CRANFIELD
INSTITUTE OF TECHNOLOGY
PILOT EXPERIMENTAL STUDY OF THE VIBRATION
CHARACTERISTICS OF
A MACPHERSON STRUT WHEEL SUSPENSION
by
April. 1971
CRANFIELD INSTITUTE OF TECHNOLOGY
PILOT EXPERIMENTAL STUDY OF THE VIBRATION
CHARACTERISTICS OF
A MACPHERSON STRUT WHEEL SUSPENSION
by -R.M. Stayner
S U M M A R Y
The vibratory force transmissibility of a strut type wheel suspension has been investigated in the laboratory. Measurements were made using an electro hydraulic vibrator and both swept frequency sinusoidal and broad band random
excitation. The development of the test rig and the analysis equipment are described briefly. The results indicate the importance of non-linearity in the response of the suspension system and the need for a more satisfactory theoretical analysis.
INTRODUCTION
EXPERIMENTAL DETAILS
1
1
General design of the rig Modifications
Sinusoidal analysis equipment Swept sinusoidal vibration tests Constant frequency test
Random vibration tests
1 1 2 2 3 3
CALCULATION OF TRANSMISSIBILITY FUNCTIONS
Swept sine forcing Random forcing
DISCUSSION OF RESULTS
Raw data Reduced data
Single frequency t e s t
Relevance of theoretical analysis
SUGGESTIONS FOR FUTURE WORK
General investigation of suspension systems Extensions to theory
Verification of experimental method Extensions to experiment Equipment improvements CONCLUSIONS 5 6 6 6 7 7 7 7 8 TABLES 1. 2. 3.
Force transmissibility from swept sine analysis Force transmissibility from random analysis Resonant frequencies: experimental observations compared with theoretical values
9 10 11 FIGURES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Block diagram: swept, sinusoidal vibration. Block diagram: random vibration.
Swept sine vibration response: vector locus
Swept sine amplitude response.
Typical repeatability of consecutive sweeps. Distortion effects.
Force in strut, 15-200 Hz., 60 lb. input force,
Force in tie-rod, lower link, 15-200 Hz., 60 lb. input force. Force in strut, 15-200 Hz., 30 lb. input force.
Force in tie-rod, lower link, 15-200 Hz., 30 lb. input force, Force in strut, tie-rod, 2-50 Hz., small displacement.
Constant frequency response to variations in forcing amplitude. Strut force, displacement.
Tie-rod force, lower link force.
Response to random forcing,
Displacement p.s.d., 0-25 Hz., larger displacement. Strut force, input force, 0-25 Hz., larger displacement.
Tie-rod force, lower link force, 0-25 Hz., larger displacement. All forces and displacement p.s.d. 0-25 Hz,, smaller displacement, Tie-rod force, input force p,s.d., 0-200 Hz,
Strut force p.s.d., 0-200 Hz.
Force transmissibility functions.
Sinusoidal forcing, 15-200 Hz., 60 lb. input force. Sinusoidal forcing, 15-200 Hz., 30 lb. input force. Sinusoidal forcing, 2-50 Hz., small displacement. Sinusoidal forcing, 4-50 Hz., large displacement, Random forcing 0-25 Hz., (large displacement). Random forcing 0-25 Hz., (small displacement)
Random forcing 0-200 Hz., strut and tie rod force only. Strut force for all types of input.
Tie rod force for all types of input. Lower link force for all types of input. Force transducer calibrations.
The vibratory forces transmitted through an automobile suspension system may be studied in the laboratory and related to theoretical analysis of the system. The work reported here concerns the development of experimental techniques useful in such a laboratory study.
Measurements were made on a test rig in which an electro-hydraulic
vibrator was used to excite a single suspension system in isolation. This rig was built to validate the theoretical analysis of a student thesis project, but has not yet been operated successfully. A brief series of experiments was carried out in which forces transmitted through the suspension system were
analysed, by several techniques, at frequencies in the range 0-200HZ. Two types of excitation were used; swept sinusoidal and broad band random. For the former, equipment was available to plot the complete vector locus of the relationship between two variables, or to track and plot the fundamental
amplitude of a distorted signal. For the randomly excited vibrations, analysis was restricted to power spectral density functions of single variables.
The details of the experimental techniques, discussed in the next section, are included as an aid to future, more complete studies using the same or
similar equipment. This leads to the procedures for obtaining transmissibility functions from the raw data, as required for evaluation of both the suspension system and the experimental methods. The results are then discussed with reference to the existing theoretical analysis of the suspension system, and finally some suggestions are made concerning possible continuation of
experimental and analytical work on this topic. Continuation of such work is encouraged by indications of variation in the system characteristics observed during this preliminary investigation. Further experiment is also required to resolve a certain lack of correlation between results of random and swept sinusoidal vibration tests.
EXPERIMENTAL DETAILS
General Design of the Rig.
The general design of the rig is fully described in the relevant A.S.A.E. thesis.* A stiff frame supports the suspension unit, as on the car, by the top of the MacPherson strut, the inner pivot of the transverse lower link and the stabilizer bar. Also attached to the frame and connected to the wheel spindle is the ram of the electro-hydraulic vibrator. Force transducers are inter-posed between the hydraulic ram and the wheel spindle and between the frame and suspension system at each attachment point. A displacement transducer is fitted between the frame and the wheel spindle.
Provision is made for forcing the wheel spindle in each of three directions, effectively vertically, longitudinally, and laterally, relative to the orient-ation of the suspension as part of the car. Only the first position was used for the tests described.
Modifications
Modifications made since the rig was originally completed concern the control and measurement functions. A two channel carrier-amplifier system was constructed for the input force transducer and for the displacement trans-ducer. The latter had been replaced by one of the inductive type as the
potentiometer type proved unreliable for extended high frequency vibration work. Displacement control was used, since for force control of the vibrator the flexibility of the system being forced led to a lack of stability. For
sinusoidal vibrations an additional servo loop can be added using the compressor amplifier of the sweep oscillator which provides the input to the electro-hydraulic vibrator. This amplifier modifies the input to the vibrator so as to maintain a constant r.m.s. amplitude of some measured parameter, in this case the force input to the wheel spindle. For random vibrations an equalizer filter set would be required to perform a similar function.
Sinusoidal analysis equipment
The equipment for sinusoidal analysis (fig. 1) comprises the sweep oscillator mentioned above and a frequency response analyser. The sweep oscillator maintains one parameter at a constant amplitude. The analyser then plots the amplitude and phase of another parameter relative to that reference as the frequency is varied, this information being displayed in vector locus form,
Alternatively the analyser may be operated simply as a tracking filter. A voltage which varies with frequency is available from the sweep oscillator so that plots of amplitude against frequency can be made. By plotting the amplitude of the fundamental component of a signal, as derived from the tracking filter, and the total signal level, also obtained from the analyser, the amount of distortion can be estimated (fig. 5 ) ,
Swept sinusoidal vibration tests.
Swept sinusoidal vibration tests commenced with the use of the vector locus plotting facility. After a few experiments to determine optimum sweep rate and time constants for the system under test, and to check repeatability, the plot shown in fig. 3 was obtained. This relates force at the strut mounting point to the input force. Repeatability of form and approximate amplitude was good, but the locus is relatively complicated and took 35 minutes to produce. A
faster sweep rate with shorter analyser time constants produced a still more complicated curve and greater variability between runs. Amplitude calibration was omitted because this type of analysis was discontinued. The vector locus
presented more information then was required, and in a form unsuitable for immediate data reduction.
Use was then made of the tracking filter to plot the amplitudes of all the forces against frequency. The voltage representing frequency is derived from the oscillator by a rather crude potentiometer and requires smoothing by a simple passive network in the connection to the X-Y plotter. A more serious short-coming is the lack of precise correlation between the voltage and a frequency counter. This necessitated marking the plots at chosen frequency increments as the sweep progressed, and rendered impossible the use of any graduated paper which might have simplified interpretation and data reduction. A frequency range of 15-200 HZ was used. The lower limit was set by the inability of the tracking filter to follow the rather unstable signals obtained at low frequencies, while the upper limit was chosen to coincide with the upper limit of the random signal analysis facility. Sweep time was reduced to 7 minutes, as the simpler function plotted requires less stability than the vector locus, for the same repeatability,
However a source of error was introduced in that the amplitude response of the tracking filter varies with frequency. This did not affect the vector plotting function as the output was used to provide phase information only, but for
tracking filter operation it presents a considerable limitation.
Repeatability of measured frequency functions was better for pairs of runs with the same direction of frequency sweep (fig. 4) than for pairs of runs with opposite directions of frequency sweep. This suggested a system response for decreasing frequency sweeps which differs from that for increasing frequency sweeps. To avoid investigation of this phenomenon at this stage, tests were restricted to increasing frequency only. The output of each force transducer, total and fundamental component, was plotted for each of two input force levels, nominally 60 lb. r.m.s. and 30 lb, r.m.s. (figs. 6 - 9 ) .
To extend the frequency range below 15 HZ, distortion information was
neglected and only total r.m.s. outputs of the transducers were recorded. This allowed frequencies as low as 2 HZ to be investigated, and the input force level to be plotted concurrently with each output using the second pen of the X-Y plotter. The lower level of input force, 30 lb. r.m.s. was used, but only two of the outputs were obtained, since the system response changed radically during this series of runs. The change, which occurred suddenly, is attributed to a reduction of coulomb friction with increase of working temperature, since displacement amplitude increased markedly. Fig. 10 shows the responses at the start of the test, while fig. 11 shows the later responses.
Constant Frequency Test
A constant frequency test was therefore carried out to investigate the effect of varying the amplitude of the input force. A frequency of 6.5 HZ was chosen as at this frequency considerable force change had been observed (fig. 12 and fig. 13). The displacement demand signal was gradually increased from zero, with the force feedback amplitude control removed. It is to be noted that the chosen force level for the previous tests, viz. 30 lb., was the maximum for system operation under friction 'lock' conditions at this frequency.
Random Vibration Tests
Random vibration tests were carried out with demanded displacements of band-limited white noise. Two ranges were chosen to suit the analysis equipment. viz. 0 - 25 HZ and 0 - 200 HZ. The input frequency content was controlled by properties of the vibrator/suspension system and no attempt was made to obtain
'white noise' characteristics for either the input force or the displacement (fig. 2 ) . An extended series of tests was not planned and so the most readily obtainable random excitation was used. All transducer outputs were recorded for
The tracking filter is made up of a set of modular equipment. The performance was reported to the manufacturer who conducted supervised tests of each component module. These were all within the quoted specifications. Similar checks were observed on other modules which, when combined in the tracking filter configuration had a far better frequency response. No cause could be found for the poor
performance of the A.S.A.E. system, but it is suggested that it be returned to the manufacturer for a more extended test so that it can be brought up to specification.
power spectral analysis, and their r.m.s, levels (for all frequencies above 2 HZ) measured with a valve voltmeter.
For the lower frequency analysis, 0 - 25 HZ (Figs. 14-17) displacement and all four force signals were recorded at each of two levels of the dis-placement signal. These were obtained for the same r.m.s. input force by approaching this force from first a higher and then a lower value. In this way it was hoped that the results could be related to those obtained with sinusoidal excitation when two types of response were observed for the same input.
The broader band analysis was re tricted to input and two output forces (figs. 18 and 19) only, by a shortage of analyser tape loops and experimental time.
CALCULATION OF TRANSMISSIBILITY FUNCTIONS
The transmissibility functions were calculated for each type of excitation so that the random and swept sine vibration results could be compared.
Comparison of the system response to different levels of the same type of forcing is also simplified.
Swept sine forcing
For the results of the sinusoidal forcing tests, the transmissibility ratios of each output force to the input force, as functions of frequency, (figs. 20 - 23) were obtained as follows:
At each frequency the amplitudes were read from the plotted results. Using calibrations of the transducers, e.g. in Ibf./volt fig. 30, and of the analyser plotted output, in volts/cm., the measured amplitudes were converted to Ibf. Ratios of two force levels thus obtained could be plotted directly as trans-missibility functions. Where suitable, frequency intervals were restricted to
those marked during the experiment, but for rapidly changing functions it was often necessary to interpolate frequency values, with some lack of accuracy.
All values were measured from total signal level curves, corrected where distortion was observed. A linear amplitude response was assumed for the analyser, for the calculations, but in fact the response of the system was some-what non-linear and results for values outside the range 0.025 - 0.075 volts are not accurate. Table 1 shows a specimen calculation for sinusoidally obtained transmissibility functions.
Random Forcing
Calculation of transmissibility functions from the results of the random forcing tests are complicated by the presentation of the results as power spectral density functions, i.e., as plots of mean squared amplitude density. In addition the variance inherent in the results must not be confused with minor system
resonance effects. Procedure was as follows:
The area under each p.s.d. curve was measured, and that amount for the area above 2 HZ was used to calibrate the power density scale. The area represents the mean square signal level, and the root mean square level was known from the voltmeter reading taken during the test. The resulting values of for example lb2/HZ/cm. were noted for each variable. Amplitude values were measured from the p.s.d. curves as cm. and ratios calculated for each frequency and pair of
in arbitrary units, which were then corrected by a constant factor, namely the square root of the ratio of the relevant pair of power density calibration values. For details see table 2 and fis. 24 to 26.
To minimise variance effects, for the 0 - 25 HZ tests the power density measurements were made as average-over-band values for bandwidths of either
1 or 2 HZ, which are an order of magnitude larger than the analysis bandwidth of approximately 0-2 HZ. For the 0 - 200 HZ test such a procedure might have reduced the precision of analysis and lost some of the resonant effects. Individual frequency values were therefore used, the analysis bandwidth being 1.5 HZ.
Note that the accuracy with which amplitudes could be estimated from the p.s.d. curves was greatly reduced for large sections of the curves where a very
low value was obtained. This is to some extent mitigated by the subsequent square root operation, but the results are still only approximate.
DISCUSSION OF RESULTS
Raw Data
The raw data from both swept sine and random excitation tests may be examined for indications of the system response. The vector plot of strut force response for an input level of 100 Ibf. (fig. 3) compares closely with the amplitude response function for an input level of 60 Ibf. (fig. 4 ) ; note loops at peak amplitude frequencies of 30, 60 and 180 HZ. The amplitude response
functions from the swept sine tests are very similar in form to the transmissibility functions, as a result of the servo-control of the input force level. Direct interpretation of the random test results is less fruitful.
The results of the swept sine tests are considered for the two frequency ranges used.
15 - 200 HZ major resonances occur at 30 HZ for the strut force and 45 HZ for the lower link force. The tie-rod force response is more complex with major resonances at 25, 60, 120 and 180 HZ.
The effect of changing the amplitude is most obvious at low frequencies, particularly with the strut and lower link forces whose lowest resonances at 20 - 25 HZ become important.
2 - 50 HZ. Again, results for larger amplitudes of motion show an increase in strut force at low frequencies. The large amplitude motion is equivalent to the previous, higher frequency sweep, whereas the lower amplitude motion is quite different in the frequency range 40 - 50 HZ. A large strut force is transmitted at the standing wave frequency of the spring with the damper locked, but apparently is absorbed when the damper is free to move.
The results of the random forcing tests, obtained as power spectral density functions are difficult to interpret. This is a result of the lack of control over the input frequency content and of the inherent variability of this form of testing. The variability could have been reduced by the use of longer signal samples, had time allowed. Nevertheless, the results of the broad band
excitation (figs, 18 and 19) indicate resonances in the frequency bands 8 - 10 HZ, 45 - 55 HZ and 80 - 110 HZ, The lower frequency analyses, 0 - 25 HZ (figs. 14 to 17) do not indicate resonances reliably, but demonstrate the response of the
vibrator/suspension system to a demanded white noise displacement control. The actual displacement cannot be maintained at frequencies above a few HZ, while the input force at low frequencies is very low if large displacements are not allowed. Tie rod and lower link forces are maintained even at low
frequencies and vary little in frequency content with amplitude of forcing. Strut force increases at low frequencies as displacement level is increased, but not at frequencies above 10 HZ, although displacement frequency spectra have similar forms for the two cases.
Reduced Data
The reduction of the raw data to obtain transmissibility functions introduced little change in the interpretation of the results of the swept sine tests.
Agreement between transmissibility function amplitudes from both sets of results was good for the tie rod force, but only fair for the low frequency test and so no comparison can be made. It may be worth noting that the tie rod force appeared least effected by amplitude variation in all the available raw data.
Reduction of the results of the random vibration tests yielded transmiss-ibility functions which, except for the tie rod, differed considerably from those obtained in sinusoidal vibration (figs. 27 to 29). Where comparisons are
available, the form of the transmissibility functions is similar, with main resonances apparent from the strut force at 20 HZ, and from the tie rod at 25 and 60 HZ, but the vibrator/system response was limited to frequencies below 130 HZ. The lower frequency random test was less informative. Differences in the forces appear related to differences in the displacement transfer function, but not to the results of the sinusoidal tests.
Single Frequency Test.
The results of the test carried out at a single frequency with gradually increasing amplitude (figs. 12 and 13) bear out the previous observation that two types of response are possible for one amplitude of input force. In this case the low frequency swept sine test had been carried out with the input controlled to be 30 Ibf., which value corresponds to the limit of one type of motion at 6.5 HZ. The sudden increase in displacement amplitude was accompanied by a decrease
in all the force amplitudes, but it is to be noted that the force transmissibility ratios did not all decrease. The force transmitted through the tie rod increased considerably.
Relevance of Theoretical Analysis
The relevance of the earlier theoretical analysis of the suspension system must be questioned in the light of the comparison afforded by table 3, In this table the predicted resonant frequencies for a simplified model of the suspension system may be compared with maxima of the force transmissibility functions. Particularly notable is the lack of predicted resonant conditions between 90 and
200 HZ, when in fact, in addition to those resonances shown, there were several which did not result in high force transmissibilities but were observed to produce
considerable displacements. The primary standing wave frequency in the main spring was observed at the calculated frequency, but produced increased force
transmiss-ibilities only through the lower link and through the strut in the high friction state.
SUGGESTIONS FOR FUTURE WORK
General Investigation of Suspension Systems
The investigation of suspension systems as vibration isolators should be a feasible experimental task. It should serve as an aid in verifying or modifying analytical models for an integrated vehicle analysis, and also as a design tool for the study of components and of temperature and ageing effects. Information could also be provided of dynamic loading applied to the vehicle structure, i.e. verification of force analysis procedures. The methods are available for such work, but further development is still required, as indicated in the following paragraphs.
Extensions to Theory
The theoretical analysis for the particular suspension used requires considerable extension to be of any practical value, A more complete model is required for prediction of many of the frequency effects observed. It should at least be three dimensional. Further degrees of freedom could be included after experimental study of individual resonances. Such a study requires the theory to yield modes of vibration for each resonance, and measurements to be made of displacements or accelerations of several co-ordinates. To be relevant to the measurements made and the results sought, the model equations of motion should be solved for transfer functions or frequency response functions relating forces at fixtures to force input to the hub. This force input to the hub, which should be a random function in order to produce realistic operating conditions, must be related to observed suspension inputs which may be available only in the form of displacement or acceleration values.
Verification of Experimental Method
Further verification of the experimental method is required before any weight can be given to the disparity between certain swept sine and random vibration results. These preliminary tests must be repeated, with a careful check on transducer calibrations and amplifier settings. What little insight that has been gained into the response of the system should be used to ensure that results are obtained from all transducers for each type of forcing. It would be particularly valuable to include the displacement in the swept sine test as a record of the system operating conditions. Random analysis should be carried out with longer sample recordings.
Extensions to the Experiment
Extensions to the experiment can be suggested in many ways. Forcing has so far been limited to one axis only, but the rig was designed for forces to be applied to the wheel spindle from any of three mutually perpendicular directions. In the first instance, each axis of forcing could be used, with a range of pre-loads on the main suspension spring. It would also be possible to force the system on two axes simultaneously to study the effect of coulomb friction in the strut on transmission of horizontal forces. Random forcing with amplitude and frequency parameters similar to road conditions may be obtained using the equaliser filter set for low frequency shaping. Effect of statistical parameters of the forcing on system response could be studied and related to swept sinusoidal responses. There is much basic information which could be gained from a series of constant frequency tests, in each of which the variation of system response with amplitude may be measured.
Equipment Improvements
Improvements can be made in the laboratory equipment to reduce approximations involved in some of the measurements and to reduce the labour of data reduction.
The swept sine tests would benefit from incorporation of a dependable frequency discriminator. A suitable module is available to fit into the frequency response analyser. The analyser would be far more valuable if the complete tracking filter arrangement could be brought up to the maker's claimed performance. This is quite feasible for the frequency response, and surely the non-linearity of the output amplitude response could be reduced. Random testing would be facilitated if equalisation filters covering the range 25 - 200 HZ were added.
Data reduction should be carried out on the digital computer. For swept sine tests the higih speed data logger could be used to digitise the frequency response curves instead of recording them on the X-Y plotter. A high speed analogue-to-digital converter is available which was bought with random signal analysis in mind. This could be used, either on-line or from magetic tape
recordings of the experiments, to enable the digital computer to be used for cross-spectral analysis, a function which the existing analogue equipment cannot perform. A suitable programme ought to be available for such analysis in the computer
library of programmes.
CONCLUSIONS
In conclusion, it is not claimed that the experimental results presented here are themselves reliable descriptions of the performance of the MacPherson strut suspension system. Rather it is hoped that as the results of only four days' laboratory measurements they are indicative of the state of development of the equipment and experimental techniques. Variations were observed in the response of the suspension system. Since these were such as the equipment was intended to measure, it is suggested that the work could be continued to some purpose,
TABLE 1
Force Transmissibility from Swept Sine Analysis
Assumed sensitivity of analyser graphical output: 1 cm. reps. 0.005 volts
Transducer calibrations: Input force, f, 1250 Ibf./volt. Strut force, s, 1545 Ibf./volt
Results, 4 - 5 0 HZ, large displacement amplitude:
Frequency HZ 4 6 7 10 14 17 20 25 30 40 47 50 Input cm. 6.1 5.8 4.2 4.3 4.5 4.4 4.5 5.1 4.8 4.5 4.6 4.5 force, f Ibf. 38.1 36.2 26.3 26.9 28.1 27.5 28,1 31.9 30.0 28.1 28.75 28.1 Strut force, s cm. Ibf. 11.4 6.4 3.5 3.0 3.0 4.5 11.2 13.2 11.1 6.1 2.5 3.4 88.0 49.5 27.0 23.2 23.2 34.8 86.5 102.0 85.8 47.1 19.3 26.3 Transmissibility Ratio s/f 2.31 1,37 1.03 0.86 0.83 1.26 3,08 3.20 2.86 1.68 0.67 0.94
TABLE 2
Force Transmissibility from Random Analysis
Specimen calculation: Strut force, 0-25 HZ, small displacement case. Spectral density calibrations:
Input force, F, measured 0.030 volts r.m.s., calibration 1250 Ibf/volt, thus 37.5 Ibf. r.m.s.
2 Area under p.s.d. curve, 5.6 cm
2 2 2 so 1 cm equivalent to (37.5) /5.6 mean squared Ibf.(lb )
Frequency axis: 1 cm, represents 2,5 HZ,
(37 5i 2 therefore, on power density axis, 1 cm. represents ^ /-'^ c lb /HZ
*) *) ^ * 6xz. 5
whence the factor F » 100 lb. /WLlcm.
and F - 10 r.m.s.lb./HZ/cm. S i m i l a r l y , for the s t r u t f o r c e , e} = 0.666 Ib^/HZ/cm. and s = 0 . 8 1 6 Ib./HZ/cm. For calculat Frequency HZ 2 4 6 8 10 12 14 16 18 20 22
ion in the table,
Power Densities Input force 0.22 0.22 0.30 0.31 0.35 0.42 0.52 0.45 1.15 1.20 1.61 the factor ^ - 0.0816 r (cm.) Strut force 2.5 2.9 3.75 3.75 5.2 4.3 5.0 3.0 6.3 6.2 6.2 Ratio H2 11.4 13.2 12.5 12.1 14.9 10.2 9.6 6.67 5.5 5.2 3.85 H 3.38 3.63 3.54 3.48 3.86 3.19 3.10 2.58 2.34 2.28 1.96 Transmissibility 0.28 0.30 0.29 0.28 0.32 0.26 0.25 0.21 0.19 0.19 0.16
TABLE 3
Resonant Frequencies; experimental observations compared with theoretical values
Experimental Observations Frequency, HZ 5 15-30 20-25 25 30-35 45 45 80-120 120 180 Transducer Strut Strut Transverse Link Tie rod Strut Transverse Link Tie Rod Various Tie rod All Conditions Sweep Range HZ 0-25 15-200 15-200 0-25, 15-200 15-200 15-200 0-25, 15-200 15-200 15-200 15-200 Displacement large small small any large large any various any any Predicted Frequency HZ 3 - 4 21.5 34-83 46.5 49 316 Frequencies Conditions no friction friction locked damper unlocked, varies with damping. spring surge any condition any condition
DISPLACEMENT TRANSDUCER //yy// VOLTAGE PROP. FREQUENCY
nni
X - Y PLOTTER TRACKING FILTERn
COMPONENT RESOLVER JUNCTION BLOCK 2 - B E A M C.R.O. - I — CARRIER AMPLIFIERSm
VALVE («XTMETERRG.I. BLOCK DIAGRAM: APPARATUS FOR SWEPT SINUSOIDAL VIBRATION.
RANDOM SIGNAL GENERATOR // /^ ^ / y ^j y / LOAD CELL 2 CHANNEL CARRIER SYSTEM - ^ //??/ DISPLACEMENT TRANSDUCER
UlU
JUNCTION BLOCK CARRIER AMPLIFIERS X - Y PLOTTERNOR ATOM I SAC STATISTICAL ANALYSER
B
VALVE VOLTMETERFIG. 3. VECTOR LOCUS PLOT STRUT FORCE I 5 - 2 0 0 Hz
RELATIVE TO CONSTANT INPUT FORCE.
2 0 so K30 2 0 0 FREQUENCY H j
FIG.4. REPEATABILITY OF AMPLITUDE RESPONSE TO" SWEPT SINE FORCING
TOTAL SIGNAL
FUNDAMENTAL COMPONENT
I
.«-aoo Hz F1G.S. DISTORTION : FUNDAMENTAL AND TOTAL COMPONENTS OF TRANSDUCER
OUTPUT ( I N P U T FORCE)(NOTE-FREQUENCY RESPONSE OF TRACKING FILTER)
'025
INPUT FOBCE NOMINAL 60 LB R.M.S. STRUT FORCE
FIG.
FREQUENCY H j
•075
i/i -OS
2
TTt ROD FORCE
UOWER LINK FORCE
SO
FREQUENCY H j
FIG. 7. FREQUENCY RESPONSE, SWEPT SINE INPUT F0RCE760LB R.M.S. I S - 2 0 0 H j
•075 .. ui 'OS 2 of
J
r^x
INPUT FREQUENCY ( N O M . 3 0 LB R.MtS) STRUT FORCE ^ \ • • > I ^ -50 FREQUENCY H jTIE ROD FORCE LOWER LINK FORCE
SO
FREOUEHCY H;
FIG. 9, FREQUENCY RESPONSE, SWEPT SINE INPUT FORCE, 3 0 L B R.M.S I 5 - 2 0 0
H^-<n OS 2
a
INPUT FORCE STRUT FORCE TIE ROD FORCE
FIG.IO.
S K) IS 20 30 «O SO FREQUENCY Hz
FREQUENCY RESPONSE, SWEPT SINE FORCING, 2-SO H^. SMALLER DISPLACEMENT MOTION.
>
3) O m & • -^ * — 7 - - -^ i " ^^/ r
f i's \
/-'
s,
s .^
'1' (
.^•-^i
< < < _ ' - C " < ^ " ^ ...— •—• —r " "
N . \ > • ' . I l . - • \ ^ I l INPU T F O STRU T F O TI E RO D A C N . S S S 1 ^ m)-.'::r::_\-:^-.-—
STRUT FORCE LBF Z •O • I o m X N TlP
10 7} m w •o O z (A mïi
O3
z
H •n 3Js
c m z o < ( 0 5s
0 .^ 0 > 5 . 1 \ ' \ / \ /• V
1 10 0r
1
1
1
f
1
1
— 18 ê
N's..
* N • N . . N . \ - . \ • \1
i
S 8 S
I ' '7 r \ ^ N \ \ m 0 \ X ^ N \ < "s • .0 0 1 l BI "0 r?;
m m z -1 N iq s c H •n 0S
m -• o ö 5 O g aO >^ 4
20 30
INPUT FORCE LBF
FIG. 13. AMPLITUDE RESPONSE AT CONSTANT FREQUENCY
INCREASING INPUT FORCE AT 6 5 Hz.
lO 15
FREQUENCY H j
^3
FIG.I4. DISPLACEMENT RS.a 0-2S Hz. LARGER AMPLITUDE 6-35x lO'' R.M.S FT.
lO 25
lO 15 FREQUENCY Hi
FIG.I5(o) STRUT FORCE RS.D. 0 - 2 5 H2 LARGER AMPLITUDE 6 7 5 R.M.S. LB. FIG. 15(b) INPUT FORCE RS.D. 3 7 5 R.M.S. LB.
( a ) TIE ROD FORCE ( L A R G E DISPLACEMENT) 2' 16 RMS LB
(b) INPUT FORCE P » D ( 3 7 5 R M S L B )
(c) LOWER LINK FORCE R S . D . 2 7 9 RMS LB
lO 15 FREQUENCY H^
2 0
25 RMS LB
d) LOWER LINK FORCE RS.D
3- 51 R.M.S LB.
yi^MMiUVMl?^'
b) INPUT FORCE RS.D 37-5 RMS LB. è) INPUT FORCE RS.D 37-5 RMS LB c) DISPLACEMENT PS.D 3 l 7 x Ió3 RMS FT. lO 15 FREQUENCY Hzf) TIE ROD FORCE P.SB.
1-85 RMS LB t o IS FREQUENCY H^ 20 25 F I G . 17 R A N D O M F O R C I N G , L O W E R A M P L I T U D E O F D I S P L A C E M E N T 0 - 2 S H j . t o o FREQUENCY Hz
FIG. I8.(a) TIE ROD FORCE R S . D . 0 - 2 0 0 H j 6 0 RMS LB.
FIG. 18(b) INPUT FORCE RS.D. 0 - 2 0 0 H7. 125 R M S LB.
zoo H(
FIG.I9. STRUT FORCE RS.D. 0 - 2 0 0 Hz 45-7 RMS LB.
SO lOO FREQUENCY H^
FIG. 20. SINUSOIDAL FORCE TRANSMISSIBILITIES IS 2 0 0 Hz 6 0 L B . INPUT FORCE.
-I a s
o<B
-so
FREQUENCY Hz
lOO 2 0 0
FIG.21. FORCE TRANSMISSIBILITIES (SINUSOIDAL) I 5 - 2 0 0 Hz 30LB INPUT FORCE. < IT >-I - 1 0 uj -6 Z • < IT
t-w
+ STRUT 0^ O TIE ROD / ^^<9 1 ' < '' ' ?'''
'. A
/ • ^ ' ^ • — - , . - ^ * — " 30 4 0 FIG.22. i 4 6 8 10 2 FREQUENCY HzFORCE TRANSMISSIBILITIES (SINUSOIDAL) 2 - 5 0 Hz-SMALL DISPLACEMENT
\ \ 1 \ \ \ > \ X \ 1 STRUT O TIE ROD 1
1
! " J J
2 3 4 5 6 B lO 2 0 3 0 SO FREQUENCY HzFIG. 23. SINUSOIDAL FORCE TRANSMISSIBILITIES 4 - 5 0 H-LARGE DISPLACEMENT. 0 < a. U) z < UJ o 4 6 8 lO FREQUENCY Hz
FIG 24. TRANSMISSIBILITY RATIOS RANDOM FORCING 0 - 2 5 Hz. LARGE DISPLACEMENT ( 0 0 0 6 3 5 R.M.S. F T )
2 DISPLACEMENT TRANSMISSIBILITY FT/LB « K ) ' TRANSMISSIBILITY RATIO O O 3 to 73 > Z (/I Z v> ta 7)
o
w 33 > Z Oo
-n O 3J n z o too
o
XlOO 2 0 0 Hz
FIG. 27 STRUT FORCE TRANSMISSIBILITY ALL INPUTS.
o 0 2 L
10 20 FREQUENCY Hz.
2 0 0
O S o 2 z < cc O I O 0 5 \
SWEPT SINE I 5 - 2 0 0 Hz LOW HIGH R A N D O M 0 - 2 5 Hz LOW " " . HIGH O 0 2
V
V-x
/ • • > .4:^
I \ f f \ ii-i-V\
•i i V lO 2 0 FREQUENCY Hz SO • . \••.v,
/.?
l O O 2 0 0FIG. 29. LOWER LINK FORCE TRANSMISSIBILITY ALL INPUTS.
1 0 0 ISO LOAD LB
