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-mechanism idiosyncrasies, detailing harmonic theory, valve lift curves, and spring vibrations.
| Identifier | ExFiles\Box 56\2\ Scan082 | |
| Date | 15th January 1929 guessed | |
| 6 VALVE-MECHANISM IDIOSYNCRASIES Valve Lift Cam Angle FIG. 10—VALVE DIAGRAM PLOTTED FROM POINT-BY-POINT READINGS The Fine Line Represents Lifts as Observed with the Telescopic Indicator at a Camshaft Speed of 200 R.P.M. The Heavy Line Represents Observations at a Camshaft Speed of 1,130 R.P.M., Showing the Bouncing of the Valve at This Speed ment harmonics are proportional, and the latter will therefore be used in the discussion immediately following. The derivation of acceleration harmonics, as well as a simplified form of harmonic analysis, is given in the appendix. EXPERIMENTAL CHECK OF HARMONIC THEORY A spring-and-valve combination that vibrated badly was chosen to check the harmonic theory. The cam contour is that shown as No. 1 in Table 1. As determined with the shutter wire attached, the spring had a frequency of 11,450 vibrations per minute. The calculated frequency of the spring was 11,800 vibrations per minute. throughout. The ninth, for example, has an amplitude less than that of the fourteenth. The one thing they all have in common is that their maximum amplitude occurs in the center of the lift curve. Plotting a chart, using for abscissa the order number of the harmonics and for ordinate their maximum amplitude, gives the peculiar curve shown in Fig. 14. This curve is that of a function alternating between positive and negative values and approaching zero from both sides. This is true of all the valve-lift curves we have analyzed, but we do not know whether it is true of all lift-curves, nor do we know the law that governs this curve. It is realized that the spring vibration is caused by a force and that, therefore, the harmonics of the valve acceleration rather than those of the displacement curve are responsible for it. For any one cam-and-spring combination, the acceleration and displacement harmonics are proportional, and therefore be used in the discussion immediately following. The derivation of acceleration harmonics as a simplified form of harmonic analysis, is given in the appendix. TABLE 1—MAXIMUM AMPLITUDE OF VALVE-LIFT HARMONICS FOR DIFFERENT CAMSHAFTS, IN INCHES Har-monic Order | Cam-shaft No. 1 | Cam-shaft No. 2 | Cam-shaft No. 3 | Cam-shaft No. 4 | Cam-shaft No. 5 1 | +0.1586 | +0.1324 | +0.1476 | +0.1476 | +0.2838 2 | +0.1670 | +0.1156 | +0.1342 | +0.1170 | +0.1958 3 | +0.0634 | +0.0664 | +0.0674 | +0.0718 | +0.0934 4 | +0.0266 | +0.0322 | +0.0174 | +0.0255 | +0.0213 5 | −0.00796 | −0.0053 | −0.0062 | −0.0044 | −0.0055 6 | −0.01054 | −0.0121 | −0.0141 | −0.0099 | −0.0121 7 | −0.01117 | −0.0132 | −0.0122 | −0.0128 | −0.0124 8 | −0.00512 | −0.0051 | −0.0064 | −0.0064 | −0.0085 9 | +0.00418 | +0.0033 | +0.0045 | +0.0044 | +0.0055 10 | +0.00372 | +0.0002 | +0.0028 | +0.0042 | +0.0040 11 | +0.00075 | −0.0006 | −0.0005 | +0.0019 | +0.0027 12 | −0.00196 | −0.0026 | −0.0021 | −0.0006 | −0.0005 13 | −0.00201 | −0.0020 | −0.0013 | −0.0019 | −0.0019 14 | −0.00124 | −0.0008 | −0.0008 | −0.0018 | −0.0013 15 | +0.00046 | +0.0011 | +0.0002 | −0.0002 | +0.0006 16 | +0.0011 | +0.0011 | +0.0014 | +0.0009 | +0.0016 17 | +0.0011 | +0.0008 | −0.0004 | +0.0008 | +0.0015 18 | +0.00062 | −0.0006 | 0 | +0.0008 | +0.0001 19 | −0.00005 | −0.0009 | −0.0004 | 0 | −0.0002 20 | −0.00052 | −0.0006 | −0.0002 | 0 | −0.0002 21 | −0.00031 | −0.0002 | −0.0001 | −0.0002 | −0.0002 22 | +0.0002 | +0.0002 | +0.0001 | −0.0001 | +0.0003 23 | +0.00062 | +0.0005 | +0.0002 | −0.0002 | 0 24 | +0.00046 | +0.0002 | −0.0001 | +0.0002 | −0.0003 25 | +0.00031 | −0.0001 | −0.0002 | 0 | 0 26 | 0 | −0.0002 | 0 | −0.0001 | 0 27 | 0 | −0.0001 | 0 | −0.0001 | −0.0002 28 | +0.00015 | +0.0002 | +0.0001 | 0 | 0 29 | +0.00031 | +0.0002 | 0 | +0.0001 | 0 30 | +0.00031 | +0.0003 | +0.0001 | +0.0001 | 0 FIG. 11—VALVE-LIFT-INDICATOR CURVES SHOWING VALVE BOUNCING 1370 R.P.M. ON 200 R.P.M. 1400 R.P.M. ON 200 R.P.M. 1430 R.P.M. ON 200 R.P.M. FIG. 12—VALVE-LIFT-INDICATOR CURVES AT CUSTOMARY ENGINE SPEEDS 780 R.P.M. ON 200 R.P.M. 100 R.P.M. ON 200 R.P.M. 1200 R.P.M. ON 200 R.P.M. 7 VALVE-MECHANISM IDIOSYNCRASIES Center of Valve Lift 8th 17th 26th 9th 18th 27th 10th 19th 28th 11th 20th 29th 12th 21st 30th 13th 22nd 14th 23rd 15th 24th 16th 25th FIG. 13—HARMONICS OF VALVE-LIFT CURVE Based on Cam No. 1, Table 1 Figs. 15 to 18, inclusive, show records of the spring vibration and valve-lift curve through a camshaft speed range of 573 to 1050 r.p.m. The speeds at which photographs were made, except that at 850 r.p.m. in Fig. 17, are those at which the maximum vibrations seem to occur. If the number of spring waves on each record is multiplied by the speed at which it was taken, a number is obtained that is within less than 1 per cent of 11,450, the observed frequency of the spring. It appears, therefore, that the actuating force is the cam harmonic, the order of which is represented by the number of waves per camshaft revolution as shown on the records. Inspection shows that the amplitudes of the waves on the records have the same general relation to one another as the amplitudes of the corresponding harmonics shown in Table 1, for cam No. 1, and in Fig. 13. The spring vibrations, therefore, correspond to the amplitudes of the harmonics of the lift curve. There remain to be checked the phase and the sign of the waves. If the experimental work checks the calculations, the maximum amplitude of a spring wave must lie on the center line of the valve-lift curve and its sign must be that shown for the corresponding harmonic of cam No. 1 in Table 1. To check this, a correction must be made for the offset, as given in the description of the valve-lift and spring-vibration indicator. In this case the offset was 0.5 in advance of the lift curve. In addition to this, a correction must be made for the time it takes a wave to travel from the end of the spring to the mid-point, one-quarter of the total wave length. This correction is in the direction of valve lift; that is, in the direction opposite to the correction for offset. The vertical line on each record shows the valve-lift center-line displaced to agree with these corrections. In every instance, the phase and the sign check with the calculated quantities. In comparing the films for the different speeds, it will be seen that the middle one in Fig. 16, representing a speed of 717 r.p.m. and harmonic No. 16, is the lowest. That is correct, since the sixteenth harmonic is of a very low amplitude. The record which appears in the center of Fig. 17 is peculiar. There is no harmonic corresponding to 850 r.p.m., and this is verified by the record. As this speed is between the strong thirteenth and fourteenth harmonics, the spring probably is excited by these. It is not in phase with the speed of the camshaft, however, and it can be seen plainly that the vibration is damped by interference as soon as the valve lifts again. The other record of special interest is the top one in Fig. 18, which represents a speed of 920 r.p.m. The result of dividing the frequency, that is 11,450, by 920 is 12.5. There can be no harmonic of this order, but Table 1 shows that this cam contour has a twenty-fifth harmonic of appreciable magnitude, and this harmonic is exciting the first overtone of the spring. No particular care was taken to attach the shutter wire to the exact mid-point of the spring, where the node exists in this type of vibration. Examination of the record discloses that the vibrations are double. This indicates that the shutter was not connected at the node and that the spring was vibrating in halves. Careful measurement of the wave spacing of all the records reveals that the waves are closer together during the period of valve lift than while the valve is on its seat. This is to be expected when it is remembered that the number of active coils of the spring is somewhat less during valve lift than while the valve is closed; the spring has, therefore, a slightly higher frequency while the valve is open. A spring that is actuated by a cam mechanism which produces one simple harmonic motion per revolution of the shaft cannot vibrate until the cam reaches a speed equal to the frequency of the spring. Such a speed is not obtainable with our apparatus; but a harmonic Amplitude of Harmonic, in. Harmonic Order Number FIG. 14—RELATION BETWEEN AMPLITUDE AND ORDER NUMBER OF HARMONICS Based on the Same Cam as Fig. 13 | ||