| Freeform surface is widely used in various industries due to its exquisite appearance and outstanding dynamic performance. Currently, the modeling technology of complex free-form surface has been quite mature, but its complex shape and high precision requirement raise the difficulty in processing. Five-axis machining is an important means of efficient processing of the complex and high performance parts in industry, and it can process continuous, smooth and complex freeform surface. Since the degrees of freedom increases, the orientation control of cutting tool and the tool path planning in processing become much more complex. Therefore, in the five-axis NC machining of parts with complex freeform surface, the research on the tool orientation adjustment and the tool path planning has important practical significance.This paper analyzed the geometry principle of free-form surface processing and proposed the second-order contact method based on the high-order contact character of surface and studied the tool orientation adjustment and tool path planning in the surface processing. Mainly including:(1) The relationship between surfaces and the individual characteristics of the surface is discussed by applying the differential geometry curves and surfaces theory. The concept of contact order for the tangent contact between surfaces is introduced and the relationship between the contact order and the principal and normal curvature of surface which is also applied to the partial reconstruction model of tool envelope surface is studied.(2) Based on the analysis of high-order contact characteristics of surface, the partial geometry model of freeform surface machining by rotary cutting tool is established starting with the contact characteristics of second-order and free-form surfaces. The function of the tool axis vector is calculated when the rotating tool envelope surface contacts with the freeform surface in a normal section and is extended to any normal sections near the contact point. Then the function of tool axis inclination angle is proposed when the second-order contact between the tool envelope surface and the free-form surface appears and the equation of the tool orientation of the state is analytically resolved.(3) According to the expression of cutting tool axis vector function obtained by the second-order contact method, open parameters concave surface is studied and its simulation is analyzed. And the curvature function curves of each discrete tool contact point which appears when second-order contact between tool envelope surface and free-form surface exists. After traversing every direction of the tangent plane, it found that the function curve of the cutting tool axis inclination angle has a common discrete point in the same discrete tool position. And in the same parameter line but different discrete tool position, the tool axis inclination angle changes stably, the tool plan is smooth and the processing is stable.(4) To optimize the processing direction by maximize the line space of processing, we switch the procedure of seeking processing direction to the matching of the minimum principal directions of curvature of the free-form surface. For the step calculation, we proposed the variable step algorithm of chord error, based on the golden section method to obtain the maximum chord error parameters by interval approximation. According to the curvature radius relation between initial tool contacts and temporary discrete tool contacts, we checked the maximum actual chord error and obtained the maximum step of processing met the tolerance in machining.(5) The results of computer simulation demonstrate the feasibility and reliability of the proposed algorithm. Followed by the laboratory analysis, we showed that the model not only satisfy the requirements of precision of the surface, but also can improve the processing efficiency to a great extent, which is of practical significance. |
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