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

Table 4

Natural frequencies of the stage with different rigidity ratios predicted by analytical calculation and finite element simulation.

Rigidity ratio of stage	Method	Yawing mode	Pitching mode	Lower rolling mode	Vertical mode	Higher rolling mode
0.41	Analytical analysis	343.2	467.9	517.3	657.3	754.3
	Finite element; analysis	323.3	459.3	477.2	604.1	677.3
	Difference	5.78 %	1.83 %	7.76 %	8.10 %	10.21 %
1.03	Analytical analysis	299.1	403.0	452.7	572.2	659.6
	Finite element; analysis	287.8	401.7	420.1	536.9	634.4
	Difference	3.78 %	0.33 %	7.21 %	6.17 %	3.82 %
2.40	Analytical analysis	245.8	325.8	346.1	469.6	584.8
	Finite element; analysis	240.3	328.1	334.3	452.8	559.2
	Difference	2.25 %	0.71 %	3.40 %	3.57 %	4.37 %
4.02	Analytical analysis	213.6	279.6	286.3	407.7	531.1
	Finite element; analysis	210.0	282.2	277.7	395.5	507.5
	Difference	1.69 %	0.92 %	3.02 %	2.99 %	4.44 %