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

Table 1

Geometric errors of precision horizontal machining center.

Component	Error term	Symbol	Component	Error term	Symbol
𝑋-prismatic joint	Positioning error	Δ𝑥𝑥	𝐵-rotary joint	𝑋 direction run-out error	Δ𝑥𝐵
	𝑌 direction of straightness error	Δ𝑦𝑥		𝑍 direction run-out error	Δ𝑧𝐵
	𝑍 direction of straightness error	Δ𝑧𝑥		Axial error	Δ𝑦𝐵
	Rolling error	Δ𝛼𝑥		Around the 𝑋 axis turning error	Δ𝛼𝐵
	Britain swing error	Δ𝛽𝑥		Positioning error	Δ𝛽𝐵
	Yaw error	Δ𝛾𝑥		Around the 𝑍 axis turning error	Δ𝛾𝐵
𝑌-prismatic joint	𝑋 direction of straightness error	Δ𝑥𝑦	Orientation error between joints	𝑋, 𝑌-axis perpendicularity error	Δ𝛾𝑥𝑦
	Positioning error	Δ𝑦𝑦		𝑋, 𝑍-axis perpendicularity error	Δ𝛽𝑥𝑧
	𝑍 direction of straightness error	Δ𝑧𝑦		𝑌, 𝑍-axis perpendicularity error	Δ𝛼𝑦𝑧
	Rolling error	Δ𝛼𝑦		𝐵, 𝑌-axis parallelism error in 𝑋𝑌 plane	Δ𝛾𝑥𝐵
	Britain swing error	Δ𝛽𝑦		𝐵, 𝑌-axis parallelism error in 𝑍𝑌 plane	Δ𝛼𝑧𝐵
	Yaw error	Δ𝛾𝑦		𝐵, 𝑌-axis offset error in 𝑍 axis direction	Δ𝑧𝐵𝑦
𝑍-prismatic joint	𝑋 direction of straightness error	Δ𝑥𝑧	𝑍-prismatic joint	Rolling error	Δ𝛼𝑧
	𝑌 direction of straightness error	Δ𝑦𝑧		Britain swing error	Δ𝛽𝑧
	Positioning error	Δ𝑧𝑧		Yaw error	Δ𝛾𝑧