Journal of Research of the National Bureau of Standards-C. Engineering and Instrumentation Vol. 63C, No. 1, July-September 1959 A Tilting Air-Lubricated Piston Gage for Pressures Below

One-Half Inch of Mercury 1

U. O. Hutton

(M ay 8, 1959)

A desct'iption is given of a tilting dead-weight piston gage constructed at the National Bureau of Standards for ranges of differential pressure up to about 0.5 inch of mercury. A resolut ion of bett er than 1 part in a hundred thousand of fuJI scale has been obtained by use of the toolmaker's sine bar m ethod of angle measurernent. The scale is a linear function of the sine. The instrument can be calibratcd from basic measurements of length and weight, IS rugged, a nd may be constructed III almost any laboratory mechanical shop. Sources of possible errors in reading are discussed in detail. Comparative t ests with certain other gages or manometers are cited wherein linearity " 'as found to be within 1 part in 10 000 and a

1. Introduction "csort to delicate sLructures and requires neither optical nor electrical amplification. The extended A need exists for pressure-measuring 01' controlling scale available is gained through the use of a microm­ devices for ranges of low pressme, particularly the eter and end gage block. pressure range corresponding to atmospheric pre sure at high altitudes. The need is more aeute where 2 . Description of Piston Gages measurement and control are both required. For the study of the press ure-deflection characteristics of In development, two modcl were constructed that diaphragms of high sensitivity, no device discussed will be referred to as Models I and II. Model II in available literature [1] seemed conveniently appli­ incorporates all the features of Model I so that a cable to the problem whcre constancy of pressure discussion of Model I i possibly not of great value; dlfference from a datum was desired for various however, its simplicity of construction and the high lengths of time up to 24 hr. Oonventional air­ sensitivity and 1'e olution attained may make it lubricated piston gages are nicely applicable to this applicable in some cases where the additional com­ problem approaching within about 0.4 in. of mercury pleAi.ty of Model II is not warranted. The fu'st of the datum pressure with a resolution of at least 1 model is of such simplicity that it may be constructed part in 10 ,000. This report de cribes a piston gage and a basic calibration made in a short time in almost to cover from about 0.5 in. of mercury to the datum any laboratory. The principles of the gage are so pressure with a resolution of 1 part in 100,000 and elementary that adherence to the details being means of pressure adju tment without resort to described is not suggested as being necessary. Dimen­ weight changing. sions and other specifi.c detail as used are included In exploring the characteristics of gages suitable for guidance in understanding the structure on which for the contemplated tests, several air-lubricated performance data is pre ented. piston gages were made from medical hypodermic 2.1. Description of Gage, Model I syringes of 25- and 100-cm3 capacity. These syringes had hollow pi tons and could be employed to as low For the piston-cylinder combination, four 100-cm 3 a pressure as 0.4 in. of mercury. Schemes for em­ syringes were obtained. Two of these were found ploying such gages with opposed pistons were aban­ to be sufficiently tight for adaptation. They were doned because of the loss of resolution as the pressure put through a hand-lapping operation where lapping difference set up by the pistons becomes small. In powder, Linde A Of J.i- ), wa used in a creamy water handling a well-lapped syringe it was observed that suspension. From }f to 2 hI' lapping was employed air lubrication for a low-density pi ton was sur­ using a combination of rotary and longitudinal mo­ prisingly adequate even if the piston was not vertical. tion with the addition of water or lapping compound Brubach's experiments [2] encouraged an attempt to as required. The lapping operation was considered devise a piston gage, the incremental loading of complete when a piston, washed and dried, would which would be adjusted by changing the angle of just fall of its own weight in its cylinder oriented in tilt instead of the weights as on the conventional a vertical position with the pistO:l at any radial angle. dead-weight testers. Distinct advantages of this It does not eem possible to overlap such a combina­ design are that it reaches high resolution without tion with this size of lapping particle using water as a lubricant because of the hydrodynamic lubrica­ tion furnished by the lapping motion; however, it I The major part of this work was sponsored by the Flight Control Laboratory, Wright Air Development Center, Wright· Patterson Air Force Base, Ohio. was always possible to remove the high areas on the 47 piston and cylinder so that the freedom-of-fall condi­ BEARING tion described was obtained. The tighter areas may BEARING MOUNT CYLINDER be recognized while lapping b~T the degree of dis­ PI STON persion of the lapping compound and after drying by TO TEST PRESSURE WEIGH1 the higher grade finish on the closer surfaces. Extra attention may be given the high areas by localized finger pressure on the cylinder and by choice of the piston orbit to bring them into frequent play. In some of the better lapped areas, white light interference fringes have been visible but this is not necessary for --- proper performance. After lapping, the cylinder and piston were cut with a diamond saw as shown in figme 1, then mounted on a sin e bar, shown in figme 2 to form a piston gage. The piston is weighted as desired and PIVOT floats without rotation in the cylinder on an air film as a bob. The cylinder is supported on another por­ FIGCRE 2. Tilting pi6ton gage, Nlodel I. tion of the original hypodermic piston employed as an air-lubricated pinion bearing. The micrometer anvil and sine pivot are at such a relative height that the piston is horizontal when the micrometer is fully 2 .2. Description of Gage, Model II retracted. The cylinder must be rotated to keep the piston As a result of the experience with Model I , a free. It was origi na ll~ ' ro tated by an ail' jet directed second grge, YrocLcl II, was built. The design was against the teeth of a 4-in. diam spur gear concen­ changed so that t be tilt can be measured over a trically mounted on the cylinder, but later by a 25-w, gO-deg angle from. the horizontal b~T means of gage 2,700-rpm shaded-pole induction motor operated at end-blocks and I-in. micrometer caliper. Thc cylin­ ~~ voltage with a rubber band (No. 32) as a belt over der on this model was made from 1.250-in. cliam the motor shaft and around Lhe cylinder. A slight precision-bore . glass tubc. The piston and bearing finger spin IS sometimes required for starting, and were prepared, by lapping, from ordinary Pyrex under the light load conditions prevailing, the rubber tubing in an attempt to avoid the slight taper that is band, as a belt, lasts several weeks and vibration or present in a hypodermic syringe. See figures 3, 4, 5. temperature transmissions from motor to cylinder rnstcad of the wood base of the original model, a are negligible. 2 X 6 X 12-in. surface platc was used as a base. This The piston is eccentrically loaded to prevent its provides a satisfactory surface on which to wring the rotation as shown in figure 2. One inch of vertical gage blod;:s used to establish the altitude of the travel of the micrometer corresponds to 40 revolu­ triangle (this being the measure of the tilt). The tions of the micrometer screw. The length of tbe pivots for the piston support bar and for the mi­ scale on the barrel of the micrometer is 1. 5 in., which crometer mOllnt are hardened steel cones and spaced gives a total scale length for 40 revolutions of 60 in. , 10.000 ± 0.002 in. apart. with a readability of 0.005-in ., corresponding to 1 in 10 ,000.

L- /" -1 , -, I /z - _I

MICROMETER

BEARING DPI STON

TEST PR ESSURE

ALT ITUDE h I

CYLI NDER SPIRIT LEVEL..---( =

FIGU RE 1. Sawing of hypoder mic ~yr ina e to obtain parts for piston gage. FIGURE 3. Tilting piston gage, Model II. 48 provided. A small fan motor with a rubber belt provides the roLational movement of the cylinder. The piston is closed with an inside fitted cap and a fixed cast lead weight, '1V l , is used and is ad­ vantageously located at Lhe upper end of Lhe piston so that its verLical componen L will be as nearly as possible through Lhe cenLer of the piston s upporting area with a t il t of 3- 4 in. ] n addition to the main wei ght, \Vl , Lhe piston is loaded wiLh an auxiliary weight, \V2, composed of lead shoL or other such movable weighLs, Lhe purpose of which will be dis­ cussed in section 5.5. A change in altitude, h of 1 in . is provided b)' each I-in. end-block placed uncler the micromeLer and each I-in. block is equivalenL Lo ]0 perce nt of the piston weight which is can 'ied by the air pocketed under t he piston. The pressure developed by the piston in this pocket is in direct proportion to altitude, h. Altitudes up Lo 8 in . have been em­ ployed. For altitudes from 8 Lo 10 in. Lhe eccen tric FIGUUE 4. Tilting piston gage, "Model I I , in zero position. posiLion of Lhe weighLs will not always overcome tbe cylinder drag and prevent roLation. The scale length of this model usin g Lhe combina­ The micrometer support mOLlnt is positioned by a Lion of Lhe m icrome tel' and end blocks is e ITe ctivel y parallelogram strucLure so that the micrometer eighL Limes the scale lengL h of 1Joclel J, a nd thus fs axis is main tain ed perpendicular Lo the surface of readable Lo 1 part in 80,000. Some experimenLs tbe base plate. The pressure connection is made have been made with a 6-in. diam reading elial such through the pivot bearing as s ho wn. A stop is as used on Lhe more prec ise mi crometers. This provided to prevenL Lhe piston being blown ouL, provides a scale length of 6,000 in. readable Lo 1/:32 and for convenience in observing tbat the level of of an inch and a zero sLabili LY of Lhe same order as the base plate is unaltered, a ensiLive spiriL level is t he resoluLion. . Two press ure connection s to the lower surface of the p iston arc provided, one for connection to Lhe chamber or space in which the pressure is to be measured and Lhe other, marked "Fill" in figure 3, Lo replenish air lost b~T leakage. A conLrollable volume shown in fi gure 4 is con !l ecLed Lo the "Fill" opening. The function of the saIL pad is di scussed in section 5.4. 3. Calibration

The pressure difference p beLween the two end s urfaces of the piston is deLermined b)' the relaLion

mg . mgh p = - ' sm A=- '- a ad where m is the mass of the weight; g, the acceleration of gravity; h, the altitude of the triangle (fig. 3); a, the effective cross-section al error of t he piston; d, the distance between Lhe pivots of Lite siLle bar and calipers (fig. 3); A, the angle of elevation of the sille bar. Tt is seen tha t my/ad is a eo nsLant for anyone design, weight of piston and at anyone location. When these constants arc known, it is only necessary to measure h to determine the pressure. If the weight mg is in grams and the other quantities in centimeters, p is in units of grams per square centi­ m eter; similarly if mg is in pounds and the other quantities in inches, p is in units of pounds per l"IGUlm 5. Tilting piston gage, ~Model II, in tilted position. square inch. 49 The piston weight is readily determined, if desired, the test pressure, using an independent connection to 1 part in 100,000. to some type of reservoir to introduce or release air In the investigation, relative readings of high for the repositioning of the piston when desired. precision and reproducibility were desired, but the When it is desired to provide a definite pressure to a basic calibration was of lesser concern. Con­ gage to be calibrated, set the altitude h with the sequently the precise determination of effective area micrometer or with micrometer and end-gage blocks was not ~ttempted. The effective area has been to give the pressure desired. This pressure will be assumed to be the mean of the cylinder and the maintained at. the test connection so long as the piston areas. The diameter of the piston was piston floats without touching either end-stop. If measured to approximately 1 part in 10,000 by an unknown pressure is to be determined, connect means of a micrometer caliper. The cylinder the apparatus in the same manner but set h, step by diameter which is difficult to measure accurately step, until all axial motion of the piston is canceled. with mechanics' micrometers had an accuracy of This can ordinarily be accomplished in less than a about 1 part in 4,000. Thus the effective area w::s minute. probably known to an accuracy of about 1 part III Tests of various sorts have been improvised to 2,000. Higher precision in this determination would determine the performance of this type of piston require not only more precise measurement but a gage. Certain tests were pcrJormed on Model I combination of piston and cylinder without measur­ and not repeated on Model II. Also, some tests able taper or dimensional irregularities. Meyers were devised after Model II was in operation and and Jessup [4] (as well as later workers) suggest were not performed on the earlier model. Test effective diameter determination by manometric results are included irrespective of theu' being methods, and with a suitable manometer available obtained on the earlier or on the more advanced this method would be perf erred to clearance measure­ model where they seemed to provide pertinent ments. Where a basic gage calibration is required, information on the gage performance. effective area determination to 1 part in 25 ,000 for a The r eadings of the piston gages were compared I-inch piston should not be too difficult. with those of several sensitive pressure-measuring There is also some change in area possible, due to instruments in order to obtain information on its internal pressure in the cylinder. Correction for performance characteristics. These were: (a) An this error may be made from empirical data. And, Ascot-Casella micromanometer [3]; (b) a vertical finally, the effective area may be slightly influenced aU'-lubricated piston gage adapted from a 100-cm 3 by the change in the eccentricity of the piston for hypodermic syringe; and (c) a sensitiv(l2-in. mer­ differen t angles of tilt. No error from this sonrce cury manometer having a null indicator based upon has been separated, but some allowance for such an a capacitance bridge [5]. The Ascot-Casella in­ error is indicated in the later tabulation. No strument has a torsion balance to measure the dimensional changes have as yet (after 1 year) been difference in the product of the pressure and area of recognizable due to either wear or secular changes. two bells floating on kerosene. The vertical component of the piston weight is proportional to the sine of the angle of tilt which requires a knowledge of both the altitude and hy­ 4.1. Zero Stability potenuse of the triaJ'lgle (see fig. 3). The leg or Particular attention was given to a study of the altitude of the triangle, measUTed by the micrometer repeatability of the gage zero since full advantage of and gage blocks, can be measured to an accuracy of the gage resolution is available here, whereas under 0.00005 in. For equal absolute accuracy in the the loaded condition stability can be determined value of the sine of the angle, the hypotenuse must only to the degree that the load may be held constant. be lmown to the same accUTacy as the altitude. The zero, as referred to, is determined under the condition of both ends of the piston exposed to 4. Performance atmospheric pressure. The altitude h is adjusted by means of the micrometer until the piston floats The base of the instrument must be maintained without axial drift. The repeatability of the zero, level. Since the resolution is equivalent to the sine determined after altering the former setting by of an angle of 2 sec of arc, the axis of the base should varied amounts, with either intermittent or continu­ be maintained to within at least 1 sec of the hori­ ous rotation, has been found to be in the same order zontal. For highest accuracy, the gage needs to be as the resolution of the micrometer reading. Six leveled on a rigid table in a room free from excessive consecutive hourly readings showed variations of drafts and where the temperature uniformity is sucb + 0.0002 to - 0.0001 in. in altitude. Daily readings that a thermal expansion error of significance will with no rotation of the cylinder during the night not exist in either the altitude or area measurements. have rppeated within the same limits for at least 5 The first step is to zero the gage. This is the days. The influence of other factors on the zero condition where the pressure connection is open to were studied and the results of the tests may be the room, and the piston in the rotating cylinder is summarized as follows: at an equilibrium position touching neither end-stop. Under this condition the axis of the piston is, of (a) There was no visible change in zero with an course, horizontal. The gage is then connected, to ambient temperature change of 5° C. so (b) A change in the axial posiLion of the piston the altitude increases; this increase in sensitivity is of Ys in. each side of the iniLial balance point caused not considered significant since the total variation is a total zero variation of 0.0002 in. within the resolution of the 2-in. manometer. (c) A doubling of the cylinder roLational speed The results of the comparison at an intermediate was observed to affect the zero by 0.0002 in. pressure range are shown in table 2. The test was (d) The piston weight was increased 5-fold without again made on Model I piston gage but with a greater observable change in the zero. load on the piston. The pressure given in column 2 (e) A piston with an end load of 500 g was reversed of table 2 was calculated from the constants of Lhc so that the load was positioned first in an outboard piston gage and the altitude following the procedure position, then inboard position. The average read­ outlined in section 3. The difference in the pressures ings, in each position, were identical with a variation calculated for the piston gage and determined from in individual readings of only 0.0002 in. readings on the 2-in. manometer are given in column 4. The difference amounts to about 1 part in 2.000 Some later tests were made with a 6-in. dial on the of the pressure and is compatible with the resolution micrometer. Altitude resolution with tIns microm­ of the 2-in. manometer and the uncertainty in the eter was 0.00005 in. and zero repeatability in tests determination of the effective area of the piston. over several days was to the same limit. With a 30-g piston weight this corresponds approximately TABLE 1. Low-pressure mnge comparison· tilting piston gage J.l!lodel I and 2-in. manometer to a pressllTe of 4 X 10- 7 in. of mercury. Tilting 2-in. manometer Increments 4.2. Comparison Tests, Pressure Controlled by gage Tilting Piston Gage Altitude Readino in. in. IIg Average For 0.2 in. 0.2000 0. 00160 ------. - - ._------The first experiments to determine the stability . 2000 .00161 O.OOtHO 0. 00160 of the reading when the pressure was controlled by . 4000 . 00320 ------. 4000 . 00320 . 00320 .00160 maintaining a constant tilt of the piston gage were . 6000 .00479 ------. 6000 . 00476 . 00478 .00158 made with the Ascot-Casella micromanometer as a .8000 . 00633 ------_.----.-- reference standard. Readings were made on the .8000 . 00635 . 00634 .00156 mieromanometer for a period of 20 min while a constant altitude, or tilt, was maintained on the a '-rho reference pressure is ) atm. piston gage during which the axial position of the TABLE 2. Intermediate 7Jressure range comparison' tiltiny piston varied X in. The micromanometer indications piston gage Model I and 2-in. manomele1' varied approximately 0.2 scale divisions with a Tilting gage 2-1n. rn a- DiJIerence full-scale reading of 250 scale divisions. This nometer indicated a repeatability of about one part in 1,000 at a pressure corresponding to about 1 percent of Altitude Pressure Pressure in. in. Hg calc. in. H g Inches I-Ig full scale on tIle piston gage. 1. 0000 0. 03741 0. 03745 0.00004 3.0000 . 11223 . 11227 .00004 Additional comparisons were made in the above 5. 0000 . 18705 . 18709 . 00004 pressure range using a hook gage with a resolution 7.0000 . 26187 .26197 . 00010 of about 0.001 in. of water as the reference standard. 9.0000 .33669 .33684 . 00015 The repeatability in readings of the piston gage was • Tbe reference pressure is 1 atm. about the same as with the Ascot-Casella microma­ nometer . The stability and reproducibility of the The results of the comparison at the highest zero position of the tilt gage was considerably better pressures thus far employed arc shown in table 3. than the readings as obtained with either the Ascot­ The test was made on Model II piston gage. Again Casella or hook gage. For this reason it was believed the pressures calculated from the piston gage altitude a more reliable reference should be used and subse­ and constants are compared 'with the pressures de­ quent comparison tests were made with the 2-in. rived from readings made on the 2-in. manometer. mercury manometer or the vertical air-lubricated H ere the pressures agree within about 3 parts in gage. 10,000, an amount far less than the expected uncer­ Comparison tests were made at three pressure tainty in deternlining the effective area of the piston. ranges obtained by varying the weight of the piston. The linearity, which is independent of the piston For each piston weight the tilt, or altitude, of the area, is within about 1 part in 10,000. piston gage was varied. In all of these tests the tilt­ TABLE 3. High preSSU1'e range comparison· tilting gage ing piston gage is acting as a pressure regulator. Jjlod el II and 2-in. manometer The pressure readings were made on the reference Tilting gage 2- in. man- D ifl"erence instrument, in this case the 2-in. mercury manometer. ometer The results of the low-pressure range comparison are given in table 1. The check readings were made Altitude Reading in in. Hg calc. In. Hg In. H g 5 min after the first reading. The resolution of the 0 0 0 0 4.0000 . 28700 .28706 . 00005 2-in. manometer is about 0.00005 in. of mercllTy. It 7.0000 . 50225 .50242 . 00017 will be seen that the increments for successive in­ creases of 0.2 in. in altitude decrease somewhat as • Tbe reference pressure is 1 atm. 51 4.3 . Comparison Tests, Pressure Controlled by T ABL E 5. Repeatability test on Model I I , Model I pelj01'ming an Auxiliary Instrument as a 1"eaulalol' •

The experimental model of a vertical piston gage Elapsed Model I Model II time was em plo~~e d at the lowest pressure of its range in a test where the pressure in the system was set and lvIinutes Altitude;". Altitude in. controlled by the vertical piston gage. The altitude 0 0. 900 0.6038 40 .900 .6038 of the tilting piston gage, adjusted to bring both 125 .900 . 6038 pistons to an approximately steady axial position was 0 4.0 2. 5587 read at intervals of time. The same point was ob­ 5 4. 0 2. 5588 10 4.0 2.5587 served over several hours and repeated the following 15 4.0 2.5587 morning. The results are shown in table 4. 30 4.0 2. 5588 55 4.0 2.5588

T ABLE 4. Comparison of lilting ail'-lubricated a piston ga1tge a. 'rhe reference pressure is 1 atm. with a vel'lical air-lubricated piston gauge

Elapsed Tilting gage Vertical mate center of the load supporting area. However, Lime piston gage wide variations are desired in tilt, say up to 75° 01' 80° from the horizontal, in which case the center of Pressure in. Pressure in. gravity of the piston may not even lie directly kr Altitude in. Hg calc. Ilg O______~ 8.6535 ______0.32321 above any portion of the bearing support area. To h ~ __ ___ ~_____ 8.6535 ______.32321 4 ______~__ 8.6545 ______.3232 1 test for this effect the piston was end loaded with 24______8.6537 ______.32321 lead weights and th e tilting piston gage connected

Average ~~ ___ _ 8.6538 0.32313 0.32321 to the 2-in. mercury manometer. The altitude of the tilting piston gage was set to 7 in" producing a • The reference pressure is 1 atm. pressure of ap pro x i matel~r 0.225 in. of Hg. The difference in height of the two mercury columns of The maximum departure in the altitude reading the manometer was observed, first with the piston of the tilting piston gage from the average was 0.0007 inserted into the tilting gage with tbe piston weight in. or less than 1 part in 10,000 . The difference between calculated pressures as determined by the at the elevated end, and then with th e piston reversed two gages is on the average 0.00008 in. of mercury end-for-end. This procedure was repeated several or 3 parts in 10,000. Again this is less than the times. expected enol' in the determinations of the effective The difference in the readings of the mercury areas of the pistons. manometer, for the orientations of the weighted This test demonstrated also the ease of b alancing piston in the tilting piston gage, corresponded to 0.000125 in. in altitude in the 7-in. deflection. This the pressures in the two gages b~~ the adjustment of the tilt altitude with the micrometer. The initial is less than 1 part in 50,000 and is about equivalent balance would be obtained within 4 min and, after to the least reading of the null indicator of the an altitude change of smaller magnitude, balance mercury column. could be restored in less th an one minute. With careful attention and with optical magnification of 5. Other Factors Affecting the Performance piston drift a balance can often be effected in one quarter of this time. A number of factors are considered which may N one of these comparative tests provided data affect the satisfactory operation of the piston gage J that shows reprodu c ibilit~~ of the reading deflection I to the precision anticipated from the performance of and in some measure may contribute to errors in the instrumen t at zero. Although the 24-hl' test pressure readings. interval in table 4 showed only a change of two parts j in 80,000, one intermediate reading in the series 5,1. Ma intena nce showed a departure of five times this. An imperfect regulation of the test pressure could be the cause for The maintenance to keep this gage 111 excellent such variations. In another test Model I tilting calibration and operating condition has been of I gage set at two arbitrary heights, was used as a pres­ very minor character. The maintenance so far req uired has been an occasional cleaning of the sure regulator and Model II was repeatedl~T adjusted to this pressure. The data are given in table 5. piston and cylinder. Cleaning has usually been I H ere the reproducibility of the setting is 1 part in at intervals of at least 1 month. As there is no 25,000. wear on the gage itself in use, the precision parts should be expected to have a long life. 4.4. O ff-Center Loading of the Piston I 5 .2. Temperature The effect on the pressure generated by the tilting piston by off-center piston loading was investigated. The most significant error believed present is that The center of gravity of the piston for small angles due to the change in effective ar ea of the piston of tilt may be readily positioned over the appro xi- through'J he thermal expansion of the materials ,of 52 which thcy al'e made. For Pyrex glass the thermal t imes greater th an L11 e effeeL when the glass smfaces expansion aHects the area less than one part in were acid treated. 100,000/°0, for which an approximate correction The ail' l ubrication of the close-fiLLing beal' ings of is read ily applied if nece sary. If wide temperature the piston gage palticularly at low pressures, Wfl,l'­ variations are anticipated and the highest accuracy rants further discussion. The horizon tal ail' piston is rcq u ired, the rna terial in the sine bar configura tion may be regarded as a journal bearing Lo which the houkl, of course, have the same temperature coeffi­ classical hydro dynamical theory of lubrication ap­ cient as the gage blocks. plies. Computations based on SommerfeU equations as given by Hersey [6] indicate the load bearing 5.3. Low-Pressure Limits of Operation capacity to be at least 10 g/cm2, more than adequaLe and the calculated coefficient of friction is a few Only e~1)101'atory tests have been conducted at perce~t , which is in reasonable agreement with reduced absolute pressures. I n these tests the expenence .. entire piston gage was placed in a pressure chamber However, a number of the factors involved in the and usually the piston gage has been at its zero operation of this instrument are not so easily treated position. by theory. T he Sommerfeld equations assume that "While the results of these tests indicate the possi­ the bearing fluid is incompressible and Newtonian, bility of operation of the piston gage at lower abso­ wi th a definite viscosi ty. At atmospheric pressure, lute pressures than anticipated, grea tel' difficulty with a bearing load of the order of 5 g/cm2 the as­ has been experienced in the dissipation of electrieaJ sumptions of incompressibility would be expected Lo charges on the piston. The usc of Llle saIL pad to apply fairly well. At reclucrd preSSU l' es, howeve1', control the humiditv was ineO:ective. A conclueLive the compress ib i lit~ T oJ the gas becolnes important. piston and eylinclef'might be a solution to this prob­ To support the bearing load the pressul'e below the lem but fabrication of these clements was not piston must exceed that above the piston b~T sOl11e undertaken. In lieu of conducting materials several :3 to 5 mm of Hg. At 1 mm of Hg ambient pressure "antistatic" agents have been employed. For the gas must, ill the crevice below Lhe piston, be example a very thin film of sulfuric acid on the compressed by several timps and the Sommerfeld glass surface has given compleLely sat i sfacLo J'~T theory would be expected to break down . Also opera tion to a pressure of a few mm of merC"lII'.\· when the mean-fl' ee path of the gas becomes com­ for at least an hour. Also, but with an accumulating parable to Lhe clearance Llle phenomenon of slip electrical charge, the pisLon gage has opera Lcd at would become i mportan t. This will also oeClli' aL 7.e1'O position for several hours at an absolute pressure am.bient pressures of the ordel' of a millimeter of Hg. of below 0.01 mm of Hg and at 0.0025 mm of Hg Down to these preSSUl'es Lhere is only a slight vitJ'ia­ for more than an hour. Remarkably the1'e was no tion of viscositr with pressure and so thel'e should indication or suggestion of "lubrication" failure. be very little difference in the coeffic ienL of fricLion The axial motion of the piston at very low pressure from tili so ul'ce. becomes very sluggish. The rotational drag on the At the vpry low ambien t pressures of a few microns piston produced by the rotatin g cylindcr first de­ of H g the ratio of load pressure to ambien t pl'rssure creases as the pressure is lowered, reaching a min i­ and also the ratio of lUcan free pa th Lo clearance are mum at about 2 mm of Hg, then as the pressure is of the order of ] 00 or a thousand Lo 1 and the classi­ lowered further there is a rapid increase in the drag callubl'ication theory would not be expected to ap­ which remains about constant to the lowest pressw'es ply. An attempt was made to setup the theory of reached. A "coefficient of friction" calculated for lubrication £01' the case in which the mean-free path this lowest pressure was 0.4 as compared to a value was very large in comparison with the clearance. of only 0.025 at the 2 mm abs preSSUl'e and 0.1 at This bogged down because of the geo ill etrical com­ atmospheric pressure. plexity but it was possible to see resemblallces to the At low pressures the static and kinetic friction ap­ classical theory. pear to be about equal, differing from the ease at The direction of eccentricity makes an angle with atmospheric pressure where it is sometimes neces­ the direction of the load which is on the order of 90 sary to start the motor r epeatedly to seCUl'e cylin­ deg. The rotation of the cylinder sets up a drift der rotation without spinning the piston. which forces gas in to Lh e con verging wedge, building The piston had been in use for many hours, thus up a pressure which will support the load. In the wearing off the high spots, before the low-pressure classical theory the gas escapes from the wedge by tests wore made, and the continued smooth opera­ the viscous flow, in the molecular case the escape tion at low pressure was only obtained when the is by diHusion. Qualita.tively the two cases are film of sulfuric acid was present. Without the acid similar, but with a different dependance on the local film it was noL ordinarily possible to keep thc piston clearance. It appears thaL at least part of the load in a floating condition at pressures bcIow 1 mm of can be supported by hydrodynamic lubrieation even Hg. This beneficial bellavior of the acid film may in the range of molecular flow. be due to its action as a lubricant 01' to its power to AnoLher mechanism might be expected at the reduce formation of electrical charges or both. The lowest pressures. The treatment with sulphuric effect of electrieal charges on the axial eontrol of the' acid probably leaves the glass with a large content clean piston was estimated to be as much as 20,000 of water which m ight out-gas for a long time when 53 first evacuated. Also the surface of the glass may be In his discussions, Professor Ott states "for low somewhat more slippery than when it is quite clean. speeds the friction decreases rapidly with speed, The preliminary considerations of theory are quite and the relative motion being greater during the obviously raising more questions than can now be back than during the forward stroke, the angular answered and it is clear that there is room for more momentum imparted during the forward stroke study. would be more than that taken away during the back stroke" and consequently the amplitude of the 5 .4. Force From Static Charges oscillation increases. This analysis was applied to an oil-lubricated bearing in the reference but In the earlier use of the gage a sluggishness La the would appear to similarly explain the encountered response of the piston was occasionally observed. oscillation on this air-lubricated device. This was connected with the phenomenon reported It was found that internal damping in the piston by Brubach [2] who states "Some of the s:yringes could be used to control tbe oscillation over a wide had a tendency to center themselves, that is, when range, so instead of using only the eccentrically the plunger was stabilized at a given point and then positioned cast lead weight, loose lead "bird shot" pushed in or out of the barrel, the plunger would were added to approximately 25 peTcent of the total return approximately to the original point of piston weight. The movement of the shot on small stabilization." It was suggested in his paper that oscillations is sufficien t to damp out any pTogres­ this action is a function of the asymmetry of the sive increase in their amplitude. cylinder or piston. However, this phenomenon was These oscillations limit the highest pressure that believed due to the accumulation of static charges on can be reached with the tilting gage. With Model II the piston and was soon connected with changes in about 0.5 in. of Hg can be developed at a tilt angle the room humidity. The sluggishness was usually of about 60° at 400 rpm of the cylinder with main­ present when the relative humidity was lower than tenance of good piston stability. HigheT pressures 50 to 55 percent and always absent at higher llU­ should be possible with closer fitting and greater midi ties. A simple method of elimination of this precision in the cylinder surfaces. A recent loading trouble was through humidity control. This was with tungsten carbide granules instead of lead has readily accomplished by inserting in the hollow bear­ allowed an angle of til t of 80° because of higher ing of the tilting gage a small blotting paper disk damping and a lower center of gravity due to the soaked in saturated sodium chloride. This main­ higher density of the material. tained the required humidity for several weeks without rewetting. Since the remedy for this 5.6. Centrifugal Force trouble was so simple an exhaustive study of the phenomenon was not made. As the cylinder rotates some rotational spin is The entire force from the electrical charges on the imparted to the air in the cylindeT. This spinning piston when at rest axially, seemed radial and no force increases with increase in the rotational speed error in the controlled pressure was observed. When of the cylinder or with increase, longitudinally, in the piston motion is required to counterbalance any distance between the piston and the bearing which volume change, the restraining force may, for a would expose more of the cylinder area to the few seconds, be a substantial proportion of the piston enclosed air. The effect of this centrifugal force weight but entirely disappears in 20 to 30 sec if a was investigated by increasing the space between new position is established. In effect it is as though the piston and the bearing from ~{s in. to JlS in., a considerable amount has been added to the in­ reading any change in altitude with the micrometer. ertia of the piston but nothing to its wcight. The The altitude change was + 0.0001 in., which is the piston behaves as though it had a frictionless spring least reading of the micrometer. As an additional control on its axis with the spring support attached check the rotational speed of the cylinder was to a frictionless dashpot. advanced from 200 rpm to 600 rpm. The reading of altitude at the higher speed was within 0.0001 5.5. Piston O scillations in. of the lower. It was concluded from these tests that any pressure developed by this centrifugal Usually the piston operates with a slight rotational force under normal conditions of operation was oscillation of several degrees; sometimes the oscil­ without significant effect. lation is entirely absent, but at other times, with some condition critical, such as tilt, piston weight, 5.7. Pressure Varia tions Due to Dynamic Sources or rotational speed, the oscillation of the piston increases in amplitude until the piston weight The piston gage itself is not sensitive to high­ carries over the top. When this occurs the piston frequency fluctuations in pressure but under certain continues to rotate at the speed of the cylinder circumstances the fluctuations created by the and the gage is inoperable. In the search for some piston gage may objectionably affect the connected history of this phenomenon a letter of Professor apparatus. These fluctuations can arise from three Ott, Ohio State University [7], relative to the failure sources; first, seismic motions, horizontal or vertical; of the Hackensack bascule bridge which he likened second, any axial component of symmetrical charac­ to "a pendulum suspended from a rotating shaft" ter imparted by the cylinder rotation; and third, was unearthed as describing a similar situation. from the mechanism used to make up losses in the 54 enclosed volume. Such an etreet in the order of rate of pumping, and in th c arne direction, as before. 2 X 10-5 in. of I-Ig has been found when following This seems to reduce the possibility of the pumping the deflectioll of a sensi Live diaphragm wiLh light being due h ere to any screw conveyor action from fringes. Effects exceedin o· one liahL fringe have surface marks or scratches on Lh e cylindrical urfaces. been ob er ved. These' flu cLuations have been (c) The weigh t on the piston had a large influence satisfactorily controlled by connecting the gage to on th e pumping raLe. At normal peed and ·wIth the diaphragm with some clamping interposed such a piston weight of 30 g a gain of 0.2 em3/min was as small bore tubing. noted; an d under the same condiLions but with a piston weight of 150 g th e rate of gain was 2.0 cm3/min. 5.8. Leakage (d) A test was made in which th e belt Lension wns progressively increased. Since th e belL pull was up­ Leakage from the enclosed volume back of the wards on the cylinder and positioned ncar the piston may tak e place past th e piston and th e outboard end of the bearing, tightening the belt would bearing since both are air-lubricated. The test decrease the bearing load and would at a certain made on Model I with a very low rotational speed point approximate an equally distributed loading. while in a vertical position showed a leakage of air Under the conditions where ligh t belt tension gave of 0.5 cm3/min at a differential pr essure of 0. 3 in. of a pumping rate of 1.0 cm 3 10ss per minute the gradual Hg. The leak decreases to zero, of course, when th e inerease in tension passed through a condition wh ere piston gage axis is horizontal. This leakage is there was no pumping and on to where th e rate was usuall~- obscmed by the pumping which oceurs. an 0.4 cm 3 gain pcr minute. The increase in b el t tension did not result in an obser vable t ilt of the 5.9. Pumping piston axis. (e) The pisLon was allowed to rotaLe with the The volume enclosed by the piston is subject to cylinder by scaling it to th e cylinder wiLh a drop change due to pumping through the air beariJlg of machine oil. The rate of volume gain was found while the cylinder is rotating and may be either into unchanged, indieating no pumping tlu·ough the or from th e atmosphere. Usually the rate of volume piston-cylinder clearance. change exceeds the r ate of leakage. In the applica­ (f) The load in the piston was now arranged as tions for which this gao·e is being developed the unsymmetrically as possible. A 11 6-g end l

This pumping action is of limited importance in Accuracy limit in inches of altitude the piston gage. The considerable discussion pre­ Factor sented here arises because of the difficulty en­ countered in the attempt to discover if any errors in Basic Relative pressure measurement arise from this action. The 1. LeveL ______O. 0001 0.00005 primary cause of the difficulty is the fact that the 2. 'l'emperaturo ______. 0001 . 0001 3. Area._. ______. 0005" . 0002 gage has a resolution some 10-fold greater than any 4. Sine ______. 0001 . 00005 conveniently available instrument on which an error 5. Static charges ______· 0001 . 0001 6. Piston oscillation. ______· 0001 .0001 from this source could be evaluated by comparative 7. Oentrifugal pressure ______.0001 . 0001 8. Dynamic preSS UTC ______. 0001 . 0001 testing. 9. Leakage ______.0001 . 0001 10. Pumping ______· 0001 . 0001 11 . Gage volume ______· 0001 . 0001 5.10. Gage Volume 12. Oentrifugal force on \\'eigbL ______. 0001 . 0001 13. Weight determination ______· 0001" . 00005 14. Zero reproducibility ______. 00005 . 00005 In apparatus where a small constant volume 15. Reading reproducibility ______. 0001 . 0001 system is required or desired the volume of this gage may be excessive, particularly when combined with In the error columns the values under "Basic" the gage leaking and pumping that have just been are assigned to cover the errol' of the instrument as a discussed. primary standard. In the column uncleI' "Rela­ The motion of the piston can be observed, if tive" the values arc based on the ability of the gage desired, by low-power optical magnifying means and to repeat a reading either as a gage or as a pressure the position change corresponding to the gain or loss regulator. The errors without asterisks are subject of 0.05 cm3 is reasonably visible, but the volume to variations dependent on random influences. The change of the gage is always significant when there is errors marked with the asterisk are unidirectional. a movement of the piston. At differential pressures The 5-in. altitude with the medium-weight piston less than 0.1 in. of Hg, the increased volume may be corresponds to a pressure reading of about 0.4 in. of contaminated by "in" pumping from the atmosphere Hg. The maximum predicted 1:'1'1'01' in the basic in which the gage is operated. measurement is 8 X 10- 5 in. of Hg and in the relative measurement is less than 4 X 10- 5 in. of Hg. 5.11. Centrifugal Force on the Piston 6. Design Modifications An axial force on the piston will exist if the cylinder rotates with any eccentricity. If eccentric motion is Although because of its simplicity, an air-lubri­ imparted to the piston, an axial component may cated bearing has been employed for the cylinder, result, affecting the apparent mass of the piston. this is by no means essential and does have t ile The construction employed, where the same straight inconvenience of considerably increasing the ex­ bore of the cylinder is used both to position the change between the atmosphere within and without cylinder on its bearing and to support the piston, is the gage. Oil-lu brieated journals or ball bearings 56 could. be employed and the pressure chamber ealed To reach the lowes t pressures the piston weigh t with O-rings. should be t he least possible. N o attempt has been Where it is desired to work from a pressure datum m ade to detrrmine the op tim um diameter of thc other than that of the room , t hi s may be ftccom­ pi Lon . A diameter on the order of 1 in . is con­ plished by several means. For in stance, idell tical vrnien L Lo work with, b u t smaller di ameters migh t air-lubricated bearings for the cylinder mfty be be employed wiLh eq nal sa Li sfacLion if tbe volum e or employed at both ends of the piston. This has been leakage of th r gage is par ticularl y signifi can t. T he done at times, bu t a very nice mechanical assembly eccen tric weighL for th e piston may he, on vari ou s is required to allow disassembly fo r cleaning or ad­ an-anl-!-'emen Ls, susprnclccl ouLside of t he cylinde r in justing the piston weigh t. If self-alincment ball order Lo provide grcaLer lr.ve rage if needed. bearings were employed this need not be a difficult The micrometer or h eigh t seLLing means migh t reassembly. be driven b~T a servomo tor to m ain tain a null piston Al ternately, a par ticularly compact structure could position. Increased resolu tion is available if the be made by making the ou ter surface of the cylinder micrometer were provided with a 6-i 11 . rcading circle the bearing face, concentric with and outside the or a digital readout, and provided that the screw piston support area and fj tted with two end pressure has commensurate accuracy. taps, as shown in fi gure 6. Alternatively the whole device may be enclosed by a belljar or to insure ease 7. Field of Application of access to the micrometer for adj ustmen t, the cylinder section only migh t be enclosed and driven Because of i ts sensitivity and in herent acc uracy through a magnetic coupling. it is believed that this gagc has application as a calibrating standard in the range of diff cr ential DRIVE BELT pressure up to at least }f-in. of mercury and p ossibl~T can be ex tended to Lwice this . Its apcriodic motion and low-temperature coeffLCien t (par ticularly if of quartz) reduces the time for a calibration. T esLs at zero differential pressure but at low absolute pressure indicate that measurements can V'V\!'VV''''''''''}-- TE ST CONNECTION be made aL absolute pressures down to a few mil­ limeLers of Hg. With further development, it appears possiblc to extend the lower pressure limit down below a 0.1 of a millimeter of Hg. As a m anometer to read an unknown pressure in Lhe above r ange, it h as considerable versatility and AIR BEAR INGS with its dead-beat characteristics allows readings l~ I GURE 6. ~Modifi e d piston gage . to be ob tained rapidly. As a pressure regulator to Symmetrical pressure connections are provided La control tbe reference pres· sure also. Tbe bearings arc outside of Lbe cylinder. re-produce precise settings, it has Lhe unique ad­ vantage of the commonly used dead weight Lester. If the reference pressure is to be a high vacuum, the highest precision would be necessary in the 8. References cylinder fi tting. Even with the smallest working clearance between the piston and cylinder the ap­ [1] W. G. Brombacher and T . W . Lashof, Bibliography and proach to the referen ce pressure would presumably index on dynamic pressure m easurement, NBS eirc. be limited by the leakage past the piston, and the 558 (1953). [2] H . F. Brubach, Some laboratory applicaLions of t he 10 \\' operation would be limited to an average pressure friction properties of the dry hypodermic syringe, R ev. that would allow an air fi lm for lubrication of the Sci. I nst. 18,363 (May 1947). piston. [3] H . R. H indley, A differential manometer, J . Sci. I nst. 24, For a reference standard, it is believed that the 295 (1947). [4] C. H . Meyers and R . S. J essup, A multiple m anom eter most desirable piston and cylinder combination and piston gage for precision m easurem ents, BS J . would be of fused quartz because of the stability of R esearch 6, 1061 (1931) RP 324. this material and also bccause of its nice working [Sl Manom eter fo r calibrating h igh-altitude pressure devices, qualitics. The fitting of the piston to the cylindcr N BS T ech. News Bull. 43, 71 (1959). [6] M . D . H ersey, A short account of t he theory of lubrica­ and area measurements might be performed to a tion, .T . Frankl. l nst. 220,93 (1935). much higher order of accw'acy than with glass. [7] P . W. Ott Letter to Eng. News R ec. 103,785 (1929). Transparency of the cylinder seems desirable for [8] S. A. McI{ee and T . R . McKec, Pressul'e distribution in observation of the piston although fo r a structure oil films of journal bearings, Trans. Am. Soc. :\1ech. Eng. APM- 51- 15, 161 (Nov. 1931). such as figure 6 an end window would suffice, in [91 F. VV . Ocvirk, Measured oil film pressure d istribution in which case Lhe cylinder and piston could both be misaligned plain bearings, Lub. Eng. 10, 262 (Oct. metallic. It is desirable for the piston and cylinder 1954). to be of iden tical materials to avoid temperature effects in the close fi ts req uired. WASHINGTON, D.C. (Paper 6301- 5)

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