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

Table 3

Change law of the warping effect on natural frequencies with respect to the aspect ratio () of the rectangular cross section.

Mode number (Hz)		1	2	3	4	5
mm; mm	FEM	521.34	899.54	915.97	970.21	1129.5
	Warping ignored	745.84	1009.3	1044.1	1122.2	1338.6
	Error (%)	43.06	12.20	13.99	15.67	18.52
	Warping included	523.25	897.71	914.36	973.88	1118.4
	Error (%)	0.37	0.20	0.17	0.38	0.98
mm; mm	FEM	718.70	1136.7	1170.0	1209.3	1339.7
	Warping ignored	817.31	1128.6	1207.1	1251.5	1511.9
	Error (%)	13.72	0.71	3.16	3.49	12.85
	Warping included	725.9	1126.5	1165.3	1203.8	1351.2
	Error (%)	1.01	0.89	0.41	0.45	0.86
mm; mm	FEM	888.27	1135.3	1318.4	1369.8	1654.8
	Warping ignored	901.25	1133.4	1316.8	1366.6	1677.5
	Error (%)	1.46	0.16	0.12	0.23	1.40
	Warping included	881.50	1132.6	1309.2	1358.4	1641.9
	Error (%)	0.76	0.23	0.70	0.82	0.77
mm; mm	FEM	1006.7	1142.0	1396.9	1454.8	1863.0
	Warping ignored	996.82	1136.7	1382.5	1437.9	1845.2
	Error (%)	0.98	0.46	1.03	1.16	0.95
	Warping included	996.66	1136.4	1382.2	1437.8	1845.0
	Error (%)	0.99	0.49	1.05	1.17	0.96
mm; mm	FEM	886.69	913.84	1152.0	1200.5	1618.1
	Warping ignored	902.91	913.55	1149.1	1196.3	1633.7
	Error (%)	1.83	0.03	0.25	0.35	0.96
	Warping included	882.74	912.38	1146.2	1192.5	1610.8
	Error (%)	0.45	0.16	0.47	0.67	0.45
mm; mm	FEM	688.94	708.39	885.52	924.77	1279.0
	Warping ignored	685.18	819.72	891.44	934.60	1291.5
	Error (%)	0.55	15.72	0.67	1.06	0.98
	Warping included	684.82	729.04	881.56	919.73	1279.3
	Error (%)	0.59	2.92	0.45	0.55	0.02
mm; mm	FEM	458.34	528.46	599.48	627.81	864.93
	Warping ignored	485.90	609.77	627.59	772.46	869.75
	Error (%)	6.02	15.86	4.69	23.04	0.56
	Warping included	457.66	527.83	598.45	625.73	862.19
	Error (%)	0.15	0.11	0.17	0.33	0.32