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

Table 5

Change law of the warping effect on natural frequencies with respect to the number of coils.

Mode number (Hz)		1	2	3	4	5
	FEM	984.59	1400.9	1738.5	2168.0	2259.2
	Warping ignored	1332.77	1713.92	1848.66	2286.35	2336.40
	Error (%)	35.36	22.34	6.34	5.46	3.42
	Warping included	973.17	1406.73	1746.22	2263.04	2271.58
	Error (%)	1.16	0.42	0.44	4.38	0.55
	FEM	521.34	899.54	915.97	970.21	1129.5
	Warping ignored	745.84	1009.30	1044.17	1122.22	1338.65
	Error (%)	43.06	12.20	13.99	15.67	18.52
	Warping included	523.25	897.71	914.36	973.88	1118.41
	Error (%)	0.37	0.20	0.17	0.38	0.98
	FEM	359.89	521.12	529.55	697.79	771.62
	Warping ignored	504.25	574.71	588.36	765.78	963.49
	Error (%)	40.11	10.28	11.10	9.76	24.87
	Warping included	353.34	515.50	523.97	685.21	764.24
	Error (%)	1.82	1.08	1.05	1.80	0.96
	FEM	270.56	330.04	335.05	533.20	582.48
	Warping ignored	359.73	364.84	393.39	577.06	731.52
	Error (%)	32.96	10.54	17.41	8.23	25.59
	Warping included	265.39	326.26	331.55	523.17	764.24
	Error (%)	1.91	1.14	1.04	1.88	0.86