Partial Meshing of Synchronous Belt Teeth

2007 ◽  
Author(s):  
Tomas Johannesson
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
Power Transmission ◽  
Transmission Error ◽  
Distribution Model ◽  
Velocity Difference ◽  
Line Segments ◽  
Tooth Stiffness ◽  
Overlap Area ◽  
Difference Effect

Synchronous belts have been used in power transmissions where synchronization is also needed since the 1940’s. In the 1960’s overhead camshaft engines were introduced and synchronous belts were used as cam belts. This made way for a new standard for belts: improvements were made in materials and profile geometry. These new belts had lower noise emissions and, at the same time, greater durability. Often, both wear and noise are generated when a belt tooth seats or unseats a pulley. A tooth is considered to be fully meshed when the whole belt pitch forms a circular arc. This is not the case for teeth in partial mesh, which occurs in seating and unseating zones. In these zones force peaks are often present. These peaks are believed to arise mainly as a result of two phenomena: one is the overlap effect due to the belt geometry not fitting the pulley, and other is the velocity difference effect. The latter is speed-dependent while the former depends on the belt and pulley profile geometries and the belt teeth positions relative to the pulley. Although force peaks of high magnitude occur, they are present at a such small part of the engagement that their contribution to power transmission can be neglected. This indicates that the positions of the belt pitches relative to the pulley pitches can be established by the load distribution from fully meshed conditions. Although the characteristics of partial mesh teeth have been improved by the introduction of new profiles and materials, problems of durability, noise and transmission error, arising from partially meshed teeth, are still present. Therefore it is important to study belt mechanics in seating and unseating zones. This paper describes a method to calculate force peakson seating and unseating. An overlap area (geometrical interference) is formed by giving belt teeth profiles displacement and checking for interference with the pulley profile. Since it is assumed that the seating and unseating force peaks do not influence the load distribution, the positions of the first and last teeth are superimposed on belt teeth profiles using the results from a quasi-static load distribution model covering fully meshed conditions. The superimposed first and last belt teeth profiles are modelled by line segments. A pulley profile is also modelled by line segments and the profiles are checked for interference. Where interference occur an overlap area is formed. The overlap is translated to a force value via correlation with belt tooth force measurements. Results from the model show good agreement with measurements when force peaks are small. This is due to the fact that the quasi-static load distribution model produces correct belt displacements for these cases. For measured force peaks of higher amplitude the seating and unseating effects are under estimated by the method. The semicircular belt geometry in combination with the hyperelastic nature of the elastomer is probably the reason. A solution is to implement a non-linear force-overlap relation. Another effect not included is the velocity difference effect. The results are sensitive to belt tooth height and radial tooth stiffness.

Low Order Static Load Distribution Model for Ball Screw Mechanisms Including Effects of Lateral Deformation and Geometric Errors

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Bo Lin ◽  
Chinedum E. Okwudire ◽  
Jason S. Wou
Keyword(s):  
Load Distribution ◽  
Static Load ◽  
High Order ◽  
Contact Model ◽  
Ball Screw ◽  
Distribution Model ◽  
Computational Time ◽  
Geometric Errors ◽  
Lateral Deformation ◽  
Low Order

Accurate modeling of static load distribution of balls is very useful for proper design and sizing of ball screw mechanisms (BSMs); it is also a starting point in modeling the dynamics, e.g., friction behavior, of BSMs. Often, it is preferable to determine load distribution using low order models, as opposed to computationally unwieldy high order finite element (FE) models. However, existing low order static load distribution models for BSMs are inaccurate because they ignore the lateral (bending) deformations of screw/nut and do not adequately consider geometric errors, both of which significantly influence load distribution. This paper presents a low order static load distribution model for BSMs that incorporates lateral deformation and geometric error effects. The ball and groove surfaces of BSMs, including geometric errors, are described mathematically and used to establish a ball-to-groove contact model based on Hertzian contact theory. Effects of axial, torsional, and lateral deformations are incorporated into the contact model by representing the nut as a rigid body and the screw as beam FEs connected by a newly derived ball stiffness matrix which considers geometric errors. Benchmarked against a high order FE model in case studies, the proposed model is shown to be accurate in predicting static load distribution, while requiring much less computational time. Its ease-of-use and versatility for evaluating effects of sundry geometric errors, e.g., pitch errors and ball diameter variation, on static load distribution are also demonstrated. It is thus suitable for parametric studies and optimal design of BSMs.

Recent Progress and Prospect on Tooth Modification of Involute Cylindrical Gear

2021 ◽  
Vol 14 ◽  
Author(s):  
Lin Han ◽  
Yang Qi
Keyword(s):  
Load Distribution ◽  
Power Transmission ◽  
Gear Tooth ◽  
Transmission Error ◽  
Gear Pair ◽  
Cylindrical Gear ◽  
Tooth Width ◽  
Modification Method ◽  
Power Transmission Systems ◽  
Tooth Modification

Background: Recent reviews on tooth modification of involute cylindrical gear are presented. Gear pairs are widely employed in motion and power transmission systems. Manufacturing and assembling errors of gear parts, time-varying mesh stiffness and transmission error of gear pair, usually induce vibration, noise, non-uniformly load distribution and stress concentration, resulting in earlier failure of gear. Tooth modification is regarded as one of the most popular ways to suppress vibration, reduce noise level, and improve load distribution of gear pairs. Objective: To provide an overview of recent research and patents on tooth modification method and technology. Methods: This article reviews related research and patents on tooth modification. The modification method, evaluation, optimization and machining technology are introduced. Results: Three types of modifications are compared and analyzed, and influences of each on both static and dynamic performances of gear pair are concluded. By summarizing a number of patents and research about tooth modification of cylindrical gears, the current and future development of research and patent are also discussed. Conclusion: Tooth modification is classified into tip or root relief along tooth profile, lead crown modification along tooth width and compound modification. Each could be applied in different ways. In view of design, optimization under given working condition to get optimal modification parameters is more practical. Machining technology and device for modified gear is a key to get high quality performance of geared transmission. More patents on tooth modification should be invented in future.

An Experimental and Theoretical Study of Quasi-Static Behavior of Double-Helical Gear Sets

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
M.R. Kang ◽  
A. Kahraman
Keyword(s):  
Load Distribution ◽  
Theoretical Study ◽  
Power Transmission ◽  
Transmission Error ◽  
Helical Gear ◽  
Static Behavior ◽  
World Congress ◽  
Helical Gears ◽  
Support Conditions ◽  
Stagger Angle

Abstract The quasi-static behaviors of a double-helical gear pair is investigated both experimentally and theoretically with the main focus on the influence of the key design and manufacturing parameters associated with double-helical gears, including nominal right-to-left stagger angle, the stagger angle deviation (error) from the nominal stagger angle, and axial gear supporting conditions. On the experimental side, a double-helical gear test setup proposed earlier (Kang, M. R., and Kahraman, A., 2015, “An Experimental and Theoretical Study of Dynamic Behavior of Double-Helical Gear Sets,” J. Sound Vib., 350, pp. 11–29). for studying dynamics of the same system is employed that allows adjustable right-to-left stagger angles, intentional stagger errors, and axial support conditions. Specific measurement systems are developed and implemented simultaneously to measure the static motion transmission error and axial motions of the gears under low-speed conditions, as well as gear root strains to determine right-to-left load-sharing factors. A test matrix that covers wide ranges of stagger angles, intentional stagger error, and axial support conditions is executed within a range of torque transmitted to establish an extensive database. On the modeling side, the measured quasi-static behavior of double-helical gear pairs is simulated by using an existing quasi-static double-helical load distribution model (Thomas, J., and Houser, D. R., 1992, “A Procedure for Predicting the Load Distribution and Transmission Error Characteristics of Double Helical Gears,” World Congress-Gear and Power Transmission, The 3rd World Congress—Gear and Power Transmission, Paris.). Direct comparison of the measurements and predictions of loaded static transmission error, axial play, root stresses, and right-to-left load-sharing factors are used to validate the quasi-static model as well as describing the measured behavior.

Log-Compound-Poisson Distribution Model of Intermittency in Turbulence

1998 ◽  
Vol 53 (10-11) ◽  
pp. 828-832
Author(s):  
Feng Quing-Zeng
Keyword(s):  
Energy Dissipation ◽  
Poisson Distribution ◽  
Turbulent Energy ◽  
Compound Poisson Distribution ◽  
Distribution Model ◽  
Velocity Difference ◽  
Scaling Exponents ◽  
Compound Poisson ◽  
Developed Turbulence ◽  
Experimental Values

Abstract The log-compound-Poisson distribution for the breakdown coefficients of turbulent energy dissipation is proposed, and the scaling exponents for the velocity difference moments in fully developed turbulence are obtained, which agree well with experimental values up to measurable orders. The under-lying physics of this model is directly related to the burst phenomenon in turbulence, and a detailed discussion is given in the last section.

Gear transmission error outside the normal path of contact due to corner and top contact

1999 ◽  
Vol 213 (4) ◽  
pp. 389-400 ◽  
Author(s):  
R. G. Munro ◽  
L Morrish ◽  
D Palmer
Keyword(s):  
Dynamic Test ◽  
Theoretical Models ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Transmission ◽  
The Novel ◽  
Transmission Systems ◽  
Helical Gears ◽  
Tooth Stiffness ◽  
Top Contact

This paper is devoted to a phenomenon known as corner contact, or contact outside the normal path of contact, which can occur in spur and helical gear transmission systems under certain conditions. In this case, a change in position of the driven gear with respect to its theoretical position takes place, thus inducing a transmission error referred to here as the transmission error outside the normal path of contact (TEo.p.c). The paper deals with spur gears only, but the results are directly applicable to helical gears. It systematizes previous knowledge on this subject, suggests some further developments of the theory and introduces the novel phenomenon of top contact. The theoretical results are compared with experimental measurements using a single flank tester and a back-to-back dynamic test rig for spur and helical gears, and they are in good agreement. Convenient approximate equations for calculation of TEo.p.c suggested here are important for analysis of experimental data collected in the form of Harris maps. This will make possible the calculation of tooth stiffness values needed for use in theoretical models for spur and helical gear transmission systems.

Investigation of Noise Features of Planetary Gear Trains Based on Human Aural Characteristic

2017 ◽  
Author(s):  
Masao Nakagawa ◽  
Dai Nishida ◽  
Deepak Sah ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Gear Tooth ◽  
Structural Complexity ◽  
Planetary Gear ◽  
Transmission Error ◽  
Sound Level ◽  
Tooth Surface ◽  
Surface Error ◽  
Planetary Gear Trains ◽  
Tooth Stiffness ◽  
Gear Trains

Planetary gear trains (PGTs) are widely used in various machines owing to their many advantages. However, they suffer from problems of noise and vibration due to the structural complexity and giving rise to substantial noise, vibration, and harshness with respect to both structures and human users. In this report, the sound level from PGTs is measured in an anechoic chamber based on human aural characteristic, and basic features of sound are investigated. Gear noise is generated by the vibration force due to varying gear tooth stiffness and the vibration force due to tooth surface error, or transmission error (TE). Dynamic TE is considered to be increased because of internal and external meshing. The vibration force due to tooth surface error can be ignored owing to almost perfect tooth surface. A vibration force due to varying tooth stiffness could be a major factor.

A Comparison of Analytical Predictions With Experimental Measurements of Transmission Error of Misaligned Loaded Gears

1992 ◽  
Author(s):  
Harsh Vinayak ◽  
Donald R. Houser
Keyword(s):  
Experimental Data ◽  
Load Distribution ◽  
Theoretical Calculations ◽  
Data Acquisition System ◽  
Transmission Error ◽  
Test Facility ◽  
Experimental Measurements ◽  
Gear Pair ◽  
Prediction Program ◽  
Dynamic Transmission Error

Abstract This paper deals with the experimental study of dynamic transmission error of a gear pair. Two aspects of the experiment are discussed : 1) design of the test facility and data acquisition system and 2) comparison of transmission error and load distribution with experimental data. Several gears were tested under varying misalignments. A prediction program LDP (Load distribution Program) was used for theoretical calculations of dynamic transmission error.

Vibration-Based Early Crack Diagnosis With Machine Learning for Spur Gears

2020 ◽  
Author(s):  
Fatih Karpat ◽  
Ahmet Emir Dirik ◽  
Onur Can Kalay ◽  
Oğuz Doğan ◽  
Burak Korcuklu
Keyword(s):  
Machine Learning ◽  
Fault Diagnosis ◽  
High Speed ◽  
Crack Detection ◽  
Power Transmission ◽  
Calculated Data ◽  
Design Parameters ◽  
Tooth Stiffness ◽  
Vibration Responses ◽  
Root Crack

Abstract Gear mechanisms are one of the most significant components of the power transmission systems. Due to increasing emphasis on the high-speed, longer working life, high torques, etc. cracks may be observed on the gear surface. Recently, Machine Learning (ML) algorithms have started to be used frequently in fault diagnosis with developing technology. The aim of this study is to determine the gear root crack and its degree with vibration-based diagnostics approach using ML algorithms. To perform early crack detection, the single tooth stiffness and the mesh stiffness calculated via ANSYS for both healthy and faulty (25-50-75-100%) teeth. The calculated data transferred to the 6-DOF dynamic model of a one-stage gearbox, and vibration responses was collected. The data gathered for healthy and faulty cases were evaluated for the feature extraction with five statistical indicators. Besides, white Gaussian noise was added to the data obtained from the 6-DOF model, and it was aimed at early fault diagnosis and condition monitoring with ML algorithms. In this study, the gear root crack and its degree analyzed for both healthy and four different crack sizes (25%-50%-75%-100%) for the gear crack detection. Thereby, a method was presented for early fault diagnosis without the need for a big experimental dataset. The proposed vibration-based approach can eliminate the high test rig construction costs and can potentially be used for the evaluation of different working conditions and gear design parameters. Therefore, catastrophic failures can be prevented, and maintenance costs can be optimized by early crack detection.

scholarly journals The Cold Rolling Load Distribution of the Nuclear Power Zirconium Alloy Based on the Self-adaptive Particle Swarm Optimization Algorithm

2021 ◽  
Author(s):  
Cao Yuan ◽  
Jianguo Cao ◽  
Wang Tao ◽  
Wang Leilei ◽  
Li Fang ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Cold Rolling ◽  
Optimization Algorithm ◽  
Load Distribution ◽  
Zirconium Alloy ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Rolling Process ◽  
Distribution Model ◽  
Swarm Optimization

Abstract Aiming at the problem of load distribution during multi-pass cold rolling of nuclear zirconium alloy strip, the load distribution model with good shape is established by the self-adaptive particle swarm optimization algorithm (SAPSO), considering the main constraint conditions including rolling force, reduction and torque in cold rolling process. Based on the penalty function method transforming the constraint problem into the unconstrained problem, the particle swarm optimization algorithm with adaptive inertia weight factor optimized the load distribution model is developed to improve the local search ability of the particle swarm optimization algorithm. Compared with the existing nuclear zirconium alloy industrial schedule, the simulation results of load distribution based on the SAPSO can keep good shape in multi-pass cold rolling process with the high prediction accuracy. The industrial experiments demonstrate that the proportional crown difference value is consistent, the plate shape flatness is good.

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