| The modern numerical control technology is one of the crucial parts in modern manufacturing technology. The important norms to value numerical control system performance are the quantity of the interpolation functions and algorithms. Traditional NC system only have line and circular interpolation functions. They have some inevitable defects, such as oversized programs, low processing efficiency, low machining accuracy because of being secondary interpolation between CAM and CNC and rising ridge in finish surface. The advantages of NURBS interpolation technology are cutting down program code, dispensing with carrying through high speed program transmission, abbreviating processing time, advancing machining quality and so on. They greatly amend unfavorable facets of traditional line and circular interpolation, enhance the function of CNC path and have the critical function to improve entirety function of CAD/CAM.1. NURBS(Non-uniform rational B-spline)offers consolidate mathematical expression for normal analytical shape and free form curve(Non-rational B spline, rational and non-rational Bezier curve are the special cases of NURBS)which is convenient for accessing and application of engineering database. This paper discusses NURBS curve and its character and calculating methods of correlation parameter and gives arithmetic and converse arithmetic when known points is used for generating NURBS curves. For cutting down real-time calculating workload of spline curve, some calculating missions which can be completed once should be completed in the pretreatment phase. This paper adopts subsection matrix expression which is convenient for calculating and programming.2. This paper put forward a new NURBS interpolation algorithm which is based on Adams differential equation,and its parameter interpolation formula. And for furthermore filling the real-time requires of NURBS curve interpolation, this paper ameliorates the parameter interpolation formula by applying combination of ahead and rearward difference in place of differential and gets the reformtiveAdams differential equation interpolation iteration formula with fast parameter recursive efficacy. At the same time the prediction–correction method is adopted. First, interpolation point and feed step length are predicted by the iteration formula. Then the error between actual step and anticipation step length is calculated. If the error is in allowable range, the predicted interpolation point is considered as the interpolation point we to be seeking, otherwise the predicted parameter is corrected until it is in the allowable range of errror.3. Determination of the self-adaptive feed step length(feed rate).(1) Determination of constrained feed step length based on chord error controlling.In machining process, the machining accuracy is the first technic target to be assured. The inevitable error begetted by substituting tiny straight lines for curve is the main error source in NURBS interpolation. The constrained feed step length based on chord error controlling changes the instance which the error become bigger when curve curvature is bigger in the machining with invariable feed step length. Its keystone is as follows: the contour error being monitored in machining, if it is in the allowable range the feed step length is calculated with the present feed, oterwise the constraint feed step length is calculated under the require of the error. In this way, the feed step length can be adjusted with the curve curvature to insure that the chord errors are in the allowable range. In order to fulfill the require of real time interpolation and avoid the burdensome calculating of the differential coefficient, this paper adopts some methods to predigest the calculation impactfully and reasonablly as follows. Because the interpolation step length of NC machining is awfully smaller than curvilinear curvature radius, so chord error can be replaced with distance between curve section centre point and chord - length centre point. Generally, the deviation is small between them, only when nearby curvilinear inflexion is quite large, but curvature of curve nearby inflexion is often small where corresponding chord error is also small. So that this method is reasonable in engineering application. Consequently the self-adaptive feed step length is determined by summarizing theory and predigestion methods hereinbefore and some other calculation methods. It has the function of chord error controlling.(2)The determination of constrained feed step length based on feed acceleration controllingBecuase the motion parts of NC tools such as cutting tools rests, tables and so on have prodigious mass, for assuring machining accuracy the machine inertiamust be considered. Because a majority of NURBS curve are non-straight line segment, so this paper discusses machine impact of normal acceleration which due to the change of feed speed direction. With the elevating of feed rate in high speed and super high speed machining, the normal acceleration in the curve machining become larger and larger especially in the curve parts with large curvature. It may be bring badly impact on the entire machining system machining process and the machining quantity of the parts becauce the impact on the NC machine is beyond of its designed capacity. In this paper the change of real-time normal feed acceleration is monitored in high speed machining interpolation. When it exceeds allowable range, it would be adjusted in time according to setting feed acceleration, namely corresponding constrained feed step length is calculated taking prescribed allowable feed rate as constrained qualification.Analyzing constrained feed step lengthΔLi1 based on chord error controlling, constrained step length based on feed acceleration controlling and setting feed step length , the final current interpolation step length is the minimum of these three numbers:The NURBS interpolation methods assuring interpolation track adopted above have ability of adjusting feed rate itself. It can control interpolation error and feed rate in the allowable range at the same time, achieve maximum feed speed under the condition that the interpolation accuracy and impact on machine tool are all in controlling range, acquire optimization between interpolation accuracy and feed rate, improve machining quality and efficiency and primely content modern CNC machine tools which need machining with high speed and high accuracy. Curve with rational form and fragment parameter equation makes calculation abnormal tedious such as curve track, its differential coefficient and curvature and so on. This paper using proper interpolation preconditioning, meliorative fast parameter recursive formula, and rational approximate calculation, effectively predigests calculation of interpolation process avoids complex calculation of derivative and curvature radius, and ensures the all right real-time character of the interpolation algorithm.For machining which have high requirement for surface quality, such as finishing, and polishing, a interpolation method of constant cutting force (homogeneous material removal rate) is adopted in this paper. It is good for advancing machining quality and increses the the service life of the cutter. At thesame time this paper improves on its original formula utilizing Adams differential equation interpolation algorithm. And then get new constant cutting force interpolation algorithm which avoids tedious curvature calculation. It advances interpolation real-time character and machining accuracy.4. This paper presents new algorithm of S shape Acceleration-Deceleration controlling. Summarizing and analyzing corresponding literature, this paper adopts time relay and Acce-Dece-symmetry method, makes use of NURBS curve symmetry to predict Deceleration-point in the real-time interpolation, combines with Adams differential equation interpolation algorithm and gets the ahead parabola- line-parabola S shape Acceleration-Deceleration controlling method. It not only has merits such as higher positon accuracy no impact and being self-adaptive and so on, but also has got rid of the conditions of using minute chords to represent curve and calculating the length of curve once with interpolation be carrying out once. It is good for improving interpolation accuracy and real-time character.5. Real-time NC machining path emulation is executed with MATLAB and VC++ software based on Adams differential equation interpolation arithmetic and the new algorithm of S shape Acceleration-Deceleration. And the arithmetics have been proved to be correct, effective and having goog real-time character. This study makes preparations for empoldering new generations of the CAD/CAM.CNC system, and not only has important theory value for advancing NC systems but also has significant practical value for engineering application.NURBS interpolation technology which has been applying in the numerical control machining domain is an item of propping technology with the development of high speed and high accuracy maching. It will greatly improve the whole development level of the numerical control machining technology. With the era going forward, its prominent technical performance will obtain even more expansive development. |
