A general closed-form analytical solution is derived for the lapping tracks with its kinematics for the concentric V-groove lapping system. The lapping tracks on the ball surface for the three contact points are fixed circles, and their lengths of the lapping tracks are linearly proportional to , , and , respectively. In practice, if the orientation is randomized as the ball enters the lap again, then the distribution of the lapping tracks are dense after many cycles, and the larger the lapping length in each cycle, the smaller is the number of cycles required achieving the maximum lapped area ratio. In the geometry design of ball lapping, the V-groove half-angle should be larger than 45¢X, but to prevent the splash of abrasives, it should be less than 75¢X.
Since the spin angular speed with its angle continuously varies with time for the eccentric lapping system, lapping tracks are not fixed circles. In practice, the lapped areas are complementary at the contact points of A and B. The total lapped area ratio is higher than 87% for a slip ratio less than 0.5. Hence, it is possible to lap all the surface of a ball by changing the slip ratio during the lapping process. Moreover, the larger the V-groove half-angle, the less is the eccentricity to achieve the optimum lapped area ratio.
In order to understand the ball motion and ball lapping mechanism in the magnetic fluid lapping system, the forces and moments equilibrium equations are derived and numerical methods are analyzed. As the balls traveling in a train are assumed to be the same size, only one ball is considered in the dynamic analysis. Results show that as the ball separates from the shaft and the float, the spin angle increases quickly and approaches to 90¢X. Hence, the ball changes its attitude and thereby generates a new lapping tracks on the ball surface. Consequently, after repeating many cycles, lapping tracks would be scoping out more space and this is one of the spherical surface generation mechanisms.
Surface waviness of ball causes a variation in the lapping load. When , it is possible to cause the ball separated from float and the lapping load is zero during the separation period. No matter how the ball separates from float, the spin angle always varies in a small range. Hence, only a very small region can be grounded due to the effect of the surface waviness. Therefore, it is not the main lapping mechanism of the spherical surface generation.
In fact, during the lapping process, many balls with different diameters are lapped. To understand the ball¡¦s lapping mechanism of the spherical surface generation, it is necessary to consider a batch of balls. For a batch of balls with different diameters, the applied load on each should be different from each other. Generally, the larger the diameter of a ball, the larger is the friction force between the ball and shaft and the ball circulation speed. Therefore, it is possible to cause the collision between the larger and the smaller balls. To understand the interaction between balls traveling in a train, the dynamic analysis of multiple balls is developed. As the ball interacts with each other, it is possible to change the spin angle, and thereby to achieve the larger variation range of the lapping tracks. During the lapping process of a batch of balls, it is also possible to cause the separation between the shaft and the ball, and it causes the ball to change its attitude and to achieve more uniform lapping tracks.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0818106-181936 |
| Date | 18 August 2006 |
| Creators | Hwang, Yih-chyun |
| Contributors | Jao-hwa Kuang, Jen-fin Lin, Yeau-ren Jeng, none, Yaw-terng Su, Rong-tsong Lee, Yuang-cherng Chiou |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0818106-181936 |
| Rights | unrestricted, Copyright information available at source archive |
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