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Determining the parameters of angular contact ball bearings under preload is the key issue to improve the accuracy and performance of high-speed spindle. The impact of gyro force and centrifugal force were considered, a static and a dynamic model for angular contact ball bearings under rigid preload were presented. By using Newton iterative method, dynamic parameters of the angular contact bearings were obtained, including eccentricity of contact ellipse, contact angle, contact force, maximum contact stress, contact ellipse radii and stiffness, etc. According to numerical simulation, relationship between the parameters, versus preload and versus rotation speed were given. The results reveal that the stiffness increases as the preload increases appropriately, the contact stress and contact ellipse radii increase as the preload increases excessively. In addition, under rigid preload this model has no bearing softening effect. This method provides valuable theoretical basis for further researches, such as calculating bearingscalorific value, calculating bearings fatigue life and optimizing bearings structure, etc. Introduction Angular contact ball bearings are commonly used in high-speed spindles. The performance of angular contact ball bearings effect the static and dynamic performance of high-speed spindles seriously [1]. These bearings require preloading in order to improve the rotational accuracy and sufficient stiffness, and reduce vibration noise, etc. Basically, there are two types of bearing preload: rigid and constant. Constant preload is using helical springs, disc springs, and other preload devices to make the bearings obtain appropriate preload force. Rigid preload is using sleeves and washers to make the inner ring and outer ring in an appropriate distance, so that the bearings have appropriate preload force [2]. In actual manufacturing process, because of lacking accurate modeling and analyzing method, it is a key problem to determine the preload force or preload distance of the bearings. Consequently, it is significant to establish a model of bearings under preload. There are many studies make researches about bearings in modeling, analyzing, testing fields. Altintas considered gyro force and centrifugal force of rotation parts, and established a model by using the finite element method [3, 4]. Lim derived 5 degree of freedom analysis model and stiffness matrix based on Hertz contact theory [5, 6]. Royston derived 5 degree of freedom vibration model based on Lim’s work. And studied the change of natural frequency and stiffness in different preload force [7]. LigangCai presented a modeling theory of angular contact ball bearings under constant preload, and verified the model through an experiment [8]. Wang Hong-jun introduced bearing softening effect under high speed rotation [9]. Wensing calculated elastic deformation according to the generalized shape function, and used software ANSYS to verify the result [10]. BaominWang analyzed mechanical properties of bearings by using Pseudo dynamic method [11]. Ali investigated the stiffness of bearings under different preload force and rotation speed through hammer test [12]. TaipingHuang used eccentric mass excitation method to obtain the equivalent stiffness of the bearings [13]. Few investigations have focused on the modeling method of angular contact ball bearings under rigid preload. This paper based on Hertz contact theory, and considered the impact of gyro force 3rd International Conference on Mechanical Engineering and Intelligent Systems (ICMEIS 2015) © 2015. The authors Published by Atlantis Press 890 and centrif preload, in state. Acco force and v contact for valuable th Dynamic m This p parameter established angle c preload m contact elli can be sol previous so radial direc Contac and Hertz c ω x, y Here, p ellipse,the the eccentr After co ω Using: L M N By integ ∫∫ ugal force. cluding con rding to N ersus rotat ce, maxim eoretical ba odel of an aper based equations and force b an be solve odel in rot pse(ei,eo), c ved by New lutions(ei, tion can be t area mod ontact theo ∫∫   , x y   is t elliptical co icity e is gi ordinate tra

A dynamics modeling research for angular contact ball bearing of high-speed spindle under rigid preload