*6.1. Disc Robotic Deburring Experiment*

In the first robotic deburring experiment, a disc deburring for an automobile hub was conducted on the original experimental platform of the robot manipulator (shown in Figure 2a). The experimental workpiece was an aluminum alloy casting blank of an automobile hub, as shown in Figure 11a, and the experimental deburring object were disc burrs of the automobile hub, as shown in Figure 11b.

It can be seen from Figure 11 that disc burrs of automobile hub were located on the inside of the mold cavity, so that these burrs were not suitable to be removed via the abrasive belt grinding. It was a good use case of a certain carbide rotary tool (i.e., a kind of high-speed machining file, shown in Figure 12) driven by the robot manipulator with a high level of dexterity of manipulation and orientation reachability. Furthermore, this kind of rotary tool with a relatively long side cutting edge is more suitable to execute the deburring for disc burrs of automobile hub. A double-cutting cylindrical round-head carbide rotary tool with the side cutting edge (shown in Figure 12b and its type is CX1020M06) was selected to carry out the deburring for disc burrs of automobile hub in the first experiment. The length of the side cutting edge and the diameter of the selected tool were 20 mm and 10 mm, respectively.

**Figure 11.** Casting blank of automobile hub: (**a**) overall appearance of automobile hub; (**b**) disc burrs of automobile hub.

**Figure 12.** Carbide rotary tools: (**a**) series of tools; (**b**) cylindrical ball nose tool; (**c**) arch ball nose tool.

Based on the proposed robotic deburring tool path planning method, the detailed robotic deburring tool location (position and orientation) planning and the detailed robotic layered deburring planning are presented as follows. The selected tool can deburr once the entire thickness of burrs due to the length of the side cutting edge is significantly larger than the thickness of burrs with range between 0.37 mm and 0.72 mm. Thus, the disc burrs of automobile hub can be removed by executing robotic layered deburring several times through the proposed robotic deburring tool path planning method.

Disc burrs vary in size and exhibit a discontinuous distribution as can be seen in Figure 11b. Through the actual measurement, the maximum width dimension, i.e., the maximum machining allowance *D*max was 7.36 mm. In the first experiment, the thickness of the single-layer deburring, i.e., the cutting depth *dp* was set as about one third of the diameter of the side cutting edge, which was taken as 3 mm. The entire allowance can be deburred completely by repeating three times. Among them, the thickness of the last deburring layer was selected as 1.36 mm to improve the deburring quality.

Furthermore, a total of eighteen discrete points were selected on the entire target curve at the edge of disc body, as shown in Figure 13. The position of each contact point of the layered deburring tool is planned by the Equations (1) and (2) along the exterior normal **n***<sup>l</sup>* (red arrows are showed in Figure 14a) of each discrete point, as shown in Figure 14a. As mentioned above, disc burrs of the automobile hub were suitable for deburring with the tool side cutting edge and the contact orientations of the layered deburring tool were planned as shown in Figure 14b. The details were: (a) the deburring direction of tool, i.e., the tool side edge vector **n** was taken as the unit inner normal vector **f** of each discrete position (i.e., cyan arrows, as shown in Figure 14b, and they were in the opposite direction of the red arrows as shown in Figure 14a); (b) the movement direction of tool (vector **o**) was planned along the unit tangent vectors τ of each discrete position (i.e., green arrows, as shown in Figure 14b) and points to the next discrete position to be deburred; and (c) the tool vector **a** was derived as **a** = **n** × **o**. Finally, the disc deburring of the automobile hub was conducted in the clockwise direction based on

the planned tool contact positions and tool contact orientations as shown in Figure 14 (symbols -<sup>1</sup> , -2 and -<sup>3</sup> represent the sequence of each layered deburring).

**Figure 13.** Target curve of disc and discrete points.

**Figure 14.** Tool locations planning of the layered deburring: (**a**) tool contact positions; (**b**) tool contact orientations.

Additionally, the proposed robotic deburring process parameter control method was applied to the robotic deburring of the first experiment in order to adjust robotic deburring process parameters with a constant cutting speed and a constant cutting force. In this experiment, the robotic spindle speed was selected to be 10,000 rpm, and the line speed of the robotic feed was set to 30 mm/s. Hence, the desired robotic spindle speed and the desired robotic spindle load were 10,000 rpm and 0.17N·m. Variation ranges *E*1, *EC*1, *E*<sup>2</sup> and *EC*<sup>2</sup> (corresponding to [−*Se*, *Se*], [−*Sec*, *Sec*], [−*Le*, *Le*] and [−*Lec*, *Lec*], respectively) were set to [−3000, 3000], [−800, 800], [−0.05, 0.05] and [−0.02, 0.02], respectively. Variation ranges of output variables, i.e., change in control voltage of the robotic spindle and change in robotic feed (corresponding to [−*Vu*, *Vu*] and [−*Fu*, *Fu*], respectively), were set to values such that [−0.3, 0.3] and [−3, 3], respectively. From (3)–(8), quantizers of *E*1, *EC*1, *E*<sup>2</sup> and *EC*2, and scaling factors of *u*<sup>1</sup> and *u*2, were obtained as *KSe* = 0.002, *KSec* = 0.0075, *KLe* = 60, and *KLec* = 150, and *KVu* = 0.05 and *KFu* = 1, respectively. Furthermore, adjustment factors α<sup>1</sup> and α<sup>2</sup> were set to α<sup>1</sup> ∈ [0.3, 0.7] and α<sup>2</sup> ∈ [0.2, 0.8], respectively. Hence, the fuzzy rules in the designed fuzzy controller for robotic spindle speed and robotic spindle load are expressed respectively as follows:

$$\begin{cases} u\_1 = -\langle \alpha\_1 E\_1 + (1 - \alpha\_1) E C\_1 \rangle \\\ a\_1 = \frac{1}{6} (0.7 - 0.3) |E\_1| + 0.3 \end{cases} \tag{14}$$

$$\begin{cases} u\_2 = -\langle \alpha\_2 E\_2 + (1 - \alpha\_2) E C\_2 \rangle \\\ a\_2 = \frac{1}{3} (0.8 - 0.2) |E\_2| + 0.2 \end{cases} . \tag{15}$$

The experimental platform and the automobile hub workpiece of the first robotic experimental deburring are shown in Figure 15. The detailed robotic experimental deburring for disc burrs of the automobile hub on the original experimental platform is shown in Figure 16. Results of layered experimental deburring disc of the automobile hub workpiece are shown in Figure 17. Finally, the results of the target planning path and actual tool path of experimental deburring for the automobile hub workpiece are shown in Figure 18 (here, the blue line and the red line are the target planning path and the actual tool path, respectively). Deviation results of target planning path and actual tool path of experimental deburring for disc of hub are shown in Figure 19, the vertical axis indicates the magnitude of the deviation, and other two horizontal axes in the horizontal plane indicate the corresponding positions of the target planning path in the deburring experiment. In addition, a figure in the form of plane polar coordinates illustrating deviation results of this experiment deburring is shown in Figure 20. The maximum deviation was 1.23 mm, and these robotic deburring results can meet the experimental deburring requirements.

The effectiveness of the proposed robotic deburring tool path planning method and the proposed robotic deburring process parameter control method were verified in the first deburring experiment. Also, it can be seen that the robotic deburring orientations were adjusted dexterously, especially in the place where the local curvature changes greatly, and the dexterous deburring ability of the robot manipulator was fully demonstrated in the first deburring experiment.

**Figure 15.** Experimental platform and automobile hub: (**a**) original experimental platform of robot manipulator; (**b**) automobile hub workpiece.

**Figure 16.** Experimental deburring disc of hub on original experimental platform.

**Figure 17.** Results of layered experimental deburring disc of hub: (**a**) first layered deburring; (**b**) second layered deburring; (**c**) third layered deburring.

**Figure 18.** Results of target planning path and actual tool path of experimental deburring.

**Figure 19.** Deviation results of target planning path and actual tool path of experimental deburring for disc of hub.

**Figure 20.** Deviation results of target planning path and actual tool path of experimental deburring for disc of hub (polar representation).
