scholarly journals Modelica Spur Gears with Hertzian Contact Forces

2017 ◽  
Author(s):  
Markus Dahl ◽  
Håkan Wettergren ◽  
Henrik Tidefelt
Keyword(s):  
Contact Forces ◽  
Hertzian Contact ◽  
Spur Gears

scholarly journals Modeling and Dynamic Analysis of Spherical Roller Bearing with Localized Defects: Analytical Formulation to Calculate Defect Depth and Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Behnam Ghalamchi ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Dynamic Model ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
Measurement Data ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Radial Clearance ◽  
Outer Race ◽  
Rolling Elements ◽  
Localized Defects

Since spherical roller bearings can carry high load in both axial and radial direction, they are increasingly used in industrial machineries and it is becoming important to understand the dynamic behavior of SRBs, especially when they are affected by internal imperfections. This paper introduces a dynamic model for an SRB that includes an inner and outer race surface defect. The proposed model shows the behavior of the bearing as a function of defect location and size. The new dynamic model describes the contact forces between bearing rolling elements and race surfaces as nonlinear Hertzian contact deformations, taking radial clearance into account. Two defect cases were simulated: an elliptical surface on the inner and outer races. In elliptical surface concavity, it is assumed that roller-to-race-surface contact is continuous as each roller passes over the defect. Contact stiffness in the defect area varies as a function of the defect contact geometry. Compared to measurement data, the results obtained using the simulation are highly accurate.

scholarly journals From Hertzian contact to spur gears: analyses of stresses and rolling contact fatigue

2019 ◽  
Vol 20 (6) ◽  
pp. 626 ◽  
Author(s):  
Guillaume Vouaillat ◽  
Jean-Philippe Noyel ◽  
Fabrice Ville ◽  
Xavier Kleber ◽  
Sylvain Rathery
Keyword(s):  
Rolling Contact Fatigue ◽  
Contact Fatigue ◽  
Spur Gear ◽  
Point Of View ◽  
Rolling Contact ◽  
Hertzian Contact ◽  
Spur Gears ◽  
Realistic Representation ◽  
Contact Fatigue Life ◽  
Surface Microgeometry

The study of rolling contact fatigue in spur gears requires a good comprehension of all the phenomena occurring at the material scale. On a numerical point of view, a realistic representation of the material and of the load repartition function of the local micro-geometries is needed. However the resulting models are often complex and time-consuming. So, this work aims at developing a model meeting these specificities. Thus, different sections of the spur gear material granular geometry are simulated first. Secondly, the contact pressure fields are computed accurately relatively to the simulated surface microgeometry. Then, the influence of several parameters on their rolling contact fatigue life is highlighted. Among friction, sliding coefficient, load variation and roughness, these individual or combined parameters are taken into account in the model, tested and their impact stressed out. Finally, a fatigue criteria based on rolling contact fatigue micro-cracks nucleation at grain boundaries is proposed in order to compare simulations and influencing parameters to the reference.

Contact Analysis of Gear Trains Using Linear Complementarity Based Compliant Contact Model

2019 ◽  
Author(s):  
Mangesh Pathak ◽  
Sourav Rakshit
Keyword(s):  
Finite Element ◽  
Computation Time ◽  
Planetary Gear ◽  
Element Model ◽  
Linear Complementarity ◽  
Contact Analysis ◽  
Contact Forces ◽  
Gear Train ◽  
Spur Gears ◽  
Gear Contact

Abstract The current computation models for gear contact analysis and wear prediction are mostly based on finite element analysis which consumes much computation time and effort. In this work, we adopt an alternative approach for gear contact analysis using linear complementarity. This approach was successfully applied to a pair of rigid spur gears and a planetary gear train (gears are considered as rigid bodies) in our previous work. In this paper, we extend our linear complementarity model to consider local deformation caused due to contact between gear teeth in mesh. Thus obtained linear complementarity model is applied to a pair of spur gears and a planetary gear train. A linear complementarity solver computes the contact forces between meshing teeth of gears. From the contact forces, sliding wear in gear teeth is predicted. Archard’s wear model is used for the wear prediction. Using this model, the contact forces are uniquely determined for the examples considered. The results of linear complementarity and finite element model for a pair of spur gears are compared. The linear complementarity model consumes much less computation time than the finite element model.

A vibration model of a rotor system with the sinusoidal waviness by using the non-Hertzian solution

2021 ◽  
pp. 146441932110659
Author(s):  
Jing Liu ◽  
Chenyu An ◽  
Guang Pan
Keyword(s):  
Accurate Method ◽  
Rotor System ◽  
Contact Forces ◽  
Contact Model ◽  
Hertzian Contact ◽  
Rigid Rotor ◽  
Nonlinear Contact ◽  
Reasonable Approach ◽  
Almost All ◽  
Hertzian Contact Model

The nonlinear contact forces and deformations between the balls and raceways can cause very complex vibration behaviours of rotor systems with the waviness in the support bearings. However, almost all previous works that used sinusoidal waviness took the Hertzian solution as the calculation method, which is not an accurate method based on Johnson’s formulation since the changes in the curvature at the sinusoidal contact surfaces. To overcome this issue, a new dynamic model of a rigid rotor system with the waviness in the support bearings is proposed. To provide a more accurate nonlinear contact force formulation for the sinusoidal waviness profile, the model used the Johnson’s extended Hertzian contact model to replace Hertzian contact model. This model can consider the time-varying curvature between the mating sinusoidal surfaces. The lubricating condition in the support bearing is also considered. A comparative study on the effects of Hertzian contact model, simplified Hertzian contact model, and Johnson's extended Hertzian contact model on the nonlinear vibrations of the rotor system is developed. The effects of the waviness amplitude and orders on the vibrations of the rotor system are discussed. The comparative simulations show that the proposed model can provide a more reasonable approach for predicting the vibrations of the rigid rotor system. Moreover, the simulations give that the nonlinear contact forces in the support bearings can greatly affect the system vibrations.

scholarly journals Dynamic analysis of railway vehicle-track interactions due to wheel flat with a pitch-plane vehicle model

1970 ◽  
Vol 39 (2) ◽  
pp. 86-94 ◽  
Author(s):  
Rajib Ul Alam Uzzal ◽  
Waiz Ahmed ◽  
Subhash Rakheja
Keyword(s):  
Contact Point ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Railway Vehicle ◽  
Vehicle Model ◽  
Lumped Mass ◽  
Dynamic Interactions ◽  
Lumped Parameter ◽  
Wheel Flat ◽  
Secondary Suspension

This paper presents the responses of the railway vehicle and track components in terms of contact forces and displacements. The considered vehicle model is a five-DOF pitch-plane lumped parameter quarter car model supported on two-dimensional track systems comprising three layers. The car body is linked with the vehicle bogie through secondary suspension springs and damper elements, which is further linked to the wheels through primary suspension springs and damper elements. In modeling of the track, the rail is considered as an infinitely long beam discretely supported by a series of springs, dampers and masses representing the elasticity and damping effects of the rail pads, ballasts, and subgrades respectively. The non-linear Hertzian contact theory is employed to accomplish the dynamic interactions between the lumped mass vehicle and the continuous rail. The drastic effect of one wheel flat to the other perfect wheel-rail contact point is also taken into account. Keywords: Wheel flat, pitch-plane vehicle, wheel-rail impact, component force. doi:10.3329/jme.v39i2.1851 Journal of Mechanical Engineering, Vol. ME39, No. 2, Dec. 2008 86-94

Probabilistic Critical Safety Wheel Wear Sizes of Chinese Railway Freight Cars

2008 ◽  
Vol 44-46 ◽  
pp. 759-764
Author(s):  
Yong Xiang Zhao ◽  
Bing Yang ◽  
Ming Fei Feng ◽  
Y. Li ◽  
M.J. Liu ◽  
...  
Keyword(s):  
Field Investigation ◽  
State Equation ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Wheel Wear ◽  
Size Change ◽  
Railway Freight ◽  
Impact Forces ◽  
Safety Effect ◽  
The Impact

Critical safety wheel wear size is investigated through considering the fatigue safety effect on RD2 type axle of China railway freight cars. The wheel wear size increase results in a rise of the wheel-rail contact forces, which increase the fatigue stress history of the axle in service. Therefore, the size must be controlled to maintain the axle safety in service before the next overhaul inspection. A field investigation was firstly made on the wear size change regularity. Then, the size related wheel-rail impact forces are solved by a non-linear Hertzian contact theory with a vehicle multi-body dynamic model. In addition, a statistical method is further developed for incorporating the impact forces into the wheelset service load history. Finally, a wear size related critical state equation is established for ensuring the axle safety in service. A stationary solution is statistically obtained for the critical wear sizes with respect to the axle circumferential crack and semi-elliptical crack. It is concluded that the critical safety wear size should be controlled in the range of 100 mm at the statistical level of survival probability 0.99 and confidence 95%.

Stress Analysis of a Touchdown Bearing Having an Artificial Crack

2017 ◽  
Author(s):  
Neda Neisi ◽  
Eerik Sikanen ◽  
Janne E. Heikkinen ◽  
Jussi Sopanen
Keyword(s):  
Stress Intensity ◽  
High Speed ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Frictional Contacts ◽  
Dynamic Friction Coefficient ◽  
Surface Failure ◽  
Propagation Analysis ◽  
Hertzian Contact Theory

The active magnetic bearings (AMBs) are often the preferred bearing solution in high speed rotating machines. Even though AMBs have numerous advantages in comparison to normal bearings they are sensitive to the power shutdowns. In the absence of electromagnetic field, the rotor collides with touchdown bearing. The high contact forces occurring between the rotor and touchdown bearing might lead to a contact surface failure in the touchdown bearings. In this study, the simulation model has been used to study the stresses of the touchdown bearing with an artificial crack. Flexibility of the rotor is modelled using the finite element method and frictional contacts are defined between the rotor and touchdown bearing. Hertzian contact theory is used to model all internal contacts in the ball bearing type touchdown bearings. This makes it possible to obtain the Hertzian contact stresses in each ball of the touchdown bearing and evaluate the stress intensity factors for a crack propagation analysis. The results show that increase in the dynamic friction coefficient between the rotor and bearing as well as increase in the air gap leads to a higher maximum Hertzian stress. As a result of the higher contact stress the stress intensity factor will increase.

Vibrations due to Impact in a Non Ideal Mechanical System With a Non-Linear Hertzian Contact Model

2014 ◽  
Author(s):  
Helio A. Navarro ◽  
Jose M. Balthazar ◽  
Reyolando M. L. R. F. Brasil
Keyword(s):  
Mechanical System ◽  
Rigid Wall ◽  
Contact Forces ◽  
Hertzian Contact ◽  
Impact Behavior ◽  
Steady State Responses ◽  
Post Impact ◽  
The Impact ◽  
The Mathematical Model ◽  
State Responses

This work analyses the post impact behavior of a mechanical system consisting of an oscillator and an unbalanced non–ideal electrical motor. The impact between the mechanical system and a rigid wall is based on the assumption that the impacting bodies undergo local deformations. The method used in the present work is similar to the Discrete Element Method for particle systems modeled with a “soft–sphere” mechanism. The contact forces are modeled using a nonlinear damped Hertzian Spring-Dashpot system. The mathematical model of the mechanical system is represented by a set of nonlinear ordinary differential equations. The transient and steady-state responses are discussed. As the motor is considered a non ideal energy source, the Sommerfeld effect is also analyzed. The impact model is first applied for a single freely falling particle and then in the proposed mechanical system. Non-dimensional expressions for the contact force and numerical simulations of the mechanical system behavior are also presented.

Non Hertzian Contact Model for Tooth Contact Analysis of Spur Gear with Lead Crowning

2014 ◽  
Vol 658 ◽  
pp. 351-356 ◽  
Author(s):  
Nicolae Pop ◽  
Spiridon Cretu ◽  
Ana Tufescu
Keyword(s):  
Mathematical Model ◽  
Significant Influence ◽  
Spur Gear ◽  
Hertzian Contact ◽  
Spur Gears ◽  
Tooth Contact Analysis ◽  
Gear Teeth ◽  
Analytical Research ◽  
Contact Surfaces ◽  
Hertzian Contact Model

The behavior of the contact surfaces between the gear teeth has a significant influence on the gear service properties. An analytical research concerning this behavior by considering a non Hertzian model was developed. A mathematical model of the surfaces of the teeth flanks for modified involute spur gears with crowning and relieving was presented. The pressure distribution, displacement and contact surfaces were analyzed, on considering the load, material characteristics and geometry of the contact surfaces and using a numerical method.

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