# Using Fuzzy Control for Feed Rate Scheduling of Computer Numerical Control Machine Tools
## 1 Introduction  
Computer numerical control (CNC) machining is a manufacturing process automatically controlling the machine tools for producing high-precision workpieces. To achieve high-speed and high-precision machining, on-site operators typically adjust the feed rate in computer-aided manufacturing (CAM) software based on their experiences derived from previous cutting experiments. Previous studies presented many advanced control methods such as optimal control and adaptive control of cutting conditions in order to improve machining accuracy [1, 2, 3]. Among them, dynamic feed rate scheduling uses two indicators for evaluating the feed rate: constant cutting force-based and processing path-based dynamic feed rate scheduling. First, in constant cutting force-based dynamic feed rate scheduling, the cutting force model is usually established depending on the cutting tool and the direction of the cutting velocity vector. In other words, the model provides a suitable feed rate instantly under a constant cutting force and spindle speed. [PERSON] et al. [4] presented a feed rate optimization method for constant peak cutting force in the five-axis flank milling process to resolve the unstable machining of parts with ruled surfaces in the aviation industry. The optimization method used least squares theory with the cutter entry angle and feed rate as variables for establishing the peak cutting force for each cutting point. Moreover, a feed rate scheduling method was also designed to quickly solve the appropriate feed rate under constant peak cutting force. [PERSON] et al. [5] proposed a mechanistic cutting force model to perform effective feed rate scheduling for indexable end milling in process planning. The developed cutting force model applied cutting-condition-independent cutting force coefficients which took run out, cutter deflection, geometry variation and size effect as consideration for accurate cutting force prediction. [PERSON] and [PERSON] [6] developed a reference cutting force model basedon considering the transverse rupture strength of the tool material and the area of the rupture surface. The experimental results revealed that the model provides an effective criterion for a feed rate scheduling system that regulates cutting force at a given criterion. All these studies have implemented a cutting force model to adjust the feed rate; however, feed rate scheduling is still associated with many difficulties, such as incompatibility of the cutting force model, sensors installation, and cost much time for collecting cutting experimental data. Secondly, the poor processing quality such as large surface roughness and insufficient contour precision is mainly attributed to an incorrect processing feed rate or large jerk produced by excessive acceleration and deceleration. These situations likely occur when machining with a larger curvature therefore producing the chord errors [7; 8]. [PERSON] et al. [9] noted that the chord error was affected by the interpolation algorithm, curvature, and feed rate. In a condition of the same feed rate, an area with larger curvature produces a larger chord error, because the interpolation algorithm of the conventional controller is constant, the feed rate must be reduced to maintain the chord error within the requirements; therefore, an offline dynamic feed rate scheduling method was proposed to alleviate the abovementioned problem. [PERSON] and [PERSON] [10] found that due to the non-uniform map between curves and parameters, it is very difficult to maintain a constant feed rate and chord accuracy between two interpolated points along parametric curves; therefore, an adaptive feed rate calculation using speed-controlled interpolation algorithm was proposed. Both simulation and experimental results for non-uniform rational B-spline (NURBS) examples were verified for the feasibility and precision of the proposed interpolation algorithm. [PERSON] et al.