Analytical and Finite Element Modeling of the Dynamic Characteristics of a Linear Feeding Stage with Different Arrangements of Rolling Guides

Table 1

Parameters of the ball screw driven stage.

Parameter	Value	Unit
Total stage mass, M	36.866	kg
Moments of inertia, 𝐽𝑥, 𝐽𝑦, 𝐽𝑧	0.45085, 0.5115, 0.95064	Kg m^2
Geometry dimensions,; 𝑒1=𝑒2=𝑒3=𝑒4=𝑒	140	mm
𝑙1=𝑙2=𝑙3=𝑙4=𝑙	83.5	mm
𝑑1=𝑑2=𝑑3=𝑑4=𝑑	27.962	mm
D, L, a, 𝑒0	20, 700, 350, 10.5	mm
Spring constant (linear guide); 𝐾=𝐾𝑖1=𝐾𝑖2 (𝑖=1,4)	139.2𝑒^6	N/m
Spring constant (ball screw); 𝐾𝑣=𝐾𝑢	0.879𝑒^6	N/m
Spring constant (ball screw); 𝐾𝜃=𝐾𝜓	0.0359𝑒^6	N-m/rad