Analysis of time-varying friction excitations in helical gears with refined general formulation

2015 ◽  
Vol 229 (13) ◽  
pp. 2467-2483 ◽  
Author(s):  
Hanjun Jiang
Keyword(s):  
Friction Force ◽  
Contact Line ◽  
Sliding Friction ◽  
Helix Angle ◽  
Universal Method ◽  
Time Varying ◽  
Contact Ratio ◽  
Friction Forces ◽  
Helical Gears ◽  
Face Width

Time-varying sliding friction force and friction torque are regarded as non-negligible excitation sources of vibration and noise in gears. The sliding friction force primarily excites the motion along the off-line-of-action direction, which transmits vibration to the housing through shafts and bearings and then radiates noise. Since the contact line intersects with the pitch line, and the directions of the friction forces are opposite on both sides of the pitch line, the calculation of the friction excitations in helical gears becomes more difficult, especially in the high contact ratio helical gears. However, there is no universal method for calculating the friction excitations in helical gears with different range of contact ratio. The changes of friction excitations in helical gears are highly dependent on the geometric parameters such as helix angle and face width among others. Yet, there exist very limited studies on these topics. In this study, a refined general formulation for the calculation of time-varying contact line and friction excitations is proposed by assuming uniform load distribution along the contact lines with time-varying normal force and friction coefficient. Key gear parameters such as modification coefficient, helix angle, and face width are analyzed to illustrate their effects on the time-varying contact line and friction excitations. The results demonstrate that the refined general formulation is effective for the calculation of the friction excitations in helical gears with different range of contact ratio, and the parametric analysis could supply some guidance for choosing gear parameters in the design of helical gears to reduce the friction excitations.

On the influence of helix angle and face width on gear windage losses

2015 ◽  
Vol 230 (7-8) ◽  
pp. 1101-1112 ◽  
Author(s):  
Nicolas Voeltzel ◽  
Yann Marchesse ◽  
Christophe Changenet ◽  
Fabrice Ville ◽  
Philippe Velex
Keyword(s):  
Computational Fluid Dynamic ◽  
Fluid Dynamic ◽  
Helix Angle ◽  
Spur Gears ◽  
Power Losses ◽  
Flow Rates ◽  
Helical Gears ◽  
Face Width ◽  
Loss Prediction ◽  
Simulated Flow

This paper investigates the windage power losses generated by helical gears rotating in pure air based on experimental results and a computational fluid dynamic code. It is found that the simulated flow patterns are totally different from those calculated for spur gears and that both tooth face width and helix angle are influential. The windage losses derived from Dawson’s and Townsend’s formulae are critically assessed using computational fluid dynamic results thus highlighting the limits of a unique formulation for accurate windage loss prediction. Finally, an analytical approach is suggested which gives good results providing that the flow rates at the boundaries of the inter-tooth domains can be estimated.

Experimental Study of Friction in a Pneumatic Actuator at Constant Velocity

1993 ◽  
Vol 115 (3) ◽  
pp. 575-577 ◽  
Author(s):  
Lee E. Schroeder ◽  
Rajendra Singh
Keyword(s):  
Experimental Study ◽  
Experimental Method ◽  
Friction Force ◽  
Constant Velocity ◽  
Sliding Friction ◽  
Pneumatic Actuator ◽  
Friction Forces ◽  
Friction Models ◽  
Semi Empirical ◽  
Force Data

This paper describes an experimental method of determining sliding friction forces in a pneumatic actuator. Several empirical and semi-empirical friction models are evaluated using measured friction force data. A repeatability study is also performed to qualitatively assess friction randomness and a change in friction regimes.

Friction Force Distribution Along Time-Varying Contact Line in Helical Gear System

2012 ◽  
Author(s):  
Wen-liang Li ◽  
Li-qin Wang
Keyword(s):  
Friction Force ◽  
Contact Line ◽  
Helical Gear ◽  
Gear System ◽  
Shape Design ◽  
Force Distribution ◽  
Time Varying ◽  
Fundamental Theory ◽  
Impact Reduction ◽  
Instantaneous Position

Based on the theory of energy minimization, a numerical algorithm was developed to calculate friction force distribution along the time-varying contact line in helical gear system. The friction force distribution varies with the instantaneous position of the meshing point and the length of contact line. The friction force was calculated on every meshing point of time-varying contact line via the algorithm. The results show the friction force becomes larger from the tooth root to the pitch point and becomes smaller from the pitch point to the tooth tip. Due to this, there is a significant shock at the pitch point which will generate noise and vibration. The changing law of friction force distribution provides a fundamental theory for modification shape design and impact reduction.

scholarly journals Effect of Helix Angle on the Gear Design Parameters in Helical Gears

2019 ◽  
Vol 8 (10) ◽  
pp. 887-890
Keyword(s):  
Helix Angle ◽  
Contact Stresses ◽  
Design Parameters ◽  
Screw Compressor ◽  
Bending Stress ◽  
Contact Ratio ◽  
Helical Gears ◽  
Gear Design ◽  
Overlap Ratio ◽  
Lower Noise

Screw compressor demands quite operation. For getting lower noise it is important to have higher contact ratio. Contact ratio can be increased by increasing the Helix angle i .e. indirectly increasing overlap ratio. The paper represents the effect of change in design parameters with respect to helix angle with the keeping same module and same centre distance. Higher helix angle leads lower bending and contact stresses. The study was conducted for screw electrical compressor. Gear was design for fixed parameters except helix angle. Also the contact stresses are analyzed (FEA) on ANSYS. The result from the calculation and FEA are compared for contact stress as well as bending stress.

Dynamic Behavior of Helical Gears with Effects of Shaft and Bearing Flexibilities

2011 ◽  
Vol 86 ◽  
pp. 26-29
Author(s):  
Kai Feng ◽  
Shigeki Matsumura ◽  
Haruo Houjoh
Keyword(s):  
Experimental Tests ◽  
Time Varying ◽  
Gear Pair ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Helical Gears ◽  
Shaft System ◽  
Proposed Model ◽  
Center Distance ◽  
Good Agreement

This study presents a numerical model of helical gears to consider the effects of shaft and bearing flexibility. A primary feature of this study is that the time-varying mesh stiffness is not just determined by the geometry of gear pair but also updated for each iteration according to the change of center distance. The effects of shaft and bearing flexibilities are discussed by comparing the dynamic response of gear pairs supported with a rigid and a flexible bearing-shaft system. The results show that the pressure angle and contact ratio are significantly changed due to the center-distance variation of gears and the gear pair with a flexible bearing-shaft system has much larger vibration. Finally, experimental tests are conducted to validate the proposed model. The predicted results show good agreement with the experimental data.

Effects of Carburized Part, Helix Angle and Face Width on Residual Stresses of Case-Hardened Helical Gears

2004 ◽  
Vol 2004.4 (0) ◽  
pp. 63-66
Author(s):  
Kouitsu MIYACHIKA ◽  
Wei-Dong XUE ◽  
Takao KOIDE ◽  
Satoshi ODA ◽  
Hiroshige FUJIO
Keyword(s):  
Residual Stresses ◽  
Helix Angle ◽  
Helical Gears ◽  
Face Width

An analytical method to determine the addendum modification parameters of involute helical gears

2011 ◽  
Vol 225 (11) ◽  
pp. 2516-2524 ◽  
Author(s):  
T Chen ◽  
W Sun ◽  
X Zhang
Keyword(s):  
Cross Section ◽  
Contact Line ◽  
Engineering Application ◽  
Element Model ◽  
Helical Gears ◽  
Accuracy Requirement ◽  
Face Width ◽  
The Moment ◽  
Cross Section Method ◽  
Good Agreement

Due to the simplified tooth profile and the complicated load distribution along the contact line, the traditional analytic method cannot satisfy the accuracy requirement while carrying out addendum modification of the helical gears. To overcome this disadvantage, a new way based on cross-section method is presented to calculate the deformation of helical tooth tip. First, the tooth is divided into copies of cross-section along face width and the moment of inertia for each section is calculated. Also, the load is distributed according to length of the contact line, and the effect of deflected load is taken into account as well. Based on these works, a general formula of helical tooth tip deformation is deduced. Then, this formula is applied to calculate the addendum modification width ac. In addition, considering that tooth tip modification will shorten the meshing line, three models used to control length of the remaining meshing line are proposed and addendum modification height hc is defined accordingly. Finally, an instance is given to verify the good agreement between results of this study and those of a finite element model. Apart from this, engineering application of this method is provided.

A Dynamic Friction Model for Unlubricated Rough Planar Surfaces

2003 ◽  
Vol 125 (4) ◽  
pp. 788-796 ◽  
Author(s):  
Xi Shi ◽  
Andreas A. Polycarpou
Keyword(s):  
Friction Coefficient ◽  
Friction Force ◽  
Harmonic Excitation ◽  
Published Data ◽  
Dynamic Friction ◽  
Time Varying ◽  
Friction Forces ◽  
Dynamic Friction Coefficient ◽  
Normal Separation ◽  
The Mean

Modeling dynamic or kinetic friction for realistic engineering surfaces continues to be a challenge, partly due to the coupling between system dynamics and interfacial forces. In this paper, a dynamic friction coefficient model for realistic rough surfaces under external normal vibrations is developed. From the system dynamic model, the instantaneous time varying normal separation at the interface is obtained under normal harmonic excitation. Subsequently, the instantaneous dynamic contact and tangential (friction) forces are calculated as a function of the instantaneous normal separation. The dynamic friction coefficient defined as the ratio of the time varying friction to the interfacial normal forces that explicitly includes interfacial damping, is also calculated. The results show that a mean increase in the instantaneous normal separation may or may not lead to a decrease of the mean friction force and the mean friction coefficient, which is supported by published data. For unlubricated elastic sliding contact conditions considered in this paper, the effect of damping on the dynamic friction coefficient is found to be negligible, whereas loss of contact causes significant apparent dynamic friction force and dynamic friction coefficient reductions. Several different interpretations of the time varying dynamic friction coefficient are presented and the implications of using a simple constant value to represent the time varying dynamic friction coefficient are discussed.

Parametric vibration of split gears induced by time-varying mesh stiffness

2014 ◽  
Vol 229 (1) ◽  
pp. 18-25 ◽  
Author(s):  
Dongsheng Zhang ◽  
Shiyu Wang
Keyword(s):  
Parametric Vibration ◽  
Design Parameters ◽  
Time Varying ◽  
Contact Ratio ◽  
Mesh Stiffness ◽  
Rotational Model ◽  
Helical Gears ◽  
Multi Scale ◽  
Rotational Vibration ◽  
The Relationship

Time-varying mesh stiffness is a significant excitation source within gear systems. Split gear (or laminated gear, phase gear) is an interesting design using equally phased gear-slices, which can remarkably reduce the mesh stiffness fluctuation like helical gears but completely avoid the axial force. This work examines a split gear pair to address the suppression of the mesh stiffness fluctuation and rotational vibration thereof, especially the relationship between the key design parameters including the number of slice, contact ratio, and damping, and the parametric vibration. For these aims, this work develops a purely rotational model, based on which the multi-scale method is employed to determine stability boundaries. The results imply that the unstable zones are related to the mesh phase determined by the number of slices and contact ratio, and these zones can be diminished by the damping. The analytical predictions are numerically verified by Floquet theory.

scholarly journals Highly Selective Biomimetic Flexible Tactile Sensor for Neuroprosthetics

Research ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Yue Li ◽  
Zhiguang Cao ◽  
Tie Li ◽  
Fuqin Sun ◽  
Yuanyuan Bai ◽  
...  
Keyword(s):  
Friction Force ◽  
Sliding Friction ◽  
Dielectric Material ◽  
Silver Nanowires ◽  
Static Friction ◽  
Tactile Sensor ◽  
Capacitive Sensor ◽  
Silver Nanowire ◽  
Friction Forces ◽  
Signal Encoding

Biomimetic flexible tactile sensors endow prosthetics with the ability to manipulate objects, similar to human hands. However, it is still a great challenge to selectively respond to static and sliding friction forces, which is crucial tactile information relevant to the perception of weight and slippage during grasps. Here, inspired by the structure of fingerprints and the selective response of Ruffini endings to friction forces, we developed a biomimetic flexible capacitive sensor to selectively detect static and sliding friction forces. The sensor is designed as a novel plane-parallel capacitor, in which silver nanowire–3D polydimethylsiloxane (PDMS) electrodes are placed in a spiral configuration and set perpendicular to the substrate. Silver nanowires are uniformly distributed on the surfaces of 3D polydimethylsiloxane microcolumns, and silicon rubber (Ecoflex®) acts as the dielectric material. The capacitance of the sensor remains nearly constant under different applied normal forces but increases with the static friction force and decreases when sliding occurs. Furthermore, aiming at the slippage perception of neuroprosthetics, a custom-designed signal encoding circuit was designed to transform the capacitance signal into a bionic pulsed signal modulated by the applied sliding friction force. Test results demonstrate the great potential of the novel biomimetic flexible sensors with directional and dynamic sensitivity of haptic force for smart neuroprosthetics.

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