8. System Assembly and Performance
8.7 Control Performance: Synchronized Motion
Tests were performed on linear axes across distances of 25 mm up to 100 mm. The distribution of the overshoot errors showed no specific trend with increases in distance. The overshoot of an axis depended primarily on the inconsistencies of localized friction characteristics close to the target position. The maximum overshoot recorded for a linear axis was 0.059 mm by the column module, while the base module displayed the highest average overshoot error of 0.018 mm. The smallest errors were displayed by the cross slide module, which displayed the smoothest motion from all linear modules due to higher quality in its manufacturing. The cross slide module was a retrofitted commercially acquired unit of hardware.
Tests on rotary axes were performed for rotations of 45o up to 360o. The highest overshoot error of 1.406o was registered by the cutting head rotary module; which also displayed the highest errors on average. The rotary table module possessed a reduction gearbox and operated at relatively low speeds, it therefore displayed the smallest overshoot errors on average.
8.7 Control Performance: Synchronized Motion
Linear Paths (Dynamic Analysis)
An investigation was performed to determine the combined accuracy for the synchronized motion of two axes. The synchronization of axes was performed by the servo communication module, which issued a synchronized start to axes by means of a general I2C call. Figure 8.14 illustrates the resultant position error from the synchronized motion of the base module and work table slide module in a MRM drilling configuration. The axes were required to move the drill spindle across a linear trajectory of 100 mm at a combined feed rate of 100 mm/min (G-code: F100 X70.71 Y70.71). The resultant error from the trajectory was calculated by equation 8.5. The equation does not account for mechanical errors and only presents the error from the perspective of the control system (tracking error).
𝐸𝑟𝑒𝑠 𝑖 = ∆𝑋𝑜 𝑖
𝑛 𝑖=1
2
+ ∆𝑌𝑜 𝑖
𝑛 𝑖=1
2
− ∆𝑋𝑚 𝑖
𝑛 𝑖=1
2
+ ∆𝑌𝑚 𝑖
𝑛 𝑖=1
2
(8.5)
The maximum resultant error in the position of the drill spindle was 0.429 mm and the trajectory was completed with an average position error of 0.069 mm. The average was computed on the magnitude (absolute value) of the errors.
Figure 8.14: Graph of Position Error (Drill Spindle) vs Time, Resultant Position of X and Y Axes -0.400
-0.200 0.000 0.200 0.400 0.600
0 10 20 30 40 50 60 70
Position Error (mm)
Time (s)
Graph of Position Error vs Time: X-Y Axes (Drilling Config)
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8.7 Control Performance: Synchronized Motion
Figure 8.15: Graph of Position Error (Tool Post) vs Time, Resultant Position of X and Y Axes
Figure 8.15 illustrates the resultant position error from the synchronized motion of the base module and cross slide module in the MRM turning configuration. The axes were required to move the tool post (and tool) across a linear trajectory of 50 mm at a combined feed rate of 100 mm/min (G-code: F100 X35.36 Y35.36). The maximum resultant error exhibited for the synchronized motion of these axes was 0.382 mm and the average error was 0.045 mm.
Circular Interpolation (Dynamic Analysis)
Figure 8.16: Arc Generated by Synchronized Motion of Base Module and Work Table Slide Module
The performance of the MRM control system was investigated for circular interpolation. A test was performed for the interpolation of an arc of radius 100 mm with a subtended angle of 90o. The test was performed with the base module as the X-axis and the work table slide module as the Y-axis in the 3-DOF drilling configuration. The arc began with the drill spindle at relative position (x=100 mm, y=0 mm) and ended at position (x= 0 mm, y = 100 mm). The arc was linearized according to the circular interpolation algorithm and the linear segments were further interpolated according to the linear interpolation algorithm. Figure 8.16 illustrates the resultant arc that was described by the drill spindle in free space (drill not engaged with work part).
-0.400 -0.200 0.000 0.200 0.400 0.600
0 5 10 15 20 25 30 35
Position Error (mm)
Time (s)
Graph of Position Error vs Time: X-Y Axes (Turning Config)
0.00 20.00 40.00 60.00 80.00 100.00 120.00
0.00 20.00 40.00 60.00 80.00 100.00120.00
Y Position (mm)
X Position (mm)
Actual Arc Generated from Measurements
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8.7 Control Performance: Synchronized Motion
Figure 8.17 illustrates the resultant position error of the drill spindle during the formation of the arc. The position error accounts for tracking errors in the control system and is calculated by equation 8.5. The position error graph is characterized by multiple peaks in the error throughout the trajectory. These peaks occur due to a rapid change in reference input to the position controller at the end of each linear segment in the arc. The arc of Figure 8.16 contained four distinct linear segments resulting in four peaks in the position error characteristic. The magnitude of the errors is highly dependant on the dominant axis (axis required to cover the greater distance) in an individual linear segment and the consistency of the error curve varied throughout the trajectory. The largest error registered for the trajectory was 0.241 mm.
The linearization of an arc generates inherent errors, causing the radius of the arc to deviate from the prescribed radius. The errors are present in the reference to the position control algorithm resulting in the final control error being a composite of both reference and tracking errors.
Figure 8.17: Graph of Position Error vs Time, Generation of Arc by X and Y Axes
Figure 8.18: Graph of Radial Error vs Time, Generation of Arc by X and Y Axes -0.300
-0.200 -0.100 0.000 0.100 0.200 0.300
0 20 40 60 80 100 120
Position Error (mm)
Time (s)
Graph of Position Error vs Time (mm): X-Y Axes
-0.2000.0000.2000.4000.6000.8001.0001.2001.4001.6001.8002.0002.2002.4002.6002.8003.0003.200
0 10 20 30 40 50 60 70 80 90 100
Error (mm)
Time (s)
Radial Errors in Circular Interpolation
Total Radial Error
Radial Error in Reference Position
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