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).
Analysis of valve spring materials, heat treatment, and design to eliminate resonant vibrations, including comparative data and frequency formulas.
| Identifier | ExFiles\Box 56\2\ Scan060 | |
| Date | 1st January 1929 guessed | |
| 12 WIRE common practice to make valve-springs from oil-tempered spring-wire. With the development of alloy steel the call arose for alloy-steel springs. The spring manufacturer naturally used the same continuous heat-treating process he had used on carbon-steel springs. The expected results were not obtained with the new steel and the old type of heat-treatment. Tests during a 5-year period show that springs made from soft wire, heat-treated after coiling, are far superior to springs coiled from heat-treated wire. Averages of life-tests of springs give the following as the comparative values of springs of different types: (1) Carbon steel, heat-treated before winding 1.0 (2) Electric-furnace chromium-vanadium steel, heat-treated before winding 0.9 (3) Carbon steel, heat-treated after winding 5.0 (4) Electric-furnace Chromium-vanadium steel, heat-treated after winding 10.0 Heat Treatment Recommended To those who are looking for the best, we therefore recommend an electric-furnace chromium-vanadium steel that is heat-treated after winding. Where price is a consideration, we believe that the results secured from a carbon steel that is heat-treated after coiling more than offset the slight increase in price due to the method of treatment. Even though extreme care is taken with the material, heat-treatment and design, failure may sometimes be encountered after comparatively short service. Failures of this sort have been traced to the resonance between the natural frequency of the spring and the frequency of the forced vibration from the camshaft. Any force tends to set up a wave motion in the spring, the wave length of which depends upon the natural frequency of the spring. When the forced vibration is of such a frequency that its wave length is a simple Table 1—Characteristics of an Original Spring that Vibrated Noisily and a Redesigned Spring in which the Trouble was Eliminated Item | Original Spring | Redesigned Spring --- | --- | --- Mean or Pitch Diameter, in. | 1.102 | 0.878 Free Length, in. | 3 1/32 | 2 23/32 Total Number of Coils | 10 1/2 | 9 Gage of Wire, Washburn & Moen No. | 9 | 10 1/2 Load, with Valve Open at 2 1/32 in., lb. | 48 | 53 Load with Valve Closed at 2 11/32 in., lb. | 29 | 29 Stress with Valve Open lb. per sq. in. | 41,200 | 57,000 Stress with Valve Closed, lb. per sq. in. | 25,300 | 31,200 Stress Range, lb. per sq. in. | 15,900 | 25,800 Rate, lb. per in. | 59.0 | 77.3 Weight of Active Mass, lb. | 0.1435 | 0.0700 Frequency or Free Vibrations per Minute | 10,750 | 17,600 multiple of the free wave-length of the spring, a condition of resonance may be created. If the wave length is long and if such that an integral number of the free wave-lengths of the spring are completed during one cycle of the valve, the applications of the force will be in phase, and the resulting wave motion in the spring will be cumulative and resonant. Ricardo has offered a convenient formula for calculating the natural frequency of a spring. Ricardo's formula is N = 531 √(R/W) where N = complete number of free vibrations per minute of the spring R = rate of spring, in pounds per inch W = weight of the active mass of the spring, in pounds The derivation of Ricardo's formula is simple and can be obtained from a consideration of a spring vibrating with its ends fixed. In this case, each half of the spring may be regarded as working independently of the other half. Then, as one half works as an extension spring, the other half works as a compression spring, and vice versa. Natural Frequency Formulas If the central coil of the spring is assumed to move through a distance of a inches, the maximum displacement will be a/2 to either side of the rest position. Each half of the spring or a compression spring, moving a distance of a/2. Since the amplitude is half the displacement, the amplitude for the half-spring will be a/4. The inertia force will then be: Fi = (W/2g) (a/48) w² where a/4 = amplitude, in inches Fi = inertia force g = force of gravity w = angular velocity of periodic force, or radians divided by seconds W/2 = weight of half the spring, in pounds Since the rate of the spring in number of pounds required to compress it 1 in. varies inversely with the number of coils, the rate of the half-spring will be 2R and the resisting force due to the stiffness of the spring will be: Fr = 2R (a/2) = Ra where a/2 = deflection of the half-spring, in inches Fr = resisting force R = rate of the spring, in pounds per inch These two forces will be equal and opposing, and, hence, by equating the two and evaluating the constants, the formula (1) is obtained. The natural-frequency formula must be employed with caution, as, notwithstanding design figures, two springs seldom have the same natural period, because of the slight variation in the gage of commercial wire, the slight difference in pitch-diameter, and differences between one spring and another in the number of active coils, all of which affect the rate in pounds and the weight of the active (Please turn to page 24) | ||