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 Load Distribution Model for Planetary Gear Sets

2017 ◽  
Author(s):  
Yong Hu ◽  
David Talbot ◽  
Ahmet Kahraman
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
Distribution Model ◽  
Component Level ◽  
Gear Mesh ◽  
Position Errors ◽  
Unequally Spaced ◽  
Planetary Gear Sets ◽  
Mesh Phasing ◽  
Gear Meshes

Here, a load distribution model of planetary gear sets is presented capable of dealing with planetary gear sets with any component level and gear set level design variations such as component supporting conditions, different kinds of gear modifications and planetary gear sets with different numbers of equally or unequally spaced planets as well as different gear set kinematic configurations while considering gear mesh phasing. It also accounts for classes of planetary gear set manufacturing and assembly related errors associated with the carrier or gears, i.e. pinhole position errors, run-out errors and tooth thickness errors. Example analyses are provided to indicate the need for a model of this type when studying load distribution of planetary gear sets due to unique loading of the gear meshes associated with planetary gear sets. Comparisons to measurements existing in the literature are provided.

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.

An Experimental Study on the Motion Transmission Error of Planetary Gear Sets

2015 ◽  
Author(s):  
B. Boguski ◽  
A. Kahraman
Keyword(s):  
Experimental Study ◽  
Power Flow ◽  
Critical Factor ◽  
Planetary Gear ◽  
Transmission Error ◽  
Ring Gear ◽  
Gear Mesh ◽  
Fixed Ring ◽  
Planetary Gear Sets ◽  
Planet Gear

An experimental study on the overall loaded motion transmission error of planetary gear sets is presented in this study. A test rig is designed and procured for the purpose of measuring the input-to-output transmission error of planetary gear sets within a range of input torque. The test matrix includes three distinct phasing conditions (in phase, sequentially phased and counter-phased) of a four-planet gear set as well as two planet tooth profile modifications. Two different power flow conditions with a fixed planet carrier and a fixed ring gear are considered. The transmission error results indicate that the phasing condition of the gear set is the most critical factor resulting in varying levels and numbers of modulation sidebands around the gear mesh orders. Planetary gear sets having in-phase planet meshes exhibit dominant gear mesh harmonic orders with little sideband activity, while sequentially-phased and counter-phased gear sets show an increase in planetary sideband orders associated with the sun, ring and planet gears. In addition, the power flow condition with fixed carrier is shown to have higher root-mean-square amplitudes of transmission error than configuration with a fixed ring gear.

A Load Distribution Model for Planetary Gear Sets

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Y. Hu ◽  
D. Talbot ◽  
A. Kahraman
Keyword(s):  
Load Distribution ◽  
Planetary Gear ◽  
System Level ◽  
Distribution Model ◽  
Gear Mesh ◽  
Position Errors ◽  
Unequally Spaced ◽  
Planetary Gear Sets ◽  
Mesh Phasing ◽  
Gear Meshes

A load distribution model of planetary gear sets presented is capable of simulating planetary gear sets having component- and system-level design variations such as component supporting conditions, different kinds of gear modifications and planetary gear sets with different numbers of equally or unequally spaced planets as well as different gear set kinematic configurations while considering gear mesh phasing. It also accounts for classes of planetary gear set manufacturing and assembly related errors associated with the carrier or gears, i.e., pinhole position errors, run-out errors, and tooth thickness errors. Example analyses are provided to indicate the need for a model of this type when studying load distribution of planetary gear sets due to unique loading of the gear meshes associated with planetary gear sets. Comparisons to measurements existing in the literature are provided.

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.

Locating Faulty Planet Gears Using External Vibration Measurements

2019 ◽  
Vol 9 (1) ◽  
pp. 14-17
Author(s):  
D Peng ◽  
W A Smith ◽  
R B Randall
Keyword(s):  
Vibration Signal ◽  
Processing Technique ◽  
Operating Conditions ◽  
Internal Vibration ◽  
Signal Processing Technique ◽  
Vibration Measurements ◽  
External Vibration ◽  
Gear Mesh ◽  
Mesh Phasing ◽  
Planet Carrier

In this study, a mesh phasing-based approach is developed to locate the positions of faulty planet gears using external vibration measurements. Previous studies have illustrated how this can be achieved using internal vibration measurements recorded from a sensor placed on the planet carrier. It was shown in these studies that the timing of identifiable fault symptoms in the vibration signal relative to the phase of the gear-mesh component depends on which of the planet gears carries a fault. A signal processing technique is then developed to locate the position of a spalled gear using internal vibration measurements. However, internally mounted sensors are not commonly used in planetary gearboxes and it is much more convenient to mount sensors externally, for example on the gearbox casing. Therefore, this study extends the concept of using mesh phasing relationships to locate faulty planet gears, this time using external vibration measurements. The updated procedure is validated using experimental data collected from a test-rig running under a range of operating conditions. The results show that the updated procedure is able to identify the locations of faulty planet gears so long as an absolute phase reference (for example from a tachometer) of the planet carrier is available.

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.

Harmonic Balance Method for Nonlinear Vibration of Compound Planetary Gear Sets

2015 ◽  
Author(s):  
Weilin Zhu ◽  
Shijing Wu ◽  
Xiaosun Wang
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Planetary Gear ◽  
Response Characteristic ◽  
Transmission Error ◽  
Balance Method ◽  
Time Varying ◽  
Algebraic Equations ◽  
Gear Backlash ◽  
Planetary Gear Sets

In this paper, a new nonlinear time-varying dynamic model for compound planetary gear sets, which incorporates the time-varying meshing stiffness, transmission errors and gear backlash, has been presented. The harmonic balance method (HBM), which is an analytical approach widely used for nonlinear oscillators, is employed to investigate the dynamic characteristics of the gear sets. The matrix form iteration algebraic equations has been established and solved by HBM and single rank inverse Broyden method to reveal the effect of transmission error and gear backlash on the frequency response characteristic of the system. Sub-harmonic resonant, super-harmonic resonant and jump phenomenon have been illustrated by several examples.

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.

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