Control Resolution, Accuracy, and Repeatability Referring back to Example 37.1 , the mechanical inaccuracies in the open-loop positioning system can be described by a normal distribution whose standard deviation = 0.005 mm. The range of the worktable axis is 550 mm, and there are 16 bits in

Question

Control Resolution, Accuracy, and Repeatability

Referring back to Example 37.1 , the mechanical inaccuracies in the open-loop positioning system can be described by a normal distribution whose standard deviation = 0.005 mm. The range of the worktable axis is 550 mm, and there are 16 bits in the binary register used by the digital controller to store the programmed position. Determine (a) control resolution, (b) accuracy, and (c) repeatability for the positioning system.

Accepted Answer

(a) Control resolution is the greater of [latex]CR_1[/latex] and [latex]CR_2[/latex] as defined by Equations (37.14a) and (37.15):

[latex]CR_1=\frac{p}{n_s r_g}=\frac{5.0}{48(4)}=[/latex] 0.0260 mm

[latex]CR_2=\frac{L}{2^B -1}=\frac{550}{2^{16}-1}=\frac{550}{65,535}[/latex] = 0.0084 mm

CR = Max {0.0260 ,0.0084} = 0.026 mm

(b) Accuracy is given by Equation (37.17):

Ac = 0.5 CR +3σ (37.17)

Ac= 0.5(0.0260) + 3(0.005) = 0.0280 mm

(c) Repeatability Re = ±3(0.005) = ±0.015 mm

Question 37.3: Control Resolution, Accuracy, and Repeatability Referring ba...

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