Decoupling Suspension System for an Oscillating Element Microbalance

1. Technical Field

This invention relates generally to instrumentation for mass measurement and more particularly to a suspension system for an oscillating element microbalance which effectively decouples the microbalance from its environment and improves the instrument's mass resolution.

2. Background Information

An extremely sensitive microbalance employing an oscillating tapered element and capable of accurately measuring the mass of very fine particles and other matter, has previously been developed. This instrument employs a tapered elongate elastic element having a first end which is adapted to support a specimen and a second larger end which is anchored so that the first end and specimen carried thereby are free to oscillate. The elongate element is excited into oscillation at a resonant frequency. The resonant frequency of the oscillating element varies in accordance with the mass loading and accordingly can be monitored and measured to determine the mass of the specimen supported by the oscillating element. Details of construction and the operating principles of such an oscillating tapered element microbalance are described in U.S. Pat. No. 3,926,271, issued Dec. 16, 1975 to H. Patashnick. An improvement which facilitates use of the microbalance for the measurement of the mass of particulate or other forms of matter contained within a medium such as air or other fluids is described in U.S. Pat. No. 4,391,338 issued on July 5, 1983 to H. Patashnick and G. Rupprecht. The contents of these two patents are incorporated by reference herein.

In practice the oscillating tapered element microbalance has proven to be a highly accurate instrument which permits on-line, real-time direct measurement of particulate mass with great sensitivity and reliability. The instrument has been successfully employed in the evaluation of diesel exhaust, dust concentration and smoke measurement and is applicable to many other situations in which particles or other extremely fine forms of matter need to be detected and weighed.

The tapered element in the above-described microbalance vibrates in a clamped/free mode. This means that at the clamped end, where the tapered element meets the housing, two problems have to be confronted. First the vibration of the tapered element causes a strain on the support system, with the result that energy flows out from the tapered element through the housing into the support system, lowering the mechanical quality factor, Q, of the tapered element. Secondly, mechanical perturbations from the environment enter through the support system and housing, changing the phase and amplitude of the tapered element vibration, and thereby degrading the accuracy of the frequency determination and the mass resolution of the instrument. These two problems are not entirely unrelated because a decrease in the Q also has the effect of allowing a broader spectrum of environmental mechanical noise to enter the microbalance.

One approach for coping with these problems has been to attach the housing of the microbalance to a larger rigid distributed mass which is then decoupled by standard means such as a foam rubber cushion from the noisy environment. Although a three-dimensional decoupling of the tapered element from environmental noise can thus be achieved, this approach is rather cumbersome and not fit for certain applications. Further, the results are far from ideal, since it has been found that decoupling from environmental noise is not simultaneously achieved with a high Q and therefore compromises are necessary.

A need thus exists for an arrangement that simultaneously solves the two problems described above, thereby allowing the full potential of the microbalance to be realized.

This need is satisfied, according to the present invention, by the provision of a strategically placed suspension system. More particularly, the housing of the microbalance is suspended from a support member by suspension means aligned with an instant center of rotation of the microbalance. The location of the instant center of rotation is a function of the microbalance's mass moment of inertia, total mass and the distance from its center of gravity to the element's free end. With such a suspension system, internal vibrational energy is prevented from leaving the microbalance while external noise is simultaneously prevented from entering, thereby effectively decoupling the microbalance from its environment.

Further, the inventors have discovered that by specially configuring the tapered element, decoupling need only be provided in one direction. In a preferred embodiment, the free portion of the tapered element is provided with an elliptical cross section, and a pair of torsion bars extending along a suspension axis which intersects the instant center of rotation and is parallel to the major axis of the elliptical cross section is employed to suspend the housing of the microbalance. The invention also contemplates the use of a plurality of spring means as suspending means in a three-dimensional decoupling system, as well as the method of mechanically decoupling the oscillating element microbalance.

Accordingly a principal object of the invention is to improve the mass resolution of an oscillating element microbalance by effectively isolating it from environmental noise.

Another object is to simultaneously maintain a high Q of the oscillating element of the microbalance.

A further object is to accomplish this improvement in performance and decoupling with a suspension system that is simple, rugged, relatively inexpensive, and usable in the many diverse applications and environments in which the microbalance can be employed.

Yet another object is to provide a novel method for decoupling an oscillating element microbalance to minimize vibrational losses while at the same time rendering mechanical noise ineffectual.

Still another object is to provide extremely sensitive mass measuring apparatus capable of measuring minute particles and of operating in real-time, on-line, in a wide variety of environments for scientific and/or industrial purposes.

Yet another object is to provide such apparatus which is compact in size, versatile in use and economical to manufacture, operate and maintain.

These and other objects, features and advantages of the invention will be more readily understood from the following detailed description when read in conjunction with the accompanying drawings, in which:

FIG. 1 is a simplified, partially cut-away perspective view of an oscillating tapered element microbalance employing the decoupling suspension system of the present invention;

FIGS. 2a-d and 3a-c are schematic illustrations helpful in understanding the principles of the present invention; and

FIG. 4 is a schematic illustration of another embodiment of the invention.

A preferred embodiment of the improved mass measuring apparatus of the present invention is illustrated in simplified form in FIG. 1. The apparatus includes an oscillating element microbalance 10 mounted and supported by a suspension system generally denoted 11.

Microbalance 10 includes an elongate elastic element 12. Element 12 is preferably tapered as shown and hollow. The larger end 13 of element 12 is anchored to the base 16 of housing 18. Although illustrated as cylindrical, housing 18 may take other shapes and configurations and is designed to at least partially enclose tapered element 12 and provide a convenient attachment point for the suspension system.

A specimen supporting substrate or filter 14 is located atop the other end 19 of tapered element 12. End 19 and the mass supported thereon are free to oscillate relative to housing 18 when excited by drive means (not shown). The frequency of element oscillation is detected and measured by suitable means (not shown).

Briefly, in operation the free end 19 of tapered element 12 is excited into oscillation at a resonant frequency. When mass is added to the free end of the oscillating element, the resonant frequency shifts downward with the magnitude of the frequency change being dependent on the mass loading. Thus, by monitoring and measuring the variation in the resonant frequency of the oscillating tapered element, very accurate mass determinations can be made. Details of the construction and operating principles of the oscillating tapered element microbalance are presented in earlier mentioned U.S. Pat. Nos. 3,926,271 and 4,391,338 and accordingly are not repeated herein.

Also shown in FIG. 1 is a preferred form of the suspension system 11 of the present invention. The suspension system includes a support member 24 and a pair of torsion bars 20 and 22. The torsion bars connect support 24 to housing 18 and serve as suspension means for the microbalance. The torsion bars preferably possess a high Q and may, for example, be made of hollow steel tubing. The outer ends of the torsion bars are fixedly secured to support 24 and the inner ends are fixedly attached to housing 18 in any well known manner.

As shown, the torsion bars 20 and 22 extend along a suspension axis SA which intersects a point S. S represents an instant center of rotation which, as more fully explained below, is located a distance L.sub.2 below the center of gravity, CG, of the microbalance. The center of gravity is located a distance L.sub.1 below the mass to be measured atop the free end of the tapered element.

The torsion bars limit movement of the microbalance to rotation about suspension axis SA, for example, in the direction, a, in response to a force F applied to a mass atop the tapered element. The torsion bars serve to provide a restoring torque and, as more fully discussed below, effectively decouple the microbalance from its environment.

Analysis of the decoupling process by the inventors has revealed that, disregarding second order effects, decoupling need only be achieved in a plane perpendicular to the longitudinal axis of the tapered element. Moreover, the inventors have found that this two-dimensional decoupling can be reduced further to a one-dimensional decoupling provided that the tapered element is formed in such a way that its vibration is restricted to one direction. This can be accomplished by providing the free portion of the tapered element with an elliptical cross section.

An example of a tapered element having an elliptical cross section throughout a portion of its length is shown in FIG. 2a. Tapered element 12 is hollow and supports a substrate or filter 14 on which is mounted a specimen 25, the mass of which is to be measured. The other, enlarged end of element 12 is anchored to base 16 of the housing of the microbalance. Plan views of the tapered element 12 at planes 2b, 2c and 2d are illustrated in FIGS. 2b, 2c and 2d, respectively. As shown, the tapered element 12 has an elliptical cross-sectional form beginning at its free end and extending throughout most of its length. The span of tapered element 12 between planes 2c and 2d exhibits a transition from an elliptical to a circular cross section.

Also shown in FIG. 2c are the two principal directions of vibration of element 12. The "soft" direction SD is the direction in which the vibration can be easily excited and which points in the direction of the minor axis of the elliptical cross sections. The "hard" direction HD is the direction of the major axis, which is difficult to excite. The preferred mode of oscillation is then in the "soft" direction, i.e. in the direction of the minor axis of the ellipse. An excitation of a vibration in the "hard" direction, i.e. in the direction of the major axis, is highly supressed in this configuration so that, for all practical purposes, a random translational displacement of the support member will only have an effect in the "soft" direction.

Referring briefly once again to FIG. 1, it will be noted that torsion bars 20 and 22 are affixed to opposite sides of the housing 18 in such a way that the microbalance is allowed to rotate around a suspension axis SA which is perpendicular to the preferred "soft" direction of the tapered element's oscillation (i.e. SA is parallel to the major axis of the elliptical cross section). Furthermore, suspension axis SA intercepts point S which represents an instant center of rotation of the microbalance. This instant center of rotation is independent of force F acting in the "soft" direction and of the mass m to be measured. The instant center of rotation S refers to a point or location on the longitudinal axis of tapered element 12 which would experience pure rotation, i.e. no translation, were the microbalance operated unsupported in a gravity free environment. This point is located at a distance L.sub.2 from the center of gravity CG where:

where I is the mass moment of inertia of the microbalance in respect to the center of gravity, M represents the total mass of the microbalance and L.sub.1 is the distance between the mass m at the free end of the tapered element and the center of gravity CG. Since L.sub.1 and M can be measured and the mass moment of inertia, I, can either be calculated or determined experimentally, the proper location of the torsion bar suspension of the housing can be determined to be L.sub.2 from the center of gravity. The attachment of the torsion bars along an axis extending through the instant center of rotation minimizes the loss of vibrational energy to the support member since the torsion bar material can be selected to minimize mechanical damping. This critical placement of the torsion bars also prevents external environmental noise from entering the microbalance.

The derivation of the length L.sub.2 as a function of M, L.sub.1 and I will now be described with reference to FIG. 3.

Referring first to FIG. 3a, a tapered element 12, located within a housing 18, is schematically illustrated as supporting a mass m. For purposes of this discussion, the microbalance is considered to have a total mass, M, and the distance between center of gravity, CG, and mass m is calculated to be L.sub.1. An inertial force F acts on the mass m perpendicular to the longitudinal axis, LA, of the tapered element, as shown in FIG. 3a. The forces acting on the system can be augmented by cancelling forces +F and -F acting at the center of gravity as shown in FIG. 3b. This distribution of forces is equivalent to a combination of the force F at the center of gravity and a torque FL.sub.1 as shown in FIG. 3c.

Next, the displacement of a point S below the center of gravity will be calculated. There are two opposite displacements acting simultaneously on point S: a displacement to the left LD caused by the force F in FIG. 3c and a displacement to the right RD introduced by the rotation of the housing around the center of gravity caused by the torque FL.sub.1. One finds: ##EQU1## since the acceleration a=F/M, and ##EQU2## since the angular acceleration .alpha.=FL.sub.1 /I.

The point S does not move under the influence of the force F at m, and is therefore an instant center of rotation if LD=RD. Substituting equations (2) and (3) and reducing leads to the following relationship ##EQU3##

By the same approach it can be shown that horizontal force F applied at S, which is equivalent to an acceleration of the device suspension transmitted through the torsion bars, has an instant center of rotation at the mass m located at the distance L.sub.1 from the center of gravity. Therefore environmental noises acting in the direction of the "soft" vibration of the tapered element do not lead to a relative motion between the mass m and the housing. This means that with the suspension introduced by this invention the tapered element cannot be excited into vibration by environmental noise, which is equivalent to a complete decoupling.

An alternate suspension system for decoupling the microbalance in three-dimensions is illustrated schematically in FIG. 4. Microbalance housing 18 incorporating tapered element 12 is suspended within a cage-like support structure 26 by a set of peripherally spaced springs (or their equivalent). Although only four springs 28, 30, 32 and 34 are shown, typically eight such springs would be employed. In the illustrated example, the spring attachments at the inner ends are brought close to point S by placing them in recesses of housing 18 to achieve a small restoring torque, while the outer ends of the springs are attached to the cage-like support structure 26. In accordance with the principles of the invention, the springs are aligned along axes that intersect at the instant center of rotation S. Of course, other equivalent structures can be used to implement the suspension system of the present invention.

In summary, the suspension system of this invention prevents internal vibrational energy from escaping and simultaneously prevents external noise from entering the microbalance. It decouples the microbalance from its environment by simultaneously overcoming the two identified difficulties associated with existing oscillating element microbalances. The invention thus serves to maintain the high Q of the tapered element and significantly improves the performance of the microbalance. In conjunction with a tapered element having an elliptical cross section, a pair of torsion bars can be employed to simply and effectively implement the invention and achieve the other objects set forth hereinbefore. A microbalance incorporating the suspension system of this invention has been found to have a mass resolution of 5.times.10.sup.-9 grams where m=50 milligrams.

Although the invention has been described in terms of two embodiments, it will be readily apparent to those skilled in this art that various modifications, rearrangements and substitutions can be made without departing from the spirit of the invention; for example, a gimballed system could be employed to achieve three-dimensional decoupling. The scope of the invention is defined by the claims appended hereto.