US2845697A - Method of manufacturing a longitudinal mode mechanical vibrator - Google Patents

Description

Aug. 5, 1958 v R. ADLER METHOD OF MANUFACTUR MODE MECHANIC ING A LONGITUDINAh. AL VIBRATOR Filed March 11, 1

INVENTOR. jEoerz c/Qaller 2% bornqg United Stats METHOD OF MANUFACTURING A LON GITU- DINAL MODE MECHANICAL VIBRATOR Robert Adler, Nortlifield, Ill., assignor to Zenith Radio Corporation, a corporation of Delaware The present invention relates to longitudinal mode mechanical resonators of the type used in ultrasonic generators and the like. More particularly, it relates to a new and improved method for adjusting the resonant frequency of such resonators to an accurately predetermined value.

As is generally known, a bar or rod formed from any of a wide variety of materials such as metals, glass, ceramics, etc., can be made to mechanically vibrate in a longitudinal mode when shock-excited by a sharp blow from a hammer moving along its longitudinal axis. The mechanical energy delivered to the resonator in this manner subsequently manifests itself as a mechanical vibration having an amplitude which is initially at a peak and which decays exponentially with the passage of time. Such vibration normally has a fundamental frequency component which is determined primarily by the physical length of the resonator and the propagation velocity of sound in the material from which the resonator is formed. Generally, the physical length of the resonator represents a half-wave length at the fundamental frequency, hence maximum particle displacement occurs at the extreme ends of the resonator while a vibration node appears at the exact physical center. In the region of this nodal plane there is no particle displacement but merely a cyclic stressing of the material in tension and compresison. The amplitude of displacement of any particular particle occupying a position intermediate the nodal plane and either end is a function of the physical distance between the transverse plane in which the particle resides and the nodal plane.

Mounting or supporting the resonator must be done in a particular manner if excessive damping of the longitudinal vibrations by the support member is to be avoided. Since vibrational energy is primarily transferred to the support member by the motion of the particles in the region of contact between the support member and the resonator, it is desirable that the support contact the resonator at a point of minimum particle displacement. As has been previously stated, such a vibrational node exists throughout a transverse plane situated at the exact physical center of the resonator. Contact between the support member and the resonator must be limited to this region if the damping effect of the support is to be minimized.

While there are many possible ways of mounting or supporting the resonator by mineral contact in this region, experience has shown that a support of the type described and claimed in the copending application of Ole Wold, Serial No. 645,310, entitled Ultrasonic Generator, filed concurrently herewith, now U. S. Patent 2,821,956 issued February 4, 1958, and assigned to the same assignee as the present application, provides excellent positional stability with substantially negligible damping. Such a support requires the removal of a small amount of'resonator material from the region of the nodal plane to form a pair of diametrically opposite relatively shallow transverse slots.

" atent O 2,845,591 Patented Aug. 5, 1958 To facilitate further explanation, it may be helpful to consider the factors which affect the fundamental resonant frequency of the resonator. As has been stated, the resonant frequency is primarily determined by the physical length and the propagation velocity of sound energy in the resonator. The latter is a function of the physical properties of the material from which the resonator is formed and hence is established and unalterable once a specific material has been chosen. Accordingly, the desired resonant frequency is normally arrived at by adjusting the physical length. Shortening the resonator decreases the period of vibration resulting in an equivalent increase in the resonant frequency. A third factor must be considered, however, if the mounting technique chosen requires the removal of a portion of the resonator material in the region of the nodal plane. While such removal has no effect on the physical length of the resonator, it does reduce the stiffness of the resonator in the nodal region, and the reduced stiffness has been found to result in a lowering of the fundamental frequency of vibration. This effect can be analogized to a pair of equal masses interconnected with a spring having a particular spring constant. If energy is imparted to the system causing the masses to oscillate in a direction parallel to the longitudinal axis of the system, the frequency of oscillation will be a function of the magnitude of the masses and the spring constant. A reduction in the stiffness of the spring results in a reduction in the spring constant and a lowering of the natural frequency of the system. While this efiect is less pronounced in the case of a resonator, since the stiffness is varied in but a relatively small portion of the system, the effect on the natural resonant frequency is qualitatively identical.

Should it be desired to mass produce, by conventional manufacturing techniques, longitudinal-mode resonators of the type so far discussed, all of these factors become of increasing importance. Normally the application to which the resonators are to be put establishes the frequency tolerance range within which all useful units so produced must fall. In many applications, this range is sufficiently narrow to render the use of conventional mass-production techniques unsatisfactory without the introduction of an additional frequency adjustment procedure to reduce the frequency spread of the resultant resonators and to center this spread withinthe preestablished useful frequency range. It is necessary that this frequency adjustment procedure be introduced subsequent to the final step in the fabrication process if it is to compensate for all tolerance effects which tend to introduce frequency variations. Additionally it is economically desirable that the procedure be capable of supplying the prerequisite frequency accuracy without the use of specialized high precision techniques or equip ment.

Accordingly, it is an object of the present invention to provide a new and improved method for adjusting the resonant frequency of longitudinal-mode mechanical resonators of the type used in ultrasonic generators and the like.

It is a further object of the present invention to provide a new and improved method for adjusting the resonant frequency of such resonators to an accurately predetermined value.

It is a still further object of the present invention to provide a new and improved method for adjusting the resonant frequency of such resonators to an accurately predetermined value without the use of precision processing or special equipment.

In accordance with the method of the present invention, a longitudinal mode resonator or vibrator is first fabricated to such dimensions that it exhibits an actual The features of the invention which are believed to be novel are set forth with particularity in the appended claims. The organization and manner of operation of the invention, together with further objects and advantages thereof, may best be understood by reference to the following description taken in conjunction with the accompanying drawings, in which like reference numerals refer to like elements in the several figures, and in which:

Figure l is an exploded view of a device constructed in accordance with the present invention;

Figure 2 is a cross-sectional view taken through transverse section 22 of Figure 1.

Figure 1 shows a partially exploded view of a longitudinal mode resonator and mounting bracket assembly. Resonator or vibrator is of circular cross-section and is shown longitudinally displaced from its normal operative position Within aperture 14 of bracket 11 to better show certain structural details.

Resonator 10 is preferably formed from aluminum or a similar metal having a low internal damping factor. A pair of shallow transverse slots 12 are positioned at the exact physical center of the resonator, each being diametrically opposite the other. A frequency adjustment hole of a predetermined depth is shown symmetrically disposed about the transverse nodal plane which passes through the exact physical centers of transverse slots 12. The factors which determine the depth-of hole 15 are discussed in considerable detail later in this specification. The relationships existing between slots 12 and hole 15 are more clearly shown in the cross-sectional view of Figure 2.

Mounting bracket 11 contains a central aperture 14 of suflicient diameter to permit the free passage ofresonator 10. A pair of resilient support members 13 formed from a single length of piano wire or the like are positioned across aperture 14 and are supportably locked to bracket 11 by slots 16 of appropriate contour.

Bracket 11 and resonator 10 are assembled by first outwardly deforming resilient support members 13 and then advancing resonator 10 through aperture 14 .until support members 13 engage slots 12. The inwardly directed forces exerted by support members 13 on resonator 10, which result from the outward deformation, serve to lock resonator 10 within aperture 14, the contact between resonator 10 and support members 13 being restricted to four'discrete points within transverse slots 12. The advantages and structural details of this mount are disclosed in the aforementioned copending application and hence further discussion is deemed unnecessary.

Several factors should be kept in mind, however, to facilitate a better understanding of the frequency adjustment method herein to be described. Conventionally, the desired resonant frequency of a resonator of this type is established by adjusting the overall length of the resonator such that it represents a half-wave length at the desired frequency of vibration. The removal of the-necessary material to form transverse slots 12 has the effect .of lowering the resonant frequency below that which would result on the basis of its length alone. As has been stated this is a result of the reduction in the stiffnessof the resonator in the nodal region. With these factors in mind, it is readily apparent that some compensation must be made in the physical length of .the resonators 4 to offset the frequency lowering effect of the transverse slots, if the resonators are to exhibit final resonant, frequences which fall within a relatively narrow predetermined range. When an attempt is made to fabricate large numbers of such resonators by conventional massproduction machining techniques, the required compensation introduces difficulties because of normal variations in the composition of the raw stock from which the resonators are formed and the tolerances associated with the fabrication process. Experience has shown that unless some means is provided for adjusting the resonant frequencies subsequent to the completion of the forming process, rejection rates are high based on frequency deviations beyond the pre-established useful tolerance range.

For resonator applications which impose reasonably exacting frequency requirements, this difiiculty is avoided by fabricating and adjusting the natural frequency of the resonators in accordance with the method of the present invention. The resonators are formed having a physical length which is a predetermined amount shorter than that dictated by the desired accurately predetermined frequency. The resulting resonators thence exhibit resonant frequencies which extend over a relatively wide finite range, the mean frequency of which is higher than the final desired frequency by a predetermined amount. The transverse mounting slots are then formed in any well known manner. This has the previously-mentioned effect of reducing the rigidity of the resonators in the nodal region, and a slight net reduction in resonantfrequency results. By properly choosing the length of the resonators, a criterion is established in which this net reduction in frequency is just adequate to shift the frequency range to a point in the frequency domain at which the'lower extremity of the range substantially coincides with the mean frequency of the pre-established useful tolerance range, i. e., the desired predetermined frequency. The resultant range of resonant frequencies exhibited by the resonators in their completed form is then divided into a plurality of adjacent zones each of a frequency width slightly narrower than the width of the pre-established useful tolerance range. The resonant frequency of each of the resonators is then checked against a standard which exhibits a resonant frequency centered in the useful tolerance range, to determine the amount by which the frequency of each of the rsonators deviates from the standard and accordingly, into which of the discrete zones it falls. In this manner, a plurality of discrete resonator groups are formed, there being the same number of groups as there are zones. All of the resonators falling into any given group are subjected to the same frequency adjustment comprising the removal of material by drilling out a portion of the resonator within the region of the nodal plane; the depth of the hole, i. e., the amount of material removed, being approximately proportional to the frequency change required to shift the mean frequency of the group to the point in the frequency domain at which it coincides with the mean frequency of the pre-established useful tolerance range. All of the resonators contained within the group are shifted by like amounts, hence all reside within the useful tolerance range by virtue of the fact that the width of each of the groups was made slightly smaller than the width of the useful range. Like adjustments are made on the resonators contained in the remaining groups with the exception that differing amounts of material must be removed from the resonators in each group, the amounts being approximately proportional to the frequency difference which exists between the mean frequency of the group and the mean frequency of the useful tolerance range.

While material may be removed from the nodal region of the resonators in a variety of ways, experience has shown that removal by drilling along a transverse axis substantially within the plane has advantages not found in other techniques. A conventional drill press can be used with a simple V-block supplying the necessary support to the resonator during the drilling operation. Appropriately adjusted stops determine the depth of the hole and hence the amount of material removed. Each of a number of drill presses corresponding to the number of groups can be preadjusted to remove the correct amount of material from the resonators contained in a particular group, thus no skill is demanded of the operator beyond that required to correlate a given resonator group with the corresponding drill press. In this manner the desired frequency adjustment is readily accomplished without the utilization of special machining techniques of a more expensive or time consuming nature.

In addition to these enumerated advantages, the fundamental concept of frequency adjustment by the removal of material from the region of the nodal plane eliminates a basic difficulty encountered in more conventional techniques. As has already been established, it is essential that the support means contact the resonator in the region of the nodal plane if excessive damping is to be avoided. If the more conventional frequency adjustment technique of varying the physical length of the resonator is used, certain strict requirements must be satisfied if the result is to be satisfactory. Care must be exercised to insure that equal amounts of material are removed from each end of the resonator if shifting of the nodal plane is to be avoided. Any unbalance in the quantities removed has the effect of shifting the nodal plane away from the plane of the transverse mounting slots toward the side of greater mass. Such a displacement of the nodal plane places the mounting slots at a point where particle displacement occurs and vibrational energy is lost to the support with a corresponding reduction in the efliciency of the resonator. Accordingly, it is readily apparent that such a method requires the use of machining techniques and skill considerably beyond that required by the method of the present invention. Additionally, the working of both faces of the resonators tends to introduce additional frequency variations due to cumulative tolerance effects which are considerably more pronounced than those associated with a relatively simple drilling operation.

Merely by way of illustration and in no sense by way of limitation the following is given as an example of the frequency accuracy obtainable in the mass production of 40 kc. longitudinal-mode mechanical resonators by fabrication and adjustment in accordance with the method of the present invention. The resonators were fabricated to a length such that an average resonator exhibited a frequency approximately 120 cycles per second above the desired 40 kilocycles per second (kc.). The remaining samples were found to occupy a range 250 cycles wide centered about 40,120 cycles per second. This range was divided into five discrete adjacent zones of 50 cycles width and the resonators falling into each of the resultant groups were frequency adjusted by drilling away an amount of material in the nodal region which was proportional to the frequency difiierence which existed between the actual mean frequency of the group and the desired 40 kc. A standard number 56 drill was used which resulted in drill stops approximately one sixteenth of an inch apart with the deepest hole passing almost through the resonators in the group requiring maximum frequency adjustment. Upon completion of the process, all of the samples were then found to fall in a tolerance range of 40 kc. plus or minus 30 cycles per second. This represents a frequency accuracy of better than plus or minus .08% obtained with conventional low precision machining techniques.

Accordingly, by utilizing the method of the present invention, longitudinal-mode mechanical resonators which have accurately predetermined resonant frequencies can be mass produced. The effects of normal manufacturing tolerances are readily compensated by a final frequency adjustment which is accomplished in a manner which eliminates the need for precision processing and hence permits the use of conventional machining techniques. Experience has shown that resonators fabricated and frequency adjusted by this method fall within the allowable frequency tolerance range with such a regularity that no final frequency check is required before they are installed in the apparatus for which they are intended.

Resonators produced by the method of the present invention are useful in ultrasonic apparatus of the type fully described and claimed in the copending application of Robert Adler, Serial No. 578,333, filed April 16, 1956, now U. S. Patent 2,821,954 issued February 4, 1958 and divisional U. S. Patent 2,817,025 issued December 17, 1957 and entitled Control System, respectively, and that of Robert Ehlers and Clarence W. Wandrey, Serial No. 645,091 entitled Ultrasonic Transmitter and, filed concurrently herewith, now U. S. Patent 2,821,955 issued February 4, 1958, all of which are assigned to the same assignee as the present application.

While a particular embodiment of the present invention has been shown and described, it is apparent that changes and modifications may be made without departing from the invention in its broader aspects. The aim of the appended claims, therefore, is to cover all such changes and modifications as fall within the true spirit and scope of the invention.

I claim:

1. The method of manufacturing a longitudinal-mode mechanical vibrator having an accurately predetermined resonant fundamental frequency which comprises: fabricating an elongated vibrator element having an actual longitudinal-mode resonant fundamental frequency slightly higher than said predetermined fundamental frequency; and removing material from an intermediate portion of said element coincident with and substantially within a nodal plane for vibrations at said fundamental frequency in an amount substantially proportional to the difference between said actual and predetermined fundamental frequencies to reduce its resonant fundamental frequency from said actual fundamental frequency to said predetermined fundamental frequency.

2. The method of manufacturing a longitudinal-mode mechanical vibrator having an accurately predetermined resonant fundamental frequency which comprises: fabricating an elongated vibrator element having an actual longitudinal-mode resonant fundamental frequency slightly higher than said predetermined fundamental frequency; and drilling away material from an intermediate portion of said element coincident with and substantially within a nodal plane for vibrations at said fundamental frequency in an amount substantially proportional to the difference between said actual and predetermined fundamental frequencies to reduce its resonant frequency from said actual fundamental frequency to said predetermined fundamental frequency.

3. The method of manufacturing a longitudinal-mode mechanical vibrator having an accurately predetermined resonant fundamental frequency which comprises: fabricating a cylindrical rod having a length slightly shorter than one-half wave length in said rod at said predetermined resonant fundamental frequency and adapted for longitudinal-mode vibrations at an actual fundamental frequency slightly higher than said predetermined fundamental frequency when supported at its central nodal plane for vibrations at said fundamental frequency; and drilling away material from said rod substantially within said central nodal plane in an amount substantially proportional to the difference between said actual and said predetermined fundamental frequencies to reduce its reso nant fundamental frequency to said predetermined fundamental frequency.

4. The method of manufacturing a longitudinal-mode mechanical vibrator having an accurately predetermined resonant fundamental frequency which comprises: fabricating an elongated vibrator element having a length 7 8 slightly shorter. than one-half wavelength in said element References Cited in the file of this patent at said predetermined fundamental frequency; testing said UNITED STATES PATENTS element to determine its actual longitudinal-mode reso- V r t nant fundamental frequency; and removing material from 2,655,069 m 3 an intermediate portion of said element coincidentwith 5 2 3 Y M 5' andv substantially within a nodal plane for vibrations at 2,728,902 Whne 1955 said fundamental frequency in an amount substantially I I proportional to the difierence between said actual and REFERENCES I v predetermined fundamental frequencies to reduce its funbQ k Sound, wood, G; 13911 & 0 damental frequency from said actual fundamental fre- 10 London, 1946, Fagcs 111-121 and 140444 felled quency to said predetermined fundamental frequency.

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