From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Page detailing formulas and design considerations for round and square wire springs.
| Identifier | ExFiles\Box 158\4\ scan0043 | |
| Date | 12th June 1936 guessed | |
| TABLE OF FORMULAS FOR ROUND AND SQUARE WIRE | | Round | Square | | Round | Square | |---|---|---|---|---|---| | P | π S d³ / 8 D | 4 S d³ / 9 D | S | 8 P D / π d³ | 9 P D / 4 d³ | | P | G f d⁴ / 8 D³ | G f d⁴ / 5.58 D³ | S | f G d / π D² | f G d / 2.48 D² | | f | π S D² / G d | 2.48 S D² / G d | d | π D² S / G f | 2.48 S D² / G f | | f | 8 P D³ / G d⁴ | 5.58 D³ P / G d⁴ | d | ³√(8 P D / π S) | ³√(9 P D / 4 S) | | P/f | G d⁴ / 8 D³ N | G d⁴ / 1.5 π D³ N | W | G d⁴ / 8 D³ N | G d⁴ / 5.58 D³ N | S = Stress. G = Torsional modulus of elasticity. f = Deflection per coil. W = Pounds per inch deflection. N = Number of active coils. D = Mean diameter of spring. d = Diameter of wire. P = Load carried. Tolerances for Spring Design By use of the mathematical equations above it is obvious no allowance is made for any variation. Commercial limits on tempered wire are plus or minus .0015 on smaller sizes—more on heavy sizes. This introduces an error, the value of which depends on the particular spring in question, and it is possible that the .003 difference which can be expected is responsible for a very definite load fluctuation. In coiling springs from commercial wire there is often a difference in O.{Mr Oldham} D.{John DeLooze - Company Secretary} from springs made off of the same coil of wire. This is due to difference in tensile strength and elastic limit of the material, with consequent variation in recoil off the same arbor. This variation will often be 3% of an inch in a spring 1 inch O.{Mr Oldham} D.{John DeLooze - Company Secretary} with cheap wires. The spring designer should allow for this in the permissible load variation, or if the springs must be extremely accurate, use the best material obtainable and have the producer apply a rigorous inspection. Wahl Formula The formulas which have been given on foregoing pages to determine the fibre stress do not consider the total stress imposed on the wire as the ratio of wire size to mean spring diameter changes. Mr. A.{Mr Adams} M.{Mr Moon / Mr Moore} Wahl of Westinghouse Electric & Manufacturing Company, Pittsburgh, developed a formula to cover this case. It was published in Mechanical Engineering and is: S max = (16 P R / 3.1416 d³) * ((4C - 1) / (4C - 4)) + .615 / C C = 2 R / d Y R = mean radius d = wire dia. in inches P = load in lbs. This formula Y has been plotted as a curve and is published on the next page with the permission of the author. By obtaining the numerical ratio of mean diameter to wire diameter a factor can be obtained from the curve which is Y in the formula. Then maximum stress = Y * (2.55 P D / d³) = Y * (16 P R / 3.1416 d³) We urge all calculations of important high duty springs as valve springs or springs having a mean diameter to wire size ratio less than eight be calculated by this formula. The formula applies equally well to round or square wire. | ||