Tham khảo tài liệu 'hydrodynamic lubrication 2009 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 82 5 Stability of a Rotating Shaft Oil Whip Fig. . Stability charts for finite length bearings for three different values of the parameter 111 18 Oil Whip Theory 83 From the stability chart the following can be said 1. The larger the eccentricity ratio the more stable the shaft is. If the eccentricity ratio is larger than in paticular the shaft is always stable. 2. The higher the critical speed the higher the stability limit is. 3. The smaller the length L diameter D ratio of the bearings the more stable the shaft is. 4. There is no such simple rule that the stability limit is equal to twice the critical speed. It can be seen from the above analysis that a low oil viscosity high bearing pressure large bearing clearance high critical shaft speed and a small L D ratio are recommended for high shaft stability. b. Stability of Large Vibrations When a shaft bends and whirls with a large amplitude the journal center performs steady revolution around the bearing center for the major part of the bearing length as shown in Fig. bb. Therefore by setting the time derivative K of the eccentricity ratio to be 0 in Eq. of the oil film force the circumferential component of the oil film force Pe can be written in the following simple form Pe K k m - 2Q where M is the rotating speed of the shaft and Q e is the whirling speed of the shaft. In the case of large vibrations or whirling stability means whether the whirling radius of the journal diverges or converges under the oil film force mentioned above and in this case twice the critical speed has an important meaning as seen from the above equation. Fig. . Modeling of large vibrations 15 For large vibrations the shaft system can be modeled by a cylinder of mass m tied to the bearing center with a spring of spring constant k as shown in Fig. . 84 5 Stability of a Rotating Shaft Oil Whip The equation of motion of the cylinder can be written as follows the coordinates of the center of the .
