Parametric Study on the Influence of Warping Deformation upon Natural Frequencies of Die Springs

Table 4

Change law of the warping effect on natural frequencies with respect to the diameter of the cylinder.

Mode number (Hz)		1	2	3	4	5
mm	FEM	836.61	1419.6	1446.5	1553.7	1760.4
	Warping ignored	1162.25	1574.61	1629.74	1752.98	2089.33
	Error (%)	38.92	10.92	12.67	12.83	18.68
	Warping included	818.03	1402.37	1428.08	1522.45	1746.51
	Error (%)	2.22	1.21	1.27	2.01	0.79
mm	FEM	366.39	625.73	638.26	680.81	778.55
	Warping ignored	517.72	701.37	726.15	780.18	930.54
	Error (%)	41.30	12.09	13.77	14.60	19.51
	Warping included	363.61	623.34	635.98	676.02	777.59
	Error (%)	0.76	0.38	0.36	0.70	0.12
mm	FEM	205.48	351.70	358.68	382.02	438.26
	Warping ignored	291.77	394.48	408.34	439.17	523.85
	Error (%)	41.99	12.16	13.85	14.96	21.58
	Warping included	204.59	350.92	357.63	380.31	437.40
	Error (%)	0.43	0.22	0.29	0.45	0.20
mm	FEM	131.12	224.78	229.20	243.94	280.38
	Warping ignored	186.48	252.72	261.06	281.29	335.25
	Error (%)	42.22	12.43	13.90	15.31	19.57
	Warping included	130.43	224.46	228.59	243.07	280.32
	Error (%)	0.53	0.14	0.27	0.36	0.02