An Analysis Methodology for Stochastic Characteristic of Volumetric Error in Multiaxis CNC Machine Tool

Table 4

The characteristic matrices of precision horizontal machining center.

The adjacent body	Body ideal static, motion characteristic matrix	Body static, kinematic error characteristics matrix
0-1; 𝑋 axis	𝐓01𝑝=𝐈4×4	Δ𝐓01𝑝=𝐈4×4
	𝐓01𝑠=100𝑥010000100001	Δ𝐓01𝑠=1−Δ𝛾𝑥Δ𝛽𝑥Δ𝑥𝑥Δ𝛾𝑥1−Δ𝛼𝑥Δ𝑦𝑥−Δ𝛽𝑥Δ𝛼𝑥1Δ𝑧𝑥0001
1-2; 𝑌 axis	𝐓12𝑝=𝐈4×4	Δ𝐓12𝑝=1−Δ𝛾𝑥𝑦00Δ𝛾𝑥𝑦10000100001
	𝐓12𝑠=1000010𝑦00100001	Δ𝐓12𝑠=1−Δ𝛾𝑦Δ𝛽𝑦Δ𝑥𝑦Δ𝛾𝑦1−Δ𝛼𝑦Δ𝑦𝑦−Δ𝛽𝑦Δ𝛼𝑦1Δ𝑧𝑦0001
2-3 tool	𝐓23𝑝=100𝑥𝑡𝑑010𝑦𝑡𝑑001𝑧𝑡𝑑0001	Δ𝐓23𝑝=𝐈4×4
	𝐓23𝑠=𝐈4×4	Δ𝐓23𝑠=𝐈4×4
0-4; 𝑍 axis	𝐓04𝑠=𝐈4×4	Δ𝐓04𝑝=10Δ𝛽𝑥𝑧001−Δ𝛼𝑦𝑧0−Δ𝛽𝑥𝑧Δ𝛼𝑦𝑧100001
	𝐓04𝑠=10000100001𝑧0001	Δ𝐓04𝑠=1−Δ𝛾𝑧Δ𝛽𝑧Δ𝑥𝑧Δ𝛾𝑧1−Δ𝛼𝑧Δ𝑦𝑧−Δ𝛽𝑧Δ𝛼𝑧1Δ𝑧𝑧0001
4-5; 𝐵 axis	𝐓45𝑝=𝐈4×4	Δ𝐓45𝑝=1−Δ𝛾𝑧𝐵00Δ𝛾𝑧𝐵1−Δ𝛼𝑥𝐵00Δ𝛼𝑥𝐵1Δ𝑧𝐵𝑦0001
	𝐓45𝑠=cos𝐵−sin𝐵00sin𝐵cos𝐵0000100001	Δ𝐓45𝑠=1−Δ𝛾𝐵Δ𝛽𝐵Δ𝑥𝐵Δ𝛾𝐵1−Δ𝛼𝐵Δ𝑦𝐵−Δ𝛽𝐵Δ𝛼𝐵1Δ𝑧𝐵0001