Calculation table of cylindrical helical compression spring

Since the calculation of the spiral spring is more troublesome, the computer can be used to compile the relevant calculation formulas into various programs for design calculations if conditions permit. In addition, in order to quickly and easily determine the size and parameters of the ammunition, this calculation table is specially compiled. The designer can directly find out the spring that is similar to the design according to the working conditions of the ball. This table includes the main parameters and dimensions of the compression springs made of 60S2Mn cold-coiled by 60S2Mn when the diameter of the spring material is less than 13mm, using carbon spring steel wire grade C; when the diameter of the material is more than 13mm. It is suitable both for variable loads under 10³ times and for cylindrical helical compression springs with variable loads of 10³-10⁵ times or shock loads. For extension springs, the P_j and f_j values are 80% of the values in the table, and the material diameter is ≤13mm.

When the tensile strength σ_b of the material is different from the value σ_b‘ in Table 12-2-18, the working limit load P_j  and the single-turn deformation under the working limit load f_j should be corrected, and the correction factor is shown in Table 12-2-18.

The working limit load P_j in the table, the single-turn deformation f_j under the working limit load, and the single-turn stiffness P_d‘ are shown in Table 12-2-17.

If the maximum working load P_n is known, use the following formula to find the calculated load P_j for different load Kinds,

P_j=K₁P_n

where K₁ is the load category coefficient

Since the spring size and parameters given in Table 12-2-19 have not yet fully considered the performance of Type 1 load springs, the calculation of Type I springs needs to be carried out in addition to this calculation table, and related verification needs to be carried out.

Table 12-2-17 Calculation formulas of P_j , f_j , P_d‘, T_p, T_j and G

Application	Working limit load Pj/N	Deformation of single loop under working limit load fj /mm	Single coil spring rate Pd‘/N*nun-1	Allowable shear stress, /MPa		Working stress T, /MPa		Shear modulus G/N,mm-2
				Compression spring	Torsion Spring	Compression Spring	Tension Spring
Variable load times<103	πd3nj/8DK	πD2Tj/KGd Or Pj/Pd‘	Cd4/8D3	0.5σb	0.4σb	Tj≤1.12Tp, take Tj=1.12Tp		79000
						0.5σb	0.4σb

 

Table 12-2-18 Correction factors for P_j and f_j when the tensile strength of the material can be different from σ_b‘

Wire Diameter d/mm	0.5	0.6	0.7	08-0.9	1.0	1.2	1,4	1.6	1.8	2.0
σb‘/MPa	2200	2100	2060	2010	1960	1910	1860	1810	1760	1710
Correction factor for Pj	σb/2200	σb/2100	σb/2060	σb/2010	σb/1960	σb/1910	σb/1860	σb/1810	σb/1760	σb/1710
Correction factor for fj	36σb/G	38σb/G	39σb/G	40σb/G	41σb/G	42σb/G	43σb/G	44σb/G	45σb/G	47σb/G

 

Wire Diameter d/mm	2.5	3	3.5	4-4.5	5	6	8	10	12	14~45
σb‘/MPa	1660	1570	1570	1520	1470	1420	1370	1320	1270	1480
Correction factor for Pj	σb/1660	σb/1570	σb/1570	σb/1520	σb/1470	σb/1420	σb/1370	σb/1320	σb/1270	σb/1480
Correction factor for fj	48σb/G	51σb/G	51σb/G	53σb/G	54σb/G	56σb/G	58σb/G	61σb/G	63σb/G	54σb/G

 

Note: σ_band G in the table are the tensile strength and shear modulus of the material used, respectively.

Table 12-2-19 Calculation table of cylindrical helical compression spring

 

Wire Diameter d/mm	Spring Diameter D/mm	Allowable Stress Tp/MPa	Working limit load Pj/N	Deformation of one loop under working limit load fj/mm	Single coil spring rate Pd‘/N*mm-1	Maximum mandrel diameter DXmax/mm	Minimum set diameter DTmin/mm	Initial tension P0 (for extension spring)/N
0.5	3 3.5 4 4.5 5 6 7	1100	14.36 12.72 11,39 10.32 9.43 8. 04 7.00	0.627 0.883 1.181 1.524 1.912 2.812 3.888	22.9 14.4 9.64 6.77 4.93 2.86 1.80	1.9 2.4 2.9 3.4 3.9 4.5 5.5	4.1 4.6 5.1 5.6 6.1 7.5 8.5	1.64 1.2 0.92 – 0.589 0.409 –
0.6	3 3.5 4 4.5 5 6 7 8	1055	22.75 20.28 18.26 16.62 15.22 13.03 11.38 10.11	0.480 0.680 0.913 1.183 1.486 2.197 3.051 4.042	47.4 29.8 20.0 14.0 10.2 5.93 3.73 2.50	1.8 2.3 2.8 3.3 3.8 4.4 5.4 6.4	4.2 4.7 5.2 5.7 6.2 7.6 8.6 9.6	3.39 2.49 1.91 – 1.22 0.843 0.622 –
[0.7]	3.5 4 4.5 5 6 7 8 9	1030	30.23 27.37 24.98 22.97 19.74 17.31 15.40 13.88	0.547 0.739 0.960 1.211 1.799 2.504 3.325 4.266	35.3 37.0 26.0 19.0 11.0 6.91 4.63 3.25	2.2 2.7 3.2 3.7 4.3 5.3 6.3 7.3	4.8 5.3 5.8 6.3 7.7 8.7 9.7 10.7	–
0.8	4 4.5 5 6 7 8 9 10	1005	38.54 35.30 32.55 28.14 24.74 22.06 19.90 18. 14	0.609 0.796 1.006 1.502 2.098 2.792 3.588 4.485	63.2 44.4 32.4 18.7 11.8 7.90 5.55 4.04	2.6 3.1 3.6 4.2 5.2 6.2 7.2 8.2	5.4 5.9 6.4 7.8 8.8 9.8 10.8 11.8	6.03 – 3.87 2.68 1.97 1.51 1.19 –
[0.9]	4 4.5 6 7 8 9 10	1005	53.05 48.77 45.13 39.14 34.54 30.89 27.92 25.46	0.524 0.686 0.871 1.305 1.829 2.442 3.141 3.930	101 71.1 51.8 30.0 18.9 12.7 8.89 6.48	2.5 3 3.5 4.1 5.1 6.1 7.1 8.1	5.5 6 6.5 7.9 8.9 9.9 10.9 11.9	–
1.0	4.5 5 6 7 8 9 10 12 14	980	63.30 58.73 51.19 45.33 40.63 36.80 33.62 28.66 24.95	0.584 0.743 1.120 1.575 2.106 2.717 3.403 5.019 6.931	108 79.0 45.7 28.8 19.3 13.5 9.88 5.71 3.60	2.9 3.4 4 5 6 7 8 9 11	6.1 6.6 8 9 10 11 12 15 17	– 9.42 6.54 4.81 3.68 2.91 2.36 1.64 –
1.2	6 7 8 9 10 12 14 16	955	82.38 73.42 66.13 60.16 55.10 47.16 41.22 36.59	0.869 1.230 1.653 2.141 2.691 3.980 5.524 7.319	94.8 59.7 40.0 28.1 20.5 11.9 7.46 5.00	3.8 4.8 5.8 6.8 7.8 8.8 10.8 12.8	8.2 9.2 10.2 11.2 12.2 15.2 17.2 19.2	13.57 9.97 7.63 6.03 4.89 3.39 2.49 –
[1.4]	7 8 9 10 12 14 16 18 20	930	109.23 98.90 90.19 82.94 71.32 62.52 55.62 50.11 45.55	0.987 1.335 1.734 2.187 2.634 4.522 6.006 7.704 9.609	111 74.1 52.0 37.9 22.0 13.8 9.26 6.50 4.74	4.6 5.6 6.6 7.6 8.6 10.6 12.6 14.6 15.6	9.4 10.4 11.4 12. 4 15.4 17.4 19.4 21.4 24.4	–
1.6	8 9 10 12 14 16 18 20 22	905	133.82 127.12 117.32 101.33 89.12 79.46 71.69 65.33 99. 94	1.098 1.432 1.812 2.706 3.778 5.029 6.461 8.076 9.864	126 88.8 64 7 37.5 23.6 15.8 11.1 8.09 6.08	5.4 6.4 7.4 8.4 10.4 12.4 14.4 15.4 17.4	10.6 11.6 12.6 15.6 17.6 19.6 21.6 23.6 26.6	24.1 19.1 15.4 10.7 7.87 6.03 4.77 – –
[1.8]	9 10 12 14 16 18 20 22 25	680	170.78 157.80 137.06 120.92 108.34 97.82 89.20 82.01 73.16	1.201 1.522 2.286 3.203 4.279 5.501 6.882 8.424 11.03	142 104 60.0 37.8 25.3 17.8 13.0 9.74 6.63	6.2 7.2 8.2 10.2 12.2 14.2 15.2 17.2 20.2	11.8 12.8 15.8 17.8 19.8 21.8 24.8 26.8 29.8	–
2.0	10 12 14 16 18 20 22 25 28	855	204.88 178.61 158.20 141.80 128.40 117.29 107.96 96.41 87.05	1.297 1.954 1.923 3.676 4.740 5.939 7.275 9.542 12.10	158 91.4 57.6 38.6 27.1 19.8 14.9 10.1 7.20	7 8 10 12 14 15 17 20 23	13 16 18 20 22 25 27 30 33	37.7 26.2 19.2 14.7 11.6 9.42 7.79 – –
2.5	12 14 16 18 20 22 28 30 32	830	320.30 285,78 257,73 234.58 215.03 198.54 177.90 161.26 151.74 143.16	1.435 2,033 2.733 3.547 4.460 5.480 7.206 9.175 10.62 12.16	223 141 94.2 66.1 48.2 36.2 24.7 17.6 14.3 11.8	7.5 9.5 11.5 13.5 14.5 16.5 19.5 22.5 24.5 25.5	16.5 18.5 20.5 22.5 25.5 27.5 30.5 33.5 35.5 38.5	63.9 47 36 28.4 23 19 14.7 – –
3.0	14 16 18 20 22 25 28 30 32 35 38	785	444.99 403.88 369.03 339.76 314.73 283.08 264.50 242.27 229.16 211.75 196.77	1.527 2.068 2.690 3.398 4.190 5.531 7.258 8.179 9.392 11.35 13.50	291 195 137 100 75.1 51.2 36.4 29.6 24.4 18.7 14.6	9 11 13 14 16 19 22 24 25 28 31	19 21 23 26 28 31 34 36 39 42 45	97.4 74.6 58.9 47.7 39.4 30.5 24.3 – – – –
3.5	16 18 20 22 25 2B 30 32 35 38 40	785	614.66 564.41 52163 484 52 437.67 398. 65 376.26 356.30 329.78 306.97 293.40	1.699 2.221 2.816 3.481 4.614 5.906 6.855 7.880 9.546 11.37 12.67	362 254 185 139 94.8 67.5 54.9 45.2 34 6 27.0 23.2	10.5 12.5 13.5 15.5 18.5 21.5 23.5 24.5 27.5 30.S 32.5	21.5 23.5 26.5 28.5 31.5 34.5 36.5 39.S 42.5 45.5 47.5	109 88.5 73.1 56.6 45.1 – 34.5 28.9 – 22.1
4.0	20 22 25 28 30 32 35 38 40 45 50	760	728. 45 679.34 615.63 562.40 531.91 504.14 467.6 435.9 417.0 376.3 342.9	2.305 2.861 3.804 4.884 5.680 6.535 7.931 9.462 10.56 13.56 16.96	316 237 162 115 93.6 77.1 59.0 46. 1 39.5 27.7 20.2	13 15 18 21 23 24 27 30 32 37 42	27 29 32 35 37 40 43 46 48 53 58	151 125 96.5 76.9 – 58.9 49.2 – 37.7 29. 8
4.5	22 25 28 30 32 35 38 40 45 5055	760	937.0 853.3 782.04 740 702.9 652.9 609.6 584.1 527.8 481.3 442.7	2.464 3.293 4.234 4.935 5.688 6.913 8.261 9.235 11.8814. 86 18.19	380 259 184 150 124 94.4 73.8 63.3 44.4 32.4 24.3	14.5 17.5 20.5 22.5 23.5 26. S 29.5 41.5 36.5 41.5 45.5	29.5 32.5 35.5 37.5 40.5 43.5 46. 5 48.5 53.5 58.5 64, 5	200 155 123 – 94.5 78.9 – 60. 4 47.7 38.6 31.9
5	25 28 30 32 35 38 40 45 50 55 60	735	1100.6 1012.5 960 912.6 850 794.6 761.8 690 630.2 580 537.3	1100.6 1012.5 960 912.6 850 794.6 761.8 690 630.2 580 537.3	395 281 229 188 144 112 96.4 67.7 49.4 37.1 28.6	17 20 22 23 26 29 31 36 41 45 50	33 36 38 41 44 47 49 54 59 65 70	236 188 164 144 120 92 72.7 58.9 48.7 40.9
6	30 32 35 38 40 45 50 55 60 65 70	710	1530.9 1461.1 1364.8 1280.3 1209.6 1117.8 1023.8 944.78 876.9 817.7 766. 1	3.230 3.741 4.572 5.489 6.047 7, 901 10.00 12.28 14.79 17.55 20.53	471 391 298 233 200 140 102 76.9 59.3 46.6 37.3	21 22 25 28 30 35 40 44 49 54 59	39 42 45 48 50 55 60 66 71 76 81	339 298 249 191 151 122 101 84.8 72.3 62. 3
8	30 32 35 38 40 45 50 55 60 65 70	710	1530.9 1461.1 1364.8 1280.3 1209.6 1117.8 1023.8 944. 78 876.9 817.7 766.1	3.230 3.741 4.572 5. 489 6.047 7.901 10. 00 12. 28 14. 79 17. 55 20.53	471 391 298 233 200 140 102 76.9 59.3 46.6 37.3	21 22 25 28 30 35 40 44 49 54 59	39 42 45 48 50 55 60 66 71 76 81	339 298 249 – 191 151 122 101 84.8 72.3 62.3
10	40 45 50 55 60 65 70 75 80 85 90 95 100	600	4615 4264 3954 3687 3448 3239 3053 2887 2736 2602 2479 2366 2264	2.991 3.934 5.005 6.212 7.541 9.01 10.60 12.33 14.19 16.16 18.30 20.55 22.93	1543 1084 790 593 457 360 288 234 193 161 135 115 98.8	26 31 36 40 45 50 55 60 65 69 74 79 84	54 59 64 70 75 80 85 90 95 101 106 111 116	1470 1163 942 779 654 557 481 419 368 326 291 261 236
12	50 55 60 65 70 75 80 85 90 95 100 110 120	635	6227 5833 5478 5147 4882 4629 4397 4189 4000 3825 3664 3383 3136	3. 801 4.740 5.779 6.930 8.176 9. 541 11.00 12. 56 14. 24 16.01 17.89 21.99 26.46	1638 1231 948 746 597 485 400 333 281 239 205 154 119	34 38 43 48 53 58 63 67 72 77 82 92 102	66 72 77 82 87 92 97 103 108 113 118 128 138	1953 1614 1356 1156 997 868 763 676 603 541 488 404 339
14	60 65 70 75 80 85 90 95 100 110 120 130	740	9693.7 9162 8689 8261 7867 7511 7180 6880 6601 6102 5675 5302	5.590 6.718 2 7.96 9.31 10. 76 12.31 13.97 15.75 18. 99 21.68 26.18 31.10	1734 1364 1092 888 732 610 514 437 348 281 217 170	41 46 51 56 61 65 70 75 80 90 100 109	79 84 89 94 99 105 110 115 120 130 140 151
16	65 70 75 80 85 90 95 100 110 120 130 140 150	740	13117 12475 11888 11349 10855 10405 9983 9591 8481 8287 7753 7285 6870	5. 64 6.70 7.85 9.09 10. 43 11.87 13.39 15.01 18.52 22.40 26.66 31.29 36.28	2327 1863 1515 1248 1040 877 745 639 480 370 291 233 189	44 49 54 59 63 68 73 78 88 98 107 117 127	86 91 96 101 107 112 117 122 132 142 153 163 173
18	75 80 85 90 95 100 110 120 130 140 150 160 170	740	16327 15623 14968 14364 13808 13292 12355 11529 10819 10172 9607 9100 8639	6.75 7.82 8.98 10.23 11.56 12.99 16.07 19.46 23.22 27.27 31.68 36.42 41.46	2426 1999 1667 1404 1194 1024 769 592 466 373 303 250 208	52 57 61 66 71 76 86 96 105 115 125 134 143	98 103 109 114 119 124 134 144 155 165 175 186 197
20	80 85 90 95 100 110 120 130 140 150 160 170 180 190	740	20698 19891 19120 18413 17733 16537 15461 14527 13690 12949 12271 11658 11114 10612	6.79 7.83 8.93 10.12 11.37 14.11 17.13 20.46 24.08 28.01 32.22 36.72 41.55 46.66	3047 2540 2140 1820 1560 1172 903 710 569 462 381 318 267 227	55 59 64 69 74 84 94 103 113 123 132 141 151 160	105 111 116 121 126 136 146 157 167 177 188 199 209 220
25	100 110 120 2 130 140 150 160 170 180 190 200 220	740	32340 30351 28557 26930 25478 24159 22979 21893 20916 19998 19175 17700	8.49 10.61 12.96 15.54 18.36 21.40 24.71 28.24 32.03 36.01 40.28 49.49	3809 2861 2204 1734 1388 1128 930 775 653 555 476 358	69 79 89 98 108 118 127 136 146 155 165 184	131 141 151 162 172 182 193 204 214 225 235 256
30	120 130 140 150 160 170 180 190 200 220 240 260	740	46570 44137 41949 39899 38073 36370 34788 33356 32025 29670 27611 25814	10.10 12.28 14.57 17.05 19.74 22.62 25.69 28.97 32.44 40.00 48.34 57.45	4570 3595 2878 2340 1928 1607 1354 1151 987 742 571 499	84 93 103 113 122 131 141 150 160 179 198 217	156 167 177 187 198 209 219 230 240 261 282 303
35	140 150 160 170 180 190 200 220 240 260 280 300	740	63386 60585 57897 55481 53204 51111 49168 45672 42622 39967 37583 35467	11.89 13.98 16.20 18.63 21.21 23.96 26.88 33.24 40.27 48.02 56.39 65.45	5332 4335 3572 2978 2509 2133 1829 1374 1058 832 667 542	98 108 117 126 136 145 155 174 193 212 231 250	182 192 203 214 224 235 245 266 287 308 329 350
40	160 170 180 190 200 220 240 260 280 300 320	740	82791 79564 76479 73653 70931 66148 61840 58109 54758 51791 49088	13.59 15.66 17.87 20.24 22.73 28.22 34.25 40.92 48.16 56.02 64.44	6093 5080 4280 3639 3120 2344 1806 1420 1137 924 762	112 121 131 140 150 169 188 207 226 245 264	208 219 229 240 250 271 292 313 334 355 376
45	180 190 200 220 240 260 280 300 320 340	740	104782 101141 97642 91325 85665 80640 76147 72056 68447 65120	15.41 17.35 19.54 24.32 29.62 35.45 41.81 48.66 56.10 64.02	6855 5829 4998 3755 2892 2275 1821 1481 1220 1017	126 135 145 164 183 202 221 240 259 278	234 245 255 276 297 318 339 360 381 402
50	200 220 240 260 280 300 320 340	740	129361 121406 112781 107718 101909 96634 91915 87571	16.98 21.21 25.59 31.07 36.71 42.82 49.43 56.48	7617 5723 4408 3467 2776 2257 1860 1550	140 159 178 197 216 235 254 273	260 281 302 323 344 365  386 407