Table 1
Angles of Rise, Degrees
1
cos
2
α
+
.8
sin
2
α
0 1.000 1 1.000 2 1.000 3 1.001 4 1.001 5 1.002 6 1.002
Table 2
Analyses of phosphor-bronze wire
B & S Gage No. Diameter Inch. Copper % Tin % Phosphorus %
10 .103 95.8 3.8 0.36 12 .0812 95.9 3.6 0.38 14 .0647 95.7 3.8 0.35 16 .0495 95.6 3.9 0.34 18 .0401 95.6 3.9 0.32
Iron: Less than 0.05 per cent in each sample.
Lead, Nickel and Zinc: Not detected.
Table 3
Modulus of torsion for phosphor-bronze wire
Gauge of Wire Average Diameter of wire, inches Modulus of Torsion, G, 106 lbs/in2
12 .0812 6.56 12 .0812 6.59 14 .0647 6.43 14 .0647 6.34 16 .0495 6.44 16 .0495 6.33 16 .0495 6.65 18 .0401 6.71 18 .0401 6.72
Table 4
Design of springs
Design No. Wire No. Diameter of wire inches Stiffness for 15 turns lbs/inch Mean Diam. of coils inches Modulus of torsion 106 lbs/inch2 Load for maximum fiber stress of 10,000 lbs. per inch2 . lbs.
IX 18 .0401 3 .36 6.7 .67 VIII 18 .0401 9 .25 6.7 1.0 VII 16 .0495 20 .25 6.5 1.9 VI 14 .0647 7.6 .50 6.4 2.1 V 12 .0812 18.7 .50 6.6 4.4 IV 10 .103 20 .68 6.5 6.3 III 10 .103 6 1.00 6.5 4.2 II 8 .128 20 .92 6.5 8.5 I 8 .128 7.6 1.25 6.5 6.5
Table 5
Dimensions of constructed springs
Spring No. Mean D.am. of Coils Inches Winding Load lbs/inch2
IX-9 .364 8300 -10 .363 -11 .363 VIII .25 8300 VII .25 5400 VI .50 4600 V .50 3280 IV .68 4150 III 1.00 4250 II .920 4250 I-1 1.472 4250 I-2 1.442 4250
Table 6
Performance of Similar Springs of Phosphor Bronze
Ident. No. No. of Turns Stiffness lbs/in. Computed Silliness lbs/in. Average Stiffness Ratio r/a Pitch Angle degrees
IX-9 15 2.54 3.0 9.0 4.5 -10 15 2.70 3.0 9.0 4.5 -11 15 2.66 3.0 .88 9.0 4.5 VIII-1 15 8.5 9.0 6.2 5.0 -2 15 8.9 9.0 6.2 5.0 -3 15 8.4 9.0 .95 6.2 5.0 VII-1 15 18.4 20.0 5.0 5.0 -2 15 18.5 20.0 5.0 5.0 -3 15 18.5 20.0 .92 5.0 5.0 VI-5 15 6.2 7.6 7.7 5.0 -6 15 6.3 7.6 7.7 5.0 -7 15 6.2 7.6 .82 7.7 5.0 V-2 15 17.7 18.7 6.1 5.0 -3 15 16.4 18.7 6.1 5.0 -4 15 18.2 18.7 .95 6.1 5.0 IV-2 8 30.7 37.5 6.6 5.5 -4 8 31.6 37.5 .83 6.6 5.5 III-4 7 11.3 12.9 .88 9.7 4.5 II-1** 11 16.8 20.4 .82 -2 5 47.2 60.0 .79 7.2 4.0 -3 8 30.0 37.5
.80 7.2 4.0 -3 5 * 48.060.0 7.2 4.0 I-1 8.25 7.32 9.00 .81 11.5 2.4 -2 8 8.25 9.82 .84 11.2 2.5
* Extrapolated from value for 8 turns.
** Without end plugs.
Table 7
Effect of heat treatment on stiffness
Spring Ident. No. Date of Test Heat Treatment Increase in Stiffness %
II-2 Feb.-24 none 0 II-2 12-27-24 none −3.4 II-2 1-10-25 210°C +2.3 II-2 1-24-25 220°C +2.3 IV-4 Feb.-24 none 0 IV-4 12-27-24 none −1.9 IV-4 1-10-25 210°C 0 IV-4 1-24-25 220°C +2.8
Table 8
Maximum Load Pounds Maximum Hysteresis Inches Hm Maximum Deflection Inches Dm
H
m
D
m
2.5 .0005 .08 .006 3.5 .0010 .11 .009 5.0 .0020 .16 .012
Table 9
Data on after-effect. Time of tests as short as possible. Springs not seasoned.
Spring Number Test No. Maximum Deflection Inches Maximum Load Pounds Number of Turns After Effect Inches Time of Start
I-2 1 .4906 4 8 .0010 3:20 PM 2 .6117 5 8 .0007 4:12 PM 3 .4891 4 8 .0001 4:33 PM I-2 1 .1522 6 6 .0011 3:11 PM 2 .1508 6 6 .0001 4:02 PM IV-2 1 .0813 2 1/2 8 .0006 1:41 PM 2 .0810 2 1/2 8 0 2:02 PM 3 .0810 2 1/2 8 0 2:10 PM 4 .0809 2 1/2 8 0 2:19 PM 5 .0811 2 1/2 8 −.0002 2:27 PM 6 .0807 2 1/2 8 0 3:30 PM IV-4 .0792 2 1/2 8 .0002
Springs seasoned
IV-2 Seasoned 200 times 1 .0828 2 1/2 8 .0007 2:32 PM 2 .0821 2 1/2 8 0 2:41 PM 3 .0822 2 1/2 8 0 2:54 PM 4 .0824 2 1/2 8 0 3:02 PM Note: Compare the data on spring IV-2 for the seasoned and unseasoned condition. IV-4 Seasoned 100 times 1 .0797 2 1/2 8 .0005 9:34 AM 2 .0795 2 1/2 8 0 9:43 AM 3 .0793 2 1/2 8 .0002 9:53 AM
Table 10
Drift data
Spring Number Load Pounds Deflection Inches Drift Inches Time Hours Ratio, Drift to Deflection Number of Turns
I-2 4 .489 .0019 17 .0039 8 IV-4 8 .2529 .00045 1 .0018 8 5 .1604 .00028 1 .0017 8
Table 11
Data on buckling
Spring Number Number of Turns Criterion B
IX-10 15 3.8 -11 15 4.7 VIII-1 15 6 -2 15 9 -3 15 14 -3 10 10 VII- 15 10 -2 15 8 -3 15 6.5 VI-5 15 9 -5 13 8 -6 15 9 -7 15 5.5 V-3 13 9 -3 11 9 V-3 9 8 -4 15 7 IV-2 8 7 -2 8 8 -4 15 15 -4 13 19 -4 10 19 -4 8 9 -4 8 8 III-4 14 15 -4 10 26 -4 7 13 II-3 14 28 -3 10 32 I-2 8 16
Table 12
Effect of seasoning on stiffness
Spring Number Stiffness Unseasoned lbs/in. Stiffness Seasoned lbs./in. Number of Cycles
I-2 .2 8.15 210 IV-2 30.7 30.0 200 IV-4 31.6 31.4 100 IV-4 31.6 31.4 800