CN110524416A - The design method and elastic collet of elastic collet - Google Patents

The design method and elastic collet of elastic collet Download PDF

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Publication number
CN110524416A
CN110524416A CN201910729512.4A CN201910729512A CN110524416A CN 110524416 A CN110524416 A CN 110524416A CN 201910729512 A CN201910729512 A CN 201910729512A CN 110524416 A CN110524416 A CN 110524416A
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CN
China
Prior art keywords
collet
elastic
sleeve
elastic collet
clamping part
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CN201910729512.4A
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Chinese (zh)
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张少军
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Guangdong Baiyun University
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Guangdong Baiyun University
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Priority to CN201910729512.4A priority Critical patent/CN110524416A/en
Publication of CN110524416A publication Critical patent/CN110524416A/en
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B24GRINDING; POLISHING
    • B24BMACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B41/00Component parts such as frames, beds, carriages, headstocks
    • B24B41/06Work supports, e.g. adjustable steadies
    • B24B41/067Work supports, e.g. adjustable steadies radially supporting workpieces

Abstract

The present invention relates to a kind of elastic collet design method and elastic collets, which comprises simplifies the structure of the elastic collet;Functional requirement to be achieved is needed according to elastic collet described in the structure determination of the elastic collet;According to the necessary clamping force under elastic collet working condition described in the Structure Calculation of the elastic collet, and according to the necessary clamping force, obtain the stress of the collet sleeve of the elastic collet;Functional requirement to be achieved, the structure of collet sleeve described in optimization design are needed according to the stress and the elastic collet of the necessary clamping force and the collet sleeve.In this way, the structure of collet sleeve guarantees that elastic collet has good dynamic stiffiness and higher grinding accuracy when high-speed grinding by optimization design to reach collet sleeve and collet chuck cooperation and zero clearance rigid contact in the case where clamping work status.

Description

The design method and elastic collet of elastic collet
Technical field
The present invention relates to technical fields of mechanical processing, more particularly to a kind of elastic collet design method and elastic collet.
Background technique
Elastic collet is a kind of on drilling and milling bed of device for securing drill bits or the tubular fixture of milling cutter, and a kind of Can device be used to a kind of special fixture of the part that fixed needs are processed on vehicle, grinding machine.With the most use at present is ER elasticity Collet chuck, c-type collet chuck etc..
Elastic collet in the prior art is when clamping workpiece and being in high-speed grinding state, the dynamic stiffiness of elastic collet It is poor, while grinding accuracy is relatively low.It is illustrated by taking the processing of engine air valve rod as an example below: engine air valve rod It is an important part of engine, for controlling the air inlet and exhaust of engine.Wherein, the valve discone antenna surface of valve stem, disk Outer circle and the machining accuracy of air valve cervix arc profile are very big to engine performance impacts.Domestic and international more advanced processing gas at present Door rod method is using CBN (Cubic BoronNitride cubic boron nitride) grinding wheel high-speed grinding (grinding speed >=100m/ S) and multiple type faces, the grinding efficiency such as the disk outer circle of clamped one time grinding outlet door rod, discone antenna surface, neck arc surface are higher.So And under high-speed grinding and large area grinding, because the dynamic stiffiness of elastic collet is poor, so that valve stem is also easy to produce vibration;Separately Outside, the rigidity of the working position of valve stem itself is relatively low, therefore valve stem is also easy to produce chatter mark, final reduction valve stem Produce precision.Therefore, a kind of bullet that can still have good dynamic stiffiness in high-speed grinding state, improve grinding accuracy is designed Property collet very it is necessary to.
Summary of the invention
Based on this, it is necessary in view of the above technical problems, provide a kind of bullet high with good dynamic stiffiness, grinding accuracy Property clip designs method and elastic collet.
A kind of design method of elastic collet, the elastic collet include collet sleeve, collet chuck and mandril, and the mandril is set to In the collet chuck, the collet chuck is set in the collet sleeve, which comprises
Simplify the structure of the elastic collet;
Functional requirement to be achieved is needed according to elastic collet described in the structure determination of the elastic collet;
According to the necessary clamping force under elastic collet working condition described in the Structure Calculation of the elastic collet, and according to Necessity clamping force, obtains the stress of the collet sleeve of the elastic collet;
Function to be achieved is needed to want according to the stress and the elastic collet of the necessary clamping force and the collet sleeve It asks, the structure of collet sleeve described in optimization design.
Technical solution is illustrated further below:
The elastic collet needs functional requirement to be achieved in one of the embodiments, specifically includes:
The collet chuck includes clamping part, and the clamping part is equipped with inner hole, the length of the clamping part itself and the inner hole Diameter ratio between 4~6 value;
The collet chuck includes the tail end being oppositely arranged with the clamping part, and the tail end is set in the collet sleeve, described The inner wall clearance fit of the cross-sectional diameter of tail end and the collet sleeve, fit clearance Δ is between the ㎜ of 0.006 ㎜~0.008 Value;
Pulling force suffered by the elastic collet is adjusted, until collet chuck tail end and collet sleeve reach rigid contact.
The elastic collet working condition according to the Structure Calculation of the elastic collet in one of the embodiments, Under necessary clamping force, and according to the necessary clamping force, obtain the stress of the collet sleeve of the elastic collet, further includes:
The intensity of the elastic collet is checked according to the necessary clamping force.
Stress and the bullet according to the necessary clamping force and the collet sleeve in one of the embodiments, Property collet need functional requirement to be achieved, the structure of collet sleeve described in optimization design specifically includes:
The wall thickness value of the collet sleeve thinnest part is set as h1
Using Finite Element Simulation Analysis, the collet sleeve under the stress of the necessary clamping force and the collet sleeve is obtained The shrinkage of thinnest part, the shrinkage and the fit clearance Δ;
If the shrinkage and the fit clearance Δ differ, continue to adjust h1Value, repeat use finite element simulation Analysis obtains the shrinkage of the collet sleeve thinnest part under the stress of the necessary clamping force and the collet sleeve, than The step for shrinkage and the fit clearance Δ, until the shrinkage and the fit clearance Δ are equal, by institute State h when shrinkage and the equal fit clearance Δ1As the thinnest part wall thickness value after the collet sleeve optimization design.
A kind of elastic collet, the elastic collet is designed according to the design method of elastic collet as described above, described Elastic collet includes:
Collet chuck, the collet chuck include the clamping part for clamping workpiece, and the inner wall of the clamping part is equipped with the first groove, The clamping part includes the arrival end for being put into workpiece, and first groove includes the first slot far from arrival end setting The inner wall junction of wall, first cell wall and the clamping part is equipped with chamfering.
First grove shaped circumferential is set to the inner wall of the clamping part in one of the embodiments, it is described fall Angle is cyclic annular chamfering, and at least two first grooves, the first groove parallel arrangement is arranged on the inner wall.
The clamping part is round table-like in one of the embodiments, and the clamping part further includes and the arrival end phase To the connecting pin of setting, the diameter of the arrival end is greater than the connecting pin.
The collet chuck further includes the ontology being connected with the connecting pin in one of the embodiments, in the ontology Portion is equipped with hollow first pipe, and the first pipe is connected with the clamping part;Airtight sealing of hole is offered on the ontology, The airtight sealing of hole penetrates through the tube wall of the ontology.
The clamping part includes clamping jaw in one of the embodiments, and the clamping jaw ring-type clamping jaw of arranging includes the One inner wall and the first outside wall surface open up first groove, the close institute of first outside wall surface on first inner wall It states and offers the second groove at arrival end.
The elastic collet further includes collet sleeve in one of the embodiments, and the drum jacket is set to the collet sleeve It is interior.
The elastic collet further includes circlip in one of the embodiments, and the collet sleeve includes first end, and described One end is arranged close to the arrival end, and the first end is equipped with cricoid third groove, and the circlip is set to the third groove It is interior;The first end is additionally provided with first through hole, and one end of the circlip passes through the first through hole and is fixed on second groove It is interior.
Above-mentioned elastic collet design method and elastic collet, at least have the advantages that
(1) in the design method of elastic collet, the structure of collet sleeve is clamping work status by optimization design to reach Lower collet sleeve and collet chuck cooperate and zero clearance rigid contact, and in practical application can by adjusting elastic collet pulling force with Make up the error of theoretical calculation and ideal model, thus guarantee when high-speed grinding elastic collet have good dynamic stiffiness and compared with High grinding accuracy.
(2) elastic collet provided in this embodiment by the inner wall of clamping part be equipped with the first groove, the first groove The inner wall junction of first cell wall and the clamping part is equipped with chamfering.The setting of first groove advantageously reduces workpiece and clamping The contact area of portion's inner wall, and then be conducive to increase unit pressure of the clamping part in clamping workpiece.In addition, collet chuck is in production It needs by grinding, the setting of the first groove advantageously reduces collet chuck and needs ground area, improves the efficiency of processing collet chuck. The setting of chamfering effectively prevent workpiece to can not be successfully feeding due to pushing up to the first groove when entering clamping part, it is ensured that on Material is gone on smoothly.
Detailed description of the invention
Fig. 1 is the elastic collet clamping workpiece that one embodiment of the invention provides and the structural representation under grinding status Figure;
Fig. 2 is the structural schematic diagram for the elastic collet that one embodiment of the invention provides;
Fig. 3 is the structural schematic diagram for the collet chuck that one embodiment of the invention provides;
Fig. 4 is the right view of Fig. 3;
Fig. 5 is diagrammatic cross-section of the Fig. 4 along the direction I-I;
Fig. 6 is the schematic enlarged-scale view at the P of Fig. 5;
Fig. 7 is the structural schematic diagram for the collet sleeve that one embodiment of the invention provides;
Fig. 8 is the force analysis figure that the workpiece that one embodiment of the invention provides is under grinding status;
Fig. 9 is the collet chuck structure schematic diagram for being used to calculate clamping jaw deformation drag that one embodiment of the invention provides;
Figure 10 is the collet sleeve stress deformation simulation analysis figure that one embodiment of the invention provides.
Description of symbols: 1, collet chuck;11, clamping part;111, the first groove;111a, the first cell wall;112, arrival end; 113, inner hole;114, chamfering;115, connecting pin;12, ontology;121, first pipe;122, airtight sealing of hole;13, clamping jaw;131, One inner wall;132, the first outside wall surface;132a, the second groove;14, tail end;2, collet sleeve;21, first end;211, third is recessed Slot;212, first through hole;22, second end;3, circlip;4, main shaft;5, mandril;6, grinding wheel;7, pull rod;8, workpiece.
Specific embodiment
In order to make the foregoing objectives, features and advantages of the present invention clearer and more comprehensible, with reference to the accompanying drawing to the present invention Specific embodiment be described in detail.Many details are explained in the following description in order to fully understand this hair It is bright.But the invention can be embodied in many other ways as described herein, those skilled in the art can be not Similar improvement is done in the case where violating intension of the present invention, therefore the present invention is not limited to the specific embodiments disclosed below.
It should be noted that it can directly on the other element when element is referred to as " being fixed on " another element Or there may also be elements placed in the middle.When an element is considered as " connection " another element, it, which can be, is directly connected to To another element or it may be simultaneously present centering elements.Term as used herein " vertical ", " horizontal ", " left side ", " right side " and similar statement for illustrative purposes only, are not meant to be the only embodiment.
Unless otherwise defined, all technical and scientific terms used herein and belong to technical field of the invention The normally understood meaning of technical staff is identical.Term as used herein in the specification of the present invention is intended merely to description tool The purpose of the embodiment of body, it is not intended that in the limitation present invention.Each technical characteristic of embodiment described above can carry out arbitrarily Combination, for simplicity of description, it is not all possible to each technical characteristic in above-described embodiment combination be all described, so And as long as there is no contradiction in the combination of these technical features, it all should be considered as described in this specification.
A kind of elastic collet design method and elastic collet are present embodiments provided, has that dynamic stiffiness is good, grinding accuracy High advantage, is described in detail below with reference to attached drawing.
A kind of design method of elastic collet, refering to fig. 1 and Fig. 2, elastic collet includes collet sleeve 2, collet chuck 1 and mandril 5, Mandril 5 is set in collet chuck 1, and collet chuck 1 is set in collet sleeve 2, and the design method of elastic collet includes:
Step S1, the structure of elastic collet is determined;
Step S2, the elastic collet according to the structure determination of the elastic collet needs functional requirement to be achieved;
Step S3, the necessary clamping force under the elastic collet working condition is obtained, and according to the necessary clamping force, Obtain the stress of the collet sleeve 2 of the elastic collet;
Step S4, according to the stress of the necessary clamping force and the collet sleeve 2, collet sleeve 2 described in optimization design it is whole Body structure.
In the design method of elastic collet, the structure of collet sleeve 2 is by optimization design, to reach in the case where clamping work status Collet sleeve 2 and the cooperation of collet chuck 1 and zero clearance rigid contact, and can be by adjusting collet pulling force to make up in practical application The error of theoretical calculation and ideal model, to guarantee that collet has good dynamic stiffiness and higher grinding when high-speed grinding Precision.
In step S1, the structure for determining elastic collet, specifically include:
Refering to fig. 1, the basic structure of the elastic collet includes collet chuck 1, collet sleeve 2 and circlip 3, and elastic collet is arranged one In a hollow main shaft 4.The clamping part 11 of collet chuck 1 be it is round table-like, 11 taper of clamping part be α, collet chuck 1 include ontology 12, ontology 12 one end is connected to clamping part 11, and the other end of ontology 12 is far from clamping part 11 and end face be diameter is d2Cylindrical surface.Folder The outer surface of headgear 2 is the outer conical surface that taper is γ, the inner wall fitting of the outer conical surface and main shaft 4.The length of clamping part 11 For L2, it is d for clamping diameter1Workpiece 8.A mandril 5 is equipped in collet sleeve 2, the diameter of mandril 5 is slightly less than the hole of collet chuck 1 Diameter, mandril 5 are fixedly connected with main shaft 4, and the main function of mandril 5 is to definitely define workpiece 8 when clamping part 11 clamps workpiece 8 Axial position.Circlip 3 is stuck in the third groove 211 of collet sleeve 2, and one end of circlip 3 is through the first of collet sleeve 2 End 21 first through hole 212 and and terminate in a second groove 132a of collet chuck 1, which is reliably to guarantee 1 collet sleeve 2 of collet chuck is unable to relative rotation during being ground workpiece 8, to prevent the loosening of collet chuck 1.
Elastic collet further includes pull rod 7, and pull rod 7 is set in one end of the separate clamping part 11 of ontology 12, and collet sleeve 2 is also wrapped Include the second end 22 being arranged relative to first end 21.When elastic collet works, pull rod 7 is under the action of angling cylinder by being set to The threaded connection of its end pulls collet chuck 1 to move towards the direction of the second end 22 of collet sleeve 2, so that collet chuck 1 is in collet sleeve 2 Under the action of clamping force, 11 contraction clip clamping of workpieces 8 of clamping part.The back stay 7 that workpiece 8 has been ground pushes collet chuck by angling cylinder again 1 moves to unclamp workpiece 8 to the direction of the first end 21 of collet sleeve 2, and workpiece 8 is unloaded by special mechanism.To guarantee mill Abrasive dust and grinding fluid do not penetrate into the mating surface of collet chuck 1 Yu collet sleeve 2 when cutting, and 4 rear end of main shaft is connected to by rotary joint to be compressed all the way Air, compressed air continues by hollow main shaft 4 and pull rod 7, and through the fit clearance of mandril 5 and collet chuck 1 when work It constantly blows to 8 direction of workpiece, to carry out effective hermetic seal.
Step S2, the elastic collet according to the structure determination of the elastic collet needs functional requirement to be achieved, specifically Include:
Step S21, the clamping part 11 of collet chuck 1 is equipped with inner hole 113, the length of clamping part 11 itself and the diameter of inner hole 113 The ratio between 4~6 value, such as clamping part 11 itself length and inner hole 113 diameter ratio value be 4,5 or 6.
Specifically, in this step, due to influencing the principal element of 8 grinding accuracy of workpiece in addition to collet chuck 1, collet sleeve 2 etc. Except the accuracy of manufacture of the core part conical surface, main there are also following several respects: first is that the L of 1 front end clamping part 11 of collet chuck2Length Degree.Theoretically, the L2Length is longer, and straightness is better.But aperture very little when due to processing valve class part, it is too long L2Value will affect the precision of manufacture.On the other hand, too long L2Value can reduce the chucking power of 11 unit areas of clamping part, Influence the reliability clamped.Simultaneously in CBN (Cubic Boron Nitride cubic boron nitride) high-speed grinding, grinding on an equal basis It cuts under loading condiction, practical grinding force can be ground lower than plain wheel 6.In view of factors above, the preferred collet chuck 1 of the present embodiment The draw ratio of 11 inner hole 113 of clamping part value between 4~6, such as the draw ratio value are 5.
Step S22, collet chuck 1 includes the tail end 14 being oppositely arranged with clamping part 11, and refering to Fig. 3, tail end 14 is set to collet sleeve 2 It is interior, the inner wall clearance fit of the cross-sectional diameter of tail end 14 and collet sleeve 2, fit clearance Δ the ㎜ of 0.006 ㎜~0.008 it Between value.
Specifically, influence grinding accuracy is straight there are one the end of separate clamping part 11 that key factor is ontology 12 Diameter is d2Cylindrical surface, the inner wall fit clearance Δ on the cylindrical surface and corresponding collet sleeve 2.It theoretically analyzes, is guaranteeing work Under the premise of collet chuck 1 can smoothly clamp with respect to collet sleeve 2 and be pushed forward release when making, the gap is smaller, positions and processes to workpiece 8 Precision is more advantageous.But in view of penetrating into the mating surface clearance condition in certain abrasive dust that may be present, so also needing to guarantee cylinder Folder 1 clamps the reliability with release, that is, the mating surface is needed to have a certain range of fit clearance Δ.Meanwhile this elastic collet is also There are an important Functional Design main points to seek to realize in the case where clamping work status through the thin-walled of the second end 22 of collet sleeve 2 Uniform shrinkage so that the end far from clamping part 11 be diameter is d2The mating surface of cylindrical surface collet sleeve 2 to reach zero clearance rigid Property contact.In summary analyze, the present embodiment by mating surface diametrically fit clearance Δ be set to 0.006mm~ 0.008mm.Only need within the scope of this to fit clearance Δ value.
The factor of collet dynamic rate is influenced other than the accuracy of manufacture of the core parts mating surfaces such as collet chuck 1, mainly also Below two aspect: first is that individually consider collet chuck 1 clamp workpiece 8 when dynamic stiffness.This 1 front end clamping part 11 of factors dictate collet chuck Length L2It is as long as possible.But comprehensively consider as the aforementioned, the draw ratio of 1 clamping part of collet chuck, 11 inner hole 113 takes between 4 to 6 Value.Second is that under clamped condition collet chuck 1 relative to collet sleeve 2 (because in contrast collet sleeve 2 is rigidly good with the contact of main shaft 4, at this time Collet sleeve 2 and main shaft 4 can be considered as a single piece) dynamic stiffness.A key element for influencing this factor is to require The diameter of the separate clamping part 11 of collet chuck 1 is d under clamped condition2Cylindrical surface and the fit clearance Δ in the hole of corresponding collet sleeve 2 It is zero, that is, reaches rigid contact.Such state needs the careful design of two aspects, first is that suitable pulling force FQ, another party Face is 2 structure of collet sleeve rationally designed, the especially wall thickness of 2 rear end of collet sleeve, between guaranteeing to collapse under this pulling force effect Gap.If the fit clearance fails effectively to collapse and eliminate under clamped condition, the dynamic that will be greatly reduced entire elastic collet is rigid Degree.But pulling force FQIt is not the bigger the better, on the one hand excessive pulling force will increase the structure size design of associated mechanisms, this is unfavorable for High-speed grinding is to the requirement compared with low rotor inertia;On the other hand, FQThe excessive collet sleeve 2 that will lead to is by excessive 4 taper hole pressure of main shaft Power N1It acts on and micro radial contraction occurs, then in FQMicro axial displacement is further generated under effect to the left.If the axial direction position Move it is more significant so that elastic collet is in pulling force FQMost of axial displacement is remained not due to inclined wedge self-lock mechanism under unloading condition It is capable of resetting, then one end of the separate clamping part 11 of elastic collet chuck 1 " will block " in the second end 22 of collet sleeve 2 at this time, need It elapses and unclamps by larger external force.This aspect is unfavorable for the reliability of automatic blanking, and another aspect workpiece 8 is upper and lower each time To can generate friction inside accurate elastic collet when material, the precision of accurate elastic collet is difficult under the operating condition of frequent loading and unloading It keeps, and the service life of elastic collet also will receive influence.
Step S23, pulling force suffered by the elastic collet is adjusted, until collet chuck 1 reaches good rigidity with collet sleeve 2 and connects Touching state.
Specifically, the pulling force F in proper rangeQIt can avoid above-mentioned adverse effect, because at this time under 8 clamped condition of workpiece The most thin position of the only second end 22 of collet sleeve 2 generates micro elastic shrinkage, and the minimum shrinkage of other thicker parts is not It is enough to make collet sleeve 2 in pulling force FQEffect is lower to occur axial displacement, waits FQThe thinnest part elastic shrinkage can be restored again after unloading, no It influences to unclamp workpiece 8.Therefore, pulling force FQValue key be under the conditions of reaching necessary clamping force, make collet chuck 1 and collet sleeve 2 Between rear end cooperation cylindrical surface reach good rigid contact state just.In view of theoretical calculation and theoretical model and reality Production has certain error, and to guarantee that elastic collet reaches good dynamic rate in practical application, the present invention is in accurate Theory meter Under the premise of calculating with simulation analysis, certain on-site parameters adjustment space has been reserved in the design, mainly in a certain range Adjust the pulling force F of angling cylinderQ, pulling force F is inferred by judging 8 grinding quality of workpiece and the whether reliable automatic discharging of workpiece 8Q Whether certain optimum value is reached.
Step S3: the necessary clamping force of the elastic collet is obtained, and according to the necessary clamping force, obtains the bullet The stress of the collet sleeve 2 of property collet, the specific steps are as follows:
Refering to fig. 1, if grinding wheel 6 and 8 rotation speed of workpiece are respectively n when being ground workpiece 82、n1(r/min), 6 motor of grinding wheel Rated power be P (W), grinding wheel 6 be ground linear velocity be V (m/s), be ground work when grinding wheel 6 with VInto(m/s) velocity radial is fed It is ground workpiece 8.If the grinding torque that workpiece 8 is subject to when being ground is T (Nm), the tangential grinding component being subject to is FT, it is subject to Radial grinding component is Fy, the axial grinding component being subject to is Fx.Since the elastic collet is applied to existing mature valve stem The rated power P of grinding process and grinding machine, 6 motor of grinder wheel has determined that.For convenient for estimation grinding force, it can be assumed that steady The acting campaign that the rated power P of 6 motor of grinding wheel is completely converted into grinding force in the limiting case when being ground surely (in fact exists The factors such as bearing friction, aerodynamic drag, P can not be totally converted, therefore this method more tends to guard).
It is analyzed as follows in more detail for grinding force: refering to Fig. 8, since the machining allowance of valve stem grinding area is substantially equal It is even, 8 forming face grinding area of workpiece can be uniformly divided near linear section AC and arc section CE in the x-direction, wherein B is in AC Point, D are the midpoints CE.And H is the midpoint of BD line.Engine valve stem diameter is d1, pan portion diameter is d3, B, D, H each point to valve The distance of the bar centre of gyration is respectively rB、rD、rH.According to the grinding area features of shape, approximate AC sections and CE sections can be ground The point of resultant force of power is attributed to B point and D point respectively.Since this two sections of grinding wheel, 6 linear velocity and grinding allowance are essentially identical, because This can be approximately considered the tangential grinding resultant force and radial grinding resultant force being respectively acting on B point and D point on this two sections of grinding areas It is equal.So as to further by the tangential grinding resultant force F of entire grinding areaTAnd radial grinding resultant force FyPosition is attributed to H Point.But for axial grinding force, due to using the direction y plunge-cutting, AC section are basic without axial grinding force, only CE sections Have.And CE sections of shapes can be approximately considered CE sections of axial grinding force and be equal to radial direction suffered by this section of region close to 1/4 section of circular arc Grinding force Fy/ 2, and its point of resultant force is located at D point, namely the axial grinding resultant force F of entire grinding areaxPosition is located at D Point, size are equal to Fy/2.Then have at this time:
P=FT× V, (1)
And T=FT×rH, (2)
Wherein,
And according to " Principle of Grinding and Cutting ", in plunge-cutting, according to the difference of 6 degree of passivation of grinding wheel, normal grinding force with Tangential grinding force ratio is generally 3:1~5:1, and the passivation of medium plain emery wheel 6 is more serious, and the ratio is bigger.Therefore, it is taken in the design Value 5:1 under the most unfavorable processing condition, it may be assumed that
Fy=5FT, (4)
And Fx=Fy/ 2=2.5FT, (5)
According to " Machine Tool Fixture Design handbook ", for the elastic collet of 8 excircle orientation of workpiece, to prevent workpiece 8 around axis Line rotates and moves along axis required clamping force WK(N) are as follows:
Wherein, K is safety coefficient, μ2For the coefficient of friction of collet chuck 1 and workpiece 8.Formula (1)~formula (5) formula is substituted into (6) formula has:
It is according to necessary clamping force W belowKThe step of stress to calculate collet sleeve 2:
Refering to fig. 1 with Fig. 8 and Fig. 9, according to " modern practical lathe design manual ", the bullet in the case where there is axially position Property collet will obtain radial clamping force WK, then the pulling force F applied to collet chuck 1 is neededQAre as follows:
Wherein,For the angle of friction of collet chuck 1 and collet sleeve 2,For the angle of friction of collet chuck 1 and workpiece 8, α is the circle of collet chuck 1 Cone angle.
And
μ1For the coefficient of friction of collet chuck 1 and collet sleeve 2.
And
μ2For the coefficient of friction of collet chuck 1 and workpiece 8.
FRThe deformation drag of 1 clamping jaw 13 of collet chuck when to clamp,
It wherein, is spring valve walled thickness (mm) refering to Fig. 8 and Fig. 9, h, d is the outer diameter (mm) of spring valve, Δ2For the folder of collet chuck 1 The diametric clearance (mm) of pawl 13 and workpiece 8, L is 1 clamping jaw of collet chuck, 13 computational length, i.e., by 13 conical surface midpoint of clamping jaw to spring valve root Distance (mm), k1For according to the conversion coefficient of 1 features of shape of collet chuck (referring to " modern practical lathe design manual ").
It is calculated below in the pressure F for clamping work status lower push rod 5Top
FTop=Wk× μ, (12)
Then tightening force suffered by collet sleeve 2: FSet is drawn=FQ-FTop, (13)
Correspondingly, the pressure that collet sleeve 2 is applied by main shaft 4:
Similarly, the pressure that 2 front conical face of collet sleeve is applied by collet chuck 1:
Step S31, the intensity of the elastic collet is checked according to the necessary clamping force, the step is specific as follows:
Step S311, the intensity for checking the tail end 14 (being dangerouse cross-section at the smallest cross-sectional of tail end 14) of elastic collet chuck 1 is wanted It asks.Specifically, the smallest cross-sectional of collet chuck 1 is located at the tail end 14 of collet chuck 1.Since the elastic collet precision of this kind of clamping workpiece 8 is wanted Friction when asking high, and working between collet chuck 1 and collet sleeve 2 is worn between collet chuck 1 and collet sleeve 2 than more serious in order to reduce Influence to clamp precision, the tension release frequency of collet chuck 1 will not be very high during service life, therefore this step is only checked The yield strength of the smallest cross-sectional, without checking fatigue strength.The stress σ at the section, which need to be checked, to be needed to meet:
Wherein, S is the area of 1 dangerouse cross-section of collet chuck, KSFor safety coefficient, σsFor the yield limit of 1 material of collet chuck.
Step S312, the stability of mandril 5 is checked.Specifically, according to the mechanics of materials about slender compression bar Theory of Stability, A length of LMandril, diameter dMandrilMandril 5 its critical pressure F that can bearTop is facedAre as follows:
Wherein, E is the elasticity modulus of mandril 5, KMandrilFor the safety coefficient for checking 5 stability of mandril, I is 5 cross section of mandril The moment of inertia have and for solid mandril 5:
Step S4, it is needed according to the stress and the elastic collet of the necessary clamping force and the collet sleeve to be achieved Functional requirement, the structure of collet sleeve described in optimization design, specifically includes:
Step S41, the wall thickness value of 2 thinnest part of collet sleeve is set as h1
Step S42, it using Finite Element Simulation Analysis, obtains under the stress of the necessary clamping force and the collet sleeve 2 The shrinkage of 2 thinnest part of collet sleeve, the shrinkage and the fit clearance Δ;
Step S43: if the shrinkage and the fit clearance Δ differ, continue to adjust h1Value, repeat using having First simulation analysis is limited, is obtained under the stress of the necessary clamping force and the collet sleeve 2 described in 2 thinnest part of collet sleeve The step for shrinkage, the shrinkage and fit clearance Δ, until the shrinkage and the fit clearance Δ Equal, when by the shrinkage and the equal fit clearance Δ h1As the thinnest part wall after the collet sleeve optimization design Thickness value.
Specifically, refering to fig. 1, the necessary pulling force F being calculated in above mentioned step S3QUnder effect, main shaft 4 is to collet sleeve 2 The pressure N of application1So that the uniform shrinkage amount of 2 rear end thinnest part of collet sleeve just reach do not apply tightening force before collet chuck 1 and folder The clearance delta of the mating surface of headgear 2, so that high dynamic rigidity and high rotating accuracy when elastic collet can achieve grinding. A series of accurately calculate described in step S2 has obtained tightening force FQPressure N under effect1Value, in this way, can be by first just setting one The wall thickness value h of a 2 thinnest part of collet sleeve1, then Finite Element Simulation Analysis is used, obtain this pressure N1Act on lower 2 thinnest part of collet sleeve Contraction magnitude, and be compared with Δ value, then the h that row adjustment is just set1Value, until the contraction magnitude is equal with Δ value.In this way Just obtain the h of optimal design1Value, then the basic size of entire collet sleeve 2 can be decided.In addition, the of the collet sleeve 2 Two ends 22 are also provided with one section of external screw thread, to have the pulling plate of same size internal screw thread by collet sleeve with one when necessary 2 disassemble from the hole of main shaft 4.
By above four steps, the design to High-speed & Precision Grinding dedicated elas-tic collet of the invention can be completed.
Illustrate how the design method of elastic collet is applied below with specific example.
Now by taking a kind of forming face grinding of engine exhaust port of certain company production as an example.8 shape of workpiece refering to fig. 1 and figure 8, gauge diameter d1=6mm, pan portion diameter d3=28mm, valve stretch out the length L of collet1=34mm, 6 line of grinding wheel when grinding Speed is V=100m/s, and 6 motor rated power P of grinding wheel is 15kW, then:
Estimate clamping force WK:
It is obtained by formula (1), is tangentially ground componentIt is ground torque Axial grinding component Fx=2.5FT=375 (N).Because collet chuck 1, collet sleeve 2 and 8 material of workpiece are steel class, take and rub Wipe coefficient μ12=0.15, safety coefficient K is set as 2.5.Then obtained by formula (6):
Calculate tightening force FQ:
This example takes α=17 ° 30 ' 30 ", 1 spring valve number of collet chuck takes 3, then is checked in, K by " modern practical lathe design manual "1 =6000.Spring valve thin-walled thickness h=4mm is taken, spring valve outside diameter d=19mm takes the diametric clearance Δ of 1 clamping jaw 13 and workpiece 8 of collet chuck2= 0.4mm designs distance L=42mm of 13 conical surface midpoint of clamping jaw to spring valve root, the then clamping jaw of collet chuck 1 when must be clamped by formula (11) 13 deformation drag: FR=888.8 (N),
Required tightening force: F is then obtained by formula (8)Q=4766.4 (N),
The pressure F of mandril 5 in the clamp state is calculated by formula (12)Top=1417 (N), then tension suffered by collet sleeve 2 Power FSet is drawn=3349.4 (N), correspondingly, pressure of the collet sleeve 2 by 4 taper hole of main shaft: N can be obtained by formula (14)1=1.677 × 104 (N)
Check the intensity of 1 dangerouse cross-section of collet chuck:
Fig. 3 and Fig. 5 are please referred to, 1 dangerouse cross-section of collet chuck of this example design is located at tail end 14, diameter at minimum outer circle For Ф 18.5mm, and inner hole 113 diameter in corresponding position is Ф 11mm, the yield limit σ of 1 material of collet chucksIt is taken as 375MPa, safety is Number KS2 are taken, then obtains the stress of the dangerouse cross-section by formula (15):
Check 5 stability of mandril:
The 5 diameter d of mandril of this example designMandril=Ф 10.8mm, long LMandril=180mm, safety coefficient KMandril2 are taken, material Elastic modulus E takes 210 × 109Pa then can obtain the critical pressure F that the mandril 5 can be born by formula (16)MandrilAre as follows:
Optimization design determines the minimum wall thickness (MINI W.) h at 2 back end cylindrical hole position of collet sleeve1:
As described in step S1, this example is by the diametric clearance Δ in 2 back end cylindrical hole of collet sleeve and 2 Correspondent cy linder face of collet sleeve It is set to 0.006~0.008mm.By tentative calculation several times, the existing minimum wall thickness (MINI W.) h by 2 back end cylindrical hole position of collet sleeve of this example1If For 1.5mm.In this way, the overall dimensions of collet sleeve 2 are decided surely.Using the method for above-mentioned steps 5, with finite element simulation point 2 stress deformation situation of collet sleeve is analysed, by obtained distribution pressure N calculated above1It is applied on 2 wall of collet sleeve, obtains stress change Shape simulation result diagram (refering to fig. 1 0).As shown in Figure 10, in the clamp state, the minimum at the 2 back end cylindrical hole position of collet sleeve Wall thickness is in radial direction and shrinks about 0.0032mm, the substantially equal to half of diametric clearance Δ, i.e., is clamping work status at this time The mating surface of lower collet chuck 1 and collet sleeve 2 can just collapse gap.Reach purpose of design of the present invention.F is provided at this timeQ=4766.4N Hydraulic gyration oil cylinder (maximum oil pressure 4MPa) its output oil pressure be about 1.2MPa.Since the pulling force of oil cylinder offer is in a certain range It is interior adjustable, it is verified through actual use, the high-speed grinding valve stem within the scope of 1.2~1.5MPa of angling cylinder operating pressure, equal energy Obtain good grinding quality.But when oil pressure is lower than 1.0MPa, 8 grinding surface of workpiece has chatter mark appearance.And when oil pressure is greater than After 1.7MPa, it may appear that occasionally there is clamping stagnation to fail effectively to unclamp workpiece 8 between collet chuck 1 and collet sleeve 2 when workpiece 8 is unclamped in oil cylinder off-load Phenomenon.These phenomenons are consistent with Such analysis of the present invention.
In one embodiment, elastic collet is designed according to the design method of elastic collet described above.It please join Fig. 3, Fig. 5 and Fig. 6 are read, which includes collet chuck 1, and collet chuck 1 includes the clamping part 11 for clamping workpiece 8, clamping part 11 inner wall is equipped with the first groove 111, and clamping part 11 includes the arrival end 112 for being put into workpiece 8, the first groove 111 packet The inner wall junction for including the first the cell wall 111a, the first cell wall 111a and clamping part 11 that are arranged far from arrival end 112 is equipped with chamfering 114。
Elastic collet provided in this embodiment on the inner wall of clamping part 11 by being equipped with the first groove 111, the first groove 111 the first cell wall 111a and the inner wall junction of the clamping part 11 are equipped with chamfering 114.First groove 111 is provided with Conducive to the contact area of reduction workpiece 8 and 11 inner wall of clamping part, and then be conducive to increase list of the clamping part 11 in clamping workpiece 8 Position pressure.In addition, collet chuck 1 production when need by grinding, the setting of the first groove 111 advantageously reduce collet chuck 1 need by The area of grinding improves the efficiency of processing collet chuck 1.The setting of chamfering 114 effectively prevent workpiece 8 enter clamping part 11 when due to It pushes up to the first groove 111 and can not be successfully feeding, guarantee going on smoothly for feeding.
In one embodiment, Fig. 5 and Fig. 6 are please referred to, 111 annular of the first groove is set to the inner wall of clamping part 11, Angle 114 is cyclic annular chamfering 114, and at least two first grooves 111,111 parallel arrangement of the first groove is arranged on inner wall.For example, folder It holds and opens up two the first grooves 111 disposed in parallel on the inner wall in portion 11, the first cell wall 111a and folder of each first groove 111 The inner wall junction for holding portion 11 is provided with cyclic annular chamfering 114.When 11 clamping workpiece 8 of clamping part, since clamping part 11 opens up The contact area of first groove 111, workpiece 8 and clamping part 11 is reduced, i.e. the setting of first groove 111 advantageously reduces work The contact area of 11 inner wall of part 8 and clamping part, and then be conducive to increase unit pressure of the clamping part 11 in clamping workpiece 8.Separately Outside, collet chuck 1 is needed in production by grinding, and the setting of the first groove 111 advantageously reduces collet chuck 1 and needs ground face Product improves the efficiency of processing collet chuck 1.Further, during entering clamping part 11, workpiece 8 is easy to contradict to the workpiece 8 On first cell wall 111a of one groove 111, but since the inner wall junction of the first cell wall 111a and clamping part 11 is equipped with ring-type Chamfering 114.Workpiece 8 can smoothly skid off the first groove 111 along cyclic annular chamfering 114, and then go deep into clamping part 11 and pressed from both sides Portion 11 is held tightly to clamp.Workpiece 8 can be effectively prevented when entering clamping part 11 due to top to first in the setting of cyclic annular chamfering 114 Groove 111 and can not be successfully feeding, guarantee going on smoothly for feeding.The inner wall angle of fillet surface and clamping part 11 is 20 °~ 40°.For example, the inner wall angle β of fillet surface and clamping part 11 is 20 °, 30 ° or 40 ° etc..It is understood that the first groove 111 number can be two, can also be one, three etc..The specific number of first groove 111 is not done in the present embodiment It is specific to limit.
In one embodiment, Fig. 3 and Fig. 5 and Fig. 7 are please referred to, clamping part 11 is truncated cone-shaped, and clamping part 11 further includes The diameter of the connecting pin 115 being oppositely arranged with arrival end 112, arrival end 112 is greater than connecting pin 115.Further, collet chuck 1 is gone back Including the ontology 12 being connected with connecting pin 115, hollow first pipe 121, first pipe 121 and folder are equipped with inside ontology 12 Portion 11 is held to be connected.The design of first pipe 121 is conducive to elastic collet and clamps elongated workpiece 8, i.e. the elastic collet is applicable in In the High-speed & Precision Grinding of clamping slender rod type workpiece 8.Airtight sealing of hole 122 is offered on ontology 12, the airtight perforation of sealing of hole 122 is originally The tube wall of body 12.Elastic collet further includes collet sleeve 2, and collet chuck 1 is sheathed in collet sleeve 2.Collet sleeve 2 and collet chuck 1 fit closely, Form mating surface.Abrasive dust and grinding fluid that workpiece 8 is generated in high-speed grinding easily infiltrate into the mating surface of collet chuck 1 Yu collet sleeve 2.For Prevent the abrasive dust and grinding fluid from entering in the mating surface of collet chuck 1 and collet sleeve 2, elastic collet accesses compressed air from the external world.Work as bullet Property collet be in clamp work status under, the compressed air is from the end of elastic collet along the fit clearance of collet chuck 1 and mandril 5 Face enters the inside of elastic collet, the airtight sealing of hole 122 on collet chuck 1, continuously blows, will grind to 8 direction of workpiece Outside bits and grinding fluid blowout collet chuck 1 and collet sleeve 2, abrasive dust can be effectively prevented and grinding fluid enters the mating surface of collet chuck 1 and collet sleeve 2 In interior and collet chuck 1, effective hermetic seal is carried out to elastic collet.Specifically, airtight sealing of hole 122 can be three and be uniformly distributed In the periphery of the ontology 12 of collet chuck 1.It is understood that airtight sealing of hole 122 can also be other numbers such as two, four, five Mesh is not specifically limited herein.
In one embodiment, referring to Fig. 4, clamping part 11 includes clamping jaw 13, the cyclic annular arrangement of clamping jaw 13.Clamping jaw 13 includes First inner wall 131 and the first outside wall surface 132 open up the first groove 111 on first inner wall 131, and the first outside wall surface 132 is leaned on The second groove 132a is offered at nearly arrival end 112.Specifically, clamping part 11 includes three identical clamping jaws 13, three clamping jaws 13 are uniformly distributed, and open up a second groove 132a, the second groove in the position close to arrival end 112 on three clamping jaws 13 132a is located at the centre position of clamping jaw 13.The effect of second groove 132a is as follows: by the material of every 13 overcentre of valve clamping jaw After material rejects one piece, then in terms of 112 direction of arrival end, the radial direction wall thickness of every 13 head middle section of valve clamping jaw wants smaller Wall thickness in its two sides.When clamping workpiece 8 collet sleeve 2 along clamping jaw 13 the first outside wall surface 132 to the first inner wall 131 Direction applies pressure to clamping jaw 13, compressive stres on each clamping jaw 13 and uneven is acted at this time, in each clamping jaw 13 Entreat region stress smaller, two side areas stress is bigger (difference that wall thickness difference determines local stiffness), such three clamping jaws 13 When clamping workpiece 8, play main clamping action is the two side areas of each clamping jaw 13, i.e. clamping of the workpiece 8 by six regions Effect.Actually three clamping jaws 13 carry out six point clampings to workpiece 8, relative to 3 points of clampings in no groove, originally The clamping jaw 13 that embodiment provides is stronger to the clamping of workpiece 8 reliable.In addition, the second groove 132a is not dismantle collet sleeve In the case where 2 dismounting collet chuck 1 is rotated using special tooling counterclockwise and provides suitable position.It is understood that clamping jaw 13 quantity can be three, can also be the other quantities such as four, five, be not specifically limited herein.
In one embodiment, Fig. 2, Fig. 7 are please referred to, elastic collet further includes circlip 3, and collet sleeve 2 includes first end 21, The first end 21 of collet sleeve 2 is arranged close to arrival end 112.The first end 21 of collet sleeve 2 is equipped with cricoid third groove 211, card Spring 3 is set in third groove 211.The first end 21 of collet sleeve 2 is additionally provided with first through hole 212, and it is logical that one end of circlip 3 passes through first It is fixed on behind hole 212 in second groove 132a.In this way, collet chuck 1 and collet sleeve 2 are achieved a fixed connection by circlip 3, can reliably protect Demonstrate,prove elastic collet under high-speed grinding working condition collet chuck 1 and collet sleeve 2 will not relative rotation, guarantee the precision of grinding.
In the design method of elastic collet provided in this embodiment, the structure of collet sleeve 2 is by optimization design, to reach It clamps collet sleeve 2 and collet chuck 1 under work status to cooperate and zero clearance rigid contact, and can be by adjusting in practical application Collet pulling force is to make up the error of theoretical calculation and ideal model, to guarantee that it is rigid to have good dynamic for collet when high-speed grinding Property and higher grinding accuracy.
In addition, elastic collet provided in this embodiment by the inner wall of clamping part 11 be equipped with the first groove 111, first First cell wall 111a of groove 111 and the inner wall junction of the clamping part 11 are equipped with chamfering 114.First groove 111 is set The contact area for advantageously reducing 11 inner wall of workpiece 8 and clamping part is set, and then is conducive to increase clamping part 11 in clamping workpiece 8 Unit pressure.In addition, collet chuck 1 is needed in production by grinding, the setting of the first groove 111 advantageously reduces collet chuck 1 and needs The area to be ground improves the efficiency of processing collet chuck 1.The setting of chamfering 114 effectively prevent workpiece 8 when entering clamping part 11 It can not be successfully feeding due to pushing up to the first groove 111, it is ensured that feeding is gone on smoothly.
Each technical characteristic of embodiment described above can be combined arbitrarily, for simplicity of description, not to above-mentioned reality It applies all possible combination of each technical characteristic in example to be all described, as long as however, the combination of these technical characteristics is not deposited In contradiction, all should be considered as described in this specification.
The embodiments described above only express several embodiments of the present invention, and the description thereof is more specific and detailed, but simultaneously It cannot therefore be construed as limiting the scope of the patent.It should be pointed out that coming for those of ordinary skill in the art It says, without departing from the inventive concept of the premise, various modifications and improvements can be made, these belong to protection of the invention Range.Therefore, the scope of protection of the patent of the invention shall be subject to the appended claims.

Claims (11)

1. a kind of design method of elastic collet, which is characterized in that the elastic collet includes collet sleeve, collet chuck and mandril, institute Mandril is stated in the collet chuck, the collet chuck is set in the collet sleeve, which comprises
Simplify the structure of the elastic collet;
Functional requirement to be achieved is needed according to elastic collet described in the structure determination of the elastic collet;
According to the necessary clamping force under elastic collet working condition described in the Structure Calculation of the elastic collet, and according to described Necessary clamping force obtains the stress of the collet sleeve of the elastic collet;
Functional requirement to be achieved is needed according to the stress and the elastic collet of the necessary clamping force and the collet sleeve, it is excellent Change the structure for designing the collet sleeve.
2. the design method of elastic collet according to claim 1, which is characterized in that the elastic collet needs to be achieved Functional requirement specifically includes:
The collet chuck includes clamping part, and the clamping part is equipped with inner hole, the length of the clamping part itself and the inner hole it is straight The ratio between diameter value between 4~6;
The collet chuck includes the tail end being oppositely arranged with the clamping part, and the tail end is set in the collet sleeve, the tail end Cross-sectional diameter and the collet sleeve inner wall clearance fit, fit clearance Δ takes between the ㎜ of 0.006 ㎜~0.008 Value;
Pulling force suffered by the elastic collet is adjusted, until collet chuck tail end and collet sleeve reach rigid contact.
3. the design method of elastic collet according to claim 2, which is characterized in that described according to the elastic collet Necessary clamping force under elastic collet working condition described in Structure Calculation, and according to the necessary clamping force, obtain the bullet The stress of the collet sleeve of property collet, further includes:
The intensity of the elastic collet is checked according to the necessary clamping force.
4. the design method of elastic collet according to claim 2, which is characterized in that described according to the necessary clamping force Functional requirement to be achieved, the knot of collet sleeve described in optimization design are needed with the stress of the collet sleeve and the elastic collet Structure specifically includes:
The wall thickness value of the collet sleeve thinnest part is set as h1
Using Finite Element Simulation Analysis, it is most thin to obtain the collet sleeve under the stress of the necessary clamping force and the collet sleeve The shrinkage at place, the shrinkage and the fit clearance Δ;
If the shrinkage and the fit clearance Δ differ, continue to adjust h1Value, repeat use Finite Element Simulation Analysis, Obtain the shrinkage of the collet sleeve thinnest part under the stress of the necessary clamping force and the collet sleeve, relatively described in The step for shrinkage and the fit clearance Δ, until the shrinkage and the fit clearance Δ are equal, by the contraction H when measuring equal with the fit clearance Δ1As the thinnest part wall thickness value after the collet sleeve optimization design.
5. a kind of elastic collet, which is characterized in that the elastic collet is described in any item according to such as above-mentioned Claims 1-4 The design method of elastic collet designs, and the elastic collet includes:
Collet chuck, the collet chuck include the clamping part for clamping workpiece, and the inner wall of the clamping part is equipped with the first groove, described Clamping part includes the arrival end for being put into workpiece, and first groove includes the first cell wall far from arrival end setting, The inner wall junction of first cell wall and the clamping part is equipped with chamfering.
6. elastic collet according to claim 5, which is characterized in that first grove shaped circumferential is set to the clamping part The inner wall, the chamfering is cyclic annular chamfering, and at least two first grooves, first groove is arranged on the inner wall Parallel arrangement.
7. elastic collet according to claim 5, which is characterized in that the clamping part be it is round table-like, the clamping part is also Including the connecting pin being oppositely arranged with the arrival end, the diameter of the arrival end is greater than the connecting pin.
8. elastic collet according to claim 7, which is characterized in that the collet chuck further includes being connected with the connecting pin Ontology, the body interior is equipped with hollow first pipe, and the first pipe is connected with the clamping part;The ontology On offer airtight sealing of hole, the airtight sealing of hole penetrates through the tube wall of the ontology.
9. elastic collet according to claim 5, which is characterized in that the clamping part includes clamping jaw, and the clamping jaw is cyclic annular The clamping jaw of arranging includes the first inner wall and the first outside wall surface, opens up first groove on first inner wall, described First outside wall surface offers the second groove at the arrival end.
10. elastic collet according to claim 9, which is characterized in that the elastic collet further includes collet sleeve, the cylinder Collet is set in the collet sleeve.
11. elastic collet according to claim 9, which is characterized in that the elastic collet further includes circlip, the collet Set includes first end, and the first end is arranged close to the arrival end, and the first end is equipped with cricoid third groove, the card Spring is set in the third groove;The first end is additionally provided with first through hole, and one end of the circlip passes through the first through hole It is fixed in second groove.
CN201910729512.4A 2019-08-08 2019-08-08 The design method and elastic collet of elastic collet Pending CN110524416A (en)

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