内圆磨床毕业设计翻译原文.doc

Investigation on critical speed and vibration mode of high speed grinderAbstractThe influences of the grinder spindle’s major structural parameters on its vibration mode were investigated. Based on the transfer-matrix method and taking into consideration the gyroscopic couple, the shear, the variable cross-section and other influential factors, a dynamic model was established for the multi-disk rotor of the rotor-bearing system of the grinder spindle. The critical speeds of first three orders, the modes of variation and other dynamic characteristic parameters of the grinder spindle were programmed and calculated. The influences of the axial pre-tightening force of the bearing, the span of the fulcrum bearing as well as the changes in the front and rear overhangs on the critical speed of the rotor-bearing system on the grinder spindle and their pattern of changes were analyzed. The results showed that the working speed of the spindle system is much lower than the primary critical speed and can therefore stay away the resonance range effectively.1. IntroductionThe spindle of high speed grinding machine tool is a typical high speed bearings-rotor dynamics system, and its rotating speed far surpasses the critical speed of the low order system. The realization of dynamic balance is associated with the performance and stability of the whole equipment. The research of rotor dynamic balance mainly involved the rigid rotor before the 1950s [1-4]. With the increase of the rotating speed and the flexibility of, the research on the method of flexible rotor’s dynamic balance appeared. The early stage method of flexible rotor’s dynamic balance was put forward by Feder, which was later called vibration balance method or modal balance method. The number of times of start-up of high-speed balance was relatively less, and is of high sensitivity. The low order mode would not be affected when the balancing of high order mode was conducted, but identification was not balanced[5-7]. The influence of bearing characteristics was especially great under large damping. It was not easy to achieve single modewhen used near critical speed in shafting balance. Later the American Goodman formally presented influence coefficient method based on least square method, and its advantages were as follows: electronic computer could be used to assist dynamic balance; the identification of unbalance factors was not affected by bearing characteristics; it could balance several vibration models simutaneously, which was more convenient especially for the balance of the shafts. However, the number of times of start-up in high speed balance was more, and the susceptibility of high order modes was reduced [8-10]. Based on the basic theories of rotor dynamics and structural system dynamics, dynamics theory model of the spindle system of high speed grinder was established using the transfer matrix method and the overall transfer matrix method in this study, and the simulation study was conducted on the influence of critical speed, vibration mode on the dynamic characteristics of main shaft systems of high speed grinder.2. Mathematical model of critical speed and vibration mode2.1 Model simplificationHigh speed spindle system is a continuous elastomer. Based on the concentration mass dynamic modeling theory of the transfer matrix method, it was necessary to simplify the quality continuous actual rotor into the rotor with a series of concentrated mass and rigid disks, which were connected by massless and flexible shaft sections in between[11-13]. Ultra-high speed grinding spindle system mainly consisted of bearings, spindle, motor rotor, and additional parts (locking nut, bearing retainer ring, encoder, sealing rings, etc.). The structural diagram is shown in Fig. 1 (1-Spindle 2- Motor rotor 3-Bearing).Figure 1. The structural diagram of spindle systemFor sliding bearing, the oil film’s dynamic coefficient matrix was as follows:The coefficient matrix of the dynamic performance of bearing block was as follows:When there was not too much difference in the stiffness and the equivalent mass of the bearing block in the direction of x, y, and coupling was relatively weak, the damping effect was negligible and the bearing was considered as isotropic:The model was converted to a fixed in-plane, and the rigidity coefficient of elastic bearing K could be calculated according to the formula below:K was the total bearing rigidity coefficient of the sliding bearing, which reflected the dynamic characteristics of the oil film, the bearing block and the foundation in a comprehensive way. The total bearing rigidity coefficient of the bearing was not constant, which was different from that of the common elastic bearing of equivalent stiffness, which was related to the whirling angular velocity of the rotor. For rolling bearing, the radial stiffness of the two bearings could form a larger angular stiffness Kθ, which was calculated according to the formula。