scholarly journals Statistical Analysis for Transmission Error of Gear System with Mechanical and Thermal Deformation Uncertainties

2021 ◽  
Vol 11 (14) ◽  
pp. 6582
Author(s):  
Joon-Ho Lee ◽  
Hee-Sun Choi ◽  
Jong-Hyeon Sohn ◽  
Geun-Ho Lee ◽  
Dong-Il Park ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Thermal Deformation ◽  
Gear Tooth ◽  
Transmission Error ◽  
Spur Gear ◽  
Geometric Error ◽  
Tooth Contact Analysis ◽  
System Uncertainties ◽  
Plastic Gears ◽  
The Impact

We establish a robust algorithm to analyze the influence of system uncertainties on the transmission error of a spur gear pair under 2D simplification. The algorithm provides a way of generating smooth cutter profiles with machining uncertainties and measuring the thermal deformation through the uncertainties in material properties. Then, it produces realizations of gear tooth profiles based on the analytical method for accuracy and computational efficiency. Numerical investigations show the statistical analysis on the tooth contact analysis by comparing steel and plastic gears. It is worthwhile remarking that the plastic gear is susceptible to the geometric error caused by thermal deformation. Moreover, although the impact of thermal deformation on steel gear may seem slim, it can have a noticeable influence when it exists with mechanical uncertainties together.

scholarly journals An Experimental Investigation of the Impact of Random Spacing Errors on the Dynamic Transmission Error of Spur Gear Pairs

2019 ◽  
Author(s):  
Muhammad Nevin Anandika ◽  
Ahmet Kahraman ◽  
David Talbot
Keyword(s):  
Frequency Spectrum ◽  
Gear Tooth ◽  
Random Sequence ◽  
Transmission Error ◽  
Spur Gear ◽  
Engineering Industry ◽  
Gear Pair ◽  
Gear Mesh ◽  
Dynamic Transmission Error ◽  
The Impact

Abstract Noise and vibration performance of a gear system is critical in any engineering industry. Excessive vibrational amplitudes originated by the excitations at the gear meshes propagate to the transmission housing to cause noticeable noise, while also increasing gear tooth stresses to degrade durability. As such, gear designers must generate designs that are nominally quiet with low-vibration amplitudes. This implies a gear pair fabricated exactly to the specifications of its blue print will be acceptable for its vibration behavior. Achieving this, however, is not sufficient. As the manufacturing of gears require them to be subject to bands of tolerances afforded by the manufacturing processes employed, the designers must be concerned about variations to the performance of their presumably quite baseline designs within these tolerance bands. This research aims at demonstrating how one type of manufacturing error, random tooth spacing errors, alter the vibratory behavior of a spur gear pair. Two pairs of spur gears are tested for their dynamic transmission error performance. One gear pair with no tooth spacing errors form the baseline. The second gear pair contain an intentionally induced random sequence of spacing errors. The forced vibration responses of both gear pairs are compared within wide ranges of speed and torque. This comparison shows that there is a clear and significant impact of random spacing errors on spur gear dynamics, measurable through examination of their respective transmission error signatures. In the off-resonance regions of speed, vibration amplitudes of the random error pair are higher than the no-error baseline spur gear pair. Meanwhile, at or near resonance peaks, the presence of random spacing errors tends to lower the peak amplitudes slightly as compared to the no-error baseline spur gear pair. The presence of random spacing errors introduces substantial harmonic content that are non-mesh harmonics. This results in a broadband frequency spectrum in addition to an otherwise well-defined frequency spectrum with gear-mesh order components, pointing to an additional concern of noise quality.

scholarly journals Meshing characteristics of a sphere–face gear pair with variable shaft angle

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985951 ◽  
Author(s):  
Lei Liu ◽  
Jinzhao Zhang
Keyword(s):  
Gear Tooth ◽  
Transmission Error ◽  
Tooth Surface ◽  
Gear Pair ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Contact Points ◽  
Shaft Angle ◽  
Meshing Characteristics ◽  
Curvature Interference

This article presents a sphere–face gear pair by substituting the convex spherical gear for the pinion of a conventional face gear pair. The sphere–face gear pair not only maintains the advantages of the face gear pair with a longitudinally modified pinion but also allows variable shaft angles or large axial misalignments. Meshing characteristics of the proposed gear pair are studied in this article. The mathematical models of the sphere–face gear pair are derived based on machining principles. The tooth contact analysis (TCA) and curvature interference check are conducted for the sphere–face gear pair with variable shaft angles. The loaded TCA is also implemented utilizing the finite element method. The results of numerical examples show that proposed gear pair has the following features. Geometrical transmission error of constant shaft angle or varying shaft angle is zero; contact points of the sphere–face gear set with variable shaft angle are located near the centre region of face gear tooth surface; there is no curvature interference in meshing; and transmission continuity of the gear pair can be guaranteed in meshing.

Tooth Contact Analysis of Planetary Gear Trains with Equally Spaced Planets

2010 ◽  
Vol 43 ◽  
pp. 279-282
Author(s):  
Kai Xu ◽  
Xiao Zhong Deng ◽  
Jian Jun Yang ◽  
Guan Qiang Dong
Keyword(s):  
Planetary Gear ◽  
Transmission Error ◽  
Spur Gear ◽  
Contact Analysis ◽  
Gear Train ◽  
Tooth Contact Analysis ◽  
Planetary Gear Train ◽  
Tooth Contact ◽  
Gear Trains ◽  
Equal Space

Based on Tooth Contact Analysis (TCA), a feasible approach for Transmission Error (TE) of planetary gear train is proposed in this paper. With a view to getting the total TE curve of the planetary gear train, a specific analysis of the TE from the planetary gear train with only one planet should be proceed firstly, the second step is to calculate each phase difference of planets in the gear train. The applicable conditions for the simplified calculation are spur gear or involute gear pairs in the gear train. Due to equal space between them, planets have the same phase angle.

Tooth Contact Analysis of Longitudinal Cycloidal-Crowned Helical Gears With Circular Arc Teeth

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Wei-Shiang Wang ◽  
Zhang-Hua Fong
Keyword(s):  
Gear Tooth ◽  
Longitudinal Direction ◽  
Transmission Error ◽  
Helical Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Circular Arc ◽  
Tooth Flank ◽  
Assembly Error

This paper proposes a new type of double-crowned helical gear that can be continuously cut on a modern Cartesian-type hypoid generator with two face-hobbing head cutters and circular-arc cutter blades. The gear tooth flank is double crowned with a cycloidal curve in the longitudinal direction and a circular arc in the profile direction. To gauge the sensitivity of the transmission errors and contact patterns resulting from various assembly errors, this paper applies a tooth contact analysis technique and presents several numerical examples that show the benefit of the proposed double-crowned helical gear set. In contrast to a conventional helical involute gear, the tooth bearing and transmission error of the proposed gear set are both controllable and insensitive to gear-set assembly error.

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.

scholarly journals Bifurcation and Chaos Analysis of the Spur Gear Transmission System for One-Way Clutch, Two-Shaft Assembly

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Zhihui Liu ◽  
Hongzhi Yan ◽  
Yuming Cao ◽  
Yuqing Lai
Keyword(s):  
Excitation Frequency ◽  
Transmission Error ◽  
Spur Gear ◽  
Transmission System ◽  
Gear Transmission ◽  
Torsional Stiffness ◽  
System Response ◽  
Gear Mesh ◽  
Gear Transmission System ◽  
The Impact

A four-degree-of-freedom nonlinear transverse and torsional vibration model of spur gear transmission system for one-way clutch, two-shaft assembly was developed, in which the one-way clutch was modeled as a piecewise nonlinear spring with discontinuous stiffness, considering the factors such as the time-varying gear mesh stiffness, static transmission error, and nonlinearity backlash. With the help of bifurcation diagrams, time domain response diagrams, phase plane diagrams, and Poincaré maps, the effects of the excitation frequency and the torsional stiffness of one-way clutch on the dynamic behavior of gear transmission system for one-way clutch, two-shaft assembly are investigated in detail by using Runge-Kutta method. Numerical results reveal that the system response involves period-1 motion, multiperiodic motion, bifurcation, and chaotic motion. Large torsional stiffness of one-way clutch can increase the impact and lead to instability in the system. The results can present a useful source of reference for technicians and engineers for dynamic design and vibration control of such system.

The Stress Analysis on Spur Gear Meshing Simulation

2013 ◽  
Vol 392 ◽  
pp. 151-155
Author(s):  
Zheng Li ◽  
Yang Chen
Keyword(s):  
Gear Tooth ◽  
Nonlinear Behavior ◽  
Element Model ◽  
Spur Gear ◽  
Contact Analysis ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Reliable Model ◽  
Nonlinear Behaviors ◽  
Meshing Process

The gear meshing is a very complicated process due to the nonlinear behaviors during the teeth contact. It is necessary to build a reliable model to simulate gear meshing process which can consider geometry and boundary conditions nonlinear behavior in gear tooth contact analysis. This paper propose a 3D finite element model to simulate the meshing process of a pair of spur gears, and then carry out the gear tooth contact analysis with the consideration of nonlinear behaviors. The results and relevant discussions will indicate and explain some significant phenomena of the gear tooth contact characteristics in gear meshing process.

A Numerical FEM Solution of Gear Root Stress in Offset Axial Mesh Misalignment

2013 ◽  
Vol 393 ◽  
pp. 375-380 ◽  
Author(s):  
Mohd Rizal Lias ◽  
Mokhtar Awang ◽  
T.V.V.L.N. Rao
Keyword(s):  
Stress Distribution ◽  
Critical Path ◽  
Gear Tooth ◽  
Contact Region ◽  
Moving Load ◽  
Spur Gear ◽  
Load Factor ◽  
Tooth Root ◽  
Load Model ◽  
The Impact

Gear offsets mesh in axial misalignment always leads to unevenness of load transferred contributing the impact of stress value and distribution along important critical path of the tooth root. Its happening due to overpress fitting when the gear is mounted onto the shaft as an interference hub fit. Current design methodology based on empirical model provide solution by approximation load factor fail to attributes in detailed regarding this phenomenon This paper determined to focus on this phenomenon in term of methodology to the stress distribution at the critical contact region of the tooth root of the gears. Pair of spur gear with real geometrical construction and condition was constructed with offset parameter. A moving load quasi-static model with a numerical FEM solution using ANSYS is presented with modification in loading variation. For verification, the stress value at the critical path of the tooth root is compared between standard high point single tooth contacts (HPSTC) loading to moving load model. As the result, a numerical FEM methodology to calculate the stress distribution of the gear tooth root in offset axial misalignment with moving load model approach is determined. The proposed method is also found reliable as an alternative solution to define an accurate load factor calculation compared to the approximation provided by the standard empirical procedure.

A Fast Finite Element Based Methodology to Predict the Temperature Field in a Thermoplastic Spur Gear Drive

2017 ◽  
Author(s):  
V. Roda-Casanova ◽  
F. Sanchez-Marin ◽  
A. Porras-Vazquez
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Mechanical Response ◽  
Error Function ◽  
Transmission Error ◽  
Spur Gear ◽  
Temperature Variations ◽  
Gear Teeth ◽  
Gear Drives ◽  
Plastic Gears

Plastic gears bring some interesting advantages compared to metal gears. However, they also have some drawbacks, many of them related to the dependency of their mechanical properties with the temperature. Among other reasons, the friction between the gear teeth causes a heat flux that heats the gears and produces temperature variations within the gear geometries. These temperature variations have effects on the mechanical response of the gears, that must be taken into account when designing plastic gear drives. In this work, two different finite element models have been proposed to perform heating contact analysis, that is a coupled thermal-stress analysis that takes into account the heating produced by friction and the non-linear properties of the material. As a result of these models, the temperature field of the gears can be determined at any running time, as well as other interesting results, such as the transmission error function or the instantaneous power loss.

scholarly journals Influence of Optimal Tooth Modifications on Dynamic Characteristics of a Vehicle Gearbox

2019 ◽  
Vol 16 (1) ◽  
pp. 6319-6331
Author(s):  
Najeeb Ullah ◽  
T. Cong ◽  
B. Huan ◽  
H. Yucheng
Keyword(s):  
Contact Stress ◽  
Gear Tooth ◽  
Transmission Error ◽  
Optimum Level ◽  
Contact Pattern ◽  
Gear Noise ◽  
Tooth Modification ◽  
Proposed Modification ◽  
The Impact ◽  
Central Gear

Considering the practical problems of gear noise and vibration, this work focuses on the gearbox of the electric vehicle as the research object to analyse the impact of gear micro-tooth modification. First of all, the effort centres itself on minimising the contact stress and making the load distribution better by implementing the tooth modification on both upper and central speed phases. The procedural analysis of gear tooth modification is executed to make the contact pattern better, so edge contact has been avoided and the load is distributed over a wide area of the tooth for both upper and central gear sets. The contact pattern is positioned in the centre of teeth and contact stress is lowered by 20% to 837 MPA. Then, the peak to peak transmission error is decreased under three proposed modification approaches. Also, contact and bending safety factors are improved as a result of tooth modification. Meanwhile, it was noticed by performing dynamic analysis that right bearings of both upper and central phases have a higher radial response for first two orders which is further decreased to an optimum level as a result of micro-tooth modification strategies.

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