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.

Dynamic Analysis of a Multi-Mesh Helical Gear Train

1994 ◽  
Vol 116 (3) ◽  
pp. 706-712 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Three Dimensional ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Gear Train ◽  
Loading Conditions ◽  
Natural Modes ◽  
Static Transmission Error ◽  
Gear Meshes

In this paper, the dynamic behavior of a multi-mesh helical gear train has been studied. The gear train consists of three helical gears, with one of the gears in mesh with the other two. A three dimensional dynamic model which includes transverse, torsional, axial and rotational (rocking) motions of the flexibility mounted gears has been developed. Two different loading conditions have been identified. In case-I, the system is driven by the gear in the middle, and in case-II, the system is driven by one of the gears at either end of the gear train. The phase difference between the two gear meshes has been determined under each loading condition. The natural modes have been predicted, and their sensitivity to the helix angle and different loading conditions has been quantified. The forced response, which includes dynamic mesh and bearing forces, due to the static transmission error excitation has been obtained. Effects of loading conditions and asymmetric positioning on the response have also been explored.

Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair

1993 ◽  
Vol 115 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A. Kahraman
Keyword(s):  
Natural Frequencies ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Helical Gear Pair

In this paper, a linear dynamic model of a helical gear pair has been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational (rocking) motions due to the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of the helix angle in the analysis.

Effect of Axial Vibrations on the Dynamics of a Helical Gear Pair

1991 ◽  
Author(s):  
Ahmet Kahraman
Keyword(s):  
Natural Frequencies ◽  
Helix Angle ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Dynamic Mesh ◽  
Gear Pair ◽  
Gear Mesh ◽  
Static Transmission Error ◽  
Helical Gear Pair

Abstract In this paper, a linear dynamic model of a helical gear pair has. been developed. The model accounts for the shaft and bearing flexibilities, and the dynamic coupling among the transverse, torsional, axial and rotational motions because of the gear mesh. The natural frequencies and the mode shapes have been predicted, and the modes which are excited by the static transmission error have been identified. The forced response due to the static transmission error has also been predicted, including the dynamic mesh and bearing forces. A parametric study has been performed to investigate the effect of the helix angle on the free and forced vibrational characteristics of the gear pair. It has been shown that the helix angle can be neglected in predicting the natural frequencies and the dynamic mesh forces. An accurate prediction of dynamic bearing forces and moments requires inclusion of helix angle in the analysis.

Static and Dynamic Transmission Error Measurements of Helical Gear Pairs With Various Tooth Modifications

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
M. Benatar ◽  
M. Handschuh ◽  
A. Kahraman ◽  
D. Talbot
Keyword(s):  
Dynamic Models ◽  
Nonlinear Behavior ◽  
Transmission Error ◽  
Helical Gear ◽  
Forced Response ◽  
Test Machine ◽  
Response Curves ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
Static Transmission Error

This paper presents a set of motion transmission error data for a family of helical gears having different profile and lead modifications operated under both low-speed (quasi-static) and dynamic conditions. A power circulatory test machine is used along with encoder and accelerometer-based transmission error measurement systems to quantify motion transmission behavior within wide ranges of torque and speed. Results of these experiments indicate that the tooth modifications impact the resultant static and dynamic transmission error amplitudes significantly. A design load is shown to exist for each gear pair of different modifications where static transmission error amplitude is minimum. Forced response curves and waterfall plots are presented to demonstrate that the helical gear pairs tested act linearly with no signs of nonlinear behavior such as tooth contact separations. Furthermore, static and dynamic transmission error amplitudes are observed to be nearly proportional, suggesting that static transmission error can be employed in helical gear dynamic models as the main gear mesh excitation. The data presented here is intended to fill a void in the literature by providing means for validation of load distribution and dynamic models of helical gear pairs.

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.

A Methodology to Experimentally Investigate the Impact of Wobble Errors on the Contact Pattern and Static Transmission Error of Helical Gear Pairs

2019 ◽  
Author(s):  
Michael Benatar ◽  
Michael Handschuh ◽  
Ahmet Kahraman ◽  
David Talbot
Keyword(s):  
Transmission Error ◽  
Helical Gear ◽  
Experimental Results ◽  
Gear Pair ◽  
Contact Pattern ◽  
Gear Mesh ◽  
Face Width ◽  
The Face ◽  
Static Transmission Error ◽  
The Impact

Abstract For a gear pair, both the contact pattern and the transmission error (TE) significantly impact durability and fatigue life. Design and manufacturing processes are often aimed at improving the contact pattern and reducing the overall TE. Other errors, such as runout and wobble, are often induced during the installation of power transmission systems, and they can alter the contact pattern and TE of an otherwise well-designed gear pair. This study provides a methodology to experimentally investigate the impact of wobble errors on the contact pattern and static transmission error (STE) of helical gears. It first provides a description of the modifications to an existing test machine. Next, it describes the gear specifications, preliminary testing matrix, data acquisition and processing procedure, as well as the experimental results obtained with regards to both the contact pattern and STE. The following are observed while describing the experimental results. For a test with no wobble and no runout, the contact pattern remains the same at every rotational position. However, by introducing even a small amount of wobble, the contact will shift from one side of the face width of the gear to the opposite side of the face width of the gear within one revolution. Introduction of wobble may increase the STE and sideband activity around gear mesh harmonics, especially as torque increases. Yet the modest increases in STE and sideband activity seen with the introduction of wobble are not enough to make definitive conclusions. The feasibility of the modified test setup has been demonstrated, and preliminary results have been presented. However, additional data collection should be completed in order to study the impact of runout and wobble on both spur and helical gear pairs with various microgeometry modifications and manufacturing errors.

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.

A Helical Gear Pair Pocketing Power Loss Model

2013 ◽  
Author(s):  
David Talbot ◽  
Ahmet Kahraman ◽  
Satya Seetharaman
Keyword(s):  
Fluid Dynamics ◽  
Power Loss ◽  
Control Volume ◽  
Fluid Pressure ◽  
Helix Angle ◽  
Helical Gear ◽  
Gear Pair ◽  
Dynamics Model ◽  
Gear Mesh ◽  
Helical Gear Pair

A new fluid dynamics model is proposed to predict the power losses due to pocketing of air, oil, or an air-oil mixture in the helical gear meshes. The proposed computational procedure treats a helical gear pair as combination of a number of narrow face width spur gear segments staggered according to the helix angle and forms a discrete, fluid dynamics model of the medium being pocketed in the gear mesh. Continuity and conservation of momentum equations are applied to each coupled control volume filled with a compressible fluid mixture to predict fluid pressure and velocity distributions from, which the instantaneous pocketing power loss is calculated. The proposed model is exercised in order to investigate fluid pressure and velocity distributions in time, as well as pocketing power loss as a function of speed, helix angle and oil-to-air ratio.

Theoretical Method for Calculating the Unit Curve of Gear Integrated Error

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Zhaoyao Shi ◽  
Xiaoyi Wang ◽  
Zanhui Shu
Keyword(s):  
Differential Equations ◽  
Optimization Algorithm ◽  
Theoretical Method ◽  
Transmission Error ◽  
Helical Gear ◽  
Contact Analysis ◽  
Gear Transmission ◽  
Tooth Contact Analysis ◽  
Static Transmission Error ◽  
Integrated Error

A theoretical method is proposed in this paper to calculate the unit curve of gear integrated error (GIE). The calculated GIE unit curve includes the quasi-static transmission error (TE) curves of the approach stage, the involute stage, and the recession stage of the ZI worm and helical gear transmission. The misalignments between the two axes of the worm and gear, as well as the modifications or errors of the tooth flanks of the gear, are considered in the procedure of calculation. Optimization algorithm is introduced to replace the solving of implicit differential equations of the conventional tooth contact analysis (TCA) method. It is proved that the proposed method is clearer and more convenient than the conventional TCA methods in calculating the GIE unit curve. The correctness and merits of the proposed method are verified by two experiments.

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.

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