Table 1 Geometric errors and corresponding numbers of the five-axis CNC machine tool.

From: Sensitivity analysis and compensation for tooth surface deviation of spiral bevel gear machine tool

Motion Axis

Geometrical errors

Serial number

X-axis

\({\delta _{x\text{X}}}\)

\({\delta _{y\text{X}}}\)

\({\delta _{z\text{X}}}\)

1 2 3

\({\varepsilon _{\alpha \text{X}}}\)

\({\varepsilon _{\beta \text{X}}}\)

\({\varepsilon _{\gamma \text{X}}}\)

4 5 6

Y-axis

\({\delta _{x\text{Y}}}\)

\({\delta _{y\text{Y}}}\)

\({\delta _{z\text{Y}}}\)

7 8 9

\({\varepsilon _{\alpha \text{Y}}}\)

\({\varepsilon _{\beta \text{Y}}}\)

\({\varepsilon _{\gamma \text{Y}}}\)

10 11 12

Z-axis

\({\delta _{x\text{Z}}}\)

\({\delta _{y\text{Z}}}\)

\({\delta _{z\text{Z}}}\)

13 14 15

\({\varepsilon _{\alpha \text{Z}}}\)

\({\varepsilon _{\beta \text{Z}}}\)

\({\varepsilon _{\gamma \text{Z}}}\)

16 17 18

A-axis

\({\delta _{x\text{A}}}\)

\({\delta _{y\text{A}}}\)

\({\delta _{z\text{A}}}\)

19 20 21

\({\varepsilon _{\alpha \text{A}}}\)

\({\varepsilon _{\beta \text{A}}}\)

\({\varepsilon _{\gamma \text{A}}}\)

22 23 24

B-axis

\({\delta _{x\text{B}}}\)

\({\delta _{y\text{B}}}\)

\({\delta _{z\text{B}}}\)

25 26 27

\({\varepsilon _{\alpha \text{B}}}\)

\({\varepsilon _{\beta \text{B}}}\)

\({\varepsilon _{\gamma \text{B}}}\)

28 29 30