Eccentricity Effect Analysis in Right-Angle Gear Dynamics

2011 ◽  
Author(s):  
Tao Peng ◽  
Teik C. Lim ◽  
Junyi Yang
Keyword(s):  
High Speed ◽  
Low Frequency ◽  
Transmission Error ◽  
Dynamic Responses ◽  
Computational Time ◽  
Model Parameters ◽  
Tooth Contact Analysis ◽  
Effect Analysis ◽  
Tolerance Specification ◽  
Assembly Error

Geometric eccentricity here refers to the radial deviation (radial runout) of pinion or gear geometric center off its rotational center or axis. Such a typical manufacturing or assembly error in gear transmission exhibits inherent effects on the gear dynamic responses. Modeling of eccentricity has rarely been done for high speed right-angle gears such as hypoid or spiral bevel gears. In this paper, two modeling methods are proposed to quantitatively represent the eccentricity in the hypoid/bevel gear dynamic analysis. The first method is based on the loaded tooth contact analysis (LTCA) for a long shaft period. The LTCA results are then used to synthesize the corresponding roll angle dependent varying mesh model parameters. A second simpler method using translational kinematic transmission error (TE) modification is proposed to reduce the computational time. The effects of eccentricity on the gear dynamic responses are then investigated. The eccentricity excited low frequency shaft order dynamics is found to affect not only the overall level of vibration but also the high frequency mesh order responses. The sideband responses are simulated and characterized. This study is expected to improve the right-angle gearing system dynamic analytical capability and assist in guiding the manufacturing or assembly error tolerance specification.

scholarly journals Quasi-Static Characteristics and Vibration Responses Analysis of Helical Geared Rotor System with Random Cumulative Pitch Deviations

2020 ◽  
Vol 10 (12) ◽  
pp. 4403
Author(s):  
Bing Yuan ◽  
Geng Liu ◽  
Lan Liu
Keyword(s):  
Degrees Of Freedom ◽  
Transmission Error ◽  
Rotor System ◽  
Dynamic Responses ◽  
Contact Ratio ◽  
Tooth Contact Analysis ◽  
Long Period ◽  
Light Load ◽  
Vibration Responses ◽  
Loaded Tooth Contact Analysis

As one of the long period gear errors, the effects of random cumulative pitch deviations on mesh excitations and vibration responses of a helical geared rotor system (HGRS) are investigated. The long-period mesh stiffness (LPMS), static transmission error (STE), as well as composite mesh error (CMS), and load distributions of helical gears are calculated using an enhanced loaded tooth contact analysis (LTCA) model. A dynamic model with multi degrees of freedom (DOF) is employed to predict the vibration responses of HGRS. Mesh excitations and vibration responses analysis of unmodified HGRS are conducted in consideration of random cumulative pitch deviations. The results indicate that random cumulative pitch deviations have significant effects on mesh excitations and vibration responses of HGRS. The curve shapes of STE and CMS become irregular when the random characteristic of cumulative pitch deviations is considered, and the appearance of partial contact loss in some mesh cycles leads to decreased LPMS when load torque is relatively low. Vibration modulation phenomenon can be observed in dynamic responses of HGRS. In relatively light load conditions, the amplitudes of sideband frequencies become larger than that of mesh frequency and its harmonics (MFIHs) because of relatively high contact ratio. The influences of random cumulative pitch deviations on the vibration responses of modified HGRS are also discussed.

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.

Running Safety Assessment of Trains on Bridges under Earthquakes Based on Spectral Intensity Theory

2021 ◽  
Author(s):  
Wei Guo ◽  
Yang Wang ◽  
Hanyun Liu ◽  
Yan Long ◽  
Lizhong Jiang ◽  
...  
Keyword(s):  
High Speed ◽  
Safety Assessment ◽  
Low Frequency ◽  
Interaction Model ◽  
Spectral Intensity ◽  
Dynamic Responses ◽  
Running Safety ◽  
High Speed Trains ◽  
Track Bridge ◽  
Multi Body

The main goal of this paper is to perform the safety assessment of high-speed trains (HSTs) on the simply supported bridges (SSBs) under low-level earthquakes, which are frequently encountered by HSTs, utilizing spectral intensity (SI) index. First, the HST’s limit displacements, which are calculated by using the multi-body train model with detailed wheel–rail relationship, varying with train speed, frequency and amplitude of a sinusoidal base excitation are obtained. Then, based on the obtained HST’s limit displacements, the spectral intensity limits (SIL) graded by the train’s running speed are calculated, and the relationship between the bridge seismic dynamic responses and the train’s running safety was established. Next, the method that utilizes the SI and the SIL indexes to evaluate the HST’s running safety was proposed and verified by comparing with the evaluation result of the train–track–bridge interaction model. Based on the proposed SI index, the HST’s running safety on the SSBs was evaluated under earthquakes, considering different pier heights and site types. The results showed that the low-frequency components of the ground motions are unfavorable to the HST’s running safety, and the height of bridge piers has a significant impact on running safety.

Temperature effect on service performance of high-speed railway concrete bridges

2016 ◽  
Vol 20 (6) ◽  
pp. 865-883 ◽  
Author(s):  
Y Tian ◽  
N Zhang ◽  
H Xia
Keyword(s):  
Temperature Effect ◽  
High Speed ◽  
Low Frequency ◽  
Numerical Approach ◽  
Service Performance ◽  
Dynamic Responses ◽  
Temperature Fields ◽  
Coupled Analysis ◽  
Element Analysis ◽  
High Speed Railway

Non-uniform temperature fields induced by time-varying solar position and heat exchange are of great significance for the bridge safety. The accurate identifications of these changes are necessary to avoid unexpected deformations and the loss of service performance. This article presents a numerical approach to determine temperature effects on train–bridge-coupled dynamics. Heat flux density of different components of a 32-m simply supported concrete bridge on high-speed railway is calculated, in which a section segmentation method is adopted for simplifications of boundary conditions. Based on heat–stress-coupled technology, temperature fields and deformation fields of the bridge are then computed via finite element analysis. Combining track irregularities and its thermal deformation as external excitations, the train–bridge-coupled analysis is solved by an inter-system iteration method. Dynamic responses of bridge and train are compared to those obtained neglecting the temperature effect. Comparative studies illustrate that temperature effect has major impacts on the bridge displacement due to the increase in low-frequency components of excitations. For the train, lateral responses are more obvious. Maximum derail factor and lateral wheel–rail force occur when the train leaves from the bridge.

A helical gear with discrete ring-involute teeth

2019 ◽  
Vol 234 (8) ◽  
pp. 1554-1568
Author(s):  
Hsueh-Cheng Yang ◽  
Wen-Jun Liang
Keyword(s):  
Contact Stress ◽  
Computer Aided Design ◽  
Transmission Error ◽  
Helical Gear ◽  
Gear Pair ◽  
Tooth Contact Analysis ◽  
Element Analysis ◽  
The Family ◽  
Aided Design ◽  
Assembly Error

This study produces a skewed-imaginary planar rack cutter with discrete conical teeth that is used to create a helical gear with discrete ring-involute teeth. A mathematical equation for the skewed-imaginary rack cutter with discrete conical teeth is firstly solved. The coordinate system for the rack cutter and gear pair is then established and a family of the rack-cutter surfaces is obtained using homogeneous coordinate transformation. The relative velocity method is used to produce the equation for meshing between the rack cutter and the gear pair. Substituting the equation of meshing into the family of the rack-cutter surfaces gives the mathematical models for the gear pair with discrete ring-involute teeth. The transmission error for the gear pair is calculated using the assembly error and a tooth contact analysis. A computer-aided design software package is used to establish solid model for the gear pair. A software interference function is used to simulate the contact condition for the gear pair for various assembly errors. Finite element analysis software is then used to determine the contact stress for the gear pair. The transmission error and the contact stress for the gear pair are insensitive to any horizontal misalignment in the assembly errors.

Numerical and experimental investigation into the mid- and high-frequency vibration behavior of a concrete box girder bridge induced by high-speed trains

2018 ◽  
Vol 24 (23) ◽  
pp. 5597-5609 ◽  
Author(s):  
Xun Zhang ◽  
Xiaozhen Li ◽  
Zhipeng Wen ◽  
Yu Zhao
Keyword(s):  
High Frequency ◽  
High Speed ◽  
Spectral Characteristics ◽  
Dynamic Responses ◽  
Model Parameters ◽  
Slab Thickness ◽  
Box Girder ◽  
Vibration Prediction ◽  
Concrete Box Girder ◽  
Concrete Box Girder Bridges

Concrete box girder bridges exhibit mid- and high-frequency (> 20 Hz) dynamic responses due to train excitations, which result in problems of noise radiation and track deterioration. This study presents a numerical model for box girder vibration prediction. Significant attention is focused on the mid- and high-frequency responses via introduction of a detailed track/bridge subsystem model. A hammer impact test was used to determine the model parameters. The model was then validated using a homologation test. The results show that the wheel/rail force and box girder mobility are the two principal factors that influence box girder vibration spectral characteristics and amplitudes. The box girder responses at cross-sections with similar dynamic characteristics vary little, as they increase moderately with the train speed. The application of a fastening system with low stiffness and high damping can effectively reduce box girder vibration. However, the elastic modulus and damping of the cement–asphalt mortar, and the thickness of the track slab and bearing base exert the smallest influences on the vibrations. The box girder slab thickness should be designed appropriately because its dynamic behavior is closely associated with the slab characteristics.

Dynamic responses of a high-speed train passing a deformed bridge using a vehicle-track-bridge coupled model

2020 ◽  
pp. 095440972094433 ◽  
Author(s):  
Hongye Gou ◽  
Chang Liu ◽  
Wen Zhou ◽  
Yi Bao ◽  
Qianhui Pu
Keyword(s):  
High Speed ◽  
Low Frequency ◽  
Coupled Model ◽  
Element Model ◽  
Vertical Vibration ◽  
Dynamic Responses ◽  
High Speed Train ◽  
Railway Network ◽  
Track Bridge ◽  
Bridge System

With the development of the railway network in a harsh environment, the additional bridge deformations accumulated over time may endanger high-speed trains passing through a bridge, since the bridge deformation directly affect the geometry of the track on the bridge, thus affecting the dynamic responses of the train. This paper investigates the effects of different types of bridge deformation on the dynamic responses of the high-speed train passing through a deformed bridge. First, a finite element model is established for a high-speed railway bridge to study the dynamic responses of vehicle-track-bridge system under bridge deformations. Then, the rail deformation caused by bridge deformation is calculated using a bridge-track deformation mapping model, and used as the excitation to the vehicle-track-bridge system to study the influence of bridge deformations on the dynamic responses of the train. Results show that the vertical bridge deformations mainly affect the vertical vehicle dynamic indices, and have negligible effect on the lateral dynamic indices. The additional bridge deformation generates an additional low-frequency excitation to the train. The bridge deformations mainly affect the dynamic responses at specific characteristic frequencies, which are independent on the magnitude of the deformation. The frequencies for bridge deformations are magnified at about 1 Hz, indicating that the additional bridge deformation may aggravate the vertical vibration of the train.

Substructure Analysis of a Flexible System Contact-Impact Event

2004 ◽  
Vol 126 (1) ◽  
pp. 126-131 ◽  
Author(s):  
Anping Guo ◽  
Steve Batzer
Keyword(s):  
Impact Analysis ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Time History ◽  
Dynamic Responses ◽  
Computational Time ◽  
Stress Wave Propagation ◽  
Model Parameters ◽  
Flexible System ◽  
Contact Impact

In this paper, the application of the substructure methodology to contact-impact analysis of flexible multibody systems is validated. Various impact model parameters that affect the model’s accuracy are presented. A contact-impact system is used that consists of a flexible cantilever bar longitudinally struck at its free end by a rigid body moving at a finite velocity. First, a dynamic model using the substructure method is established. Second, the initial conditions of the system’s dynamic responses during contact-impact are derived. Finally, a numeric contact-impact simulation is performed. The excellent agreement between the numeric solutions to both the substructure model and the analytical solutions demonstrates that the substructure model can successfully describe stress wave propagation within flexible bodies during contact-impact. The method can also clearly display the contact force time history and deformation distribution along the bar during contact-impact time and correctly predict the displacement of the contact surface of the flexible bar and the contact duration of the two bodies. It is shown that a larger substructure number will improve the accuracy of the numerical solutions, but an excessive number will lower the model’s accuracy since increasingly fine substructures increase the number of modal coordinates and lead to more serious computational round off errors and longer computational time.

Analysis of the Transmission Error of Face-Gear Drives

1997 ◽  
Author(s):  
S. D. Chung ◽  
S. H. Chang ◽  
S. S. Lu
Keyword(s):  
Mathematical Model ◽  
Angular Displacement ◽  
Transmission Error ◽  
Contact Analysis ◽  
Generation Process ◽  
Face Gear ◽  
Tooth Contact Analysis ◽  
Tooth Contact ◽  
Analytical Geometry ◽  
Assembly Error

Abstract Based on the face-gear generation process, the analytical geometry of face-gear drive with its mathematical model for tooth contact analysis of face-gear and spur pinion meshing was derived. In this paper, contact path and transmission error due to assembly misalignment were analyzed by using the proposed mathematical model and the tooth contact analysis. The effect of assembly error along the axis of face-gear, misalignment of crossed and angular displacement between axes of spur pinion and face-gear were all investigated. The results are illustrated by several examples.

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