CA2024668A1

CA2024668A1 - Method and device for automatically sharpening cutting blades

Info

Publication number: CA2024668A1
Application number: CA002024668A
Authority: CA
Inventors: Jean Etcheparre; Bernard Etcheparre
Original assignee: Lectra Systemes SA
Current assignee: Lectra SA
Priority date: 1989-09-15
Filing date: 1990-09-05
Publication date: 1991-03-16
Also published as: FR2652029A1; JPH03104599A; EP0418163A1; FR2652029B1; DE69010435D1; ATE108113T1; DE69010435T2; EP0418163B1; ES2058848T3

Abstract

ABSTRACT OF THE DISCLOSURE
The present invention relates to a device for sharpening an elongated cutting blade presenting a sharp edge, wherein it comprises at least one grin-ding wheel provided at least on the surface with abrasive material, said grinding wheel having a cylin-drical body presenting a V-sectioned peripheral groove, said grinding wheel being mounted to rotate freely about an axis contained in a plane generally parallel to the sharp edge of the blade and perpendicular to the median plane of the blade, and said axis being inclined by a predetermined angle with respect to the normal to the median plane of the blade, said sharpening device further comprising means for placing the blade and the grinding wheel in contact and means for relative displacement of the blade and the grinding wheel in a direction parallel to the sharp edge of the blade.

Description

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FIELD OF THE INVENTION
The present invention relates to a method ancl device for automatically sharpening cutting blades.
BACKGROUND OF THE INVENTION
It is known to use automatic cutting machines for cutting stacks of materials in sheet form, such as fabric for example, in the garment industry. These ma~hines are generally constituted by a cutting table on which is deposited the stack of material, or mat-tress; by a mobile assembly consisting of a beam disposed transversely above the table and sliding on longitudinal guides; by a cutting carriage sliding along the beam; by a cutting head fixed on the cutting carriage. The diffferent mobile elements are motorized by servo-motors for example, and receive orders from a numerical control. The cutting head may thus be displaced to any point of the cutting table, along pre-established paths. The cutting head generally consists of a mechanism for vertically vibrating ~ a sharpened blade, which mechanism may rise and descend so as to cause the blade to penetrate or exit at the desired spot in the stack of material. The blade may rotate about its vertical axis. Rotation is servo-controlled so that the blade always remains correctly ~5 oriented with respect to the path. In order that the blade may cut all the folds of the stack of mate-rial, said blade must penetrate into the cutting table, which therefore comprises a coating to that end.
As cutting proceeds, the blade progressively loses its cutting power. It is therefore necessary to re-sharpen it regularly, the time between two sharpenings essentially depending on the abrasive character of the material cut. Such sharpening must be rendered automatic in order not to disturb the -2- ~ 2 Ll ~ ~ $

automatic operating cycle of the cutting machine~
To that end, several solutions exist of which certain have been emp].oyed for a very long time on manual electric shears used in the garment industry (called "tip-top"): abrasive strips or small rotating cylindri-cal grinding wheels The performances of these sharpe-ners are relatively limited. More particularly, their dimensions are too large and their speed of sharpening too slow. They also require a motorization o~ the abrasive element, whether it be a grinding wheel or a strip, which complicates the mechanism.
The present invention has for its object a sharpe-ning process and device overcoming the drawbacks of the conventional devices and proposing the following advantages:
- no need for motorization - rapid sharpening - reduced dimensions - automatic compensation of wear - excellent quality of sharpening - no precise adjustment to be made.
S~MMARY OF THE INVENTION
According to the invention, the sharpening device for elongated cutting blade presenting a sharp edge, ~5 is characterized in that it comprises a grinding wheel provided at least on the surface with abrasive material, said grinding wheel having a cylin~ical body presenting a V-sectioned peripheral groove, said grinding wheel being mounted to rotate freely about an axis TT contained in a plane generally paral-lel to the edge of the blade and perpendicular to the median plane CXZ of the blade, and said axis inclined by a predetermined angle P with respect to the normal CY to the median plane of the blade, said sharpening device further comprising means for placing the blade and the grinding wheel in contact and means for relative displacement of the blade and the grinding wheel in a direction parallel to the edge of the blade.
In order to create the relative movement of the blade with respect to the grinding wheel, there are two modi operandi. The first consists in maintai-ning the blade fixed, in high position, and in displa-cing the grinding wheel, firstly in a horizontal movement to come into contact with the blade and then a vertical movement to displace it along the sharp edge of the blade. An automatic cycle may be effected, allowing several passages until correct sharpening is obtained. Contrary to the first, the second mode consists in maintaining the grinding wheel fixed in height and in displacing the blade in front of the grinding wheel. Displacement of the blade may result in particular from the longitudinaI
vibration of the latter. This solution has the advan-tage of simplifying the sharpening device by elimina-ting the need for a member for producing the vertical displacement of the grinding wheel with respect~to the blade. One or the other solution will be chosen as a function of the design of the cutting head assem-~5 bly.
Sharpening is effected in accordance with thefollowing principle: the sharp edge~of the blade is brought into contàct with~the outer edges oE the groove of the grinding wheel~.~Due to thé~inclination of the grinding wheel, contacts are made on the two opposite sides of~the b~lade. Relative displacement between the~blade and~thè gr1nding~wheel creates, by friction, rotation of the grinding wheel. The abrasive grain structure of the grinding wheel then ~
35 machines the blade along lncllned~paths~wlth respect ~ ~;

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to the sharp edge, hence sharpening. As sharpenlng continues, the blade becomes worn and advances towards the inside of the groove of the grinding wheel.
The dimensions of the grinding wheel depend on several factors of which the principal ones are as follows:
- angle of sharpening of the cutting blade - length of the zone to be sharpened - maximum dimensions not to be exceeded 1~ - amplitude of the relative vertical movement of the grinding wheel and of the blade.
All the other parameters follow from one another.
It will be observed that an infinite number of solu-tions exist. The solution retained will be a compromise respecting the different parameters.
The sharpening of a cutting blade mobile in rotation about its longitudinal axis raises another technical problem.
In fact, during cutting, the blade makes a rota-~0 tiol- about its vertical axis imposed by the blade-holder unit, so that the direction of the sharp edge of the blade at the moment of sharpening cannot be foreseen; the position of the grinding wheel with respect to that of the blade must therefore be recti-~5 fied at each sharpening.
It is a further object of the present invention to solve this problem by simultaneously imposing on the grinding wheel the same movements of rotation as on the ~ de.
~ This object is attained~according to the lnvention by a grin-Jiny wheel fixed by means of a hor;izontal spindle on a plate fast in rotation with the blade-holder unit so that the groove of the grinding wheel is constantly o~posite~he sharp edge of the blade.
BRIEF~DESCRIPTION~OF THE DRAWINGS
The invention wlll be~more readily understood - : - ~, ~ .. . .
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on teading the following description with reference to the accompclnying drawings, in which:
Figure 1 is a side view of a cutting machine equipped with the sharpening device according to the present invention.
Figure 2 is a lateral view taken in the direction of arrow 2-2 of Figure 1.
Figure 3 is a lateral view similar to that of Figure 2, illustl-ating the process of sharpening.
Figure 4 is a lateral view similar to that of Figure 2, illustrating a variant of the sharpening device.
Figure 5 is a front view of a blade part and of a grinding wheel for sharpening according to the 15 invention.
Figure 6 is a view in horizontal section taken along line 6-6 of Figure 5.
Figure 7 is a schematic view in perspective illustrating the geometrical relations between the ~0 blade and the grinding wheel Figures 8, 9 and 10 show another embodiment of the device of the invention in which the grinding wheel is rendered fast in movement with the blade.
DETAILED DESCRIPTION OF THE DRAWINGS
Referring now to the drawings, the cutting machine illustrated in Figure 1 comprises a fixed table 10, disposed on a frame (not shown) and adapted to receive a stack of materials in sheet form, or mattress 12, with a view to cutting it along~a predetermined line.
Above the table is disposed a beam 14, mounted for longitudinal displacement over table 10 and driven ~by means (not shown) in right-left direction in Figure 1, symbolized by arrow L.
On beam 14 is mounted a carriage 16 which moves 35 along the beam,~ with the ald~of means (not shown), .
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in transverse direction with respect to the table, in the forward-rearward direction in Figure 1, or right-left direction in Figure 2, symbolized by arrow T. A blade-holder unit 18 is mounted laterally on the carriage 16, via vertical displacement ways 20, in order to be able to move vertically on the carriage, therefore with respect to table 10, as illustrated by arrow H in the Figure, by drive means (not shown).
The blade-holder unit contains a member 21 for 10 gripping a vertical cutting blade 22, means for impar-ting to the blade a vibrating movement in the vertical sense symbolized by double arrow W, and means for imparting to the blade a movement of rotation about a vertical axis as symbolized by arrow R.
The object of such rotation of the blade ~s to maintain the sharp edge of the blade constantly oriented along the tangent to the path imposed by the longitudinal and transverse drive members associa-ted with the beam 14 and with carriage 16 respectively.
The upper face of the table is covered with a layer 24 of supple, penetrable matf3rial, for example a coir mat, that the tip of the blade 22 may penetrate in order to enable the whole thickness of the stack o~ sheet material 12 to be cut.
~5 Beneath carriage 16 is dlsposed a presser foot 26 mobile vertically between a raised position, illus-trated in broken lines, at a certain distance from the table 10 to allow the material 12 to be positioned on or removed from table 10, and a lowered posltion in contact with the material placed on the ta~le.
This presser foot 26 has a double function.
The first function is to press the stack of material 12 around~the blade 22 to prevent the stack from following the movement~s of vertical vibration of the blade. The~second function is to correctly guide :

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the blade 22 as close as possible to the stack 12 so as to avoid bendings of the blade 22 due to the horizontal cutting efforts.
Displacement of the presser foot 26 between its raised and lowered positions is ensured by guides 28 and a drive member (not shown).
To allow simple and rapid sharpening of the blade without notably interrupting the cutting process, it is provided according to the invention to mount on the carriage 16 a sharpening device 30 constituted as follows:
A plate 32 is fixed to the carriage 16 on orle side of the blade 22. A grindir!g ~Yheel 34 for sharpe-ning is mounted mobile opposit.e blade 22 and may be moved away or nearer it thanks to a drive member, for example a jacX 36 as shown;
In this embodim~nt, two grinding wheels 34, 35 for sharpening are provided, disposed one above the other and mounted idly on a bif~rcated support 33 at the end of the rod of jack 36 in order to ensure that the ~rinding wheels 34, 35 are both correctly in contact with blade 22.
The structure and arrangement of the grinding wheels will be described in detail hereinafter. As ~5 illustrated in Figure 3, blade 22 is sharpened at regular intervals in the following manner:
- the longitudinal and transverse displacements of beam 14 and of carriage 16 are stopped, - the vertical vibration (W) of blade 22 is stopped, - blade 22 is pivoted (R) until the sharp edge 23 thereof is opposite~the grinding wheels 34, 35 ~or sharpening. ~ : :
This operation is all:the more difficult as the mate~ial is hard and~thick, ;

- the grinding wheels 34, 35 are brought into contact with the sharp edge 23 of blade 22, - blade 22 is caused to effect at least one vertical rising stroke (H) of desired amplitu~e, by raising the blade-holder unit 18 with respect to carriage 16, in order to sharpen blade 22 over a desired length from its tip 21, - the grinding wheels 34, 35 are moved away from blade 22, - the blade is re-oriented in its initial position, - blade 22 is re-lowered in the material 12 to be cut, - ver~ical vibration (W) of blade 22 is resumed, - the longit-ldinal and transverse displacements of beam 14 and of carriage 16 are resumed.
As illustrated in Figure 4, i.t may be provided in a varianl: embodiment t.hat blade 22 remains fixed during sharpening and that grinding wheels 34, 35 move vertically.
~0 ~o that end, plate 32 and jack 36 for displacement of grinding wheels 34, 35 are mounted mobile along vertic~l guides ~0 of carriage 16, under the control of a drive member, for example another jack 42~. ~
When blades 22 are relatively fine and capable:
~5 of bending considerably upon contact with grinding wheels 34, 35, it will advantageously be provided to dispose against the blade~and opposite the grinding wheels, a rear stop 44 against which the blade abuts, which prevents:it from bending.
As illustrated ~in Figure 2,~it~may be~question of a simple stop with fl~at bearing surface~made~ of~
wear-resistant material,~agai:nst which the~edge of ::~
blade 22 opposlte the sha~rp~edge 23 slldes~durlng sharpening.
According to a vari`ant~embodiment (not shown), : : : :

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this stop may be in the form of a roller.
In the case of the variant embodiment of Figure 4, the rear stop 44 should be mounted on a vertically mobile support jointly with the plate 32 and the jack 36 holding the grinding wheels.
As illustrated schematically in Figure 5, each grinding wheel 34, 35 is in the form of a flattened cylinder and comprises a V-shaped groove 46 on its periphery. It is mounted so that its axis TT is in-clined with respect to the horizontal. In this way,when the grinding wheel approaches blade 22, it comes into contact with the opposite sides 48, 50 on either side of the sharp edge 23 of the blade at two points B, B' spaced apart vertically from the lateral edges of the groove.
The grinding wheel 34, 35 is made to comprise abrasive grains at least on the surface at the outer edges of the groove 46. To that end, either a grinding wheel may be made of a material containing abrasive ~ grains in a binding agent, or a coating containing abrasive grains may be fixed by any appropriate method on the surface of a blank made of non-abrasive material.
Thanks to the relative vertical movement of blade 22 and of grinding wheel 34, 35, the latter ~5 is driven in rotation and the abrasive grains exert on the blade a machining at the zones of contact along inclined paths with respect~to edge ~23, which effects sharpening.
The method of calculation allowing optimum dimen-sioning of the grinding wheel 34, 35 for`a blade22 of given dimensions,~ wll~l now~be set~forth.
If reference is made~to the schema;tic;perspective view of Figure 7, point C-cor~responds~to~the centre of the grinding wheel, axis CX is the horizontal~
axis which lntersects the ~olrc~le~o~f the;~bot~tom~of~

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-10- ~C ~ 2 ~ s groove 46 and the sharp edge 23 of the blade at a point D, axis CY is the horizontal axis perpendicular to the preceding one; axis CZ is the ver-tical axis passing through centre C; the plane CXZ therefore representing the median plane of blade 22. Axis TT
of the grinding wheel 34 is contained in plane CYZ
~nd makes an angle P with axis CY.
The V-groove defines a circle 52 of groove bottom of radius Ri and two circular edges 54, 56 of radius R and distant by a distance a, the sharp edge 23 of blade 22 making contact with one and the other of the edges at two points B and B' vertically distant by a distance e.
Point B projects on axis CZ at a point A distant from the centre C by a distance e/2 and on axis TT
at a point G distant from the centre C by a distance a/2.
The frustum of cone defining the groove wall on which lies point B has for apex a point E on axis ~0 TT, at a distance b from centre C.
This point E projects in a horizontal plane containing the straight line AB at a point F.
Point H is located at the intersection of the generatrix EB and of the circle 52 of groove bottom and point J is the projection of point H on segment BF.
Let Q designate the half-angle of aperture of the groove 46, Xt the horizontal distance between axis CE and the sharp edge 23 of the blade; Ri the radius of the circle 52 of groove bottom; Qa the apparent half-angle of the groove 46 of the grinding wheel, seen vertically by blade 22; and N the half-angle of cut of blade 22.
1 - Relation between the dimensions of the grinding wheel: ~
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According to the right-angled trapezium CGBH:
GB = CH a 2 Tg Q

viz. R = Ri + 2 Ta Q (1) 2 - Distance between the two points of contact of 10 the sharp edge of the blade:
According to triangle ACG, CG / AC = sin P
viz. a = e sin P (2J

15 3 - Distance between the blade edge and the vertical axis: ~
According to triangles ABC and BCG:
CB2 = AB2 + AC2 = GB2 + CG2 viz. xt2 + (e/2)2 = (a/2J2 +`R2 20 and, replacing a by e sin P:according to relation (2):

Xt = [ R2 - (e/2 cos pJ 2 ~ 1~ ( 3J
4 - Apparent angle of the groove : :
According to triangle~BGE, GE = GB tan Q ~ :

viz. a/2 + b = R tan Q
or b = R tan Q - a/2 In triangle~ABF,~
Af = b cos~P ~

and ~tan Qa = Xt Xt ' , hence, by carrying the expression of b given by rela-tion (3):
tan Qa = (R tan Q - a/2) cos P/Xt (4) 5 - Conditions to be fulfilled for correct functioning:
1) The half angle of cut of the blade must be less than the apparent angle of the groove:
viz. N < Qa (5) 2) The sharp edge of the blade must not be in contact with the bottom of the groove, viz. Xt ~ Ri (6) - Numerical example:
Numerical values corresponding to a concrete case will be taken here.
Dimensions of grinding wheels which are compatible with the available environment are flrstly arbitrarily fixed. Thereafter, all the calculations are made with these values: as a function of the results ob-tained, certain values may be slightly amended and the calculation re-made until satisfactory values are obtained.
For the present example, the followlng values will thus be taken:
N = 15 P = 15 ~S e = 24 mm R = 17 mm According to (2), the following is deduced:
a = 24 x sin 15 = 6.2 mm ~a = 6.2 mm~
According to (3j, Xt is calculated~
Xt =;12.4 mm According to (S), N ~ ~Qa or tan N ~< tan Qa~
The condition~therefore be:co~es, ~uslng~ ( 4 ):

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t < (R. tan Q - a/2).cos P
an N Xt from which is extracted:

tan Q ~ R ( tan N Xt + a) Vi2 . tan Q ~ 0.384 or Q ~ 21.
~ccording to (6), Xt ~ Ri According to (1), Ri = R ~ 2 t Q

therefore Xt > R ~ 2 t Q

or ~ 2.(R - Xt) ~ hence tan Q ~ O 674 or Q < 34~
1~ Angle Q is therefore limited by:
21 ~ Q < 34 In order to have a maximum duration of use of the blade, the difference~(Xt - Ri) should be as large as possible, which comes back to choosing Q
closer to 21 than 34.
Q = 22.5 for example.
Ri = 9.5 mm may in that case be calculated.
The exact dimensions~of the grlndlng~wheel:are ;
then~
~ R = 17 mm : ~ :
a = 6.2 mm Q = 22.5 Ri = 9.5 mm P = 15.

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During sharpening, blade 22 penetrates slightly in the groove 46 but the sharp edge 23 theoretically remains at distance Xt from axis OZ. In fact, as the edges of the groove 46 undergo slight wear, a slight decrease in this distance Xt is in practice observed as use proceeds, but this is not detrimental since values are chosen such that Xt - Ri is as large as possible.
The advantage of disposing two or more grinding wheels in the sense of the sharp edge is that of allowing sharpening over a sufficient length whilst reducing the amplitude of the relative displacement of the blade.
These grinding wheels will be borne by an appro-priate number of bifurcated supports.
Figures 8 to 10 show another embodiment of theinvention, in which the blade-holder unit 18 is ren-dered fast in movement with the grinding wheel 34.
To that ond, the grinding whe~el 34 (or th~ grin-ding wheels mounted in series on the bifurcated support38) is fixed on the plate 52 via a horizontal spindle 54; in addition, this plate 52 presents a device for guiding the blade 22 and bears the presser foot 26 which may be actuated by means of a jack 58. During ~5 cutting, the plate 52 is animated by the same movement of rotation as the one imposed by the blade-holder ~
unit 18 on the blade 22 and thus takes the sharpening system along in this movement. The groove of the grinding wheel 34 is therefore constantly opposite 3~ the sharp edge of the blade. In Figure 9, just before sharpening, the presser foot 26 rises agai~nst the plate 52 thanks~to jack 58, which forces the cam 60 to compress the return spring 62 l~ocated~on the guide 54. In this way~, the sharpening system is posi-tioned correctly opposite~the cutting edge of the :

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blade. Sharpening may then take place in the positionshown in Figure 10.
According to this advantageous variant, the sharpening process is as follows: blade 22 is placed in high position and is then automatically oriented with its cutting edge facing the groove of the grinding wheel.
Grinding wheel 34 is automatically disposed by servo-control of the rotation of the grinding wheel by that of the blade as shown in Figure 9.
Blade 22 is then vibrated exactly in the same manner as during cutting; grinding wheel 34 is then brought, in a horizontal movement, in contact with the blade, and is maintained in this arrangement for a very short time.
Finally, after having released thc grinding wheel 34, the cutting process may be resumed without it being necessary to stop the vibration of the blade 2~.
Since sharpening is effected according to this method with the blade in high position, advantage ma~ therefore be taken of the idle times of cutting (for example during the displacement between t~wo pieces), where the blade is necessarily in high posi-~5 tion to effect sharpening. Sharpening is thus in "masked time", which avoids losses of time and optima-lizes the speed of the machine.
The relative displacement of the blade 22~and of the grinding wheel 34 is, according to t;his~method, directly connected with the~amplitude of longitudinal vibration of the blade; thls datum must therefore be taken into account~in the calculation of the optimum dimensioning of the system. The other operational parameters set forth in~the generà1 presentation naturally remain applicable.

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Let W be the amplitude of longitudinal vibration of the blade. Each point of contact (B and B') sharpens on either side of the blade a length equal to W.
As an "overlapping" of the two sharpened zones is desired, the following condition must be respected:
e C W
It will suffice to take for example an "overlap-ping" of 1 mm:
e = W - 1 (e and A in mm) The cutting parameters set:
W = 25 mm N = 15 In that case, e = 24 mm (value used previously during the numerical application made within the framework of the general method).
Another parameter intervening in the dimensioning and configuration of the system is the length of sharpened blade. Let L be the length of sharpened blade. Since there is an "overlapping", L = e + W
Knowing that e depends only on the dimensions and inclination of the grinding wheel which may be ch~sen, e may be adjusted as a function of the blade length which it is desired to sharpen, as long as this length remains less than 2W, since e must not exceed W. If, on the other hand, L exceeds 2W, it is provided to place in series a number n of grinding wheels with the result that the~length of sharpened blade reaches the desired value. The distance~between two successive grinding wheels is such that the "over-lapping" of two zones sharpened by different grinding wheels is equal to the "overlapping" of twozones shar-pened by the same grinding wheel. The total length of sharpened blade is then given by formula:
~5 L = (2n-l~e~ +~W

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Claims

1. A device for sharpening an elongated cutting blade presenting a sharp edge, wherein it comprises at least one grinding wheel provided at least on the surface with abrasive mate-rial, said grinding wheel having a cylindrical body presenting a V-sectioned peripheral groove, said grinding wheel being mounted to rotate freely about an axis contained in a plane generally parallel to the sharp edge of the blade and perpendicular to the median plane of the blade, and said axis being inclined by a predetermined angle with respect to the normal to the median plane of the blade, said sharpening device further comprising means for placing the blade and the grinding wheel in contact and means for relative displacement of the blade and the grinding wheel in a direction parallel to the sharp edge of the blade.

2. The sharpening blade of Claim 1, wherein it comprises at least two grinding wheels juxtaposed in the direction of the sharp edge of the blade.

3. The device of Claim 1, wherein two or more grin-ding wheels are borne by one or more bifurcated sup-ports.

4. The device of any one of Claims 1 to 3, wherein the means for relative displacement of the blade and of the grinding wheel comprise a means for displa-cing the blade in the direction of its sharp edge opposite a fixed grinding wheel.

5. The device of any one of Claims 1 to 3, wherein the means for relative displacement of the blade and of the grinding wheel comprise a means for displa-cing the grinding wheel in the direction of the sharp edge of the blade.

6. The device of any one of Claims 1 to 5, wherein it is borne by a carriage, in the vicinity of a blade-holder unit provided with means for orientation of said blade in rotation and with means for driving the blade-holder unit in the longitudinal direction of the blade.

7. The device of any one of Claims 1 to 6, wherein it comprises a rear stop on that side of the blade opposite said grinding wheel.

8. The device of Claim 4, wherein the means for relative displacement of the blade and of the grinding wheel comprise means for vibrating the blade.

9. The device of Claim 6 or 8, wherein the grinding wheel is fixed by means of a horizontal spindle on a plate fast in rotation with the blade-holder unit, with the result that the groove of the grinding wheel is constantly opposite the sharp edge of the blade.

10. A process for sharpening an elongated cutting blade presenting a sharp edge animated by a movement of rotation about its longitudinal axis and opposite a sharpening device comprising a plate supporting a grinding wheel provided at least on the surface with abrasive material and having a cylindrical body presenting a V-sectioned peripheral groove, mounted to rotate freely about an axis inclined by a predeter-mined angle with respect to the normal to the plane of the blade, said process comprising the following steps of:

- servo-controlling the plate supporting the grinding wheel by the movement of rotation of the blade, - bringing said grinding wheel in contact with the sharp edge of the blade, and - relatively displacing the grinding wheel and the blade in the longitudinal direction of the blade.

11. The process of Claim 10, wherein the grinding wheel and the blade are displaced relatively by placing the latter in longitudinal vibration.