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Improving contour accuracy is one of the significant goals of industrial machining. This paper proposes a contour error estimation and compensation algorithm for five-axis computer numerical control (CNC) machine tools based on modified numerical control (NC) codes. The expected path analyzed by NC data and the actual trajectory collected by sensors are spatially mapped by the hidden Markov model (HMM). Next, an evaluation function that hybrids the tool tip position and tool orientation change trend is proposed as the index of contour error estimation. Finally, spatial iterative learning control (ILC) is used to compensate the contour error, and high-precision machining instructions are obtained after multiple iterations. Experiments with different trajectories are performed on a five-axis platform to verify the proposed algorithm’s effectiveness. The results show that the proposed algorithm without using planned trajectories, has the same good control effect as traditional methods, which must know the planning trajectory for simple trajectories. At the same time, the method proposed in this paper has better performance than existing algorithms based on tool tip position nearest principle at sharp corners. In conclusion, on the basis of not depending on the planning trajectories, this method has a better compensation effect for the overall accuracy of trajectories and is easier to implement in industrial applications.

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Abstract. The two basic value embodiments to guarantee the procedural law are reflected in its fairness and efficiency. The efficiency function of procedural law can improve the jurisdiction efficiency effectively, which is the both the character of procedural law itself, and the basic rule to implement the effect function of procedural law. Compared with the foreign countries, the procedural law in China has not been so perfect, and there is no perfect concept of procedure procedural justice and the overall structure of procedural law is not so scientific and reasonable, restricting the full use of efficiency function of the procedural law; only by continuously perfecting the procedural law can the efficiency function of the procedural law be fully played and applied in the law reasonably. Aimed at the efficiency function of the procedural law, the author makes a brief analysis and explains his own opinions for reference by the peers.