Harwood Engineering Company, Inc.

A System for Viscosity Measurements at Pressures up to 3 GPa and Elevated Temperatures

by L.H. Abbot, D.H. Newhall, V.A. Zilberstein, & J.F. Dill

(J.F. Dill of Air Force Aero Propulsion Laboratory, Dayton, Ohio, not a member of Harwood Engineering Co., Walpole, Massachusetts)

A falling body viscometer was developed to measure viscosity of lubricants between 10^-1 to 10⁵ Pa.s at high pressures (up to 3 GPa) and temperatures of 20-200°C. The viscometer was incorporated into a variable-support pressure vessel mounted in an 0-frame press. A solenoid is used to raise the falling soft iron plunger to its upper position, where it closes a pair of contacts. On deactivating the upper solenoid, the plunger falls to the lower position to close a second pair of contacts. Fall times are measured by a timer in 0.1s increments. Viscosity of a few fluids, namely a synthetic turbine engine oil, a mineral oil, white gasoline, and a 1:1 mixture of the mineral oil and white gasoline were measured to demonstrate capability of the system. For the synthetic turbine engine oil, isoviscous curves for 10², 10³, and 10⁴ Pa.s are presented on a P-T diagram and estimates are made of the viscosity at which dynamic effects can be expected.

Introduction

Perhaps the first significant study of the pressure dependence of lubricant viscosity was that of Hyde⁽¹⁾. In his work with the Lubricants and Lubrication Inquiry Committee of the Dept. of Scientific and Industrial Research in London, Hyde measured the viscosity of several lubricating oils up to 0.15 GPa (1.5 Kbar). A major advance occurred in 1926 with the publication of Bridgman's work⁽²⁾, using the falling weight method to study viscosity in 43 pure liquids to 1.2 GPa (12 Kbar). Unfortunately, no lubricants were included in this list, and Bridgman was primarily interested in the mechanism of viscosity rather than engineering data. In 1928, M.D. Hersey, who was influential for many years in promoting pressure viscosity research, used a rolling ball technique to study the viscosity of lubricants under pressure⁽³⁾. Working with a group at Penn State, R.B. Dow⁽⁴⁾, who had been a student under Bridgman, produced about a dozen papers on the viscosity of liquids under pressure, most of them oils. R.V. Kleinschmidt of the Harvard Engineering School Faculty had done research on viscosity in Prof. Bridgman's laboratory, and when the ASME Research Committee on Lubrication undertook to sponsor a major investigation⁽⁵⁾ on lubricants under pressure, it was logical to locate it at Harvard under the guidance of Prof. Kleinschmidt, with Bridgman only a few doors away. In 1949, Bridgman extended his own viscosity research with a study of 14 liquids at pressures up to 3 GPa⁽⁶⁾. As before, Bridgman's primary interest was in the influence of molecular structure and interactions on viscosity rather than in engineering applications. A group led by D. Bradbury and M. Mark⁽⁷⁾ measured the viscosity and density of 55 well-defined lubricants to 12 Kbar and 218°C. Fairly extensive work on turbine engine lubricants has been performed in the last 10 years by Bossert an Hopkins⁽⁸⁾ at Midwest Research Institute under Air Force sponsorship. Other recent work worth noting has been performed by Winer⁽⁹⁾, Barlow⁽¹⁰⁾ and Hutton⁽¹¹⁾. Probably the study of liquid viscosities below 10³ Pa·s. With recent advances in technology, been that performed by J.D. Barnett and C.D. Bosco⁽¹²⁾ in which pressures of up to 60 Kbar were reached. The fluids under study here, however, were not lubricants.

In all the work cited, the majority of lubricant viscosity data has been restricted to pressures below 1.5 GPa and viscosities below 10³ Pa·s. With recent advances in technology, however, it is not uncommon to have lubricant contact pressures of 2 GPa and higher. Also, with the realization that viscoelastic effects can be important in elastohydrodynamic lubrication, it has become apparent that viscosity data in the range of 10³ to 10⁵ Pa·s (where lubricant "molecular response" times become comparable to contact transit times) would be very useful in understanding the nature of these effects. There is also still a need for work on the basis of lubricant viscosity, since there is still no reliable method for predicting a material's viscous behavior without actually measuring it. It was with these considerations in mind that Harwood Engineering undertook a project under the sponsorship of the Air Force Aero Propulsion Laboratory to develop a viscometer system capable of measuring viscosities to between 10³-10⁵ Pa·s at pressures of up to 3 GPa and temperatures of 20-200°C. Included in this system is a densitometer capable of measuring over the same range. This article will discuss the design of this system and present preliminary results on the viscosity of several fluids during initial system testing.

System Design

The pressure generating system consists of two 138 MPa air-operated pumps housed in a cabinet with valving and plumbing to both advance and retract both jacks. An indicator light on the front of this panel is tripped by the stroke indicator to warn of possible over-extension of the pressure generating piston which could damage the contents of the high-pressure chamber. Also contained in this cabinet is a polar plot chart recorder for reading the output from a manganin coil provided for pressure calibration of the load cell system at room temperature. This room temperature calibration is performed to permit pressure measurement using the load cell at elevated temperatures.

A second cabinet contains a temperature controller for measurements at elevated temperatures. Heating is provided by a set of band heaters clamped around the support cylinder. Control is achieved by monitoring an iron-constantan thermocouple located between the heaters and the support cylinder. Also mounted in this second cabinet is a two-channel strip-chart recorder for monitoring cell temperature and pressure, a timer for measuring viscometer plunger fall time and a set of lights which indicate the position of the plunger in the viscometer. On the strip chart recorder, one channel indicates the output of the load cell used for measuring pressure. Since the system was intended primarily for use at elevated temperatures, the load-cell approach had to be used. A manganin coil could not be used because of the temperature dependence of the resistance of manganin which makes it unsatisfactory for pressure measurement far from room temperature. Use of the load cell provides an accuracy of ±5 percent at pressures up to 3 GPa (30 Kbar), with pressure reproducibility probably closer to ±1 percent. The second channel is attached to a chromel-alumel thermocouple which is located directly below the experimental volume and is used to measure sample temperature. A chromel-alumel thermocouple was chosen because it is relatively insensitive to pressure⁽¹³⁾. Temperature was measured within ±0.5°C.

With the basic 3 GPa (30 Kbar) press, an experimental chamber 19.05 mm diameter by approximately 127 mm long is available in which different experiments can be performed by plugging in various experimental modules⁽¹³⁾. The system developed here consists of three viscometer modules for various viscosity ranges and one density module. A number of viscometer designs were considered before the final design was settled upon. A bellows and capillary design developed by Abbot⁽¹⁴⁾ was rejected because it was felt that a solenoid powerful enough to extend the bellows at high pressure could not be fit into the pressure chamber. Serious consideration was given to the rotating vane concept (c.f. Bridgman⁽⁶⁾) or a rotating cylinder. However, rotary solenoids required for the purpose are not strong enough to operate against the drag expected at high viscosities. Continuous rotation by a miniature motor was also considered but rejected because of potentially high heating due to motor power losses.

The final design settled upon was the falling plunger type viscometer. The plunger is in the form of a cylinder with tapered ends. In many systems where a falling plunger design is used, the viscometer is cycled by rotating the pressure vessel. Due to the size of the 3 GPa (30 Kbar) 0-frame press, (approximately 17.8kN (4000 lbs), the method did not seem feasible. The viscometer, Figure 2, was therefore, constructed using a soft-iron plunger which falls vertically within two solenoids placed end to end and surrounded by a a steel shell to complete the magnetic circuit. The upper, stronger solenoid is actuated to raise the plunger to its upper position. When the plunger reaches its upper position, a pair of contacts is closed switching on a panel light. On deactivating the upper solenoid, the plunger falls to the lower position to close a second pair of contacts and turn on a second panel light. Circuitry is provided to start a timer when the upper contact is made. This provides the measurement of plunger fall times. The lower solenoid can be used as an addition to the pull of gravity to speed up the fall of the plunger, which for high viscosities can last for hours. The viscometer modules include a socket with seven lug jacks which can be plugged onto the matching anodes of the closure at the bottom of the 30 Kbar vessel. The connections provide for the operation of the two solenoids, timing of the fall of the plunger and for the measurement of temperature by means of a type K, chromel-alumel, thermocouple. The viscometer modules fit loosely in the bore of the 3 GPa (30 Kbar) vessel, leaving approximately 5.7 x 10^-²m for travel of the piston as it builds up pressure. It is advisable to track the amount of piston travel, even though the limit switch is provided to prevent damage due to overtravel. The viscometer  modules are inserted and removed from the closure by means of an extractor rod which threads into the upper pole-piece. All three viscometer modules had nominal bore diameters of 6.35 x 10^-³m (0.25 in) and an overall internal length of 7.324 x 10^-²m (2.8835 in). The plungers all had a length of 6.848 x 10^-²m (2.696 in) to give a fall distance of 4.76 x 10^-³m (0.1875 in). The plunger diameters were varied to suit the range over which reasonable fall times could be obtained. While all three modules were tested, the majority of the measurements reported here were made with the largest plunger which had a diameter of 5.565 x 10^-³ (0.2191 in.) in its cylindrical section with a sample volume of 35 x 16^-6m³.

Analysis

Equation 1

In the derivation of this equation, it is assumed that the falling body is a right-circular cylinder. In reality, the fall weight has been tapered at both ends to improve fluid flow properties around it. This tapering of the ends slightly affects the fall time as given by Equation 1. The end effects can be accounted for by multiplying the geometric factors in Equation 1 by a constant. This leaves the basic relationships between viscosity and fall time of the form:

Equation 2

While a densitometer was also constructed as part of this program, the majority of testing was done on the viscometer. The density data needed for viscosity calculations were obtained from one of three sources. For the calibration fluid, data were available from previous reports on the same fluid⁽⁸⁾. Where necessary, the existing density data were extrapolated to higher pressures using a fit to an equation of the form:

Equation 3

Equation 4

For the studies of white gasoline, estimates of the density were made from Bridgman's data on n-octane⁽⁶⁾. For the hydraulic oil and the mixture of hydraulic oil and white gasoline, densities were measured at room temperature and atmospheric pressure. The densitometer developed under this program was then used to measure the change in density with pressure. These data are considered only approximate and therefore are not reported here.

Accuracies are assigned as follows:

 

k	± 0.15
t	±0.1 s
r	±0.01
r, L	negligible
T	±1° (readability ±0.25°)
P	±5 percent*

 

Experimental Results

Measurements were made at ambient temperature (20°C), 38°C, 99°C, and 149°C for the synthetic turbine engine oil. All other measurements were made at ambient temperature (20°C for the mineral oil base and 24°C (76°F) for white gasoline and the 1:1 mixture). For each combination of pressure and temperature, 5 to 10 readings of fall-time were obtained and an arithmetic average of the readings was used as a measure of fall-time. The standard deviation for these results was found to be ± 10 percent. At several temperatures and pressures, an attempt was made to assess the effect of solenoid heating on the measured fall-time. This was done by making a series of fall-time measurements for different time of exposure to the solenoid. The plunger was held for periods of 5 and 10 minutes before being allowed to drop. Results of these measurements indicated that at ambient temperature heating by the solenoids could decrease fall-times by as much as 25 percent, but at elevated temperatures little effect was detected. The thermocouple inside the viscometer also indicated no substantial temperature rise when the solenoid was on.

Data taken in the synthetic turbine engine oil are plotted in Figure 3 for temperatures of 38°C, 99°C, and 149°C. Also included are data by Bossert and Hopkins⁽⁸⁾. It can be seen that all the data are in good agreement. Figure 4 presents ambient temperature results for the hydraulic oil, the mineral oil, white gasoline and the 1:1 mixture of mineral oil and white gasoline.

Discussion

Fall-times could be reduced at higher velocities by using a hollow cylinder to further reduce drag. The viscosity range could also be extended by introducing a differential transformer system such as that used by Barlow⁽¹⁰⁾ to measure very small fall distances.

While only limited lubricant-viscosity data were obtained during this program to develop and test a new high-pressure viscometer, they are sufficient to provide some interesting insight into the probable behavior of hydraulic fluid under typical operating conditions which it might encounter. This fluid is a polyol ester base stock typical of MIL-L-7808G lubricant base stocks. As such, it is typical of lubricants used in Air Force turbine engine applications. The other liquids are employed in high-pressure technology and, in the present instance, served to provide further insight into the behavior of the system.

While much work has been done on the importance of viscoelastic and glassy behavior in EHD contacts, little data have been available on realistic lubricants under the actual conditions found in EHD. Work performed by Trachman⁽¹⁶⁾, Miller⁽¹⁷⁾, Heyes and Montrose⁽¹⁸⁾, and Johnson and Tevaarwerk⁽¹⁹⁾ among others has provided a good analytical base in this area. The most notable experimental work directed at assessing the importance of glassy behavior in an EHD contact based on lubricant physical data is that of Winer⁽²⁰⁾ et al. In this work, measurements of the high frequency acoustic velocity were utilized to determine the location of the static glass transition point in lubricants. In these measurements, glassy behavior was observed (a drop in the pressure dependence of the acoustic velocity) when the time for the local liquid structure to change (i.e. the structural relaxation time) in the materials being studied became long in comparison to the time allowed for system equilibration (typically 15 min). These experiments determined the pressure and temperature dependence of the static glass transition (generally 10¹¹ to 10¹² Pa·s; i.e. 10¹² to 10¹³ poise). For any lubricant which reaches this kind of viscosity statistically, very large dynamic effects would certainly be observed. In terms of "glassy" behavior in the rapid transient conditions of an EHD contact, any time that either compressional or shear structural relaxation times are comparable to the contact transit time, viscoelastic effects should be expected to be important in the lubricant performance. This can be seen in the use of Deborah number by Johnson and Tevarrwerk⁽¹⁹⁾. In any practical lubrication situation, it would be useful to be able to estimate whether viscoelastic effects will be of importance in determining behavior. For a high-speed bearing, contact transit times will be in the range of 10-100 ms (calculated from the ratio of the contact width to the surface speed). Since this is the total time for a fluid element to pass through the EHD contact, it might be expected that important dynamic effects would be present on a time scale of perhaps one tenth the the total contact time since, even on this time scale, a fluid will still experience large pressure changes. This would imply that for dynamic effects to be significant in an EHD contact, a fluid should have an average structural relaxation time of at least 1-10 ms.

This time can be related to the viscosity using the relation

Equation 5

Nomenclature

Footnotes

References