US1503824A

US1503824A - Hasaiohic analyzes

Info

Publication number: US1503824A
Authority: US
Publication date: 1924-08-05
Anticipated expiration: 1941-08-05

Description

Aug 9 1,503,824 'l'. C. FRY

HAHMONI C ANALYZ ER Filed Dec. l1, 1920 5 SheetS-Sheet l /nVe/770r: Ther/7 fon E. Fry,

T. G. FRY

HARMONC ANALYZER 5 Sh'eets-Sheet 2 Filed Dec. 1l, 1920 Aug. s 1924.

T. C. FRY

HARMONLC ANALYZER l [if Mii um 'um e@ U.

,y 2 M 2 (I1 -l It I o z IM W n t W f/ HWI Patented Aug. 5, 119.24.

UNITED STATES.

THOL'N''ON C. RY, OF V/"YO'ENG, NE"

COMPANY, NCORPORTED, 0F NE/J il" JERSEY; ASSIG-NOR TO 'WESTERN ELECTRIC ;.ORIL N. Y., A CORIPORATION OF NEV YORK.

Api. licaton filed Eeceinber 11, 1920.

To all whom t may concern.'

Be it lrnown that l, Tr-ronN'roN C. Far, a citizen ot the United States, residing' at l/Vyoming, in the county ot Esser, State cit New Jersey, have invented certain new and useful Improvements in Harmonic dnalyzers, ot which the 'following is a. tnll. clear, concise, and exact description.

This invention relates to machines designed tor the interpretation or analysis ot plotted curves, and particularly to that class of machines commonly referred to as harmonic analyzers.

The object otthis invention is to provide a machine which will enable a detailed studyY to be made of such curves, as those plotted to represent wave motions with tar greater accuracy than is possible with the machines 'formerly 4in use.

Further objects ot the invention are: to limit the movement of the tracing' element to one direction only; to move th anie on which is placed the drawing' early ng the curve to be analyzed, at rightanfgles to the movement ot said tracing' element; to eraploy a constant source ot power connected positively to said trame and also to a plurality or integrating mechanisms; and to associate said tracingv element with the integrating' mechanisms by suitable means.

The construction ot the machine in accordance with the present invention will be more readily understood by reference to the drawings, in which Fig. l shows a plan view of the whole machine; 2 represents the side view; 3 shows an enlarged view of a portion ot Fig. 2; il shows the means employed to register the relative movements of the machine; and Fig'. 5 shows the device employed in tracingl the plotted curve. v

The mechanical construction ot the machine will first be described. Mounted or one end ot the iron base 6 is motor '.7 which is utilized as a source ot power. rfi-.t the other end ot the base 6 is provided a 'traine 8, which is fitted with board 9 and adapted to receive the drawing paper 10 upon which the curve ll, to be interpreted, is drawn. Between the trame 8 and the motor 'l is situated a plurality of integrating and planimeter units. These will he hereinatter more fully described.

Enclosed within the ,e'car hoi: l2 are suitable gears to translate the motion imoaiw to them 'from the motor 7 by means of shalt 13 to the shaft 14e. The worm l5 on shat't lll is adapted to engage spur gears 16 mounted on shalt 17 (see Fig. The shaft 17 is provided with worms, such as 18 and 19. adapted to engage with worin gears 20 secured to vertical shafts. ln Fin'. 3 one oit these worm gears 2O is represented as being attached to the shaft 2l. rEhe shai't 2l is provided with bearings secured to the trame a3, said frame beine' vertically mounted in any suitable manner upon the base '6. Collar 24 is utilized to prevent vertical displacement olI the shatt 2l. rit the upper end of the shaft 2l are mounted two gears 253 and adapted to engage gears and respectively. The rotation ot these nears is communicated by means oit shatts and to intermediate gears 3l and 3Q, These gears are detachably `mounted upon their respective shafts in order that they may be replaced by other interchangeable `tears adapted to be mounted in suitable position for engagement with any ot the series ot gears shown at 33 and 34C respectively. The motion received by any one ot the gears be longing to, say the series represented by 33, is imparted to the trame 35, which causes the sphere 36, mounted therein, vto revolve abort its vertical axis. The spheres 36 rest on discs 37 which are secured to sha'lts The. shafts 38 are adapted to be rotated by the rictional engagement between belt 39 and pulleys d0, as will be described in greater detail hereinafter. Attached tothe trame are two sets ot integrating apparatus, whose enact location as regards the sphere will be more readily seenby reference to Fig. Ll.

ln Fig. et sphere 3G is represented as being' in Contact with three discs 1li, l2 and 43. lThe disc ell is used in 'order to secure the sphere in an absolutely correct position and yet render it tree to move about either axis. lt is used, in other words, merely as a o'n.ide. lt will be noted that dises 4t2 and are adapted to operate similar mechanisn'is, but that they are in engagement with the sphere at right angles to eac-h other. Considerinp: the mechanism associated with disc 4t2, tor the purpose ot illustration, it will be seen that the motion imparted thereto :troni the sphere is communicated directly to the shaft lf-l upon which is placed the ,graduated wheel 45. rThe pointer is used to more llL) clearly indicate the relative turning of the wheel 45. In order to obtain a more accurate reading than the graduations on will permit, the scales 47 and 48 are provided. The motion of shaft 44 is imparted to a series of gears 49 by means of the worm 50, thus indicating any fractional displacement not recorded by the wheel 45.

The plan view, as shown in Fig. 1, represents ten separate units, such as have just been described, and are numbered 101, 102, 103, 104, 105, 106, 107, 108, 109, and 110. The only difference in the construction of these units is in the size of the gears making up the series 33, 34, etc.

Shaft 14, which is adapted to be actuated by the motor 7 through the series of gears contained in case 12, and which is adapted to actuate the integrating mechanism, as already hereinabove described, is in addition utilized to impart a horizontal motion to the fra-me 8 by means of the spur gear 51. The base 6 is provided with two parallel grooved tracks 52 and 53 in which rollers 54 and 55, attached to the frame 8, are adapted to move. Mounted on base 6, free and clear of the movable frame 8, are pieces 56 and 57 to which parallel bars 58 and 59 are secured. These bars act as a guide for the tracer 60, which is most clearly shown in Fig. 5. The construction of the tracer 60 is extremely simple, the handle 61 being provided in order that motion may be imparted to said tracer by the hand of the operator. The two pulley wheels 62 and 63 are` so spaced that they will lit readily between the guide bars 58 and 59. The pointer 64 is adapted to engage with the plotted curve to be interpreted and, therefore, is made as pointed as the accuracy of the machine as a whole warrants. Lug 65 is provided with a hole through which belt 39 slidably passes, while lug 66 is so constructed as to permit of a permanent connection between it and belt 39. Belt 39 also passes around pulley 67, which is so mounted on piece 57 that it may be moved either to the left or right according to whether or not belt 39 is excessively tight or loose.

It will be noted from the above description that in tracing out curve 11, the motor causes the board to move under the tracer 60 along' the so-called X axis. The operator, with his hand on the tracer', causes it to move along the Y axis a sufficient amount to enable the point 64 to continuously engage the curve 11. The motion of the tracer 60 is imparted to shafts 38 by means of belt 39 and pulleys 40, said motion thus being imparted to the spheres 36 through the agency of discs 37. rlhus these spheres are rotated about a horizontal axis. Simultaneously with this movement, the sphere is also rotated about its vert-ical axis by virtue of the motion communicated to it from the motor through

shafts

14, 21 and frame 35, and the gears associated therewith.

The diameter of the gears constituting series 33, 34, etc. and the gears corresponding to 31, 32, etc., bear a definite relation to the wave length of the curve 11, as drawn. Thus, the lowest gear of these series associated with unit 101, is of such a diameter that when the intermediate gear, similar to 31, 32, etc. is placed in engagement therewith, it will make one complete rotation while the tracer is moved one wave length. In like manner, the lowest gear of the series associated with 102 is of such a diameter that when in engagement with its intermediate gear it will make two complete rotations while the tracer moves the same distance. Similarly, the lowest gears in units 103 to 110 will rota-te three to ten times respectively, under the same conditions. The second gear associated with unit 101, when engaged will rotate eleven times; that of unit 102, 12 times, and so on, It will, therefore, be apparent that the top gear of unit 110, when engaged, will rotate one hundred times, while the tracer moves over one wave length. By placing the intermediate gears in engagement with the lowest gears of each unit, the spheres 37 associated therewith will be rotated upon tracing over the curve I1 once, as follows:

Unit 101, once, Unit 102, twice, etc.

Or, if it is desired to rotate the spheres from eleven to twenty times, the gears immediately above the lowest pulleys would be engaged by the several intermediate gears. lt can readily be seen that many di iferent combinations of rotations may be had by adjusting the intermediate gears.

Although one specific arrangement of the gears associated with each nuit has been de scribed, it may be that the specific problem at hand will require a different dispositiam of them. It is not intended, therefore, to limit the present invention te the exact positioning of the different gears.

The method of opt'raliiug the machine will now be described. For the salte of clearn ness, it will be assumed that the specific problem at hand is the analysis of a periodic electrical wave into its various harmonics. It is to be understood that this machine is not limited to the interpretation of electrical waves, but may be utilized in thel analysis of other wave motions, such as sound, light, etc., or in obtaining the trigoiioinetric series expansion of any portion ot'Y any cnrvrl i'vhatsoever, regardless of the origin or significance of said curve.

The periodic wave is first drawn on suitable paper in such a manner that a complete wave length will cover exactly a given distance. For purpose of reference, we will Cit assume that for the particular machine shown herein, this distance is T There is no limit to the other dimensions of the curve save that it must, ot course, be such that the whole curve is on the paper. The diagram should be placed, as indicated .in Fig. l, i. e. so that the axis of the curve is perpendicular to the guide bars 58 and 59. The tracer 60 is moved along the guide bars Vhere; T is the Wave length; n. the number of cycles of sine or cosine Waves during one cycle ot' the original curve; t the elapsed time reckoned from any instant and A, to A ,l and B to Bn are the coetli'cients Which must be determined by integration. In case the curve is not periodic, any portion of it, or length T, may be so expressed. The term A is given by the formula.

and must be separately determined. Moreover, as the curve 11 has neither the kind of symmetry to the Y axis as is possessed by sine or cosine curves, it is resol fable into aseries of sine curves and a series oiE cosine curves, However, when the electrical Waves which occur in practice have only odd harmonics, the terms signifying the even ones in the above equation may be dispensed With.

The various coefficients Al, A3, etc., A1 and B1, B3 etc. Bn are the quantities to be determined by the machine Which forms the subject of the present invention. riChese coeiiicients may be expressed as follows:

2 VT 21V/ift AnTJO y sin -T-{Zt and 2 "T 2am BD=TJO y cos -rdt The Yfunction of the machine is, therefore, to perform the above integration. The A integrations are read from the recording' mechanism associated With disc 1&2, and the aB integrations from that associated with disc a3.

From the statement ot Flouriers theorem, as given above, it will be apparent Why the present machine makes use of such motions as have already been discribed. The X and Y values or" the given curve 11 appear .in the Fourier series as angular quantities, and such transformation may readily be secured by compounding the motions as have heretoi'ore been described. Then the pointer has been moved along the curve li a distance ot dy and the plane of disc Llf2 is at an angle at) With the X or time axis, the sphere 3G will be turned, by the motion im- 58 and 59 until its pointer G-L touches the curve l1., where it intercepts the X axis, i. e. the axis of the curve itself. The three scales ot both recording mechanisms associated with each of the ten spheres are adjusted to give Zero readings.

Now, curve ll being a periodic Wave, it may be expressed according to Fouriers theorem, as follows:

parted to it from the motor 7, an amount proportional te (Zai, and such movement will be registered by both 42 and it the radius o1 sphere 3G be r, the point oi contact between disc 42 and sphere 3G will be at a distance r sin yn() from the axis ot sphere 36 and the motion of disc 42 will be proportional to Zfz/ sin n0. In like manner the motion of disc @L3 will be proportional to Zg/ cos n0. It will be apparent then that when pointer G4 moved over the entire curve 'll` the numbers registered by discs i2 and 43 Will be proportional to the coetlicients as expressed in Fouriers series, i. e. A and B11. The dimensions ot the parts are so chosen that these readings Will give Au and Bn in centimeters. Thus it is clear that as the pointer 64C traces out the curve, each ly is multiplied by sine at) or cos n.0 which is eected by the machine by converting flg/ into tivo components at right angles to each other, one of Which is at an angleot n() with the X or time axis.

The relation between the given curve il and that transcribed by any given point of the sphere 36, such as ttor example the point ot contact between the sphere 36 and the disc Ll2 may be readily shown by constructing a curve using as ordinates 1^ sin n and r cos y110. The lines drawn from the end of such curve to the origin ot the diagram will make an angle with 'i axis, which vvill be designated it ive then assume some quantity such s Z, which has the following relation to All, Bu, and

The Fourier series may be expanded thus:

The line above referred to as being drawn from the origin otl the diagram to the end of the curve will then be Z1. It, now, the axis ot the sphere 36 makes a turns While the pointer 64 moves over one complete period of the curve ll, the value of the line above referred to will become n- Z1 and it will make an angle of Zn with the Y axis. By utilizing the entire set of ten spheres provided in this machine, together with its associated gears, the values of Cn and can up to 71.2100 may be determined.

While a specific construction is described hereinabove, it is to be understood that it is intended to cover any obvious mcdilications of same, which come within the scope ot the appended claims.

lfl-Jhat is claimed is:

l. A harmonic analyzer co 'iprising a base member, a. movable trame and a plurality ot integrating mechanisms mounted on said.

base member, and "i source ot power connected with said trame and mecluinisn'ls :tor imparting motion thereto.

i5. fr harmonic analyzer comprising a plurality oil integrating mechanisms each o' said mechanisms consisting of a sphere associated with ineens adapted to rotate said sphere about its vertical axis, and means adapted to rotate said sphere about its horizontal axis, said first mentioned means being actuated by a constant source ot power.

3. A harmonic analyzer c miprising a base menilier, a movable trame n'iounted on said base member and adapted to carry the paper upon which the curve to be integrated is drawn, a plurality of integrating devices mounted on said base member, and common means for actuating said integratii'ig devices and said trame.

1l. A harmonie analyzer comprising a movable trame, a plurality oit spheres, means lor rotating said spheres upon their vertical ailes, and a common source oi" power adapted to impart motion to said trame and spheres whereby said spheres are caused to rotate upon their horizontal axes.

5. A harmonic analyzer comprising a movable trame, a plurality of integrating mechanisms having different speeds ot rotation, a movable tracing element, said Ytrame said tracing element adapted to be Y ianisms tor in'iparting motion thereto, and means controlled by said tracing element 'tor actuating said integrating mecha-- nisms,

6. er harmonic analyzer comprising a movable Atranne, a plurality et integrating mechanisms having ditlerent speeds o. rotation, two horizontally disposed guides, a tracing elemei'it adapted to be moved between said guides over said trame, a source ot power connected with said frame and said mechanisms lor in'iparting motion thereto, and means associated with said tracing element for imparting motion to said integrating mechanisms.

.7. A harmonic analyzer comprising a movable trame, a plurality oi integrating mechanisms having ditlerent speeds ot rotation, a tracing element cooperating with said 't'ran'ie, means tor imparting motion to said integrating mechanisn'is and said trame, and means tor communicating motion imparted to said tracing element to said integrating mechanisms.

8. A harmonic analyzer comprising a trame, a plnralit'7 o't integrating mechanisms having diii'erent speeds ot rotation, a tracing element adapted to cooperate with said frame, a motor to impart motion to said integrating' mechanisn'is and to said trame, and means adapted to communicate motion imparted to said tracing element to said integrating mechanisnis.

(l. ii harmonic analyzer comprising a movable trame, a plurality oit integrating mechanisn'is having dililerent speeds of rotaV` tion, means common to said trame and said integrating mechanisms for imparting motion thereto, and means adapted to vary the relative movements et said trame and said integrating mechanisms.

lO. A harmonic analyzer comprising a movable trame, a plurality ot' integrating mechanisms having different speeds oi" rotation, e of said mechanisn'is consisting ot a sphere associated with means adapted for rotating said sphere upon its verti al axis, and means tor imparting motion to said movable 'trame and to said integrating mechanisms whereby said spheres are caused to rotate upon their horizontal axes.

il, A harmonic analyzer comprising an integrating mechanism including a sphere, means tor revolving said sphere upon its vertical anis, means for moving said sphere upon its horizontal anis, a dise associated vfitl sait sphere, and a recording mechanism associated with said disc.

A harmonic analyzer comprising a movable frame, a plurality ol integrating mechanisms having dii'lerent speeds ot rota tion, a motor, a shaft driven by said motor` and a series ot gears adapted to be associ# ae-i with said sha'tt as desired to impart motion thereto, said shaft communicating to said'mechanisms the motion oi? said movable trame,

i3. A harmonic aiialyzcer conuirising a series ot gears ot varying diameters, an integrating mechanism comprising a sphere associated therenith, a shaft adapted to mount iiiterchangeable gears oit varying sizes for e aging said gears, and means ilor imparting motion to said last mentioned shaft.

lil. A harmonic analyzer comprising a movable trame, a source o't power associated therewith, a series of gears ot varying diameters associated therewith, a vertical shalt adapted to mount one oi a series of interchangeable gears adapted, respectively, to engage any one of said series ot gears, and an integrating' mechanism including a sphere driven by each of said first mentioned series of gears.

15. A harmonic analyzer comprising an integrating mechanism including a sphere, a pair of guides in spaced relation, a tracing element adapted to be moved between said guides and in contact with said movable frame, a disc contacting with said sphere, and means for communicating to said disc the motion imparted to said tracing element.

16. A harmonic analyzer comprising a movable frame, a source of power associated therewith, a series of gears associated therewith, an integrating mechanism associated with said gears, a shaft provided with a worm gear, and a second worm gear located on ashaft disposed at right angles to said irst-namedshaft, said second-named shaft adapted to impart motion communicated thereto to said integrating mechanism.

17. A harmonic analyzer comprising a motor, a series of gears associated therewith, a plurality of integrating mechanisms having different speeds of rotation associated with said gears, a shaft provided with a worm gear associated with said series of gears, and a second worm gear located on a shaft disposed at right angles to said first mentioned shaft, said second mentioned shaft adapted to impart motion communicated thereto to said integrating mechanisms.

18. A harmonic analyzer comprising a movable frame, a plurality of integrating mechanisms having different speeds of rotation, a pair of guides in spaced relation, a tracing element adapted to be moved between said guides and in contact with said movable frame, means for causing the relative movement of said frame and said tracing element at right angles to each other, and means controlled by said tracing element for actua-ting said integrating mechanisms.

19. A harmonic analyzer comprising an integrating mechanism including a sphere, means for revolving said sphere upon its vertical axis, actuating mechanism comprising a .plurality of gears and shafts, a disc associated with said actuating mechanism and cooperating with said sphere, and an indicating` mechanism associated with said disc.

20. A harmonic analyzer comprising a motor, a series of gears associated therewith, a movable frame actuated by said motor, a plurality of integrating mechanisms having different speeds of rotation associated with said gea-rs, a shaft provided with a worm gear associated with said series of gears, a second worm gear located on a shaft disposed at right angles to said first mentioned shaft, said second mentioned shaft adapted to impart motion communicated. thereto to said integrating unschanisms, an indicating mechanism associated with each of said integrating mechanisms, and means associated with said integrating mechanisms for actuating the respective indicating mechanisms.

21. harmonic analyzer comprising a movable frame adapted to carry the paper upon which the curve to be integrated is drawn, a plurality of integrating devices having different speeds of rotation, common means for actuating said integrating devices and said frame, a plurality of indicating mechanisms, and means associated with each of said integrating devices for actuatin one of said indicating mechanisms.

A. harmonic analyzer comprising a movable frame, a plurality of spheres, means for rotating said spheres upon their vertical axes, a common source of power adapted to impart motion to said frame and spheres whereby said spheres are caused to rotate upon their horizontal axes, a plurality of indicating mechanisms, a disc associated with each of said spheres and adapted to impart to said indicating mechanisms the` motion communicated to said spheres, and means for adjusting the relative movements of said frame and said spheres.

in witness whereof, l hereunto subscribe my name this 4th day of December A. D. 1920.

THORNTON C. FRY.