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최대 10 단어까지만 선택 가능합니다.
제안 방법
- A modeling program for spindle-bearing system has been developed for spindles supported by multiple bearings of different types. An indeterminate spindle bearing system with angular contact ball bearings and cylindrical roller bearings is investigated to demonstrate the program. The simulation results show that the developed program can well predict the bearing stiffness and spindle dynamic behavior under general loading conditions.
- The above scheme is used for formulating the relationship of the spindle shaft deflections and reaction forces. It is obvious that the developed scheme could be applicable to a variety of cross-section areas, with different materials and also with general loadings.
- This paper extends the earlier work proposed by Hong et al.10 to develop a new scheme for calculation of bearing stiffness and spindle shaft reaction forces. The most important contribution of this work is modifying the spindle load and deflection formulation using the so-called modified transfer matrix method.
이론/모형
- Jorgensen and Shin9 analyzed the angular contact bearing stiffness and natural frequencies of the spindle with the radial load applied. In their study, the spindle shaft was discretized into lumped elements with which the influence coefficient method was applied to find the load deflection relationship. This method could be applied only for spindles supported by two bearings or two sets of bearings in which each set of bearings is modeled as a stiffness matrix at a single node.
- In this section, simulation is performed using Matlab to demonstrate the proposed method. Two kinds of bearings such as angular contact bearing B7014 and cylindrical bearing NU1014, are considered throughout the simulation work.
- outlined a general method for modeling of spindle-angular contact bearing systems. The combination of bearing dynamic characteristics and spindle shaft using finite element method was performed to derive the dynamic equations for spindle-bearing systems, which were then iteratively solved by the Newton Raphson technique. Although their method was verified to be accurate, much computational effort was required to solve non-linear equations simultaneously.
- 10 to develop a new scheme for calculation of bearing stiffness and spindle shaft reaction forces. The most important contribution of this work is modifying the spindle load and deflection formulation using the so-called modified transfer matrix method. The overall computational procedure is in the same manner as that in Hong et al.
- It is noted that the Euler-Bernoulli beam theory does not give accurate deflection results, particularly in the case of thick beam, since the rotary inertia and shear deformation are not taken into account. Therefore, this section aims to improve the computational accuracy by using the Timoshenko beam theory.
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