A Dynamic Analysis of Cage Instability in Ball Bearings

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Takashi Nogi ◽  
Kazuaki Maniwa ◽  
Noriko Matsuoka
Keyword(s):  
Friction Coefficient ◽  
Dynamic Analysis ◽  
High Speed ◽  
Contact Stiffness ◽  
Ball Bearings ◽  
Analysis Program ◽  
Outer Race ◽  
Group Speed ◽  
Rotational Direction ◽  
Inner Race

Cage motions in ball bearings are investigated using a dynamic analysis program. Increases in the cage friction coefficient induce unstable motions of the cage. The instability is more likely to occur under high load and low‐speed conditions due to less ball-race sliding. A simple theory of cage instability is developed, and a critical cage friction coefficient formula is proposed, which is a function of the cage mass, ball-race traction, ball-cage contact stiffness, cage rotational speed, and number of balls. The prediction of this formula agrees with the results of the dynamic analysis. With a nonuniform separation between the balls, a high-speed whirl is superimposed on the normal whirl with the ball group speed. The direction of the high-speed whirl is the same as the cage rotational direction in inner race rotation (IR), but they are opposite in outer race rotation (OR). These results agree with some experimental results in the literature and validate the dynamic analysis.

scholarly journals Investigation of Factors Influencing the Structural Vibration in Ball Bearings

2000 ◽  
Vol 6 (5) ◽  
pp. 321-331 ◽  
Author(s):  
Kapil Mehra ◽  
Kambiz Farhang ◽  
Jayanta Datta
Keyword(s):  
High Speed ◽  
Structural Vibration ◽  
Ball Bearings ◽  
Appreciable Change ◽  
Outer Race ◽  
Nonlinear Springs ◽  
Lumped Parameter ◽  
Intermittent Contact ◽  
Parameter Approach ◽  
Inner Race

Hertzian equation for elastic contact is utilized along with lumped parameter approach to obtain the equations that govern the structural vibration of ball bearings. The lumped parameter formulation is obtained by treating various elements with mass lumped at their centers of gravity and the contact as nonlinear springs with nonlinear spring rates.Effects of preload, ball rotational speed, and damping are studied using the formulation. It is found that in the presence of preload, irrespective of the load magnitude, contact is maintained with both the inner and the outer races. Hence, responses obtained with and without the check for ball/inner race and ball/outer race interferences are identical. In addition, no appreciable change is observed in the responses when the preload value is varied from 1 to 10 N. At high speed of operation, the balls are found to maintain contact with the outer ring, whereas intermittent contact with the inner ring occurs for brief periods of time. Introduction of lubricant is found to dampen the oscillations considerably.

Numerical investigation of the oil–air distribution inside ball bearings with under-race lubrication

2021 ◽  
pp. 135065012110105
Author(s):  
Le Jiang ◽  
Yaguo Lyu ◽  
Wenjun Gao ◽  
Pengfei Zhu ◽  
Zhenxia Liu
Keyword(s):  
High Speed ◽  
Ball Bearing ◽  
Volume Fraction ◽  
Volume Flow Rate ◽  
Ball Bearings ◽  
Outer Race ◽  
Rotating Speed ◽  
Oil Distribution ◽  
Hole Configuration ◽  
Inner Race

Oil distribution inside the under-race lubricated bearing is crucial for lubrication and cooling of high-speed ball bearings. An under-race lubricated ball bearing is modeled to numerically investigate the effects of operating parameters and feed hole configuration on the distribution behavior of lubricant oil. The results of the numerical simulation indicate that the average oil volume fraction changes with a convex trend as the outer race rotating speed increases, while it changes monotonically with the inner race rotating speed, oil volume flow rate, and oil temperature. The extent of oil spreading on the outer race, cage, ball, and inner race decreases successively. Optimizing the feed hole configuration according to the average oil volume fraction is helpful to achieve precise lubrication of the under-race lubricated ball bearing.

scholarly journals Operating Limitations of High-Speed Jet-Lubricated Ball Bearings

1976 ◽  
Vol 98 (1) ◽  
pp. 32-39 ◽  
Author(s):  
E. V. Zaretsky ◽  
H. Signer ◽  
E. N. Bamberger
Keyword(s):  
Contact Angle ◽  
Flow Rate ◽  
Parametric Study ◽  
High Speed ◽  
Ball Bearings ◽  
Test Results ◽  
Outer Race ◽  
Lubricant Flow ◽  
Thrust Load ◽  
Inner Race

A parametric study was performed with 120-mm bore angular-contact ball bearings having a nominal contact angle of 20 deg. The bearings either had an inner- or an outer-race land riding cage. Lubrication was by recirculating oil jets. The oil jets either had a single or dual orifice. Thrust load, speed, and lubricant flow rate were varied. Test results were compared with those previously reported and obtained from bearings of the same design which were under-race lubricated but run under the same conditions. Jet lubricated ball bearings were limited to speeds less than 2.5 × 106 DN. Bearings having inner-race land riding cages produced lower temperatures than bearings with outer-race land riding cages. For a given lubricant flow rate dual orifice jets produced lower bearing temperatures than single orifice jets. However, under-race lubrication produced under all conditions of operation lower bearing temperatures with no apparent bearing speed limitation.

Development of Friction Drive Transmission

2005 ◽  
Author(s):  
Xiaolan Ai ◽  
Matthew Wilmer ◽  
David Lawrentz
Keyword(s):  
Friction Coefficient ◽  
Power Density ◽  
High Speed ◽  
Contact Stiffness ◽  
Outer Ring ◽  
The Sun ◽  
Input Shaft ◽  
Input And Output ◽  
Actual Operating ◽  
Output Torque

Friction drive is a mechanical device that utilizes friction force to transmit torque and power. Since the power is transferred through shearing a thin layer of highly pressurized lubricant film formed between the mating surfaces. Friction drive possesses desired performance attributes that pertain to its unique operating principles. These attributes include high mechanical efficiency, minimal backlash, low noise and vibration and high-speed capability. The power density of a friction drive can be very high when operated at elevated speeds. These performance features, in conjunction with its inherent manufacturing simplicity, make friction drives suitable candidates for a host of applications. The current global technology trend towards electrification and increasing use of electric machines in auxiliary drives for both automotive and industrial applications presents a good opportunity for friction drives as a cost-effective alternative to conventional gear drives. The smooth high-speed performance feature of friction drives allows the use of more efficient high-speed motors to reduce motor size and thus improve system power density. A novel cylindrical friction drive was developed [1,2] for electric oil pump applications. The friction drive is to be integrated with an electric motor to provide necessary speed reduction. The friction drive, as shown in Figure 1, is comprised of an outer ring, a sun roller, a loading planet, two supporting planets and a stationary carrier. The sun roller is set eccentric to the outer ring to generate a wedge gap that facilitates a torque actuated loading mechanism for the friction drive. The loading planet is properly assembled in the wedge gap with frictional contact with the sun roller and the outer ring and is elastically supported on the carrier. By altering the ratio of the support stiffness to contact stiffness, the actual operating friction coefficient of the friction drive can be changed to suit for desired performance regardless the wedge angle. This provides a grater freedom for design optimization. Design analysis was presented and a FE model was developed to quantify design parameters. Prototypes of the friction drive were fabricated for testing. Major geometry parameters are listed in Table 1. Extensive testing was conducted to evaluate its performance. Figure 2 shows the schematic of test apparatus. It is comprised of a drive motor, a high-speed spindle, and a hydraulic brake pump. The motor drives the spindle through a rubber belt and a pair of pulleys. The spindle shaft connects to the input shaft of the friction drive thought an input torque meter. The output shaft of the friction drive couples to the hydraulic pump through an output torque meter. The torque meters pick up both speed and torque signals at input and output shafts of the friction drive, respectively. Thermo-couples are mounted to monitor temperatures at planet support shafts and at bearings of input and output shafts. An accelerometer was placed on the back plate of a mounting bracket to which the friction drive was bolted. It monitors the vibration signals of the friction drive for reference and safety purposes. A data acquisition system was used to collect and process all signals at predetermined sampling rate. The friction drive offered a consistent smooth and quite performance over a wide range of operating conditions. It was capable of operating at an elevated speed of up to 12000 rpm with adequate thermal characteristics. Figure 3 shows the steady sate temperature contour map as function of input shaft speed and output shaft torque. Results demonstrated that the friction drive has high power transmission efficiency under various test conditions. The peak efficiency exceeded 97%. Figure 4 plots the overall system efficiency as a function of output torque for various input speeds. Results also confirmed that the stiffness of the elastic support has an important impact on performance. The elastic support stiffness, in conjunction with, the contact stiffness determines the actual operating friction coefficient at the frictional contacts.

The Effect of Waviness on Vibrations Associated Witli Ball Bearings

1999 ◽  
Vol 121 (4) ◽  
pp. 667-677 ◽  
Author(s):  
Nizami Aktu¨rk
Keyword(s):  
Computer Program ◽  
Ball Bearings ◽  
Surface Waviness ◽  
Outer Race ◽  
Rolling Surface ◽  
Frequency Domains ◽  
Axial Vibrations ◽  
Experimental Researches ◽  
Inner Race ◽  
Time And Frequency Domains

In this paper, the radial and axial vibrations of a rigid shaft supported by a pair of angular contact ball bearings is studied. The effect of bearing running surface waviness on the vibration of the shaft is investigated. A computer program was developed to simulate inner race, outer race, and rolling surface waviness with the results presented in time and frequency domains. Results obtained from the similation programme are quantatively in good aggrement with various authors’ experimental researches.

Investigation of Dynamic Processes in Ball Bearings with Defects

2013 ◽  
Vol 198 ◽  
pp. 651-656 ◽  
Author(s):  
Marijonas Bogdevičius ◽  
Viktor Skrickij
Keyword(s):  
Mathematical Model ◽  
Ball Bearing ◽  
Dynamic Processes ◽  
Experimental Investigations ◽  
Ball Bearings ◽  
Outer Race ◽  
Rolling Element ◽  
Inner Race

The paper considers the dynamics of ball bearings with defects. A mathematical model of a ball bearing with defects is offered. The performed theoretical and experimental investigations of ball bearings with defects are described. Five cases of various defects are investigated, including the defective outer race, the defective inner race, the defective rolling element, the defective inner and outer races, the rolling element and a separator, the worn-out ball bearing.

scholarly journals Parametric Study of the Lubrication of Thrust Loaded 120-MM Bore Ball Bearings to 3 Million DN

1974 ◽  
Vol 96 (3) ◽  
pp. 515-524 ◽  
Author(s):  
H. Signer ◽  
E. N. Bamberger ◽  
E. V. Zaretsky
Keyword(s):  
Parametric Study ◽  
Contact Angles ◽  
Inlet Temperature ◽  
Ball Bearings ◽  
Outer Race ◽  
Lubricant Flow ◽  
Endurance Tests ◽  
High Degree ◽  
Inner Race

A parametric study was performed with 120-mm bore angular-contact ball bearings under varying thrust loads, bearing and lubricant temperatures, and cooling and lubricant flow rates. Contact angles were nominally 20 and 24 deg with bearing speeds to 3 million DN. Endurance tests were run at 3 million DN and a temperature of 492 K (425 deg F) with 10 bearings having a nominal 24-deg contact angle at a thrust load of 22241 N (5000 lb). Bearing operating temperature, differences in temperatures between the inner and outer races, and bearing power consumption can be tuned to any desirable operating requirement by varying 4 parameters. These parameters are outer-race cooling, inner-race cooling, lubricant flow to the inner race, and oil inlet temperature. Preliminary endurance tests at 3 million DN and 492 K (425 deg F) indicate that long-term bearing operation can be achieved with a high degree of reliability.

Chaotic dynamics of cylindrical roller bearing supported by unbalanced rotor due to localized defects

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1898-1908
Author(s):  
Pravajyoti Patra ◽  
V Huzur Saran ◽  
Suraj P Harsha
Keyword(s):  
High Speed ◽  
Nonlinear Differential Equations ◽  
Roller Bearing ◽  
Major Elements ◽  
Mass Model ◽  
Outer Race ◽  
Vibration Signature ◽  
Discrete Spectra ◽  
Cylindrical Roller ◽  
Inner Race

This article presents a nonlinear vibration signature study of high-speed defective cylindrical roller bearings under unbalance rotor conditions. Qualitative analysis is conducted considering a spall defect of a specific size on major elements such as outer race, inner race, and rollers. A spring-mass model with nonlinear stiffness and damping is formulated to study the dynamic behavior of the rotor-bearing model. The set of nonlinear differential equations are solved using the fourth-order Runge–Kutta method to predict the characteristics of the discrete spectra and analyze the stability of the system. The results show that higher impulsive forces are generated because of outer race defects than defects in the inner race and roller. This can be explained as every time the roller passes through the defect in the outer race during rotation, the energy is released. However, in the case of both the roller and inner race defects, the impulsive force generated in the load zone is averaged because of the force generated in the unloading zone. The route to chaos from periodic to quasiperiodic response has been observed and analyzed that vibration signature is very much sensitive not only to the defects of bearing components but also to the rotor speed.

Study on Transverse Linear Stiffness of Bridge Piers in a High-Speed Railway

2012 ◽  
Vol 594-597 ◽  
pp. 1489-1493
Author(s):  
Heng Li ◽  
Hong Duan ◽  
Xiao Zhen Li ◽  
Chun Sheng Shan
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
High Speed ◽  
Coupled System ◽  
Dynamic Responses ◽  
Bridge Piers ◽  
Railway Bridge ◽  
Analysis Program ◽  
High Speed Railway ◽  
The Relationship

Based on the theory of vehicle-bridge coupled vibrations, the influence of transverse linear stiffness of double column piers on dynamic response of the train and bridge is investigated. A dynamic model of vehicle-bridge coupled system is established to analyze a high-speed railway bridge by BDAP software (Bridge Dynamic Analysis Program). By comparing the dynamic responses of piers which have different transverse linear stiffness, the characteristics of the relationship between the transverse linear stiffness of pier, the height of pier and transverse dynamic response are summarized, additionally some suggested values for transverse linear stiffness of piers are given to offer guidance for the design and construction of high-speed railway bridge.

An Experimental Research on the Vibration Reduction of Ball Bearings by Superfinishing Process

2016 ◽  
Vol 693 ◽  
pp. 1509-1516
Author(s):  
Wen Tao Liu ◽  
Yun Zhang ◽  
Zhi Jing Feng ◽  
Dong Feng Wang
Keyword(s):  
Experimental Research ◽  
Vibration Reduction ◽  
Ball Bearings ◽  
Considerable Influence ◽  
Medium Frequency ◽  
Outer Race ◽  
Excitation Frequencies ◽  
Inner Race

An experimental research on the reduction of vibration of ball bearings is provided in this paper. The waviness of inner race and outer race are decreased by superfinishing process, and their excitation frequencies are obtained. After the bearings’ vibration is tested, the powers of vibration distributed in different frequency regions are computed. The results reveal that the waviness excitations have a considerable influence on vibration of ball bearings in medium-frequency ranges, and the vibration can be reduced greatly by superfinishing process.

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