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Engineering Tribology Episode 2 Part 2

Tham khảo tài liệu 'engineering tribology episode 2 part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 250 Engineering Tribology and a specific damping coefficient e.g. Cix is calculated according to AW C x w W x 5.103 After determining all the necessary values of stiffness and damping coefficients the vibrational stability of a bearing can be evaluated. There are various theories of bearing vibrational analysis and the obtained stiffness and damping coefficients can be used in any of these methods. A very useful theory for vibrational analysis of a journal bearing was developed by Hori 7 . In this theory a simple disc of a mass m mounted centrally on a shaft supported by two journal bearings is considered. The disc tends to vibrate in the x and y directions which are both normal to the shaft axis. The configuration is shown in Figure 5.30. Figure 5.30 Hori s model for journal bearing vibration analysis. There are two sources of disc deflection in this model the shaft can bend and the two bearings are of finite stiffness which allows translation of the shaft. This system was analyzed by Newton s second law of motion to provide a series of equations relating the acceleration of the rotor in either the x or the y direction to the mass of the disc shaft and bearing stiffnesses and bearing damping coefficients. The description of this analysis can be found in 7 . The equations of motion of the disc can be solved to produce shaft trajectory but this is not often required since the most important information resulting from the analysis is the limiting shaft speed at the onset of bearing vibration. The limiting shaft speed is derived from the Routh-Hurwitz criterion which provides the following expression for the threshold speed of self-excited vibration or the critical frequency as it is often called o 2 __ A1A3A52__ c A12 À2Á52 - A1A4A5 A5 yA1 where A1 A2 A5 are the dimensionless stiffness and damping products o is the dimensionless bearing critical frequency. The bearing critical frequency is also given by o c c g c 0-5 5.104 5.105 TEAM LRN Computational