Refined Calculation of the Bearing Stiffness and Load in the Presence of Radial Clearance

2020 ◽  
Vol 49 (7) ◽  
pp. 591-603
Author(s):  
F. G. Nakhatakyan ◽  
A. K. Puzakina ◽  
D. F. Nakhatakyan
Keyword(s):  
Radial Clearance ◽  
Bearing Stiffness ◽  
Refined Calculation

Parametric studies on dynamic stiffness of ball bearings supporting a flexible rotor

2019 ◽  
Vol 25 (15) ◽  
pp. 2175-2188 ◽  
Author(s):  
Tikam Chand Gupta
Keyword(s):  
Numerical Integration ◽  
Dynamic Stiffness ◽  
Mathematical Formulation ◽  
Rolling Element Bearing ◽  
Radial Clearance ◽  
Integration Scheme ◽  
Time Step ◽  
Average Value ◽  
Bearing Stiffness ◽  
Time Invariant

Most of the researchers in the field of dynamics of the rolling element bearing have considered bearing stiffness as time invariant and/or not related to dynamics of the bearing. In the present paper, the bearing stiffness has been taken as function of dynamic response at every time step of numerical simulation and a detailed parametric study is performed to investigate the effect of flexibility of the rotor shaft, rotational speed, and internal radial clearance on the instantaneous and average value of dynamic stiffness of the ball bearing. The mathematical formulation is based on the Timoshenko beam finite element theory. Gravity and bearing forces are considered as external forces acting on a free-free flexible shaft. A stable Newmark- β numerical integration scheme coupled with Newton–Raphson method is used for numerical integration and for convergence to an accurate value of bearing stiffness. The results showing the variation of different components of bearing stiffness as a function of time-invariant parameters has improved the understanding of the dynamic behavior of the bearing during motion. The variation pattern of bearing stiffness coefficients is observed to be sensitive to direction of rotation. The amplitude of periodic change of these coefficients increases with the increase of the stiffness ratio of shaft and the decrease of radial clearance.

The Impact of Different Axial Oil Chamber Design on Hydrostatic Spindle

2015 ◽  
Vol 789-790 ◽  
pp. 296-299
Author(s):  
Shao Hsien Chen ◽  
Shang Te Chen ◽  
Chien Cheng Hsu
Keyword(s):  
High Precision ◽  
Large Scale ◽  
Development Trend ◽  
Ball Screw ◽  
Precision Machining ◽  
Radial Clearance ◽  
Axial Stiffness ◽  
Key Technologies ◽  
Bearing Stiffness ◽  
The Impact

High-precision machining and large-scale tool are the most primary development trend of current machine tool and hydrostatic products are key technologies of high-precision machining equipments. However, these equipments mostly process miniature components, thus the adopted tools are relatively small and the spindles mainly use are mainly built-in types of HSK32 to HSK25 with revolutions speed over 25,000rpm. Some processing equipments are even equipped with hydrostatic or gas-static spindles. The study extends the axial oil chamber to radial ones to expand the action area of axial oil pressure and form a closed oil seal edge by combining the radial clearance. Consequently, the axial bearing stiffness can be enhanced to enlarge the application scope of hydrostatic spindle. The design mode can enhance axial stiffness of spindle modules or strengthen the stiffness of hydrostatic spindle in a ball screw.

Analytical and Experimental Study of Externally Pressurized Air Lubricated Journal Bearings

1962 ◽  
Vol 84 (1) ◽  
pp. 159-165 ◽  
Author(s):  
Jason R. Lemon
Keyword(s):  
Journal Bearing ◽  
Design Parameters ◽  
Radial Clearance ◽  
Proper Selection ◽  
One Dimensional ◽  
Supply Pressure ◽  
Bearing Stiffness ◽  
Bearing Design ◽  
Gas Journal Bearing ◽  
Selection Of

A simplified analysis for calculating the characteristics, such as stiffness, flow, and load of an externally pressurized gas journal bearing, is obtained through a standard one-dimensional flow approach altered to take into account the effect of circumferential pressure variations. From this analysis, it is revealed that bearing stiffness has an optimum which, it is further shown, can be chosen through a proper selection of bearing design parameters, such as radial clearance, upstream resistor, and supply pressure. As the analysis is developed each assumption is experimentally verified. The final predictions of the analysis are also verified. It is felt that the analysis is sufficiently simple to allow comparison of many different bearing configurations, while sufficiently complete to compare very well against experimental measurements in all respects. A comparison is made between the recessed and nonrecessed bearing.

Numerical and Experimental Investigations on Preload Effects in Air Foil Journal Bearings

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Marcel Mahner ◽  
Pu Li ◽  
Andreas Lehn ◽  
Bernhard Schweizer
Keyword(s):  
Friction Torque ◽  
Fluid Film ◽  
Radial Clearance ◽  
Experimental Investigations ◽  
Hysteresis Curves ◽  
Numerical Predictions ◽  
Wide Range ◽  
Reaction Forces ◽  
Bearing Stiffness ◽  
Definition Of

A detailed elastogasdynamic model of a preloaded three-pad air foil journal bearing is presented. Bump and top foil deflections are herein calculated with a nonlinear beamshell theory according to Reissner. The two-dimensional pressure distribution in each bearing pad is described by the Reynolds equation for compressible fluids. The assembly preload is calculated by simulating the assembly process of top foil, bump foil, and shaft. Most advantageously, there is no need for the definition of an initial radial clearance in the presented model. With this model, the influence of the assembly preload on the static bearing hysteresis as well as on the aerodynamic bearing performance is investigated. For the purpose of model validation, the predicted hysteresis curves are compared with measured curves. The numerically predicted and the measured hysteresis curves show a good agreement. The numerical predictions exhibit that the assembly preload increases the elastic foil structural stiffness (in particular for moderate shaft displacements) and the bearing damping. It is observed that the effect of the fluid film on the overall bearing stiffness depends on the assembly preload: For lightly preloaded bearings, the fluid film affects the overall bearing stiffness considerably, while for heavily preloaded bearings the effect is rather small for a wide range of reaction forces. Furthermore, it is shown that the assembly preload increases the friction torque significantly.

Study on bearing stiffness characteristics with residual stress in carburized layer

2020 ◽  
pp. 095440622096079
Author(s):  
Junshuai Liang ◽  
Ning Li ◽  
Jingyu Zhai ◽  
BaoGang Wen ◽  
Qingkai Han ◽  
...  
Keyword(s):  
Residual Stress ◽  
Contact Stiffness ◽  
Roller Bearing ◽  
High Load ◽  
Axial Stiffness ◽  
Fe Model ◽  
Low Load ◽  
Bearing Stiffness ◽  
Carburized Layer ◽  
Stiffness Characteristics

In this study, a layering method of carburized ring is presented. A finite element (FE) model for analyzing bearing stiffness characteristics is established considering the residual stress in the carburized layer. The residual stress in the carburized layer of a double-row conical roller bearing is tested and the influence of the distribution of residual stress in carburized layer on the bearing stiffness is investigated. Results show that the residual stress in the carburized layer increases the contact stiffness of the bearing by 5% in the low-load zone and 3% in the high-load zone. The radial stiffness of the bearing is increased by 5% in the low-load zone and 3% in the high-load zone. The axial stiffness is increased by 6%, and the angular stiffness increased by 4%. The larger the thickness of the carburized layer, the greater the residual compressive stress in the carburized layer, the deeper the position of the maximum residual stresses in the carburized layer will lead to the greater stiffness of the bearing.

Parameters research on time-varying stiffness of the ball bearing system without race control hypothesis

2021 ◽  
pp. 095440622110179
Author(s):  
Yongzhen Liu ◽  
Yimin Zhang
Keyword(s):  
Ball Bearing ◽  
Combined Loading ◽  
Time Varying ◽  
Noticeable Effect ◽  
Rotating Speed ◽  
Bearing Stiffness ◽  
Vibration Mechanism ◽  
Control Hypothesis ◽  
Full Consideration ◽  
Bearing System

When the ball bearing serving under the combined loading conditions, the ball will roll in and out of the loaded zone periodically. Therefore the bearing stiffness will vary with the position of the ball, which will cause vibration. In order to reveal the vibration mechanism, the quasi static model without raceway control hypothesis is modeled. A two-layer nested iterative algorithm based on Newton–Raphson (N-R) method with dynamic declined factors is presented. The effect of the dispersion of bearing parameters and the installation errors on the time-varying carrying characteristics of the ball-raceway contact and the bearing stiffness are investigated. Numerical simulation illustrates that besides the load and the rotating speed, the dispersion of bearing parameters and the installation errors have noticeable effect on the ball-raceway contact load, ball-inner raceway contact state and bearing stiffness, which should be given full consideration during the process of design and fault diagnosis for the rotor-bearing system.

Energy-saving design of variable-displacement bi-directional pump-controlled electrohydraulic system

2020 ◽  
pp. 095965182097389
Author(s):  
Samir Kumar Hati ◽  
Nimai Pada Mandal ◽  
Dipankar Sanyal
Keyword(s):  
Energy Saving ◽  
Absolute Error ◽  
Fast Response ◽  
Maximum Energy ◽  
Radial Clearance ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Displacement Pump ◽  
Variable Displacement ◽  
Axial Piston

Losses in control valves drag down the average overall efficiency of electrohydraulic systems to only about 22% from nearly 75% for standard pump-motor sets. For achieving higher energy efficiency in slower systems, direct pump control replacing fast-response valve control is being put in place through variable-speed motors. Despite the promise of a quicker response, displacement control of pumps has seen slower progress for exhibiting undesired oscillation with respect to the demand in some situations. Hence, a mechatronic simulation-based design is taken up here for a variable-displacement pump–controlled system directly feeding a double-acting single-rod cylinder. The most significant innovation centers on designing an axial-piston pump with an electrohydraulic compensator for bi-directional swashing. An accumulator is conceived to handle the flow difference in the two sides across the load piston. A solenoid-driven sequence valve with P control is proposed for charging the accumulator along with setting its initial gas pressure by a feedforward design. Simple proportional–integral–derivative control of the compensator valve is considered in this exploratory study. Appropriate setting of the gains and critical sizing of the compensator has been obtained through a detailed parametric study aiming low integral absolute error. A notable finding of the simulation is the achievement of the concurrent minimum integral absolute error of 3.8 mm s and the maximum energy saving of 516 kJ with respect to a fixed-displacement pump. This is predicted for the combination of the circumferential port width of 2 mm for the compensator valve and the radial clearance of 40 µm between each compensator cylinder and the paired piston.

Analysis of Bouncing Vibrations of a 2-DOF Tripad Contact Slider Model With Air Bearing Pads Over a Harmonic Wavy Disk Surface

1999 ◽  
Vol 121 (4) ◽  
pp. 939-947 ◽  
Author(s):  
Kyosuke Ono ◽  
Kan Takahashi
Keyword(s):  
Contact Stiffness ◽  
Disk Surface ◽  
Design Parameters ◽  
Air Bearing ◽  
Static Contact ◽  
Tracking Ability ◽  
The Coefficient Of Friction ◽  
Bearing Stiffness ◽  
Perfect Contact ◽  
Contact Slider

In this study, the authors numerically analyzed the bouncing vibrations of a two-degree-of-freedom (2-DOF) model of a tripad contact slider with air bearing pads over a harmonic wavy disk surface. The general features of bouncing vibrations were elucidated in regard to the modal characteristics of a 2-DOF vibration system and design parameters such as contact stiffness, contact damping, air hearing stiffness, the rear to front air bearing stiffness ratio, static contact force and the coefficient of friction. The design of a contact slider was discussed in terms of tracking ability and wear durability. In addition, two sample designs of a perfect contact slider with sufficient wear durability were also presented.

scholarly journals Experimental and Numerical Investigation about Small Clearance Journal Bearings under Static Load Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Carlo Alberto Niccolini Marmont Du Haut Champ ◽  
Fabrizio Stefani ◽  
Paolo Silvestri
Keyword(s):  
Three Dimensional ◽  
Journal Bearings ◽  
Radial Clearance ◽  
Small Scale ◽  
Test Rig ◽  
Small Clearance ◽  
Dimensional Simulation ◽  
Dynamic Loading Conditions ◽  
Static And Dynamic Loading ◽  
Good Agreement

The aim of the present research is to characterize both experimentally and numerically journal bearings with low radial clearances for rotors in small-scale applications (e.g., microgas turbines); their diameter is in the order of ten millimetres, leading to very small dimensional clearances when the typical relative ones (order of 1/1000) are employed; investigating this particular class of journal bearings under static and dynamic loading conditions represents something unexplored. To this goal, a suitable test rig was designed and the performance of its bearings was investigated under steady load. For the sake of comparison, numerical simulations of the lubrication were also performed by means of a simplified model. The original test rig adopted is a commercial rotor kit (RK), but substantial modifications were carried out in order to allow significant measurements. Indeed, the relative radial clearance of RK4 RK bearings is about 2/100, while it is around 1/1000 in industrial bearings. Therefore, the same original RK bearings are employed in this new test rig, but a new shaft was designed to reduce their original clearance. The new custom shaft allows to study bearing behaviour for different clearances, since it is equipped with interchangeable journals. Experimental data obtained by this test rig are then compared with further results of more sophisticated simulations. They were carried out by means of an in-house developed finite element (FEM) code, suitable for thermoelasto-hydrodynamic (TEHD) analysis of journal bearings both in static and dynamic conditions. In this paper, bearing static performances are studied to assess the reliability of the experimental journal location predictions by comparing them with the ones coming from already validated numerical codes. Such comparisons are presented both for large and small clearance bearings of original and modified RKs, respectively. Good agreement is found only for the modified RK equipped with small clearance bearings (relative radial clearance 8/1000), as expected. In comparison with two-dimensional lubrication analysis, three-dimensional simulation improves prediction of journal location and correlation with experimental results.

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