| This thesis presents the study on a new hybrid linear and rotary fast tool servo (L/RFTS) stage in diamond turning machine for cutting optical free-form surfaces. This fast tool servo (FTS) consists of a rotary fast tool servo (RFTS) and a linear fast tool servo(LFTS). It not only possesses the features of high acceleration, high bearing capability and stiffness, but also can ensure the system run steadily, because of utilizing air bearing and an innovative kind of air lead-rail. By using the rotary encoder with high resolution and new measuring technique with two optical gratings enable the FTS measure the rotary angle of the tool-arm and linear displacement of the lead-rail precisely.According to the function requirement of FTS system, the author of this thesis designs the entire structure of this L/RFTS, and develops its 3D model by CATIA. To machine optical free-form surfaces by diamond turning, the cutting tool must move synchronously with the spindle rotation (the bandwidth of the L/RFTS must be at least 2 times larger than the frequency of the spindle roration), this demands L/RFTS for extremely high acceleration of both rotary and linear motion. Therefore, besides trying to decrease the mass and inertia of every part, the author chooses the brushless DC motor which has a high torque-inertia ratio and low revolving speed as the driving motor for the RFTS, and choose the linear motor with iron core that has large thrust as the driving motor for the LFTS. The computing results demonstrated that the RFTS could gain an acceleration of 46g, and the LFTS could obtain an acceleration of 7g.Cutting optical free-form surface by diamond turning machine is belong to ultra-precision cutting, so if one wants to gain perfect machining accuracy, it requires the L/RFTS possess a great performance. The air bearing and air lead-rail have the advantage of high accuracy, large carrying capacity, high stiffness and no friction. Therefore, according to the static design theory of air bearing, this thesis designs the air bearing as the bearings for the tool-arm shaft in the RFTS, and air lead-rail for the LFTS. When the supplied air pressure is 1.1 MPa～1.4MPa,the largest carrying capacity of the air bearings in the RFTS can reach to 170N,the highest stiffness can be 50N/μm,and their needed air flow is 62 cm~3/s ,but the load of the RFTS is just about 20N,less than 100N.The carrying capacity of the air lead-rail of LFTS can reach to 1200N, the highest stiffness can be 950N/μm, and its needed air flow is 102.4 cm~3/s, and the load for the LFTS is less than 500N.This thesis also designs the structure of the tool-arm for mounting the diamond tool. Its total stroke is nearly 50 mm, by the sum of its own stroke and the stroke of the lead-rail. Meanwhile, it also has the characteristic of low inertia, high stiffness, and being easily manufactured. Its first mode of resonance is 3401.4Hz, which explains that the tool-arm has a high dynamic stiffness Also, the author designs the tool height adjustment in this thesis.This thesis also conducts the structural finite element analysis on the air lead-rail and the tool-arm by ANSYS. Through static analysis, analyzes the deformation of efficient surface of the air lead-rail is much less than 0.1μm under gravity, and less than 3μm under gravity and air pressure. But when apply the maximum driving force of the linear motor to the lead-rail, the deformation of the slide of the lead-rail is much less than 3μm, however, the deformation of the base of the lead-rail is much more than 3μm. Hence, the thesis improves the structure of the lead-rail. The modal analysis of the lead-rail and the tool-arm are carried out, which analyzes the first to twentieth modes of resonance of the lead-rail and the tool-arm, and then reveals the weak parts of those components. The first mode of resonance of the base and slide of the lead-rail are 2681.6Hz and 5698.2Hz, respectively, so the bandwidth is very high.Finally, the thesis discusses the improvement on the structure of the air lead-rail. After the modification of its structure, their weak parts have been eliminated, and what most important is the deformation of the base of the lead-rail is less than 3μm, under the gravity, air pressure and the maximum driving force of the linear motor. Meanwhile, the mass of the slide of the lead-rail has also been decreased, which enable the acceleration of the LFTS exceed original requirement of 5g that the acceleration can reach to 7g. In addition, the first mode of resonance of both the base and slide of the lead-rail also change into 1909.5Hz and 6966.5Hz.Compare to the original design, the first mode of resonance of the base has decreased, but the first mode of resonance of the slide has increased than before, in that case, both of their first mode of resonance are still high, and there is a large numerical difference between the two first mode of resonance, so it's more impossible to have the resonance on the above-mentioned two components.
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