This paper studies the stiffness characteristics of preloaded duplex angular contact ball bearings. First, a five degrees-of-freedom (5DOF) quasi-static model of the preloaded duplex angular contact ball bearing is established based on the Jones bearing model. Three bearing configurations (face-to-face, back-to-back, and tandem arrangements) and two preload mechanisms (constant pressure preload and fixed position preload) are included in the proposed model. Subsequently, the five-dimensional stiffness matrix of the preloaded duplex angular contact ball bearing is derived analytically. Then, an experimental setup is developed to measure the radial stiffness and the angular stiffness of duplex angular contact ball bearings. The simulated results match well with those from experiments, which prove the validity of the proposed model. Finally, the effects of bearing configuration, preload mechanism, and unloaded contact angle on the angular stiffness and the cross-coupling are studied systematically.
The double-row self-aligning ball bearing commonly runs with angular misalignment between the inner and outer rings, and the angular misalignment significantly affects the bearing performance. However, the effect of angular misalignment on the dynamic characteristics of the double-row self-aligning ball bearing has not been studied thoroughly. This paper investigates the effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing. The quasi-static model for the double-row self-aligning ball bearing is established with five degrees of freedom, namely, three translational displacements along x, y, and z directions and two tilting angles around x-axis and y-axis. The internal clearance between balls and raceways is included in the presented model. The formulation of the three-dimensional stiffness matrix for the double-row self-aligning ball bearing is analytically derived, and is verified by comparing with the available dada in published literature. Finally, the stiffness of the double-row self-aligning ball bearing under various angular misalignment conditions is analyzed systematically. The results show that the tilting angles vary the contact angles and contact forces of the compressed balls in the double-row self-aligning ball bearing, thus affect the bearing stiffness; the bearing stiffness decreases with the internal clearance; the angular misalignment significantly impacts the stiffness of the bearing running at a low speed.
The purpose of this study is to investigate the dynamics of motorized spindle, in which the tilting effect of tandem duplex angular contact ball bearing is considered. First, the quasi-static model of the duplex angular contact ball bearing is developed based on the Jones's bearing model. Then, the model is numerically solved using the Newton–Raphson method to obtain 16 stiffness coefficients (including the tilting ones). Later, a modified transfer matrix method is used to establish the dynamic model of the motorized spindle system with 16 stiffness coefficients. Finally, experiments have been performed to detect the stiffness of the tandem duplex angular contact ball bearing and the unbalance response of the motorized spindle. Results show that the modified transfer matrix method can be used to analyze the dynamic behavior of the motorized spindle supported on tandem duplex angular contact ball bearings, the tilting effect of the tandem duplex angular contact ball bearing affects the dynamic behaviors of the motorized spindle, and the theoretical dynamic characteristics using the proposed model agree with the experimental ones.
This paper studies the static and dynamic coefficients of an externally pressurized porous gas journal bearing. The finite difference method is used to solve the Reynolds equation of the bearing to obtain the static load capacity. The linear perturbation method is adopted to derive the perturbation equations considering four degrees-of-freedom (4DOF), namely, the translational movements in x and y directions and the rotational movements around x and y directions. The effects of various parameters on the dynamic behaviors of the journal bearing are studied. These parameters include the bearing number, the supply pressure, the feeding parameter, the length-to-diameter ratio, the porosity parameter, the eccentricity ratio, and tilting angles. Simulated results prove that the proposed method is valid in estimating the static and dynamic characteristics of a porous gas journal bearing with 4DOF.
The support is a key factor affecting performance of face-grinding spindle. However, advantage of traditional rolling element bearing is not highlighted when it is for large-size face grinding. This technical brief aims to develop a combined support for the face-grinding spindle consisting of a water-lubricated hydrostatic thrust bearing and two types of radial rolling bearings, and the flexible rotor dynamics of the spindle with the combined support is analyzed using the modified transfer matrix method. The results show that the rotational stiffness of water-lubricated hydrostatic thrust bearing can increase the radial stiffness of the face-grinding spindle, so the small-size rolling bearings can be utilized as the radial support for the spindle by aid of such rotational stiffness. A comparative study of comprehensive performance between the spindle supported by rolling bearings and the replacement spindle designed with our proposed combined support shows that the proposed one has technical advantage of large axial load-carrying capacity, low frictional power loss, low temperature rise and etc.
The purpose of this paper is to investigate the dynamic characteristics of a high speed motorized spindle for internal grinding of slender holes. The modified transfer matrix method is used to establish the dynamic model of the motorized spindle rotor system including the additional stiffness of the non-contact rotary union. The linear perturbation method is adopted to derive the perturbation equations for the flow passing through the gap in the non-contact rotary union. The finite difference method is used to solve the Reynolds equation and the perturbation equations to obtain the four dimensional stiffness matrix of the non-contact rotary union. Finally, the effect of the non-contact rotary union on the dynamic behaviours of the motorized spindle are studied.
A mixed lubrication model of conical spiral-groove bearings is established by integrating partial fluid lubrication theory and G-W statistical theory. Considering the effect of bearing surface roughness, the equivalent average Reynolds equation is derived based on average flow model, which is solved by boundary fitted coordinate system and finite difference method. The G-W contact model is used to calculate the axial force and friction force produced by the contact of multi asperities. The coefficients of friction are calculated and measured under different rotational speed and the theoretical results are in accordance with the test results. The results show that comparing with bearings with deep groove, ones with shallower groove have lower transition speed and lower friction coefficient at low speeds.
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