US1799634A - Wave transmission - Google Patents

Description

April 7, 1931. E. L. NORTQN 1,799,634

WAVE TRANsMIssIo Filed Nov. 25, 1924 Rufio Patented 'Apn 7, 1931 UNITED STATES PATENT orrlca EDWARD L. NORTON, OF NEW YORK, N. Y., ASSIGNOR TO WESTERN ELECTRIC COMPANY, INCORPORATED, F NEW YORK, N. Y., A CORPORATION OF NEW 'YORK WAVE TRANSMISSION Application led November 25, 1924. Serial No. 752,082.

This invention relates to transmission of vibratory or wave motion, especially frequency selective propagation of such motion, and aims to obtain selection between adjacent ranges of frequencies mechanically in a simple manner.

Another object is to obtain mechanical selective propagation of a range of frequencies between substantially equal impedances.

Another object is to control the time of pr-opagation of wave motion between two points, in a simple manner, for instance, in order to obtain a desired delay in the propagation of the wave motion or a desired in- 1 crease in the time of propagation between the two points.

In the design of mechanical wave filters, it is convenient and practicable to follow the analogy of electric wave filters in the cases of low-pass and band-pass structures. For high-pass filters the mechanical equivalent has been more difficult to secure, requiring the use of a structure having a mass in each shunt arm and no mass inthe series arms. In accordance with the invention, there is provided a type of mechanical high-pass filter which depends upon a different principle than the ordinary lumped structure, is very simple and inexpensive in construction and Ilolas a relatively high loss in the attenuated and.

In the embodiments of the invention specifically illustrated in the accompanying drawings, mechanical torsional vibrations of a range of frequencies are selectively propagated along a rod or wire of uniform circular cross-section, naturally bent into the form of a circular loop or into the form of a plurality of circular loops constituting a helix.

In the drawings, Fig. 1 is an elevation of a system embodying one form of the invention; Fig. 2 is a curve showing the attenuation frequency characteristic of the mechanical wave filter of Fig. 1; Fig. 3 is a perspective view of a portion of a system embodying a modification of the form of the invention shown in Fig. 1; and Fig. 4 represents the electrical analogue of the mechanical transmission system.

Referring especially to Fig. 1, 4 is a circular loop of round wire which serves as a highpass mechanical filter. The wire is subjected to torsional mechanical vibrations by a piezoelectric crystal 5. The torsional mechanical vibrations selectively transmitted by the wire 4 are transmitted from the wire to a piezoelectric crystal 6. The crystals 5 and 6 are mounted on a heavy base 7. The crystal 5 may be a composite Rochelle salt or sodium potassium tartrate crystal such as is described in an article by A. M. Nicolson on the piezoelectric eifect in the composite Rochelle salt crystal, publishedpin the Proceedings of the American Institute of Electrical Engineers, November, 1919. The crystal 5 may have the usual girdle electrode 8 for connection to one terminal 9 of a source of electro-motive force variations, and an internal electrode 10 for connection tothe other terminal, 11 of the source. The connection between the elec` trode 10 and the terminal 11 may include the base 7, which may be of metal, for inst-anceV brass. The electrode 10 may be a bolt or the like, passing through the crystal and in coincidence with the longitudinal axis of the crystal, and supporting the crystal on the base 7, the crystal being clamped between the base and a plate 12 by means of a nut 13 threaded on the bolt 10. The plate 12 is preferably metallic, and may, if desired, be cemented to the adjacent basal plane of the crystal. The opposite basal plane of the crystal may be cemented to the base 7. The cement employed may be melted and super-cooled Rochelle salt, which will set in a short time, upon the agitation incident to ,its application to the surfaces to be united. The bolt 10 is rigidly connected to the loop 4 by a connector 14. The internal electrode crystal 5 and the method ofmounting the crystal are similar to the crystal and mounting method disclosed and claimed in the applications of A. M. Nicolson, Serial No. 655,800, filed August 6, 1923, and issued as Patent No. 1,562,578, No- 95 vember 24, 1925, and Serial No. 683,643, filed December 31, 1923, and issued as Patent No. 1,574,302, February 23, 1926, both assigned to the assignee of this application.

The crystal 6 is similar to crystal 5 and is 100 similarly mounted on the base 7 and connected to the loop 4.

In the operation of the system shown in F ig. 1 when electro-motive force variations are impressed across terminals 9 and 11, the crystal 5' is caused to undergo elastic twisting vibrations about iits principal or longitudinal axis, and the bolt 10 and connector 14 transmit this vibratory twisting motion to thead-y jacent end of the loop 4, thus setting that end of the loop into elastic torsional vibration. It has been found that the loop acts as a highpass mechanical filter. The vibrations of the frequencies lying Within its pass range are transmitted to the internal electrode of the crystal 6, setting that electrodey and crystal into mechanical torsional vibrations about the longitudinal axis of the crystal. rlhis vibration of the crystal 6 generates electromotive force var iations across terminals 15 and 16 which are connected to the girdle electrode and the internalelectrode, respectively, of the crystal.

The propagation constant of the high pass filter constituted by the loop 4 is, for any frequency/ aan or for a single turn,

epm] 2) f Where s=distance along the Wire a=radius of helix E=Youngs modulus of material l ,a=coeilicient of rigidity and fais the cut-o frequency, Which is defined by: i

. Where p is the density of the material.

Above the cut-olf frequency the expression for the propagation jconstant (for the filter or4 for a single loo-p) becomes imaginary, and is the expression'for the phase shift (for the iilteror fora single loop). The velocity of propagation along the loop'or helix, at any frequency f .Well Within the pass range, is equal to (2m-f) divided by the phase'shift at that frequency. Below the cutfo frequency the expression for the propagation constant is real, and is the expression for the attenuatransmission unit, by C. W. Smith, both in The Bell System Technical Journal, July, 1924, published bythe American Telephone and Telegraph Company, New -York.)

The characteristic impedance of thevstructure approaches that of a straight Wire as the frequency increases. Representing this impedance by Z0, We have for a round Wire, d being the diameter ofthe Wire. The characteristic impedance remains nearly enough constant for large values of frequency When these large values lie in the transmission range so that it is in practice usually necessary to consider only this one value of this impedance. Representing the diameter of the helix by D, the design formulae are:

These formulae together with (2) give all the information required in the design of the filter. n

As an example, suppose a high-passmechanical filter is required to cut off at 3,500 cycles and Work betweenimpedances of 200() mechanical ohms in torsion. (A mechanical ohm is 1 dyne per unit velocity, that is, 1 dyne per cm. per sec.; and in torsion, as here considered, a mechanicalohm is 1 dyne per cm. per second, both the force and the velocity being taken at 1 cm. radius.) SupposeV the material of the loopto be of steel and that an attenuation of 10() TU is required for loW frequencies.

The constants for steel are approximately The attenuation of a single loop'V of 'steel wire from Formula is 7.13 napiers or 62 TU for low frequencies. Since 100 TU loss is required, we use two complete turns. The complete filter then consists of two turns of .ll8 steel wire in a helix 13.1 in diameter. The structure cuts off at 3,500 cycles and has the required 100 TU attenuation at frequencies below about 2,100 cycles.

The fact that the propagation constant for the filter is as defined in Equation (l) above, may be seen from the following considerations:

" lf b is the angular displacement in the plane of the cross-section of the wire, s the distance along the wire, L, the moment of inertia of the section Vabout its axis, ,a the coeliicient of rigidity and p the density of the material, we have, for a round straight wire, (equating the potential reaction and the kinetic reaction, as usual, to obtain the wave propagation equation),

lf the wire is naturally bent in the arc of a circle, the term on the loft, corresponding to the potential energy factor must be changed, owing to the fact that as the wire is twisted torsionally about its longitudinal airis, half of the material at every cross section is put into the condition of tension and half into the condition of compression, the direction of these tensions and compressions being perpendicular to the cross sectional plane, i. e.

if longitudinal, the dividing line between tension and compression, for small twists, being approximately the sectional diameter which is colinear with the radius of curvature. The restoring force in this case is a function of 2') alone, rather than of its derivatives.

Letting Il be the moment of inertia of a cross-section of the wire about its diameter; a, the radius of the circle in which the wire is naturally bent; and E, Youngs modulus for the material, the potential energy due to compression and extension of the material is y i/aELGY- Differentiating this with respect to I) to find the restoring force gives Equation (7) then becomes 626 EI 326 @(3-82 l (ya (8) of a circular cross-,section 11:1/210, and' furthermore, since b is a harmonic function of the time, Equation (8) may be written:

wave and the other the reflected wave. As we are interested only in the propagation constant, the second term is neglected, the solu-` tion in this case beingi b ,Be-9) where B is the value of Zi when 8:0, and

E Y Sj-Zazwzll (u) Equation (ll) is readily reduced to the form of Equation The eects described by the foregoing equations may be explained in physical terms as follows: In a straight cylindrical rod upon which a torsional vibratory force is impressed the vibratory motion is opposed by the inertia reaction of the particle masses and by the torsional elasticity of the rod. The mass re-` action of the particles tends to absorb some of the impressed force, while the elasticity serves to transmit the force from particles in one cross-sectional layer to those in the next.

The uniform rod is thus similar to a system of e line, or series, masses coupled in tandem by springs, forming coupling, or shunt, elasticities, but dueto the homogeneous struc` ture of the line the individual sections are infinitesimally small. rlhe terms fseries and shunt, adapted from the terminology of electrical circuits, aptly describe the mechanical reactions with respect to their eects upon the transmitted motion. SeriesV reactions, or restrains, do not diminish the velocity of the motion, but tend to absorb some of the impressed force, whereas shunt reactions tend to absorb some of the velocity while transmitting thel force without diminution.

lVhen the uniform rod is curved longitudinally, as by bending in the arc of a circle, each cross-sectional element of the rod is deformed into a wedge shaped disc. A twisting movement propagated along the rod tends to rotate the elemental discs about their centers, and in so doing additional restraining forces are called into play. As the narrow edge of the disc is moved out of its original position, the material there is stretched and the dis* placement is resisted by a longitudinal tensile force. At the wide edge of the elemental disc the rotational displacement is opposed by a corresponding compressional force. That these forces are series restraints tending to oppose the transmission of the impressed force, may be seen from the following considerations: Let it be assumed that the material of the rod is ininitelyresistant to compression or extension, it is then obvious that the elemental discs cannot be rotated out of their original positions, and consequently no motion can be transmitted. The line therefore behaves as though the individual mass particles were restrained by infinitely great series elasticities. On the other hand, if the resistance to compression and extension is Zero the transmlssion of torsional vibrations 1s affected 1n no way whatever by the curvature of the line, that is, the series elastic restraint is Zero.V

At low frequencies of Vibration the series elastic reaction predominates over the series mass reactions and corresponds to a chain of K series and shunt elasticities, both distributed uniformly along the length. Such a struc ture is effective to attenuate vibratory waves.

Fig. 4 illustrates an electrical transmission line analogous to the mechanical line of this invention. To represent the uniformly dis` f tributed character of the impedance elements of the ,mechanical line, the equivalent electrical line is assumed composed of an infinite number of` sections each Vrepresenting an innitesimally small portion of the line. Consider the section between the dotted lines AA and BB. rBhe series inductance Ll, corresponds to the massnof an elemental section of the mechanical line, the shunt ca-` l acit f 8C2 corres ,onds inversel f to the tora a l y. tion are as follows:

Where 8m represents the length ofthe line corresponding to the section. The change of potential from A to B is equal to the sum of the baclrE. M. Es in the inductance SLI, and

the'capacity SG1. By well known relationships this may be expressed as where g, denotes the electrical displacement 1n the line at AA', i. e., the quantity of electricity in coulombs traversing the line at AA',

n o, the Voltage across the line at AA', and

,o, represents the increment of potential in the section. rI he charge in thev shunt caf pacity 8C2 -8g`=fv02m, from which n --z (13) K combining Equations 12 and 13 gives and" il The lower cut-ofin frequency, f1', by Equation (19), is constant,independent of the length v8x, represented by the section- The upper cut-od frequency, f2, however, becomes higher as the length 8a" is decreased; and when 8m 1s zero,las in asmooth line, f2 is innite, the .lsitliucture then being. eectively a high-pass er. Y Theelectrical analogue of the mechanical system is not easy to visualize for the reason that no electrical structure having uniformly distributed series capacity is known. Such a structure, if it could be realized, however, would be governed by Equation (14).

Equation (14) expressing the law of action and reaction in the electrical line, is seen to be of the same form as Equation (8). Electrical displacement gvcorresponds tothe me- 115 chanical displacement b; the quantity ,vlo in Equation (8) corresponds to l Oz in Equation (14) and may therefore be termed a shunt elastance; the quantity 25 corresponds to 1 and therefore represents a series elastance;

`of Equation (11i). If theelectricaldisplacement-be assumed a harmonic function of time, i. e., Q=g0 sin wt, Where Q0 is the maximum displacement and 1:271- times frequency,

gi: Substituting (17) in (14) u `C12 5x2 O1 Which can be Written,

P x (.02L102 1 The quantity'on the right of Equation (20) changes from a real to van imaginary value at the frequency 1 T f1 2"rh/Llei Which therefore demarks the. transmission and attenuation ranges.

' The theoretical attenuation frequency characteristic of the filter described above is shown in Fig. 2, and agrees With the attenuation frequency characteristic as determined experimentally. The ordinates of the curve in Fig. 2 are attenuation units, each attenuation unit being approximately 8.7 of the TU referred to above.

Fig. 3 illustrates af system employing two loops 2() and 21 similar to the loop 4 of Eig. 1, and constituting a helix having double t-he attenuation produced by a single loop. Not only the attenuation for the frequencies out side the pass range, but also the time of propagation for the frequencies of the pass range, is directly proportional to the number of loops employed, and this increase in time of propagation is of importance Where it is desired t0 employ the filter as a delay path or means for increasing the time of propagation between translating devices connected to its ends.

In the system of Fig. 3, an electro-mechanical motor element 25, shown as of the type disclosed in H. C. Egerton Patent 1,365,898, January 18, 1921, is employed instead of the piezo-electric motor element 5 of the system of Fig. 1. Any suitable type of motor element andgenerator element may be utilized,

teme: mechanicali highepass lter comprisin either Fig. 1 or Fig. 3. Thus, the generator element (not shown) for connection to the -similar to the motor 25, or may be a piezo-` electric generator such as the gencrator of Fig. 1. Preferably, the motor and generator should each have its impedance match that of the loop or helix constituting the filter element. The amplitude of vibration at each frequency of the pass range Will then beA sustained at its initial value throughout the travel of that vibration along the path.

The frequencyv selective device of this invention, although of general application as a filter or a means for delaying Wave propagation, is especially adapted to serve as a mechanical grouping lter in carrier telegraph or telephone systems.

What is claimed is:

1. A circular helix of round Wire With means coupled thereto for imparting to said 4Wire torsional vibrations to be transmitted along the Wire.

2. In combination, a circular helix of round Wire with means coupled thereto for imparting to said Wire torsional vibrations to be transmitted along the Wire, the material and the diameterof said Wire being such that itscharacteristic impedance, at the frequencies freely transmitted by the Wire, substantially equals the value of the impedance presented to said Wire by said means at one of said frequencies. `V

3. A mechanical Wave filter, comprising a curved rod of circularcross-section, the radius of curvature of the rod having a pre` computed value dependentupon the elastice ity and the density of the material of the rod and a limitingv'alue of a range of frequencies it is desired to transmit Without attenuation, said radins of curvature, elasticity, and` density having such values that the rod transmits with practically negligible attenuation sinusoidal mechanical vibrations of allrfrequencies lying on one side of said limiting 'frequency` While substantiallyjatiatenuatingmechanical fvibrations ofineighbolring? ifrequencies-lying:fon ether `@other side; iof

saidflimiting:frequency# il. In almecha'mcal'waveetransmissr means forwibrating In: ae mechanical ve transmission syS- iohrpass slilter comprising a?? curved f Lhan fofguniformly distributed yconstants, fthe? va'lue i of :doungs modulus `lof the materiali the@densityi andthewrate': of xcurvature @being .proportioned .with l`respect to arpredeterminecl` cut-:off i fiequencyl so `that ,torsional fvibrations; ,ofl` alli frequencies :lflbOve said cut-off frequency are freelytransnritted through.saidT filtergaW-hile :torsionalvibra.-

tions of substantially all frequeiiciesbelow said cut-olf frequency are highly attenuated.V 6. As a frequency selective wave transmission means, a mechanical line comprising a solid medium having elasticities both in series and in shunt with respect to the line of propagation of vibrationsimpi'essed on said line, said series elasticity being distributed in accordance with a continuous function of the length along the line.

7. As a frequency selective wave transmission means, a mechanical line in accordance with claim 6 in Awhich both seriesY and shunt elasticities are distributed according to continuous functions of the length along the line. r

8. As a frequency selective wave transmission means, a mechanical line in accordance with claim 6 in which the series elasticity is distributed uniformly along` a substantial portion of the length of the line.

9. As a frequency selective wave transmission-device, a mechanical lline comprisingan elongated solid member constituting a wave transmission path in which the properties of mass and elasticity are distributed according to continuous functions of the length, said elongated member being curved ylongitudinally wliereby torsional vibratory motion therein is opposed by a plurality of elastic restraints of different types. y

10. ,As a frequency selective wave transmission means, a mechanical line comprising an elongated Vsolid member constituting a wave transmissionpath in which the properties of mass and elasticity are distributed aci cordin g to continuous functions of the length,

said elongated member being curved longitudinally whereby torsional vibratory motion therein is opposed by a series elastic restraint.

l1. As al frequency selective wave transmission means, a mechanical line comprising I an elongated vsolid member constituting a wave transmission path in which the properties of mass and elasticity are uniformly dis-- tributed throughout a substantial portion of y the length, said elongated member being curved longitudinally whereby torsional vibratory motion therein is opposed by a uniformly distributed series elasticity.

12. A selective wave transmission means 'comprising a mechanical line having elasticiband frequency selective means comprising a mechanical line, and means for impressing mechanical `vibrations thereon, said line being adapted` by its cross-sectional configuration to oppose one kind of `elastic restraint on!A vibratory motion impressed thereon, and by its longitudinal configuration to oppose anproportioned with respect to the limitingfrequencies of a preassigned range whereby the line is adapted to tran-smit vibrations within said range with substantially noV attenuation and to attenuate frequencies outside of said. range. Q f

14. In a wave transmission system, frequency selective means comprising a uniform mechanical line of elastic material, and means for impressing torsion-al vibrations thereon, said line being curved longitudinally whereby torsional vibratory motion is opposed by a series elastic restraint., and the degree of curvature being proportioned with respect to the torsional elasticity and the mass of the line to provide a desiredv Wave propagation characteristic. y Y n 15. In a wave transmission system, fres quency selective means comprising a uniform mechanical line of elastic material, and means forfimpressing 'torsional vibrations thereon,

the line being proportioned in accordance with a preassigned frequency, whereby the line is adapted to transmit freely vibrations of frequencies above the preassigned value and to attenuate vibrations of lower frequencies. Y

In witness whereof, I Vhereunto subscribe my namey this 18th day of November A. D., n 1924.

ties in series and in -shunt with respect to the Y line of wave propagation, said elasticities being distributed according to continuous functions of the length of the line, and being proportioned, together with the mass coefficients kof the line, in accordance with the limits of a preassigned range of frequencies, whereby Ythe line is adapted to transmit freely waves of frequencies within said range, and to attenuate waves of frequencies outside said range. Y n y A13. In a wave transmission system, broad-v EDWARD L. Noirroii. e

with the ma-ss. and the; torsional elasticity of

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