Effect of Preload on the Vibrations of EHL Angular Contact Ball Bearings: Theoretical and Experimental Results
Abstract
:1. Introduction
2. Shaft—ACBB System Theoretical and Experimental Modelling
2.1. Theoretical Modelling
2.1.1. EHL Angular Contact Ball Bearing Modelling
2.1.2. Rigid Rotor Supported by ACBB System
2.2. Experimental Studies
3. Results and Discussion
3.1. Simulation Results
3.1.1. Effect of Preload in Time Domain
3.1.2. Effect of Preload in Frequency Domain
3.2. Experimental Results
Effect of Preload
3.3. Comparison
4. Conclusions
- Vibration amplitudes and BPV peak-to-peak amplitudes are decreased by increasing preload. This attenuation on the amplitute of BPV is reached to 10 times. However, at the same time, the natural frequency of system is shifted a higher value. This shifting is apparently seen in the results of both proposed theoretical model and experimental study.
- It is observed that increased preload has reduced the visibility of the bearing variable compliance frequencies and harmonics in the frequency spectrum.
- Axial vibration bandwidth is increased approximately two times with increased preload. However, vibrations in the z-axis exhibit a more complex behaviour with increasing preload. An increase in the contact angle with preload can cause an increase in the axial mode vibrations.
- Using signal processing with envelope spectrum gives better results in obtaining of bearing variable compliance frequencies. Kurtosis is increased four times by using a signal processing technique.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
Dimensionless semimajor and semiminor axis of contact ellipse | |
A | Distance between raceway grove center, m |
c | Viscous damping factor, Ns/m |
Elastic contact deformations, m | |
Elastic contact deformations at contact centre, m | |
Ball diameter, m; pitch diameter, m | |
Modulus of elasticity, reduced module of elastacity, N/m2 | |
Frequency, ball passage frequency, Hz | |
Normal EHL contact force; dissipative force; elastic restoring force; Hertz normal force, N | |
G | Dimensionless materials parameter, |
Film thickness m; central film thickness, m | |
H | Dimensionless film thickness, |
k | Stiffness factor, N/m |
m | Number of balls, kg |
n | Rotational speed of the spindle, rpm |
M | Mass of shaft, kg |
p | Pressure, Pa |
Preload, N | |
Radii of curvature, m | |
R | Curvature sum, ball centre focus radius under zero load, m |
Q | External forces, N |
u | Surface velocity in direction of motion , m/s |
U | Dimensionless speed parameter, |
t | Time, s |
W | Dimensionless load parameter, |
Coordinate axis, m | |
Pressure-viscosity coefficient, Pa | |
Instantaneous contact angle; unloaded contact angle; | |
preloaded contact angle, rad | |
Mutual approach between contacting bodies m | |
Complete elliptic integral of the second kind | |
Ellipticity parameter, a/b | |
Complete elliptic integral of the first kind | |
Viscosity, Pa s | |
Curvature, | |
, | Angular velocity, cage angular velocity, rad/s |
The angle between the fixed and moving reference axis, rad/s | |
Rock angle of the shaft about x axis, rad | |
Rock angle of the shaft about y axis, rad | |
Abbreviations | |
ACBB | Angular Contact Ball Bearing |
EHL | Elasto Hydrodynmic Lubrication |
BPF | Ball Pass Frequency |
BPV | Ball Passage Vibrations |
BSF | Ball Spin Frequency |
DSP | Digital Signal Procecessing |
PLC | Programmable Logic Controller |
Appendix A. Bearing Modelling
Appendix B. Bearing Geometry
Appendix C. System Data for Numerical Computation
Description | Dimension |
---|---|
Type | Angular Contact Ball Bearing |
Outer Raceway Diameter | m |
Outer Ring Diameter | m |
Inner Ring Diameter | m |
Inner Raceway Diameter | m |
Pitch Diameter | m |
Inner Ring Groove Radius | m |
Outer Ring Groove Radius | m |
Bearing Width | m |
Ball Diameter | m |
Number of Balls | |
Unloaded Contact Angle | m |
Young Module | GPa |
Poisson Ratio | |
Type | Rigid Shaft |
Diameter | m |
Length | m |
Mass | kg |
Lenght between Bearings | m |
Lenght CG to Bearing | , m m |
Lubricant Properties | Pas, Pa |
Measurement Place | Accelometer No | Sensivity (mv/ms2) | Sensivity (mv/g) |
---|---|---|---|
Idle side Horz. y-axis | AI8 1438 | 0.818 | 8.02 |
Idle side Vert. x-axis | AI1 1439 | 0.797 | 7.83 |
Motor side Vert. x-axis | AI9 1437 | 0.797 | 7.82 |
Appendix D. Variable Compliance Frequancies of Bearing
Speed (rpm) | Cage Freq. (Hz) | BSF (Hz) | BPFO (Hz) | BPFI (Hz) |
---|---|---|---|---|
200 | 1.4023 | 7.843984 | 18.229699 | 25.1036 |
400 | 2.8046 | 15.687969 | 36.459398 | 50.2073 |
600 | 4.2069 | 23.531953 | 54.689097 | 75.3109 |
800 | 5.6091 | 31.375938 | 72.918795 | 100.4145 |
1000 | 7.0114 | 39.219922 | 91.148494 | 125.5182 |
1200 | 8.4137 | 47.063907 | 109.378193 | 150.6218 |
1400 | 9.8160 | 54.907891 | 127.607892 | 175.7254 |
1600 | 11.2183 | 62.751876 | 145.837591 | 200.8291 |
1800 | 12.6206 | 70.595860 | 164.067290 | 225.9327 |
2000 | 14.0228 | 78.439845 | 182.296989 | 251.0363 |
2200 | 15.4251 | 86.283829 | 200.526687 | 276.1400 |
2400 | 16.8274 | 94.127814 | 218.756386 | 301.2436 |
2600 | 18.2297 | 101.971798 | 236.986085 | 326.3472 |
2800 | 19.6320 | 109.815783 | 255.215784 | 351.4509 |
3000 | 21.0343 | 117.659767 | 273.445483 | 376.5545 |
Appendix E. Effect of Preload on the Natural Frequency
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Bal, H.; Ateş, K.; Karaçay, T.; Aktürk, N. Effect of Preload on the Vibrations of EHL Angular Contact Ball Bearings: Theoretical and Experimental Results. Lubricants 2022, 10, 46. https://doi.org/10.3390/lubricants10030046
Bal H, Ateş K, Karaçay T, Aktürk N. Effect of Preload on the Vibrations of EHL Angular Contact Ball Bearings: Theoretical and Experimental Results. Lubricants. 2022; 10(3):46. https://doi.org/10.3390/lubricants10030046
Chicago/Turabian StyleBal, Hikmet, Kerem Ateş, Tuncay Karaçay, and Nizami Aktürk. 2022. "Effect of Preload on the Vibrations of EHL Angular Contact Ball Bearings: Theoretical and Experimental Results" Lubricants 10, no. 3: 46. https://doi.org/10.3390/lubricants10030046