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).
Mathematical and oscillogram analysis of valve-spring surge and harmonics.
| Identifier | ExFiles\Box 56\2\ Scan087 | |
| Date | 15th January 1929 guessed | |
| where A₀ is a constant term, or the average ordinate of the curve; A₁ is the amplitude of the fundamental; Aₙ is the amplitude of the nth harmonic; t is the time, in seconds, and ω is the angular velocity of the fundamental, in radians per second. The harmonic forces themselves are in reality acceleration forces, or the second derivatives with respect to time for the various terms of the above series. It is apparent, however, that these harmonic forces will always be proportional to Aₙ. For the purposes of this paper, the two lift-curves of Fig. 5 were analyzed for harmonics, and the resulting values of the harmonics are listed in Table 1. The most interesting points in the two analyses are that the twelfth harmonic has a very appreciable value for the lift curve of cam No. 2 but a very low value for that of cam No. 1, and that the ninth harmonic has comparatively high value for cam No. 1 but has a very low value for cam No. 2. OSCILLOGRAMS CHECK MATHEMATICAL ANALYSIS It is not the purpose of this paper to dwell upon the mechanics of the harmonic analysis of the lift curve. This subject is treated in detail in the paper on Idiosyncracies of Valve Mechanisms, by Ferdinand Jehle¹ and W. R.{Sir Henry Royce} Spiller². However, it is important to note that the values of the harmonics as shown in Table 1 check in magnitude with the intensity of the surge at resonant speeds, as shown by the telemeter oscillograms. It is particularly interesting to note that, where the harmonic analysis gives a positive value for Aₙ, the free wave has a crest at the maximum-lift point; and, where the analysis assigns a negative value to Aₙ, the free wave has a trough at the maximum-lift point. This is interesting because, in analyzing the valve-lift curve for harmonics, it was assumed that harmonics which had an additive effect to the fundamental were positive, while those which had a substractive effect were negative. However important and interesting the surge points may be, the non-resonant speeds at points intermediate of the resonant points must not be overlooked. In studying the operation at non-resonant speeds, cognizance must be taken of the fact that resonance itself is a peculiar phenomenon. If the damping characteristics of the spring approach zero, the resonant speed for any harmonic will be very sharp and critical. In this case, at any speed between two resonant speeds the spring will not vibrate in its natural period, provided no higher harmonics are present which would tend to excite the spring. In the actual case, damping enters into the spring operation and alters materially the hypothetical case mentioned. Damping has the effect of flattening ¹ M.S.A.E.—Research engineer, White Motor Co., Cleveland. ² M.S.A.E.—Laboratory engineer, White Motor Co., Cleveland. 4 [Rotated Text Left] FIG. 6—OSCILLOGRAM OF SPRING NO. 1 WITH CAM NO. 1, FROM 1750 TO 750 R.P.M. Full-Size Detail Sections of This Oscillogram Are Shown in Figs. 8 to 11 [Page 2] ELECTRIC TELEMETER AND VALVE-SPRING SURGE 5 and spreading the resonance curve, so that the surge amplitude is large at speeds considerably removed from the resonant point in either direction. In further investigation of the actual case, let us consider a spring vibrating in response to a strong tenth harmonic. Assume also that there is a strong eleventh harmonic but no harmonic between the two, such as the twenty-first, which would tend to cause the spring to vibrate in halves. In the case thus set up, the spring would respond vigorously to the tenth; and, if the camshaft speed be permitted to drop, the surge amplitude would tend to decrease because of the damping characteristics of the spring. During this period of surge slightly more than 10 free waves elapse between valve lifts, so that the wave motion from the preceding lift arrives somewhat out of phase. This gives a slightly interfering effect and decreases the surge slightly. The maximum interference is obtained when 10½ waves elapse between valve lifts, because then the wave motion from the preceding lift arrives exactly one-half out of phase. As the speed decreases beyond this point, slightly more than 10½ waves elapse between valve lifts, the interference is less, and the surge amplitude builds up. As the speed further decreases, the interference effect is lessened until a point is reached at which there are 11 complete waves between lifts. At this point the wave motion is again in phase, and we have another point where the surge-amplitude is a maximum. If we further extend this supposition to include the operation of the spring from a resonant speed influenced by a weak twentieth harmonic to the next resonant speed due to a weak twenty-first, we may find that, although the same method of reasoning holds good, the surge will be completely damped out long before 20½ waves are reached and the maximum-interference speed is reached, and that beyond this point the slightly out-of-phase wave-motion is not of sufficient intensity to start vibration of the spring. Under these conditions it can be expected that at low speeds the spring will be wholly free from surge at non-resonant points, but that at high speeds it will never be wholly free from surge, the spring vibrating under the influence of a strong, though slightly out-of-phase, harmonic just passed or just about to be attained. These ideas as to non-resonant speeds are important, and they are rather well shown by the telemeter oscillograms, which bring out the importance of non-resonant light speeds because, in nearly every case, the residual surge at these speeds is considerably greater than the surge at low resonant-speeds. The effect of the design of the spring upon these non-resonant-surge values will be discussed later. The oscillograms reproduced in Figs. 6 to 20 were taken to show the way in which different springs oper- [Rotated Text Right] FIG. 7—OSCILLOGRAM OF SPRING NO. 1 WITH CAM NO. 2, FROM 1750 TO 750 R.P.M. A Full-Size Section of this Oscillogram Is Shown in Fig. 12 [Bottom Section] ENLARGED DETAILS OF OSCILLOGRAMS To Reproduce the Complete Oscillograms, It Was Necessary To Reduce Them So Much that Details Are Lost, and the Extremes of the Vibrations Are Indicated by White Dots. Sections of Figs. 6 and 7 Are Shown Above, Reproduced the Same Size as the Originals Fig. 8—Tenth Harmonic, at 1650 R.P.M. Fig. 9—Twenty-First Harmonic, at 785 R.P.M. Fig. 10—Twelfth and Twenty-Fourth Harmonic at 1375 R.P.M. Fig. 11—Sixteenth Harmonic, at 1030 R.P.M. Fig. 12—Twelfth Harmonic at 1375 R.P.M. [Text within Oscillograms] 8: 1650 R.P.M. 10TH 9: 785 R.P.M. 21ST 10: 1375 R.P.M. 12TH & 24TH 11: 1030 R.P.M. 16TH 12: 1375 R.P.M. 12TH | ||