The Role of the Discrete Fourier Transform in the Contribution to Gear Transmission Error Spectra from Tooth-Spacing Errors

1987 ◽  
Vol 201 (3) ◽  
pp. 227-229 ◽  
Author(s):  
W D Mark
Keyword(s):  
Fourier Transform ◽  
Fourier Series ◽  
Error Analysis ◽  
Discrete Fourier Transform ◽  
Transmission Error ◽  
Spur Gear ◽  
Contact Ratio ◽  
Elastic Deformations ◽  
Exact Agreement

An expression is derived for the Fourier series spectrum of the transmission error arising from tooth-spacing errors on a single spur gear meshing with a perfect involute mating gear for the case of a contact ratio of unity and no elastic deformations present. This expression is found to be in exact agreement with previously derived results. The expression illustrates the role of the discrete Fourier transform in transmission error analysis and interpretation.

scholarly journals Analysis on Meshing Characteristics and Transmission Error of Elliptic Gears

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Changbin Dong ◽  
Yongping Liu ◽  
Yongqiao Wei ◽  
Beibei Yun ◽  
Dawei Li ◽  
...  
Keyword(s):  
Great Influence ◽  
Transmission Error ◽  
Spur Gear ◽  
Analysis Model ◽  
Contact Ratio ◽  
Cylindrical Gear ◽  
Pressure Angle ◽  
Object Based ◽  
Meshing Characteristics ◽  
Eccentricity Error

As an important parameter to distinguish noncircular gear from cylindrical gear, eccentricity is very important for the meshing characteristics and transmission error of noncircular gear. In order to study the transmission characteristics of the elliptic gear, a pair of elliptic gear in the reversing device of a new type of drum pumping was taken as the research object. Based on the analysis of the transmission pressure angle and instantaneous contact ratio of the elliptic gear, the eccentricity error was introduced into the analysis model of transmission error. The influences of the eccentricity on the transmission pressure angle, instantaneous contact ratio, and transmission error were analyzed, and the analysis accuracy is verified by the finite element method. The results show that the eccentricity has a great influence on the transmission pressure angle, instantaneous contact ratio, and transmission error of the elliptic gear, and the eccentricity error has a significant influence on the transmission error. In order to ensure the normal meshing condition of the elliptic gear, the eccentricity should be less than 0.7071, and the maximum instantaneous contact ratio is 1.809. The research results can provide some guidance for the following noncircular spur gear transmission test and transmission error research.

Comments on Errors of DFT Spectrum

2014 ◽  
Vol 568-570 ◽  
pp. 189-192
Author(s):  
Feng Han ◽  
Yao Lin Liu ◽  
Zhen Liu ◽  
Hai Dong Zeng
Keyword(s):  
Fourier Transform ◽  
Error Analysis ◽  
Energy Loss ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis ◽  
Analytical Error ◽  
Error Estimators ◽  
Asynchronous Sampling ◽  
Parseval’S Theorem ◽  
Further Development

Discrete Fourier transform (DFT/FFT) spectrums contain a variety of inherent errors in asynchronous sampling. Spectrum analysis with the accuracy above 10-3 are generally challenging issues. This work divides the DFT procedure into four signal transforms and exams six spectrum errors originated from these distortions. Besides the review of traditional errors, a so-called energy loss-gain (ELG) error is briefly introduced, which is proved to be a considerable error on the basis of Parseval's theorem. With the help of full error analysis mentioned here and the further development of analytical error estimators, it is expectable to obtain a DFT spectrum with a specified accuracy.

Further Evaluation of Spur Gear Tooth Profile Designs Used in Heavily Loaded Transmissions

2011 ◽  
Author(s):  
Nihat Yıldırım ◽  
Hakan I˙s¸c¸i ◽  
Abdullah Akpolat
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Tooth Profile ◽  
Design Parameters ◽  
Preference Order ◽  
Spur Gears ◽  
Tooth Root ◽  
Contact Ratio ◽  
Practical Applications

Aerospace applications require special procedures for component design and manufacturing. Spur gears of different designs, because of their simpler geometries, are used in vital units-transmissions of helicopters and alike aerospace vehicles. In this study, performances of various profile designs of previously researched low and high contact ratio spur gears with some realistic design parameters are studied. Effects of the realistic parameters of variable tooth pair stiffness, relief shape, and adjacent pitch error on Transmission Error (TE), tooth loads and root stresses are presented; composition of these parameters determines the efficiency of the gearbox assembly. Detail of minimization of tooth root stress through optimized/proper design of relief is described. More comprehensive comparison of the gear tooth profile design cases is done to be able to guide aerospace transmission designers for practical applications with realistic parameters for each of the design cases. A preference order is done among the design cases, depending on effect of some design parameters on the results such as tooth loads, tooth root stresses, TE curves and peak-to-peak TE values.

Effect of Involute Contact Ratio on Spur Gear Dynamics

1999 ◽  
Vol 121 (1) ◽  
pp. 112-118 ◽  
Author(s):  
A. Kahraman ◽  
G. W. Blankenship
Keyword(s):  
Transmission Error ◽  
Spur Gear ◽  
Design Guidelines ◽  
Forced Response ◽  
Contact Ratio ◽  
Test Rig ◽  
Response Curves ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
Selection Of

The influence of involute contact ratio on the torsional vibration behavior of a spur gear pair is investigated experimentally by measuring the dynamic transmission error of several gear pairs using a specially designed gear test rig. Measured forced response curves are presented, and harmonic amplitudes of dynamic transmission error are compared above and below gear mesh resonances for both unmodified and modified gears having various involute contact ratio values. The influence of involute contact ratio on dynamic transmission error is quantified and a set of generalized, experimentally validated design guidelines for the proper selection of involute contact ratio to achieve quite gear systems is presented. A simplified analytical model is also proposed which accurately describes the effects of involute contact ratio on dynamic transmission error.

scholarly journals Determining the Weights of A Fourier Series Neural Network on the Basis of the Multidimensional Discrete Fourier Transform

2008 ◽  
Vol 18 (3) ◽  
pp. 369-375 ◽  
Author(s):  
Krzysztof Halawa
Keyword(s):  
Neural Network ◽  
Fourier Transform ◽  
Fourier Series ◽  
Computational Complexity ◽  
Discrete Fourier Transform ◽  
Dynamic Systems ◽  
Low Computational Complexity

Determining the Weights of A Fourier Series Neural Network on the Basis of the Multidimensional Discrete Fourier TransformThis paper presents a method for training a Fourier series neural network on the basis of the multidimensional discrete Fourier transform. The proposed method is characterized by low computational complexity. The article shows how the method can be used for modelling dynamic systems.

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