tailieunhanh - Hydrodynamic Lubrication 2011 Part 5

Tham khảo tài liệu 'hydrodynamic lubrication 2011 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 72 5 Stability of a Rotating Shaft Oil Whip The oil film force of a finite length bearing can also be written in the following form similar to those of an infinitely long bearing and a short bearing 20 Pk - 6u R LRj c w - 2ở pK1 KPK2 w - 2Q pQ1 kPq Pq 6jJR LRj Tn ll i. i. ii . p 1 p 2 p 1 lii l p 2 HI . Il I n í 11 . Hi ill n. illi ll lii i ii ifii i iinii in this case P K P K P Q and P Q are functions of K With Hie bearing difffensions as parameters. These are usually calculated numerically. Linearization of the Oil Film Force To discuss the linear stability of a shaft the oil film force is linearized beforehand in the neighborhood of the equilibrium point of the journal center Oj0 K0 Q0 . Fig. . Rectangular coordinates radial direction circumferential direction Equations and are used to express the oil film force. Then variable substitutions K K0 K Q Q0 Q are made in these expressions and assumptions that new variables K Q and their time derivatives K and Q are so small that their second power third power . and products can be disregarded give the linearized oil film force PK and PQ as follows PK - 6u Rj LRj X c 2ko2w i 2 2ko 2ko 2 ko2 1 -K02 I K0 2 K02 1 -K02 Oil Whip Theory 73 4ko20 2k in 8 2 K02 1 - K02 1 - K02 3 2 2 n 2 K02 Pe 6u 1 LRj X cl nKou 11 1 2k0 Ko . 2 k02 V1 - k02 1 k0 2 k02 1 - k02 2nK0 e 4k0K 2 k02 V1 - k02 2 k02 1 - k02 _ Now to consider the journal motion in the rectangular coordinate system x y shown in Fig. let us transform the above components of the oil film force to the rectangular components Px and Py using the following expressions Px Pk - Peo Py Pe PkO - CK0 CK0 where Pe0 and PK0 are the stationary values of the oil film force at the equilibrium point . the constant terms of Eqs. and . Now let us perform the variable transformation K Xj c 0 yj CK0 Kj Xj c and e j ýj CK0 and assume that Xj yj Xj and y j are sufficiently small considering small vibrations. Then the