Stiffness characteristics of crossed roller bearings with roller roundness deformation

2021 ◽  
pp. 1-23
Author(s):  
Van-Canh Tong ◽  
Seong-Wook Hong
Keyword(s):  
Stiffness Matrix ◽  
Load Distribution ◽  
Misalignment Angle ◽  
Angular Misalignment ◽  
Internal Load ◽  
Roller Bearings ◽  
Bearing Stiffness ◽  
Axial Clearance ◽  
Stiffness Characteristics ◽  
External Loads

Abstract This study investigated the stiffness characteristics of crossed-roller bearings (XRBs) subjected to various loading and boundary conditions. A five degree-of-freedom XRB model was adopted that considers the effect of roller roundness deformation, which was developed by the authors in a prior study. The analytical formulation for a fully occupied (5 × 5) stiffness matrix of XRB was obtained. Extended simulations were performed to determine the XRB stiffness and internal load distribution considering the effects of the external loads, axial preloads, axial clearance, and angular misalignment. The numerical results confirmed that the bearing stiffness possessed significant nonlinearity with respect to the external loads. Increasing the axial clearance reduced the stiffness of the bearing under radial and moment loading, but it did not affect the stiffness of the pure axially loaded bearing. The stiffness of the bearing with axial clearance increased consistently with the misalignment angle. The stiffness behavior of the preloaded bearing depended on the misalignment angle.

Stiffness Study of a Parallel Link Robot Crane for Shipbuilding Applications

1989 ◽  
Vol 111 (3) ◽  
pp. 183-193 ◽  
Author(s):  
N. G. Dagalakis ◽  
J. S. Albus ◽  
B.-L. Wang ◽  
J. Unger ◽  
J. D. Lee
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Stiffness Matrix ◽  
Main Part ◽  
Laboratory Model ◽  
Stiffness Measurement ◽  
Parallel Link ◽  
Stiffness Characteristics ◽  
External Loads ◽  
Theoretical Results

This describes the first phase of an effort to develop a robot crane for shipbuilding applications. The focus of this phase is on the study of the stiffness characteristics of this robot as a function of its geometry payload and height. A brief description of the design of the main part of the robot crane consisting of a six-wire parallel link manipulator is given. The stiffness of the manipulator to side loads and moments was studied. The nonlinear and linearized mathematical model of the manipulator stiffness matrix is derived. Stiffness measurement tests were conducted using a small size laboratory model. The results of these tests for various external loads, heights, and payloads are given. Computer simulation and theoretical results are also discussed.

Mechanical analysis of spherical roller bearings due to misalignments between inner and outer rings

2016 ◽  
Vol 231 (17) ◽  
pp. 3250-3262 ◽  
Author(s):  
Yu Xing ◽  
Hua Xu ◽  
Shiyuan Pei ◽  
Xi Zhang ◽  
Wei Chang
Keyword(s):  
Carrying Capacity ◽  
Mechanical Performance ◽  
Interpolation Method ◽  
Bending Moment ◽  
Contact Angles ◽  
Hertzian Contact ◽  
Equilibrium Equations ◽  
Angular Misalignment ◽  
Roller Bearings ◽  
External Loads

This research presents a theoretical model to analyze the mechanical performance of spherical roller bearings, taking account of the angular and centroidal misalignments between the inner and outer rings. The angular misalignment can be improved by spherical roller bearings self-aligning feature to a certain degree. The interpolation method is used to determine the self-aligning contact angles of the different rollers. The centroidal misalignment is described by the angular and distance deviations. Non-Hertzian contact theory is applied to model and calculate the rollers load-distribution and total contact angles as well as the displacement of the inner ring. The loads of the rollers with the misalignments features and the external loads are included in the equilibrium equations, which is solved by Newton-Raphson method. This research shows spherical roller bearings self-aligning ability can balance the additional bending moment caused by the angular misalignment, which is at the cost of reducing its carrying capacity. But this carrying capacity will be improved to a certain degree by a proper axial load. It also illustrates that any kinds of centroidal misalignments are harmful for the service life of bearings. But the location of the misalignments can be roughly inferred by the external loads and the displacement of the inner ring, which is helpful for spherical roller bearings fault diagnose and elimination.

Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part I: General Theory and Application to Ball Bearings

1989 ◽  
Vol 111 (1) ◽  
pp. 142-148 ◽  
Author(s):  
J. M. de Mul ◽  
J. M. Vree ◽  
D. A. Maas
Keyword(s):  
General Theory ◽  
Load Distribution ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Contact Analysis ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Roller Bearings ◽  
Rolling Element ◽  
Bearing Stiffness

A new, general and consistent mathematical model of highly modular character is presented for calculation of the equilibrium and associated load distribution in rolling element bearings. The bearings may be loaded and displaced in five degrees of freedom. High speed rolling element loading is considered, internal friction is neglected, the material is assumed linearly elastic and the bearing rings are modelled as rigid except for local contact deformation. Either classical Hertzian contact analysis or modern non-Hertzian contact analysis of sophisticated or approximate character is used as applicable. The bearing stiffness matrix is computed analytically and used internally in the iterative bearing equilibrium calculation; its final values may be used for other purposes such as (rotor) dynamics analysis. In Part I, the general theory and application to ball bearings is presented. In Part II, application of the general theory to roller bearings and an experimental verification are presented.

Optimum initial axial compression due to preload in an arrangement of two tapered roller bearings Part 1: Analysis

2000 ◽  
Vol 214 (2) ◽  
pp. 125-133 ◽  
Author(s):  
I Bercea ◽  
D Nélias ◽  
S Cretu
Keyword(s):  
Fatigue Life ◽  
Axial Compression ◽  
Support System ◽  
Load Distribution ◽  
Numerical Procedure ◽  
Internal Load ◽  
Roller Bearings ◽  
System Survivability ◽  
Tapered Roller ◽  
Tapered Roller Bearings

This study is focused on a bearing arrangement made of two tapered roller bearings and a shaft, supporting a combination of axial and radial loads. The paper is divided in two parts. This part presents first a numerical procedure to obtain the internal load distribution within tapered roller bearings. The internal load distribution is required to estimate the bearing fatigue life. Afterwards, a numerical method and the related algorithm for a load support system constituted of a shaft and two tapered roller bearings are described. The effect of the initial axial preload (or total axial compression) is taken into account. In consequence the method proposed can be used to select an adequate axial preload in order to increase the system survivability. An example of model implementation, i.e. application to the transfer shaft of an automobile automatic transaxle, is presented in Part 2 of the paper.

Effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing

2019 ◽  
Vol 234 (4) ◽  
pp. 946-962 ◽  
Author(s):  
Keke Geng ◽  
Shengye Lin
Keyword(s):  
Stiffness Matrix ◽  
Degrees Of Freedom ◽  
Ball Bearing ◽  
Three Dimensional ◽  
Contact Angles ◽  
Static Model ◽  
Contact Forces ◽  
Angular Misalignment ◽  
Double Row ◽  
Bearing Stiffness

The double-row self-aligning ball bearing commonly runs with angular misalignment between the inner and outer rings, and the angular misalignment significantly affects the bearing performance. However, the effect of angular misalignment on the dynamic characteristics of the double-row self-aligning ball bearing has not been studied thoroughly. This paper investigates the effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing. The quasi-static model for the double-row self-aligning ball bearing is established with five degrees of freedom, namely, three translational displacements along x, y, and z directions and two tilting angles around x-axis and y-axis. The internal clearance between balls and raceways is included in the presented model. The formulation of the three-dimensional stiffness matrix for the double-row self-aligning ball bearing is analytically derived, and is verified by comparing with the available dada in published literature. Finally, the stiffness of the double-row self-aligning ball bearing under various angular misalignment conditions is analyzed systematically. The results show that the tilting angles vary the contact angles and contact forces of the compressed balls in the double-row self-aligning ball bearing, thus affect the bearing stiffness; the bearing stiffness decreases with the internal clearance; the angular misalignment significantly impacts the stiffness of the bearing running at a low speed.

The effect of angular misalignment on the stiffness characteristics of tapered roller bearings

2016 ◽  
Vol 231 (4) ◽  
pp. 712-727 ◽  
Author(s):  
Van-Canh Tong ◽  
Seong-Wook Hong
Keyword(s):  
Computational Procedure ◽  
Angular Misalignment ◽  
Practical Applications ◽  
Roller Bearings ◽  
Radial And Axial Displacements ◽  
Tapered Roller ◽  
Tapered Roller Bearings ◽  
Stiffness Characteristics ◽  
Moment Load ◽  
Frequency Behavior

The effect of angular misalignment between inner and outer raceways on the stiffness characteristics of tapered roller bearings (TRBs) is investigated. A computational procedure is introduced to solve the equations of TRB in the presence of angular misalignment. A dynamic analysis of a spindle supported by TRBs is also performed to investigate the natural frequency behavior by the stiffness variation due to angular misalignment. An extensive simulation demonstrates the effect of angular misalignment on the TRB characteristics such as roller–raceway contact loads, radial and axial displacements, and induced moment load. Computational results show that angular misalignment alters TRB stiffness characteristics and results in the splitting of the spindle natural frequencies by inducing anisotropic behavior of the TRBs. The proposed model and computational procedure are effective in estimating TRB characteristics and thus would aid in selecting TRBs or determining TRB loading conditions in practical applications.

Equilibrium and Associated Load Distribution in Ball and Roller Bearings Loaded in Five Degrees of Freedom While Neglecting Friction—Part II: Application to Roller Bearings and Experimental Verification

1989 ◽  
Vol 111 (1) ◽  
pp. 149-155 ◽  
Author(s):  
J. M. de Mul ◽  
J. M. Vree ◽  
D. A. Maas
Keyword(s):  
General Theory ◽  
Experimental Verification ◽  
Load Distribution ◽  
High Speed ◽  
Degrees Of Freedom ◽  
Contact Analysis ◽  
Hertzian Contact ◽  
Roller Bearings ◽  
Rolling Element ◽  
Bearing Stiffness

A new, general and consistent mathematical model of highly modular character is presented for calculation of the equilibrium and associated load distribution in rolling element bearings. The bearings may be loaded and displaced in five degrees of freedom. High speed rolling element loading is considered, internal friction is neglected, the material is assumed linearly elastic and the bearing rings are modelled as rigid except for local contact deformation. Either classical Hertzian contact analysis or modern non-Hertzian contact analysis of sophisticated or approximate character is used as applicable. The bearing stiffness matrix is computed analytically and used internally in the iterative bearing equilibrium calculation; its final values may be used for other purposes such as (rotor) dynamics analysis. In Part I, the general theory and application to ball bearings is presented. In Part II, application of the general theory to ro´ller bearings and an experimental verification are presented.

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.

scholarly journals Associations between Well-Being State and Match External and Internal Load in Amateur Referees

2021 ◽  
Vol 18 (6) ◽  
pp. 3322
Author(s):  
Eñaut Ozaeta ◽  
Javier Yanci ◽  
Carlo Castagna ◽  
Estibaliz Romaratezabala ◽  
Daniel Castillo
Keyword(s):  
External Load ◽  
Contact Time ◽  
Well Being ◽  
Ground Contact ◽  
Internal Load ◽  
Match Play ◽  
Power Meter ◽  
Ground Contact Time ◽  
Training Impulse ◽  
External Loads

The main aim of this paper was to examine the association between prematch well-being status with match internal and external load in field (FR) and assistant (AR) soccer referees. Twenty-three FR and 46 AR participated in this study. The well-being state was assessed using the Hooper Scale and the match external and internal loads were monitored with Stryd Power Meter and heart monitors. While no significant differences were found in Hooper indices between match officials, FR registered higher external loads (p < 0.01; ES: 0.75 to 5.78), spent more time in zone 4 and zone 5, and recorded a greater training impulse (TRIMP) value (p < 0.01; ES: 1.35 to 1.62) than AR. Generally, no associations were found between the well-being variables and external loads for FR and AR. Additionally, no associations were found between the Hooper indices and internal loads for FR and AR. However, several relationships with different magnitudes were found between internal and external match loads, for FR, between power and speed with time spent in zone 2 (p < 0.05; r = −0.43), ground contact time with zone 2 and zone 3 (p < 0.05; r = 0.50 to 0.60) and power, speed, cadence and ground contact time correlated with time spent in zone 5 and TRIMP (p < 0.05 to 0.01; r = 0.42 to 0.64). Additionally, for AR, a relationship between speed and time in zone 1 was found (p < 0.05; r = −0.30; CL = 0.22). These results suggest that initial well-being state is not related to match officials’ performances during match play. In addition, the Stryd Power Meter can be a useful device to calculate the external load on soccer match officials.

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