the evaluation of excitation induced by mesh stiffness variation for helical gear design purposes. The model uses linear finite-element (FE) method to calculate tooth deflections, including tooth foundation flexibility. The model combines Hertzian contact analysis with structural analysis to avoid large FE meshes. Thus, mesh stiffness variation was obtained in the time and frequency domains, which gives flexibility if comparison is made with measured spectrums. Calculations showed that a fairly low number of elements suffice for the estimation of mesh stiffness variation. A reasonable compromise was achieved between design trends and calculation time.

scholarly journals Geometry Modification of Helical Gear for Reduction of Static Transmission Error

2018 ◽  
Vol 167 ◽  
pp. 02013
Author(s):  
Jeonghyun Park ◽  
Changjun Seo ◽  
Kwangsuck Boo ◽  
Heungseob Kim
Keyword(s):  
Transmission Error ◽  
Helical Gear ◽  
Necessary Condition ◽  
Mesh Stiffness ◽  
Profile Modification ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Excitation Mechanisms ◽  
Gear Systems ◽  
Gear Mesh Stiffness

Gear systems are extensively employed in mechanical systems since they allow the transfer of power with a variety of gear ratios. So gears cause the inherent deflections and deformations due to the high pressure which occurs between the meshing teeth when transmit power and results in the transmission error. It is usually assumed that the transmission error and variation of the gear mesh stiffness are the dominant excitation mechanisms. Predicting the static transmission error is a necessary condition to reduce noise radiated from the gear systems. This paper aims to investigate the effect of tooth profile modifications on the transmission error of helical gear. The contact stress analysis was implemented for different roll positions to find out the most critical roll angle in view point of root flank stress. The PPTE (peak-to-peak of transmission error) is estimated at the roll angles by different loading conditions with two dimensional FEM. The optimal profile modification from the root to the tip is proposed.

An Analytical Investigation of Rattle Characteristics of Powder Metal Gears

2019 ◽  
Author(s):  
Elizabeth Slavkovsky ◽  
Murat Inalpolat ◽  
Anders Flodin
Keyword(s):  
Transmission Error ◽  
Analytical Investigation ◽  
Time Varying ◽  
Evaluation Tool ◽  
Mesh Stiffness ◽  
Gear Design ◽  
Gear Mesh ◽  
Internal Excitation ◽  
Gear Mesh Stiffness ◽  
Gear Rattle

Abstract This study employs an analytical model of a gear pair with transverse-torsional dynamics that allows analysis of single-sided, double-sided, and random rattle situations to contrast rattle characteristics of isotropic PM gears with a baseline steel gearset. This model utilizes time-varying gear mesh stiffness and transmission error as the internal excitation sources and time-varying operating torque as an external excitation. The gear rattle performance of PM gears is investigated under different torque conditions and operating speeds. The system kinetic and potential energy is assessed as an evaluation tool that can indicate the severity of different rattle conditions. The dynamic response of two different versions of an existing PM gear design are compared with a baseline traditional steel gear.

A model for analyzing stiffness and stress in a helical gear pair with tooth profile errors

2016 ◽  
Vol 23 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Qibin Wang ◽  
Yimin Zhang
Keyword(s):  
Contact Stress ◽  
Transmission Error ◽  
Helical Gear ◽  
Tooth Root ◽  
Mesh Stiffness ◽  
Tooth Contact ◽  
Gear Mesh ◽  
Profile Errors ◽  
Gear Mesh Stiffness ◽  
Root Stress

A model is introduced for analyzing the influence of tooth shape deviations and assembly errors on the helical gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress. The helical gear is approximated as a series of independent spur gear slices along axial direction whose face-width is relatively small. The relative position relationships among those sliced teeth in mesh are developed with tooth profile errors and the stiffness of the sliced tooth is calculated by the potential energy method. From the equilibriums of the forces, gear mesh stiffness, loaded transmission error, tooth contact stress and tooth root stress are calculated. Then two cases are presented for validation of the model. It is demonstrated that the model is effective for calculating the stiffness of helical gear pairs. Finally, the effects of the tooth tip reliefs, lead crown reliefs and misalignments on the gear mesh stiffness, transmission error, tooth contact stress and tooth root stress are analyzed. The results show that mesh stiffness decreases, loaded transmission error, the maximum tooth contact stress and the maximum tooth root stress grow with the increasing tooth tip relief, lead crown relief and misalignment. And tooth edge has concentrated tooth contact stresses with a gear misalignment.

Study on Helical Tooth Profile Modification of Planetary Gear Transmission on the Basis of Gear Transmission Error

2011 ◽  
Vol 86 ◽  
pp. 47-50
Author(s):  
Yu Tang ◽  
Shan Chang ◽  
Zhi Qiang Wang ◽  
Kun Zhang
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Tooth Profile ◽  
Gear Transmission ◽  
Mesh Stiffness ◽  
Profile Modification ◽  
Gear Mesh ◽  
Tooth Profile Modification ◽  
Planetary Transmission ◽  
Gear Mesh Stiffness

In order to minimize the fluctuation of gear transmission error (GTE) about the planetary gear transmission. A method was developed to deciding tooth profile modification curves of planetary transmission. According to the condition of the invariable design load, computing the dynamic characteristics of the planetary transmission system under modified and un-modified gear. At the same time, the compare is carried through of the dynamic characteristics for modified and un-modified gear. The results of the dynamic calculation indicate that the profile modification method can make the amplitudes of gear mesh stiffness change calmness and reduce the amplitudes of gear mesh stiffness by this method in paper. At last, the conclusion can be obtained that the tooth profile modification can reduce the vibration and noise of the planetary transmission system.

Multilevel Optimization of the Geared Rotor-Bearing System for Multi-Objectives With Critical Speed Constraints

2004 ◽  
Author(s):  
T. N. Shiau ◽  
J. R. Chang ◽  
W. B. Lu
Keyword(s):  
Critical Speed ◽  
Transmission Error ◽  
Mesh Stiffness ◽  
Error Response ◽  
Critical Speeds ◽  
Gear Mesh ◽  
Unbalance Response ◽  
Multilevel Algorithm ◽  
Gear Mesh Stiffness ◽  
Bearing System

This paper presents the multi-objective optimization of a geared rotor-bearing system with the critical speeds constraints by using an efficient multilevel algorithm. The weight of each rotor shaft, the unbalance response, and the response due to the transmission error are minimized simultaneously under the critical speed constraints. The design variables are the inner radii of the shaft, the stiffness of bearings, and the gear mesh stiffness. The finite element method (FEM) is employed to analyze the dynamic characteristics and the method of feasible direction (MFD) is applied in the optimization of the single objective stage. Based on the sensitivity analysis that gear mesh stiffness has almost no influences on the critical speeds of the uncoupled modes of two shafts, an efficient multilevel algorithm composed of system and subsystem levels is developed. In the cycle of iteration, the minimization of the shaft weight is performed in the subsystem level with the critical speed constraints of only uncoupled modes of two shafts and the unbalance response and the transmission error response are reduced in the system level with the critical speed constraints of only coupled modes. It is indicated from the numerical results that the shaft weight, the unbalance response, and the transmission error response via the multilevel technique (ML) are all reduced much more than those via the weighting method (WM) and the goal programming method (GPM).

Dynamics of a Truck Gearbox

1992 ◽  
Author(s):  
J. Perret-Liaudet ◽  
J. Sabot
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Transmission Error ◽  
Gear Transmission ◽  
The Finite Element Method ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Gear Mesh Stiffness

Abstract This work is concerned with numerous numerical simulations of the overall dynamic behaviour of a parallel helical gear transmission. These results are compared to vibratory measurements made with a simplified gearbox test rig. The dynamic modeling of the elastic components of the gear transmission (gears, shafts, bearings, housing) is realized using the finite element method. Fluctuated gear mesh stiffness is introduced owing to stiffness matrix which describes the elastic coupling between the pinion and the wheel. The kinematic transmission error is introduced as a vibratory excitation source. The equations of motion are established in a truncated modal base deduced from the average characteristics of the structure. A new computing method, called “Spectral Method”, is used for analytical study of a simplified gearbox whose housing is a simple rectangular plate. The numerical results allows us to conclude on the dominent phenomenon of the overall dynamic behaviour of the gear transmission. They exhibit in particular the main characteristics of the transfer between the static transmission error and the vibratory response of the gearbox. A series of vibration measurements made on a gearbox close to that used for the numerical simulations, has confirmed this characteristics.

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.

Parametric Instability in Planetary Gears With Frequency-Modulated Time-Varying Mesh Stiffness

2014 ◽  
Author(s):  
Xinghui Qiu ◽  
Qinkai Han ◽  
Fulei Chu
Keyword(s):  
Parametric Instability ◽  
Operating Conditions ◽  
Time Varying ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Planetary Gears ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Speed Fluctuations ◽  
Gear Mesh Stiffness

A rotational model of planetary gears is developed which incorporates mesh stiffness variation and input speed fluctuations. Gear mesh stiffness is approximated by rectangle wave and different harmonic orders are considered. Because of speed fluctuations, the mesh stiffness is frequency modulated. The parametric instability associated with frequency-modulated time-varying stiffness is numerically investigated. The operating conditions leading to parametric instability are identified using Floquet theory and numerical integration. Whether the general laws derived for steady speed to suppress particular instabilities are applicable for fluctuating speed is verified. The effects of speed fluctuations on parametric instability are examined.

An Analytical Study of the Effect of the Contact Ratio on the Spur Gear Dynamic Response

1999 ◽  
Vol 122 (4) ◽  
pp. 508-514 ◽  
Author(s):  
Anette Andersson
Keyword(s):  
Dynamic Response ◽  
Transmission Error ◽  
Spur Gear ◽  
Spur Gears ◽  
Contact Ratio ◽  
Constant Stiffness ◽  
Gear Mesh ◽  
Critical Rotational Speed ◽  
Stiffness Variation ◽  
Gear Mesh Stiffness

A model was used, where the total gear mesh stiffness was approximated by two constant stiffness levels, in order to analyze the influence of the contact ratio on the dynamic response of spur gears. Due to the stiffness variation there is parametric excitation of the transmission error, which generally causes tooth separation at certain critical rotational speeds. The present paper discloses a method to analytically calculate which contact ratio to use in order to avoid tooth separation near a specific critical rotational speed. [S1050-0472(00)02604-0]

Parametric Instability of Planetary Gear Transmission Mounted on Discrete Support Struts With Minimum Ring Gear Rim Thickness Design

2018 ◽  
Author(s):  
Peng Guan ◽  
Hans DeSmidt
Keyword(s):  
Parametric Instability ◽  
Planetary Gear ◽  
Gear Transmission ◽  
Ring Gear ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Stiffness Variation ◽  
Parametric Instabilities ◽  
Gear Mesh Stiffness ◽  
Flexible Ring

This research explores parametric instabilities of the PGT driveline system and a stability-based method for ring gear rim thickness design. Parametric excitation of a planetary gear transmission (PGT) driveline system arises from two sources: 1) gear mesh stiffness variation, 2) Interaction between moving planets, flexible ring gear and boundary struts. Many researchers have studied the parametric instability of planetary gear transmissions due to gear mesh stiffness variation, however, the effect of interaction between moving planets, flexible ring and discrete boundary struts on parametric instabilities has not been fully studied before. Especially, for sufficiently thin ring gears, this kind of effect becomes even more significant. To illustrate the novel PGT rim design proposal, firstly, a structural dynamics model of a complete PGT driveline system with elastic ring gear supported by discrete boundary struts is established. Secondly, by applying Floquet method, the parametric instability behavior due to the second parametric excitation source is fully investigated. Lastly, the design guidelines for planetary gear transmission ring gear rim thickness are proposed based on system stability from a dynamical viewpoint. The analysis and results provide new and important insights into dynamics and design of lightweight planetary gear transmission ring gear rim.

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