Effects of Eccentricity on Transmission Errors of Trochoidal Gears

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Hiroyuki Ohta ◽  
Ayumu Yamakawa ◽  
Yoshitake Katayama
Keyword(s):  
Transmission Error ◽  
Experimental Results ◽  
Transmission Errors ◽  
Cam Gear

This article deals with the effects of eccentricity on transmission errors of trochoidal gears (consisting of a roller gear and cam gear). For the tests, three types of roller gears and three types of cam gears (which had different eccentricity) were used. The experimental results showed that the peak to peak values of transmission errors had a tendency to be greater under a larger eccentricity. The measured transmission error waveforms fluctuated with periods 1/fr, 1/fc and 1/zrfr (in which fr and fc are the rotational frequencies of the roller gears and cam gears, while zr is the number of rollers). The peaks with nfr (n = 1, 2, 3, …), nfc, nzrfr, nzrfr ± mfr (m = 1, 2, 3, …) and nzrfr ± mfc appeared in the measured transmission error spectra. The amplitudes of peaks with fr and nzrfr ± mfr increased as er increased, while the amplitudes of peaks with fc and nzrfr ± mfc increased as ec increased. The transmission errors of test gears with eccentricity were estimated by the multibody analysis (MBA). A reasonable correlation exits between the calculated results obtained by the MBA and the measured experimental results.

scholarly journals Computerized Design and Generation of Low-Noise Helical Gears with Modified Surface Topology

1995 ◽  
Vol 117 (2A) ◽  
pp. 254-261 ◽  
Author(s):  
F. L. Litvin ◽  
N. X. Chen ◽  
J. Lu ◽  
R. F. Handschuh
Keyword(s):  
Gear Tooth ◽  
Error Function ◽  
Transmission Error ◽  
Low Noise ◽  
Surface Topology ◽  
Helical Gears ◽  
Transmission Errors ◽  
Bearing Contact ◽  
Pinion Gear ◽  
Tooth Surfaces

An approach for the design and generation of low-noise helical gears with localized bearing contact is proposed. The approach is applied to double circular arc helical gears and modified involute helical gears. The reduction of noise and vibration is achieved by application of a predesigned parabolic function of transmission errors that is able to absorb a discontinuous linear function of transmission errors caused by misalignment. The localization of the bearing contact is achieved by the mismatch of pinion-gear tooth surfaces. Computerized simulation of meshing and contact of the designed gears demonstrated that the proposed approach will produce a pair of gears that has a parabolic transmission error function even when misalignment is present. Numerical examples for illustration of the developed approach are given.

Optimal Machine-Tool Settings for the Manufacture of Face-Hobbed Spiral Bevel Gears

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Vilmos V. Simon
Keyword(s):  
Contact Pressure ◽  
Optimization Problem ◽  
Transmission Error ◽  
Search Method ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Transmission Errors ◽  
Bevel Gears ◽  
Spiral Bevel ◽  
Loaded Tooth Contact Analysis

In this study, an optimization methodology is proposed to systematically define the optimal head-cutter geometry and machine-tool settings to simultaneously minimize the tooth contact pressure and angular displacement error of the driven gear (the transmission error), and to reduce the sensitivity of face-hobbed spiral bevel gears to the misalignments. The proposed optimization procedure relies heavily on the loaded tooth contact analysis for the prediction of tooth contact pressure distribution and transmission errors influenced by the misalignments inherent in the gear pair. The load distribution and transmission error calculation method employed in this study were developed by the author of this paper. The targeted optimization problem is a nonlinear constrained optimization problem, belonging to the framework of nonlinear programming. In addition, the objective function and the constraints are not available analytically, but they are computable, i.e., they exist numerically through the loaded tooth contact analysis. For these reasons, a nonderivative method is selected to solve this particular optimization problem. That is the reason that the core algorithm of the proposed nonlinear programming procedure is based on a direct search method. The Hooke and Jeeves pattern search method is applied. The effectiveness of this optimization was demonstrated on a face-hobbed spiral bevel gear example. Drastic reductions in the maximum tooth contact pressure (62%) and in the transmission errors (70%) were obtained.

On the Correlation Between Dynamic Transmission Error and Dynamic Tooth Loads in Three-Dimensional Gear Systems

2015 ◽  
Author(s):  
Nina Sainte-Marie ◽  
Philippe Velex ◽  
Guillaume Roulois ◽  
Franck Marrot
Keyword(s):  
Experimental Evidence ◽  
Three Dimensional ◽  
Transmission Error ◽  
Test Rig ◽  
Transmission Errors ◽  
Linear Dependency ◽  
Lumped Parameter ◽  
Dynamic Transmission Error ◽  
Time Variations ◽  
The Relationship

A three-dimensional dynamic model is presented to simulate the dynamic behavior of single stage gears by using a combination of classic shaft, lumped parameter and specific 2-node gear elements. The mesh excitation formulation is based on transmission errors whose mathematical grounding is briefly described. The validity of the proposed methodology is assessed by comparison with experimental evidence from a test rig. The model is then employed to analyze the relationship between dynamic transmission errors and dynamic tooth loads or root stresses. It is shown that a linear dependency can be observed between the time variations of dynamic transmission error and tooth loading as long as the system can be assimilated to a torsional system but that this linear relationship tends to disappear when the influence of bending cannot be neglected.

Quality of Service of Data Broadcasting Algorithms on Erroneous Wireless Channels

2011 ◽  
pp. 421-436
Author(s):  
Paolo Barsocchi ◽  
Alan A. Bertossi ◽  
M. Cristina Pinotti ◽  
Francesco Potortì
Keyword(s):  
Quality Of Service ◽  
Polynomial Time ◽  
Wireless Channels ◽  
Transmission Error ◽  
Packet Transmission ◽  
Optimal Solutions ◽  
Bernoulli Model ◽  
Data Scheduling ◽  
Transmission Errors

Broadcasting is an efficient and scalable way of transmitting data over wireless channels to an unlimited number of clients. In this chapter the problem of allocating data to multiple channels is studied, assuming flat data scheduling per channel and the presence of unrecoverable channel transmission errors. The behavior of wireless channels is described by the Bernoulli model, in which each packet transmission has the same probability to fail and each transmission error is independent from the others. The objective is that of minimizing the average expected delay experienced by the clients. Optimal solutions can be found in polynomial time when all data items have unit lengths, while heuristics are presented when data items have non-unit lengths. Extensive simulations, performed on benchmarks whose item popularities follow Zipf distributions, show that good sub-optimal solutions are found.

Dynamic Gear Loads Due to Coupled Lateral, Torsional and Axial Vibrations in a Helical Geared System

1999 ◽  
Vol 121 (2) ◽  
pp. 141-148 ◽  
Author(s):  
S. H. Choi ◽  
J. Glienicke ◽  
D. C. Han ◽  
K. Urlichs
Keyword(s):  
Load Condition ◽  
Coupled System ◽  
Transmission Error ◽  
Lumped Mass ◽  
Mass Model ◽  
Shaft Line ◽  
Transmission Errors ◽  
Lumped Mass Model ◽  
Vibration Problems ◽  
Axial Vibrations

In this paper we investigate the rotordynamics of a geared system with coupled lateral, torsional and axial vibrations, with a view toward understanding the severe vibration problems that occurred on a 28-MW turboset consisting of steam turbine, double helical gear and generator. The new dynamic model of the shaft line was based on the most accurate simulation of the static shaft lines, which are influenced by variable steam forces and load-dependent gear forces. The gear forces determine the static shaft position in the bearing shell. Each speed and load condition results in a new static bending line which defines the boundary condition for the dynamic vibration calculation of the coupled lateral, torsional and axial systems. Rigid disks and distributed springs were used for shaft line modeling. The tooth contact was modeled by distributed springs acting normally on the flank surfaces of both helices. A finite element method with distributed mass was used for lateral and torsional vibrations. It was coupled to a lumped mass model describing the axial vibrations. The forced vibrations due to unbalances and static transmission errors were calculated. The eigenvalue problem was solved by means of a stability analysis showing the special behavior of the coupled system examined. The calculation was successfully applied, and the source of the vibration problem could be located as being a gear-related transmission error. Several redesign proposals lead to a reliable and satisfactory vibrational behavior of the turboset.

High-Speed Serial Data Transmission Error Control Based on Fuzzy Classification

2018 ◽  
Vol 22 (7) ◽  
pp. 1077-1081
Author(s):  
Zhimin Zhang ◽  
Keyword(s):  
Energy Consumption ◽  
Packet Loss ◽  
Data Transmission ◽  
High Speed ◽  
Error Control ◽  
Transmission Error ◽  
Fuzzy Classification ◽  
Control Data ◽  
Transmission Errors ◽  
Serial Data

At present, the error control method for high-speed serial data transmission obtains the errors by comparison and then controls them. If the data transmission channel is not denoised, the packet loss and error codes become serious, and energy consumption increases. The use of fuzzy classification is proposed to control data transmission errors. The method uses the combination of wavelet transform and transform domain difference to double denoise the channel, and it completes the clustering of data transmission errors by fuzzy classification. Considering packet loss, error codes, and energy consumption in data transmission error control, when the communication distance between two nodes is small, automatic repeat request is used to control data transmission errors. As the distance between nodes increases, forward error correction is used to control data transmission errors. When the communication distance gradually increases, data transmission errors are controlled by hybrid automatic repeat request. Experiments showed that the proposed method can reduce the data transmission error, control energy consumption, packet loss rate, and bit error rate, and enhance the denoising effect.

Experimental Validation of a Dynamic Numerical Model for Timing Belt Drives Behavior Simulation

2000 ◽  
Author(s):  
Lionel Manin ◽  
Daniel Play ◽  
Patrick Soleilhac
Keyword(s):  
Numerical Model ◽  
Dynamic Behavior ◽  
Operation Time ◽  
Transmission Error ◽  
Numerical Results ◽  
Experimental Results ◽  
Medium Size ◽  
Behavior Simulation ◽  
Dynamic Transmission Error ◽  
Timing Belt

Abstract The behavior of timing belts used in automotive applications have to be defined and predicted at the preliminary design phases. Numerical simulations replace progressively experimental determinations that are time and money consuming. The object of the work was to qualify from experimental results a timing belt drive numerical model. The model simulates the dynamic behavior versus time of any kind of tooth belt power transmissions. The model architecture, originalities and capabilities have been already presented, and the purpose is now to compare in details numerical and experimental results. The experimental qualification has been carried out on a laboratory test bench with a medium size engine valve controlled distribution made of 3 pulleys and a tensioner. Tensions, camshaft torque, pulleys speeds and angular acylisms, dynamic transmission error between camshaft and crankshaft pulleys have been measured. Numerous tests have been made for different running conditions by changing : speed, angular acyclism, camshaft torque, setting tension. Several phenomena and influence of parameters have been identified, as the pulley eccentricity effect on camshaft torque, span tensions, and transmission error. Part of the experimental results are used as entries of the model : camshaft torque, crankshaft instantaneous speed, transmission error due to pulley eccentricities. Further, comparisons with the numerical results were made. Experimental and numerical results of tension, angular acyclism, dynamic transmission error, versus operation time are compared for the different tests performed. The agreement is good and shows that the model developed allows to simulate dynamic behavior of timing belt with high degree of confidence.

Transmission Error in Synchronous Belt With Resonance Under Installation Tension

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Masanori Kagotani ◽  
Hiroyuki Ueda
Keyword(s):  
Transmission Error ◽  
Speed Ratio ◽  
Experimental Transmission ◽  
Transmission Errors ◽  
Belt Drives ◽  
Concave Shape ◽  
Mode Vibration ◽  
The Difference ◽  
The Moment ◽  
Good Agreement

Synchronous belt drives generate resonance on the belt spans between the driving and driven pulleys when the transverse natural frequency of the belt, matches the meshing frequency of the belt tooth and the pulley tooth. The resonance of the belt spans affects the accuracy of rotation transmission. In the present study, the mechanisms generating the transmission error in synchronous belt drives under installation tension and a pulley speed ratio of 1:1 are investigated theoretically and experimentally for the case in which the belt spans generate first mode vibration due to resonance. In addition, the change in the shaft load caused by resonance is examined. The calculated and experimental transmission errors show good agreement, and so the validity of our analysis is confirmed. Transmission error is generated by the difference in displacement between the upper and lower belt spans due to the convex or concave shape, the difference in the amount of belt climbing at the beginning and end of meshing, and the generation of torque due to the moment of inertia on the driven side. The transmission error has a period of 1/2 of one pitch of the pulley, and the generated change in the shaft load, which is the sum of the displacement due to the convex or concave shape of the upper and lower spans and the sum of the belt climbing at the beginning and end of meshing, has a period of one pitch of the pulley.

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