CA2122155A1 - Improved collet and method for optimizing gripping action thereof - Google Patents

Abstract

A method (70) for manufacturing a machine tool collet (10) and a machine tool collet (10) having design parameters optimized to maximize its gripping strength. The collet (10) is of the type having a plurality of gripping jaws (16) spaced around a longitudinal axis (18) with resilient material between the jaws (16). The method (70) includes calculating the total torque generated on a bar passing through the collet (10) for a given collet configuration, including the torque generated just prior to a toggle condition occurring between the jaws (16) and the bar and the maximum moment force generated at a toggle condition. At least one of the design parameters of the collet (10), such as jaw thickness or number of jaws, is varied and the total torque generated is recalculated until the total torque reaches a maximum value for the given collet configuration.

Description

!94/0~53 2 1 2 2 1 5 5 PCT/US93/07155 ITLE OF T~E INVENTION
IMPROVED COLLET AND METHOD FOR
OPTIMIZING ~RIPPING ACTION THEREOF
BACKGROUND OF THE INVENTION

The present invention relates to a collet, and more particularly to an improved collet having optimized parameters to maximize gripping strength, and a method for making same.
U.S. Patent No. 2,346,706 to Stoner and assigned to the Jacobs Manufacturing Company describes a collet having a plurality of flat-~ided gripping members. The gripping members are held in relative position equally spaced about a common axis. The spaces between the gripping members are filled with an adherent resilient material, such as rubber or rubber composition. The gripping members are also transversely perforated. In this case, the resilient rubber material not only fills the space between adjacent gripping members, but it also passes through the perforations in the gripping members thereby forming a plurality of longitudinally spaced continuous annular rings which hold the gripping members in desired relative positions. This collet was a significant improvement over the conventional split steel collets and is widely recognized today by those skilled in the art and commonly known as the Rubber-Flex~ collet.
However, prior to applicant's present invention, it was not known to optimize the gripping strength of the Rubber-Flex0 collet by determining optimum design parameters for the gripping blades or "jaws." Although a number of jaws having varying thicknesses were utilized in the collets, it was not commonly believed that gripping strength could be maximized by deducing the optimum number of gripping jaws for a given configuration which would fit around the inner diameter of the collet while maintaining at least a minimum amount of the resilient material between the gripping jaws.
Additionally, the thickness of the gripping jaws was SUBS I ~Tl I~E SHEE~ (RULE 26) WOg4/0~53 2 1 2 2 1 5 5 PCT/US9~/07155 ~

generally not considered as effecting gripping strength.
Typically, the jaw thickness was dictated by the size or inside diameter of the collet. In other words, smaller diameter collets had thinner jaw blades.
U.S. Patent No. 5,123,663 to Mizoauchi discloses a method for determining the minimum number o~ sagme`nts for a metal collet by determining the range of a central angle (theta) where the geometrical moment of inertia for each segment is constant with respect to a line passing through the centroid of the section perpendicular to a radial direction of the collet. The patent discloses that the range of angle theta is less than 30 regardless of the thickness of the segment. Once the central angle of about 30~ is attained, any further increase in the number of segments will only increase the number of manufacturing steps and lower the tensile strength a cylindrical portion of the collet.
OBJECTS AND 8~MNARY OF q~HE INVE~ION
It is a principle object of the present invention to provide an improved collet of the type having independent grippinq members molded in a rubber composition whereby the gripping strength of the collet is maximized.
A further object of the present invention is to provide a method for determining the design parameters for gripping jaws in a collet of the type having independent gripping jaws molded in a rubber composition.
It is also an object of the present invention to provide a collet having an optimized gripping strength which is compatible to con~entional collet sizes and requirements and interchangeable with conventional split steel collets.
Yet a further object of the present invention is to provide a process for determining the ideal gripping jaw thickness and number of jaws to optimize the gripping strength of a collet design.
Still a further object of the present invention is to provide a design optimization tool for optimizing the ' -``94/0~53 PCT/US93/071~5 design of a collet and which may be utilized on a personal computer.
And yet another object of the present invention is to provide a method for predicting collet torque slippage useful for maximizing a collet design.
It is also an object of the present inv~ntion to provide a collet torque slippage analysis method for determining the optimum characteristics or design parameters for a collet of specific dimensions and requirements.
Yet a further object of the present invention is to provlde a collet torque slippage analysis method for determining the optimum parameters for the gripping jaws within the collet for a collet of conventional dimensions and requirements.
And still a further object of the present invention is to provide an analysis method for improving the gripping strength of the wide variety and sizes of conventional collets.
And yet another object of the present invention is to provide an analysis method for determining maximum collet torgue for a collet configuration having predetermined design parameters, the method being useful in optimizing design parameters of the collet.
Still a further object of the present invention is to provide a system for optimizing collet design parameters, the system being useful in predicting optimum collet parameters to maximize gripping strength of the collet.
It is also an object of the present invention to provide a machine tool collet wherein at least one of the structural dimensions or characteristics of the gripping jaws of the collet is optimized for maximizing the gripping strength of the collet.
Additional objects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the SU~ rl, UT~ SH~

W094/0~3 PCT/US93/0715~ ~
212215~ 4 .
description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. To achieve the objects and in accordance with the purpose of the invent~on, ~s embodied and broadly described herein, a method is provided for optimizing the gripping strength of a collet of the type having a plurality of gripping jaws spaced around a common axis with resilient material between the gripping jaws. The method according to the invention comprises the steps of determining the radial force of the grippinq jaws upon a bar disposed through the collet, the radial force being dependent upon an axial force applied to the collet, and determining the tor~ue developed on the bar from the radial forces of the gripping jaws just prior to a toggle condition occurring between the gripping jaws and the bar. The method further calls for determining the total moment force generated between the gripping jaws and the bar at toggle condition for a given toggle angle. Acaording to the ~method of the invention, the toggle angle is varied until the total moment force between the gripping jaws and bar at toggle condition reaches a maximum value. The method further calls for determining the total torque on the bar from the torgue prior to toggle and the maximum total moment force at toggle condition.
By employing the method of the present invention, an optimum design for a given collet configuration can be determined by varying paràmeters of the collet design and determining the total torque on the bar until a maximum torque value is determined for a given collet configuration.
The present method may be utilized in determining the optimum design for all known collet configurations, including the ER and TG collet configurations.

~94/0~3 PCT/US93/071~5 In a preferred embodiment of the method according to the present invention, the method includes the step of varying the thickness of the gripping jaws for a given collet configuration to determine the thickness of gripping jaw generating maximum total torque for a given collet configuration. Likewise, the method~ay include the step of varying the number of collet jaws for a given collet configuration to determine the number of gripping jaws generating maximum total torgue for a given collet configuration. The method may further include t~e step of varying the jaw material, for example from steel to plastic, to determine the optimum material for maximizing gripping strength.
In further accordance with the purpose of the present invention, a method is provided for determining the optimum design for a given collet configuration and comprises the step of calculating the total torque generated on a bar passing through the collet of a given collet configuration having predetermined design parameters, the total torque including torque generated just prior to toggle occurring between the gripping jaws and the bar and the maximum moment force generated between the gripping jaws and the bar due to toggle. The method also calls for varying at least one design parameter of the collet and recalculating the total torque generated until the total torque generated reaches a maximum value for the given collet configuration.
In further accordance with the purpose of the invention, a system is pr~ovided for optimizing collet , design parameters for a type collet having a plurality of gripping jaws spaced around a common axis with resilient material between the gripping jaws, whereby a bar passing through the collet is securely held by the gripping jaw~.
The system comprises means for variably inputting design parameters of the collet of a given configuration. Means are also provided for calculating the radial force of the collet gripping jaws upon the bar, the radial force bein~

SU~STI~UT~ SH~-tT (~ULE 26) W094/0~3 PCT/USg3/0715~

dependent upon an axial force applied to the collet through a collet holder and collet nut. Means are further provided for calculating the torque developed on the bar from the radial forces of the gripping jaws just prior to toggle between the gripping jaws and the bar.
The system includes means for calculating the ~oment generated due to toggle between the gripping jaws and bar at a predetermined toggle angle. Means are provided for varying the toggle angle in the moment calculating means until the moment generated reaches a maximum value. The system also calls for means for summing the maximum moment at toggle and torque developed just prior to toggle to give a total torque developed on the bar by the gripping jaws for the inputted design parameters of the collet. In this way, the total torque developed on the bar can be maximized by varying at least one design parameter through the design parameter inputting means so that an optimum set of design parameters can be determined.
In a preferred embodiment of the system according to the invention, a computer is provided with the radial force calculating means, torque calculating means, moment calculating means, toqgle angle varying means, and summing means comprising respective software executed by the computer. ireferably, tbe computer includes a library of known design parameters for various known collet configurations for use by the software. The means for variably inputting design parameters is interfaceable with the computer so that at least one of the design parameters of the collet can be varied. Preferably, the computer further includes a library of known parameters for various collet nut geometries, with the radial force calculating means using the collet nut parameters to compute axial force imparted to the collet.
Still in further accordance with the objects of the invention, a collet torque slippage analysis program is ~--94/0~3 2122155 PCT/US93/07155 provided for calculating torque developed ~y a collet held by a collet nut and collet holder.
In further accordance with the invention, a machine tool collet which is actuated by engagement with a conical surface of a collet holder in a collet nut is provided. The machine tool collet comprise~_a resilient material for holding a plurality of gripping jaws in a desired spaced relation. The collet further includes gripping means for optimally holding a machine tool within the collet. The gripping means includes a plurality of gripping jaws held by the resilient material in a desired longitudinally and angularly spaced relation about the longitudinal centerline axis through the collet. The gripping jaws have an exposed inner face parallel to the centerline axis whereby the plurality of gripping jaws define an inner radius of the collet. The gripping jaws also have an angled or slanted exposed outer face whereby the plurality of gripping jaws defines a conical outer surface to engage the collet holder conical surface. The gripping jaws further comprise at least one structural dimension or characteristic, such as thickness, number, or material, optimized for maximizing the gripping strength of the collet.
In a preferred embodiment of the machine tool collet, the gripping jaws have a thickness optimized to maximize the gripping strength of the collet. Likewise, in another preferred embodiment, the gripping jaws are of a precise number optimized to maximize the gripping strength of the collet. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.
~IEr~N OF TRE D~WINGS
Fig. l is a perspective view of a collet according to the present invention, particularly a collet formed according to the process and method of the invention;

SU~ 2~ F~ 2~) W094/0~53 PCT/US93J071~5, ~

Fig. 2 is a partial component view of the collet depicted in Fig. l, particularly illustrating the gripping jaws of the collet;
Fig. 3 is a front end view of the collet shown in Fig. 2;
Fig. 4 is a flow chart diagram depictin~Lthe~
sequence of steps and calculations according to the method and process of the invention;
Fig. 5 is a simplified schematic representation of the system according to the invention incorporating the process and method of Fig. 4;
Fig. 6 is a flow chart diagram depicting the steps and calculations according to the method for calculating torque at toggle condition;
- Figs. 7a and 7b are diagrammatic depictions of collet thread geometries, particularly depicting the analysis parameters used in calculation of axial force;
Fig. 8a is a simplified component view of a gripping jaw cooperating with a collet holder to grip a bar, particularly illustrating the condition of toggle;
Fig. 8~ is a diagram illustrating the contact width between a ~aw and the bar;
Fig. 9 is a diagrammatic sketch particularly pointing out the analysis parameters usPd to calculate torque just prior to toggle;
Fig. lO is another simplified diagrammatic sketch illustrating the concept of roll angle and maximum roll angle used in calculation of torque at toggle condition;
Fig. lla is a detailed diagrammatic sketch ` illustrating the analysis variables used in the calculation of torque at toggle condition; and Fig. llb is a similar to Fig. lla and shows the parameters used in elastic deformation toggle analysis.
- DETAI~ED DE8CRIPTIQN OF T~E PREF~RRED EMBODIMENTS
Reference will now be made in detail to the presently preferred embodiments of the invention, one or more examples of which are illustrated in the ~ ~94/ ~ 53 PCT/US93/0715S

accompanying drawings and figures. Each example is provided by way of explanation of the invention, not limitation of the invention. In fact, it will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope ~ spirit of the invention. For instance, features or steps illustrated or described as part of one embodiment of the method of the invention, can be used on another embodiment of the method to yield a still further embodiment of the method. Thus, it is intended that the present invention cover such modifications and variations as come within the scope of the appended claims and their equivalents. The numbering of components in the drawings is consistent throughout the application, with the same components having the same number in each of the drawings.
The method and apparatus according to the present invention relate to a collet of the type illustrated in Figs. 1 through 3. Collet 10 is actuated by engagement with the conical surface of a collet holder and collet nut (not shown). Those skilled in the art understand the operation of collet 10 with a collet holder and collet nut.
~;Collet 10 comprises resilient material 12 for holding a plurality of gripping jaws 16 in a desired spaoed relation~relative to each other. Preferably, res$1ient material 12 extends through perforations 28 within gripping jaws 16 s~ as to form essentially '~concentric rings of resilient material 12 through gripping jaws 16.
-~`Collet 10 also comprises gripping means A for optimally holding a machine tool within collet 10. In a ~;preferred embodiment, gripping means A comprises a plurality of gripping jaws 16 held by the resilient material 12 in a desired longitudinally and angularly spaced relation about longitudinal centerline axis 18 sues, ~ S~E~T (P~iJ~

W094/0~53 PCT/US93/0715~ ` ~
2122155 lo through collet 10. The gripping jaws have an exposedinner face 20 parallel to centerline axis 18, whereby the plurality of jaws 16 define an inner radius 22 of collet 10. The shaft or bar of a machine tool to be held by collet 10 is inserted through inner radius 2~ of collet 10.
Gripping jaws 16 further include an angled exposed outer face 24 whereby the plurality of jaws 16 define a conical outer surface 26. Conical outer surface 26 matches the conical surface of the collet holder (not shown~.
According to the method and process of the invention described in this section, applicant has determined that the gripping strength of the present collet is significantly increased compared to conventional collets by analyzing the torque generated by the collet on the machine tool or a test bar and optimizinq the design parameters of gripping jaws 16 so as to generate maximum torque for a given collet configuration. Thus, gripping jaws 16 comprise at least one structural characteristic or dimension optimized to maximiæe the gripping strength of collet 10. The structural characteristics or dimension of jaws 16 may include, for example, the thickness of jaw 16, the number of jaws 16 within collet 10, or the type of material from which jaw 16 is formed.
For example, a standard ER25 collet configuration has collet geometries based on DIN sta~dards, such as inner radiuæ, outer radius, angle of outer conical surface, ,etc. Once a particular collet configuration is selected, the industry standards and reguirements are basically dictated by the appropriate engineerinq standards.
However, applicants have determined that by optimizing certain design parameters of the collet gripping jaws, the gripping strength of a collet of that particular configuration can be maximized.
Applicant has also particularly determined that a degree of toggle between the gripping jaws and machine S~STI~U ~ E S~E~ (RUL~ 26) ' ~94/0~3 2 1 2 2 1 S 5 PCT/US93/071~

tool or bar is desirable in that it provides a maximum torque generated between the collet jaws and bar.
Applicant has incorporated this desirable condition in his analysis in determining the optimum design parameters for the gripping jaws for maximizing total torque between the collet and tool held within.
The method and system for implementing the same according to the invention is represented generally in flow chart form in Figs. 4 to 6. The analysis steps indicated in the figures will be discussed in detail below. Table 1 provided below i5 a list of the variables and their meaning and default value used in the analysis steps.

.. ~ . . ~
~ .

2 215 S pcr/us93/o71 Table 1: Variables Analysis Variab~e Program Variable Default Value Meaning Tm~r TN Input Torque applied to nut . _ . _ W w (Calculated) ~esulnng axialforce . .
wjaw WJAW (Calculated) ~suIting ax~alforce _ _ . _ rm RM Inp~t Thread mean radius _ _ _ _ rc RC Input Collet bearing radius (l1I of Table 4 of DIN 6499) _ , ._ fn FN 0.1~ ~ric~ion coef. for nut threads fcb FCB 0.1~ Fricnon coef. for collet thrus~ bearing fc FC 0.1S Fr~cnon coef. for jawlholder interface ~, _ _ _ fD FB 0.1~ Friction coef. for barl jaw interface _ an (CalculatedJ Thread too~h angle (normal to thread) a AM2, ALPHAN, 30. Thread toothangle TANGLE (through screw axts) . -A ` AL~ (Calcula~ed) Lead or helix angle _ ., Pm PM lnput Thread p~tch (h of Table 1 of DIN 6341) . AC, ALPHAC Angle of collet Fr~ial FYJ (Calculatedj Radial Force on bar ~ Frat~aia FYJ (cQlculatedJ Radial Force on bar per j~
ra~laljaWJ; FYJOB f radiall~scg Radial ~orce on bar l l per jaw per segment TCFPW T J (Calculated) Resul~ing torque per jaw due to friction NjaWs N Input Num~er of jaws ~ _ TTJNjaWs TCFjaW Total torque for all jaws due to friction , Rb RB InputRadius of bar t T InputJaw thiclrness 94~05453 3~ 1 2 2 1 PCl/US93/0715~s Table l (.continued).
_ .-- _ hl H1(Calculared) Width of jaw at fronr of t ollet _ . _ ..
h~ HI(Calculated) J¢w width ar ith seg-ment _ Rc~ RClInpu~ Ourer radius offron~
f collet (~ d2 of ~a6le 3 of D1~ 6499) (Rc)i (Calculated) Al~erage outer radius of collet at ith seg-_ ment Ra RA Input Outer radius of back of coflet (~ dll of ~able 3 of DIN 6499) nncr RI CInput Inner radius of collet N~cg NSEG20 Num~er of segments along jaw length b _ B(l cos ac)/Nscg Segment length AL Input Engagement length of collet and collet holder 4ar LBARlnput Engagement length of jaw and bar _ THETA (Calculated) Bar rotation angle DTHETA (Calcufated lncrement in toggle or bar rotation angle THETLM (Calculated) Maximum rotanon angle for ith segment E~w E JAW 30.E+06 Young's modulus of jaw material Vjaw NU J03 Polsson's ra~a of the jaw material . .. : _ _ Ebar EBA~30.E+06 Yaung's wdulus of ., I , ~ , l ~ bar material V~ar NUB 03 Poisson's rano of the bar matenal .. . ...
~carJall BEA~L 350000 Allowable beanng stress of jaw material . .. .
ca~Jj S I GMA (Calculatet)Bearin8 stress at blade corner for ith = segment fFrad al)~ (Fra~tk~l)m FPY (Calculated)New radial force for segmenl and each it~ration m _ ., r. ~

3 13a PCI'/US93/0715~
2 1 2 2~La~ cont in~l.ed ) x, XI (Calcs lated)Moment arm for ith . . ._ . _ MTjaw MTJ (CalculatedJ Moment per jaw due to toggle only ~ MT~OtaI MT ~VjawsMTJaWTotal moment due to toggle only _ . ~ , ~ ..
T~PJJ~ TWOT ~Calculated) Torque per juw just prior to toggle ;~i~ MTWOT NJaws7iPTJ Total torqlle Just prior ro toggle . , _ TTtot~ TT TlpTlD~a4MTtota~ Total torque including to~le . . , ,_ a SCw (Calculated) Semi-contact width for Hertz cont~ct , _ . _ tcoar TCOAT .002 Wetted -surface coating thiclcness of rubber . .
. _. ' . _. .. . . __ . .. __ . . ..... __ ,. .
. , _ r _ .
_ ~ .
. - _ . _ _ , ~ __ S~ t ' ~ 5 t'i~ lL~ 26) '`'094/0~53 PCT/US93/071~

It should ~e understood that tlle ollowing description of the analysis steps according to the method and process o~
the present inYent~on is but a preferred embodiment oE tl1e present m~thod and not meant as a limitatlon thereof. The values calculated ln tlle ~teps may be calculate~ Dr ~ -pred~cted in any manner of proces6, all of w11ich all wlth the scope and 6pirit of this ~nvention. ~ddltionally, t1~e order of analysis steps presented is not l~mlted to tl1e order dlscu6sed but, can include any effective order.
Referrlng to ~ig. 4, the varlous collet parameters and default values are entered at step 69, including collet holder and nut parameters, jaw design variables, material allowable st~e~ses, coe~ficient oE friction for collet nut, holder, and b~r, test bar parameters, etc. ~t step 71 tlle maximum number of gripping ~aws is determined for a given collet configuration and given jaw thickness. The maximum number of jaws is estimated using the inner radius oE tl1e collet, the ~aw thickness, and tlle rubber coating thickne6s on each side o~-the ~aw as follows:
(Np~r~n~ cl( 2~ R~ ) Althougl1 not usad particularly ~n the analysis, the angle of resilient material 12 between the jaws may be calculated a~suming a uniform equal spacinq between the ~aws and a un~form resilient material coating thickness on each jaw Eace acoording to the following equation:
'1 2~oat rubll~r = ~ In/l~r ~ 8 di~cussed above, tl-e co~llet lO is engaged with a collet holder and collet nut (not s1~own in the figures).
Engagement between the colle~ nut and collet 1~older ~mparts an axial force to the collet. ~s a result of thi~ axial force, a radial force is developed between eacl1 jaw 16 an~ a test bar or machinQ tool 8haft througl~ the collet. The ax~al ~orce or thrust developed due to tightenillg oE the ... . . , . . "~, ~ . .

WO94/0~53 PCT/US93/07155 f~j 2122155 `

collet nut onto the collet ~1older is dependent upon tlle geometry of the tllreaded surEaces o~ tl~e collet nut. l'l~e notatlon Eor t~ll6 geometry ls ind~cated in Figs. 7a and 7b.
Tl1e thread geometry parameters may be obtained Erom englneerinq 6tandards, such as the June, l9~9 DIN b~l standard (T~ designation) or ISo 6~ matric scre~ tllread standard (M designatlon). The values for tl1e collet nut tbread geometry parameters obtained or calculate~ fro~ t!~e englneering standards are preferably stored in a library 68 for later retrieval and analys~s.
~ t step 73, the parameters for a partlcular collet conEiguration are defined, pre~er~bly from 6 tored ln formation ln~a library 66 (Fig.3). T1-e collet geometry parameter~ are based on DIN standards and are basically deflned once a particularly collet co11figuration is ~elected. The analyst is prompted to select a particular collet design or configuration and tl1e system or program then de~inec the various geometr~c data needed for t11e analysis. For example, table 2 is provided below as an example of collet geometry standards obtalned from VIN 649 for an 8- cone for an ERll, En25, En32, and En~0 collet de~i~nation.
li~ble 2. Collet Geometry Standslrds from D~ 6499 (8-degree Cone).
Collet ~2-241, dS-~4Op~ dll-24, ll-~ 4~ 4~ 4~ , sign mm mm mm mm mm mm mm :: ERll 11.0 95 7.5 18.0 2.0 2.5 S.0 :ER25 25.0 22.0 18.0 34.0 2.3 S.0 115 ER32 32.0 29.2 23.5 40.0 2.7 5.5 14.9 ER40 ~40.0 36.2 303 46.0 3 ~ ~ 7.0 18.5 The axiali~orce calculatlo11 is executed at step 7~.
The total torque applied to the collet nut on tl~e collet holder equal~ t!-e sum o~ tl1e torque nQcQssary to develop an axlal thrust on the collet and tl~e torque necessary to overcome the collet thrust bearing riction. The applied torque to the collet nut is given by the equation:

~ 94/0~53 PCT/U~93/0715~

16, Tn~ r~(2~ r COS-n---In l~) J~
If the term in~de the parenthesis is de~lned a~:
¦2;l r,~,fn + Lcosa Q ~ rm COS~n ~ fn L~
then using tllQ rela~ionsllip ~or tan 2, tllQ ~nverse relatlon i~ obtained:

Q ~ n~
l ~ ~ + cos~" J
As su~h, the expr~siotl E~r tlle applie~ torque t~ tlle ~llUt may be written as:

Q + W f~bRC - W rm (Q + fcb rRC) tllen solved for the axial force on tlle entire collet W to obtain:

rm (1 ~ f b R~) Now assuming tha~ only tlle j2WS carry any load and tl-~t eac1 ~aw iE identiaal and located ~deally so that ~acll jaw i8 l~aded in the same manner alld in the same amount. That is, the axial force per ~aw is:
wi~ = Vw ~ J~rws It should b~ understood ~hat tll~ ab~ve c~lculat~ons are but o~e means of prQdiatillg the axlal orce spplied to the colle~. The axial force may actually be predetermined and stored in an appr~priate library ~or retrieval and analysis.
The radial force calculation is perormed a~ step 75.
As a result o'f the axial force whicll develops due to the tightening Q~ the collet nut, a normal force develops Sl~ S~ 'JLE c~) W094/0~53 PCT/US93/0715~.r~
212215~

between the collet holder surface and eacll gri~ping jaw~
Tlle total frlc~ional Eorce between the collet jaws a~-~collet holder is the product of this nor~al ~orce and tlle coefficient o~ friction between the -Jaws and collet l~older.
That i6, ~ ~ -r~ V _ rc rJ~v Summ~ng foroes ~n the ax~l and radlal directiolls glves the following two equatlons in two unlcnowns:
t ~ FaT~al = fb F~ Wj~v + FjVa sinczc + fc Fj~a cos~c = O

.
~ ~ Frod~al = FJ",d I ~ FJ)aVcosac + fc FJ~,,aVS~ C = O
From thQ~e two equation6, expresnions for tl~e normal force between the collet holder and eacl~ jaw, for tlle radial ~orce transmitted between ea~l~ jaw and tlle bar, and for tlle axial force are obtained and gi~en by:
wiaW
F.~a v _ _ _ _ ~ ~b +f~)cos~c + (1 -f~)si~~
F~ WV(cosa~ - fcs~c) - . FiaW, = FP~a~V sinac In step 76, the torque due to Coulomb Eriction force per each gr~ppinq ~aw i5 calculqted for tl~e conditlon of no slippage between the bar and gripping jaws. Slippage is essentially the condition wllere the gripping jaws have ~'roc~ed" to such a degree that tlley.are basically no longer apply,~ng force to the test bar`whicll tllerefore is essentlally free to xotate within the collet. ~lle radial force transmltted between tlle ~Jaws and thQ test bar llas asso¢iated f~iational ~orces that develop at tl-e inller ace between eacll ~aw and the bar. Tll~ toxque due to ~lle Coulomb f~iction force per ~aw is calculated as follows:`

TCF Ff R~ = fb Fiad~al ~b `` S~ S i 1 1 U~ S~ (RULE 26~

`~94/05453 PCT/US93/0715~

The total torque developed w~thout ~llppa~e is tl~ls value times the number of ~aw~ ln the collet, according t~ the following~

TCF = ~ VS TjCF = Nja~s FJ~ Rb = ~ s fb FJ~ Rb The torque results from the frlctional forces actlng between the bar and each ~aw edge. Tl-e frictional force is aalculated based on Coulomb's Law of Frictioll whicll ls independent of contact area. ~s such, in this part of tl~e analysis, thQ thickness of the jaw and tl~e engagement lengtl along the inner ace between tlle bar and ~)aw edges do not eEfect tlle torque resultlng ~rom Coulomb frictlon ~orces.
At step 77, it ~s predicted whetller slip will occur between the test bar and tlle jaws based on tlle geometry oE
tbe ~aws. Sl~p will occur wllen:
tanal >fb , whc~ a1 = ~n~l(ht) = ~n-l(R - R~

It ls desired to inform tha analyst w~lether the parameter~
for thR ~aw blade IjQ has selected will re~ult in slipplng betw`een t1le ~w blades and test bar.
.

A8 ~illu~tra~ed in Fig. 8a, at some degree oE slipping etween tbe~aws and bar, the ~aw will "toggle" or "rock"
and 108e contact Witll tlle bar and collet holder at certain points along thQ length of the jaw. ~t toggle conditlon, the contacting sur~ace area w~ll be reduced. ~ degree o~
togglihg between the ~aws and bar may be desired in tJlat torque de~eloped between tl~e ~aws and bar is ac~ually increased.
To accobnt Por differe~lces due to geometric param~ter~
of the ~aws, such as ~aw th1ckness, in the torque " .~

W094/0~53 PCT/US~3/07155; ' 212215~

calculatlon, the conditions "ju~t prior" to toggle are examined accordlng to all ela~tic contact analy61s (ller~zlan Contact ~naly6is). ~asically, tl-e test bar is treated as a long cylinder in contact witll a Elat semi~ Ein1te plane sub~ected to a line oE Eorce P as sllown ~n,F~ 8b.~ The contact reglon between the cyllnder al~d plane is equal to twice th~ semi-contact width (2a) ~or the ent~re cyllnder length. The semi-contact widtll ~a) ls calculated accordlng to the following:

a =
V ~E' where E' = [ ~ ~r + ~_ I

FJaw p =, ~ial L~, Thls approach l~ val~d as long as tbe jaw thlcklless is much larger than twice the 6emi-contact width.
In step 78 according to the present method, torque i8 oalculated at a oondition ~ust prlor to toggle between tlle ~aws and bar. ~s illustrated ln Fig. 9, ~ust prior to toggle occUrrin~, the line oE action o the radial orce 8hlft8 to `the outer corner o each 3aw. Since the depth of the~aw varie~ alonq the engagement length thereo, the dl6tance or height of the segment must be oalculated. ~he engageaent length between tl-e jaw and t~-e collet holder is pro~ected~onto the bar and then tl~is lengtll is divided into a number of ,segments (N~) which may be set at defaul~
value 8uch a~ 20. Then, by summing Eorces in the radial and tangential directions and summlng moments about tl~e center oE the bar, tho torque just prior to toggle for eacll segment is obtnlned. 5ummlnq thes- values for eacl~ seqment gives , SU~S tlTUTE Stli t~ LE 26 ~ 94/0~53 PCT/~S93~07155 tlle total torque just prlor to toggle for eacll ~aw. Tl~ls approach g~ves tlle following equation~:

TjPT = ~, ((FPW~I) Rb(fb + CSaPW(SinClJaW l ~? ) CF + ~((F,ad",l) RbCOSaJ~W(Sjna~
The total torque d~veloped ~ust prior to toggle is tllis value tlmes the number oE ~aws in tlle collet, accord~ng to tlle following:
TJPTJ = Np~vs Tj,pT
Method Y0 further includes step 79 ~or calcul~ting torque at tog,gle conditlon between the jaws and bar. l`lle torque ¢alculation at ~oggle ~ondition analy~is ~s charted in detail in Fig. 6. Since tlle~toggle may not extend along the full le~gth of each ~aw, the ~aw is divided at step 10 into a nu~ber of ~egments N,~g along tlle length thereof.
The calculations proceed as a double loop. For each increment ln ~ar rotation, or "toggle angle," the elastic deformation for each segment oE a jaw is compute~ as well as its radial ~rictional for¢e.
At 8tep 101, the toggle angle Eor each jaw is deter~lned. ~8 81;0WI1 in F~g. 10, tl~e toggle angle is cal~ulated basRd on the semi-contact width obtained from tlle llertz contaat analy8is. The toggle angle is the angle through whlch.a jaw can rotate within the distallce defined by ~h8 ~emi-corltact width. l'lle toygle angle is calculated as ~f ollows: , [ 1~ ab,a~" = tan~l(Ra ) aSC", = a~ ai~V = ap", ~

SU~ T. ~TUTE SHEEl (P~ULE 26) W094/0~3 PCT/US93/071S5~` ~

generated due to elastic deformation of the jaws and torque due to elastic radial (Coulomb friction) force once the jaw edge has "yielded." Thus, the analysis considers plastic deformation of the jaws as well. It should be understood that the type of material from which the jaws are formed will thus effect the t~r~ e at toggle analysis since yielding or plastic deformation is a factor of the allowable stress for the type material.
Material composition of the jaws is thus a design parameter of the jaws which can be varied to optimize the gripping strength of the collet.
The following analysis of the torque calculation at toggle condition is represented sequentially in flow-chart form in Fig. 6. Once the jaw has been segmented at step 100 and the toggle angle calculated at step 101 as above, the analysis is executed for each segment.
Although the calculations will be explained in detail below, the basic steps are as follows. At step 103, the segment Ni is checked for previous yielding and slip. If such occurred, this segment is ignored at 104 and the next segment analyzed, and so forth. If yielding and slip did not occur, the torque for the segment due to elastic deformation is calculated at 105. This torque is summed for all segments at 106. At step 107, the segment is checked for initial yielding. If æuch has not ~occurred,~then no more torque is being generated and, at 108,~ the analysis skips to the next segment. If yielding has o¢curred, the jaw shortening is recalculated at step ; ,10~ to a;ccount for plasti~ deformation. Then, at step 110, slip is checked at the plastic deformation condition. If slip occurs, no torque is generated and the anàlysis skips to the next segment at step 111. If s~ip does not occur, the torque generated due to elastic radial force (Coulomb force) at the yielded condition is calculated at step 112. This torque is summed for all the segmentæ at step 113. The next segment is analyzed at step 117.

SUBST~ E SHEET (RULE 26) ~94/0~53 PCT/US93/07155 At step 114, the total torque at toggle condition is calculated for all jaws from the sums of step 113 and 106. If this total torgue is not a ma~imum valve at 115, then at 116 the toggle angle is incremented at the analysis repeated for that segment. The total torgue at toggle condition is not a maximum if it is ~ess than the previous value, the previous value therefore being the maximum value.
The calculations and instructions for executing the steps just described are as follow~:

Sl~B~'T~TE SHEET ~ULE 2~) WO 94/05453 Pcr/uS93/0~15~ t ~3 Initialize variables IPASS=O. I};'LDj=O for all segments Increment the bar rotanon angle ~ a~ where initial value of ~ car and a~ = abcar andsetlPASS-lPASS+l Calculale the length of each segment along the jaw length assum~g uniform spacing b=l/Ns~g where I is the engagement length of the collet and c~ollet holder.
Calculate ~It = 2t- a - Rb6~

Foreach segment i = 1. Ns~g, first check to see if IYLD; is less than zero. If it is, then this jaw segment is not in contact with the bar and so go to the next segment. If it is greater than or equal to zero then proceed. Set the i~eration counter for segment yielding to zero (m=0) and do the following calculations:
Average outer radius of collet for the i'h segment - (Rj = RCI ~ 2N (R~l ~ R~) Width of jaw at the ith segment hi = (Rc)j--Rb ~ ~lcar where ~cl~ar = RcnnCr ~ Rb Calcula~e the roll angle for the i-h segment ~roll = alcw = tan ~ tan l~hJ
Calculate the maximum rotation angle for ~he ith segment ~-~uu = tsn~l~
If 6~ 2 ~ then go to the next segment.

Angle benveen line AC and Tight edge of j8w (before toggle) for i~h segment (ai)~ - tan ~ I (h~ ~
Length of the line AC for the ith segment before toggle f~
l- cos(a2)j Angle between line A C and right edgè of jaw (after toggle~ for i'h segment (a2n)l = (a2)i + ~
Length of the line A ' C for the i-h segment after to~gle hj cos(~Z 2n) i SUB~TI~-~TE SHEE ~ (RULE 26) D 94/OS4~3 PCI/US93/0715 21~ 21221~;~

Shortening of this diagonal line for the i'h segment averaged over each jaw is (~n)i = 'i (Zn)i Lf (~n~i c O then go to the next segment.

From s~ength of matenals, the defonna~on of an axially loaded member is (PL)/(EA). l~us the force related to this shortening and acing along the line A'C is ~Fzn)j = ( j)mv i where A = 2clb Total radial force at the jaw comer for ~he i'h segment (F~ ((F~ )i + (Fzn)j) CS(a2n)i Bearing stress for the i'h segment (abncar) = ( ~l~i Checlc tor yielding of the ith segment. If ( b~ar)O bca Then calculate the moment ann from the c,enter of the bar to the f~rce ~i = (Rb ~ (hj tan(~2n)i ~ (2 t ~ a) ) ~(a2n)i) sin (a2n) Calculate the moment for the irh segment (M~ = X; (F2n), ~ccumulate the moments for all segments along the jaw MT ~ MT + (M~)~
C;o to rlext segment SliBSTîTl )TE SHEET~(~Ui ~

WO g4/054~3 2 1 2 2 1 5 5 PCr/US93/071~

If it is greater than or equal to the allowable bearing s~ess then decrease the deformations and re-calculate the fo~ce and bearing stress. ,~
Set yield flag rYLDj=lPASS where IPASS is the pass number for incrementing the toggle angle (Sn)m = (~n)i ~ m ~W~ a = (~n)i ~ Si If the new deful .llation is less than zero, then set it to the deformatiûn of the previous estimate (~n)j form = l (S )'n = ~ (~n)i form > 1 Calculate the new force related to tne new shortening (~n)m EjaW Am m ( aJ ) Calculate new total radial force at the jaw corner for the i'h segment ( rad~ (( rr~dia()i ( zn)~ ) ( 2n i Calculate new bearing s~ress (Obcar~in--l ~dl51)~

Check for yielding of the ilh segment. If ('n Y')i > o~
then adjust the iteration counter ~o m=m~l and loop back to re-calculate the def~mations~ the radial force~ and bearing stress.
Ma~num of 100 iterations is set.
.
If this new beanng stress is less than the allowable value for the beanng stress, then the amount of y~elding is dete~mined.

S~Pi~TI, UTE SHEE~ (RULE 26) ' '`3~

t 94/054~3 P~r/uS93/071~5 If this is the in~al yielding (Zcp); = O
then calculate the maximum length of line A'C. At this condi~on the points O, Al, and C are colinear and the line A'C has a maximum length of -~
(Zn)i = (Ln)i ~ ((5n)j + (~n)~
Now assign (Z~p); = (Zn)l Otherwise use the previously calculated value Calculate the elastic shortening of line A'C

d (:~P)j (2 S1n~ Rb) (~P)~ ICD
where kD is the length required for contact.

If d' is greater than zero then calculate the corresponding elastic f~r~e due to this elashc sholtening.

(FV~)I = (Z ~ where A = 2ab Now calculate the moment due to the Coulomb f~iction force for the ith segment (MS); = Rb fb (FZA)j Accumulate the momenE
M7~ = Mr + ~M.');
Go to next segment.

If d' is less than or equal to zero then this segment has lost contact with the bar. Set the yield flag to a negative value IYLD~ = -IYL~;
Go ~o next segment.

Calculate the tot~l moment due to "toggle" for all j8WS in the collet ~T = NPWS MT
Calculate the total torque TT'-al -- TlPaT~ + Ml~al Increment ~ and repeat " toggle" calculations until MT lal is a maximum.

.. . ...... ~ . . , . .~ ,~ .

W094/0~3 PCT/US93/071~S ~

For each increment of toggle angle, the total moment due to toggle is calculated for all jaws in the collet.
If this total moment is not a maximum value, then the toggle angle is incremented and the toggle calculations re-executed until the maximum torque at toggle is determined. The total torque on the bar i~he sùm of the torque just prior to toggle and the total moment at toggle.
The gripping strength of the collet is directly related to the total torque generated on the bar or tool extending through the collet. Thus, it should be understood that by varying the design parameters of the collet jaws and calculating total torque for each parameter change, an optimum set of parameters can be determined for maximizing collet gripping strength. For example, the graph provided below illustrates the effect on total torque, and thus gripping strength, of varying the jaw thickness for an ER25-8 collet configuration in increments of O.Ol inches. It was assumed that the default values of table l are acceptable and that the applied torque to nut on the collet holder was 350 in.-- lbs. It was also assumed that, at most, only lO jaws should be used in the design and that both extremes in bar or tool shaft diameter should be considered. As the graph illustrates, as jaw thickness increases, there is àn increase in total torque ~including toggle) up to a thickness of approximately O.lO inches. Above this thickness, the total torque decreases. The effect of bar diameter on the total torque for a given jaw thickness is also indicated. Thus it should be readily understood how the analysis method and system according to the present invention can optimize jaw thickness to maximize gripping strength of the collet.

:~

SU~ n~ t-, t~.lJLE26) PCr/US93/071!i:~
21221~5 ~8 SO I _ _ __ __ l I~ lc(c~- 0.~5~ l.
0 i~

2~ ~ I;nl~ îc~ I S i;~ ~ \
. A~ lic~ ol~lllo e 35U il~ s I\ \
O cOcfrlcic~l Or tli~lioll 011 ~)nl ~ V. 1~ \\
o Ntlll~l~cr o( ~lw5 3 1O \\
l~ul~l~cr co~ llick~lcss = .~02 iln I
(~l) 0.10 0.15 0.20 0. 5 J;tw lllic~ es~ illCl~CS

The graph provided below illustrates the effect of varying the number of jaws for an ER2508 collet conf~gurat~on assuming a jaw thickne~s of 0.07 inches. ~s the graph shows, generally as the num~er of jaWc increases, there is an increase in total torque. ~owever, between lO
and 14 jaws the total torque increased only 9%. Also, the graph illustrates to 15 ~aws, and depending on the degree of resilient material on the jaw faces, the maximum number o~
jaws may decxea~e.
l~pplie~ t lor-llle ~ 35U ill.-llJs Cos~rlciclll ol ~l icl;oll Ol~ l~nr = ~, î 5 J~w Illlckllcss :~ .07 i~l.
- ~00 llu~ cr con~ u I~ lcss 2 .()02 il).
~ U;ur r~inlllclcr - .315 ill. ; ~/
, ~30~ .

- 20~
/~
/
~/

0. 1 2 3 ~I S 6 7 0 ~ 10 11 12 u Nt~ l)cr or j;lWS
U~E SHE-t~ (RULt ~;)J

W094/054~3 2 1 2 2 1 5 5 PCr/US93/07~

The above graphs illustrate the effect of varying only one parameter while assuming default or constant values for the other jaw parameters. The analysis method may also be executed to determine the optimum combination of parameters, such as thickness, number, and type material, for the jaws of a given configur~t~on. ~
The analysis method of the present invention is preferably configured in a system 50, generally depicted in Figs 4 and 5. Means 52 are provided for varying the jaw parameters so as to optimize particular parameters.
Means s4 are provided for calculating the radial force of the collet jaws upon the bar, as explained above. Means 56 are for calculating torque developed on the bar just prior to toggle between the jaw and bar, also as ëxplained above. Means 58 are provided for calculating the maximum moment at toggle condition and for calculating the total torque developed on the bar 60. In a preferred embodiment, the various means comprise applicable software 64 for executing the calculations with system 50 being a computer, generally 62. System 50 preferably comprises a library 66 of parameters known for the wide variety of conventional collet configurations, and library 68 for collet nut geometry parameters~
Interface mean~, generally 52, are provided for allowing a~n analyst to generate DIN ASME standard data, define default values, input collet parameters, etc.
As described above, the present invention includes a machine tool collet having gripping means for optimally holding a machine tool. The gripping means include jaws I ., I i having at least one parameter optimized for maximizing the gripping strength of the collet. For example, collet 10 may have the number of jaws 16, or thickness of jaws 16, or material composition of jaws 16 optimized. Table 3 below is a list of machine tool collets having qripping meàns for optimally holding a tool according to the appended claims. For a given collet configuràtion, the collets listed comprise an optimized jaw thickness and SU~ TE S'~ RULE 26) . ~94/0~53 2 1 2 2 1 ~ 5 PCT/USg310715~

optimized number of jaws for maximizing the gripping strength of the collet. For example, for an ER25-8 collet configuration, a machine tool collet of the present invention includes ten jaws and a jaw thickness of 0.0745 inches.
Table 3: Collets COLLET JAW NO. OF
MODEL CAPACITY THICKNESS JAWS
TG25 (IN.)0.0469 0.0550 4 1/64" INCRØ0625 0.0550 4 0.0781 0.0550 4 0.0938 0.0550 4 0.1094 0.0550 4 0.1250 0.0550 4 0.1406 0.0550 4 0.1563 0.0550 4 0.1719 0.0550 4 0.1875 0.0550 4 0.2031 0.0745 4 0.2188 0.0745 4 0.2344 0.0745 4 0.2500 0.0745 4 TG50 (IN.)0.12S0 0.0550 4 1/32" INCRØ1563 0.0550 4 0.1875 0.0550 4 0.218~ 0.0550 4 0.2500 0.0745 5 0.2813 0.0745 5 0.3125~ 0.0745 5 0.3438 0.0745 5 0.3750 0.0130 5 0.4063 0.0130 5 0.4375 0.0130 5 - 0.4688 0.0130 5 o.5000 0.0130 5 SIJE~ Tr SHEF~ t~.U~E 26) W094/~53 PCT~US93/0715~ , I
21221~

Table 3 (continued) COLLET JAW NO. OF
MODEL CAPAITY THICKNESS JAWS
TG75 (IN. ) 0.0625 0.0745 4 1/32" INCR. 0.0938 0.0745 4 0.1250 0.0745 , 4 0.1563 0.0745 4 0.1875 0- 0745 4 0.2188 0.0745 4 0.2500 0.1000 4 0.2813 0.1000 4 0.3125 0.10~0 4 0.3438 0.1000 4 0.3750 0.1~00 ~j 0.4063 0.1000 6 0.4375 0.1000 6 .4688 0.1000 6 0.5000 0.1000 6 0.5313 0.1300 7 0.5625 0.1300 7 0.5938 0.13~0 7 0.6250 0.1300 7 0.6563 0.1300 7 0.6875 0.1300 7 0.7188 0.1300 7 0.7500 0.1300 7 TG100 (IN. ) Q.0940 0.1000 6 1/32" INCR. 0.1253 0.1000 0.1565 0.1000 6 .1878 0.1000 6 0.2190 0.1000 6 0.2503 0. ~000 6 0.2815 0.1000 6 0.3128 0.1000 6 0.3440 0.1000 6 SU~S I ~ u t E SH~ET (RU~ 26) ,~ 0~53 2 1 2 2 1 ~ 5 PCT/US93/0715~

Table 3 (continued) COLLET JAW NO.
MODEL CAPAC~TY THICKNESS JAWS
0.3753 0.0745 12 0.4065 0.07~5 . 12 0.4378 0. Q745 ~ 12 0.4690 0.0745 i2 0.5003 0.0745 12 0.5315 0.15U0 8 0.5628 0.1500 8 0.5940 0.1500 8 0.6253 0.1500 8 0.6565 0.1500 ~ .6878 0.1500 8 0.7190 0.1500 8 0.7503 0.2000 9 .7815 0.2000 0.8128 0.2~00 9 0.8440 0.2000 9 0.8753 0.2000 g 0.9065 0.2000 9 0.9378 0.2000 9 0. ~690 0. ~000 9 `1.0003 0.2000 9 TG150 (IN. ) 0.5000 0.1500 3 l/32" INCR. 0.5313 0.1500 3 0.5625 ~ .1500 3 0.5938 0.1500 3 ! , O ~ 6250 0 - 1500 3 0.6563 0~ 1500 3 0.6875 0.1500 8 0.7188 0.1500 8 0.7500 0 ~ 1500 8 0.7813 0.1500 8 0.8125 0.1500 8 SUB~ 3.~, ~` SHEET (P~3 E 26) .. , .. ..... ...... ... . . .. . ~ ... .. . ~ .. . . ~ . .. .

W094/0~53 2 1 2 2 1 S S PCT/US93/071~ , Table 3 (continued~
COLLET JAW NO. OF
MODEL CAPACITY THICKN~SS JAWS
0.8438 0.1500 8 0.8750 0.2000 8 0.9063 0.2000 1 8 0.9375 0.2000 8 0. g688 0.2000 8 1.0000 0.2000 8 1.0313 0.2000 8 1.0~25 0.2000 E~
1.0938 0.2000 1.1250 0.2000 1.1~63 0.2000 - 1.1875 0.2000 ~3 1.2188 0.2000 11 1.2500 0.2000 11 1.2813 0.2000 11 1.3125 0.200~ 11 1.3438 0.2000 ll 1.3750 0.2000 11 1.4063 0.2000 11 1.4375 0.2000 11 1.4~88 0.20~0 11 1.5000 0.2000 ll ERll (~M) 0.50 0.0550 4 0.5 MM INCR. 1.00 0.0550 4 1. 0 0.0550 4 2.00 0.0550 4 2.50 0.0550 4 3.00 0.0550 4 3.50 0.0550 4 4.00 0.0550 6 4.50 0.0550 6 5.00 0.0550 6 Sl.~ i';3T~ S~EET ~F~UI E 26) ~ 94/0~53 2 1 2 2 1 S S PCT/US93J0715~

Table 3 tcontinued) COLLET JAW NO. OF
MODEL CAPACITY THICKNESS JAWS
5.50 0.0550 6 6.00 0.0550 6 6.50 0.0550 ,~ ~ 6 ER16 (MM) 0.50 0.0550 4 0.5 MM 1.00 0.0550 4 & 1 MM INCR. 2.00 0.0550 4 3.00 0.0550 4 4.00 0.0550 5 5.00 O.0550 5 6.00 0.0550 5 7.00 0.0550 B

- 8.00 0.0550 8 g. OO 0.0550 8 ER20 (~M~ 1.00 0.0550 4 1 MM INCR. 2.00 0.0550 4 3.00 0.0550 4 4.00 0.0550 4 5.00 O.0550 6 6.00 O~ 0550 6 7.00 0.0550 6 8.00 0.0550 6 9.00 0.1300 5 10.00 0.1300 5 11.00 0.1300 5 12.00 0.1300 5 ER25 (NM) 1.00 ~ 0.0745 5 1 MM ~INCR. 2.00 0.0745 5 3.00 Q.0745 5 4.00 0.0745 5 5.00~ 0.0745 5 6.00 0.0745 5 7 r 00 O . 0745 5 sues ~ . i U i E SHtET (R'~LE 26) W(~ 94/054~3 PCr/US93/0715~ .

Ta~le 3 (continued) COLLET JAW NO. OF
MODEL CAPACITY THICKNESS JAWS
~ .00 0.0745 10 9.00 0.0745 10 10.00 0.0745 ~`10 11.00 0.0745 10 12.00 0~ 0745 10 13.00 0.2000 5 14.00 0.2000 5 15.00 0.2000 5 ER32 (NM) 2.00 0.0745 5 1 MM INCR. 3.00 0.0745 5 4.00 0.0745 5 5.00 0.0745 5 6.00 0.0745 5 7.00 0.~300 4 8.00 0.1300 4 9 - 00 0.1300 4 1~.00 0.1300 4 11.00 0.2000 4 12.00 0.2000 4 13.00 0.2000 4 14.00 0.2000 4 15. ~0 0.2000 4 16.00 0.2000 6 17.00 0. ~000 6 18.00 0.2000 6 - 19.00 0.2000 6 E~40 ~MM) 3.00 0.1300 4 1 MM INCR. 4.00 0.1300 4 .00 0.1300 4 6.00 0.1300 4 7.00 0.1300 4 8.00 0.1500 4 SU~ I ITUTE SHEE I (RULE 26) V; '~4/05453 2 1 2 2 1 P~r/US93/07 Table 3 (continued) COLLET JAW NO. OF
MODEL CAPACITY T~ICKNESS JAWS
9 . 00 0. 1500 4 10. 00 0. 1500 4 11. 00 0. 1~00 ~' - 4 12 . 00 0 . 1500 4 13 . 00 0. 2000 5 14 . 00 0 . 2000 5 15. 00 0. 2000 5 16 . 00 0 . 2000 5 17 . 00 0 . 2000 5 18 . 00 0 . 2 000 5 19 . 00 0 . 2000 7 - ~0 . 00 0 . 2000 7 21 . 00 0 . 2000 7 2~ . 00 0. 2000 7 23 ~ 00 0 . 2000 7 24 . 00 0 . 2000 7 25. 00 0. 2000 7 ERSO (MM) 10. 00 O. 1300 5 2 NM INCR. 12 . 00 0.1300 5 14 . 00 0. 1300 5 15. 00 0. 1300 5 16. 00 0. 1300 5 18 . 00 0. 1500 5 20. 00 0 . 1500 5 22 . 00 0. 1500 5 24 . 00 ~ 0. 1500 5 26. 00 0 . 2000 7 28 . 00 0 . 2000 7 30 . 00 0. 2000 7 32 . 00 0. 2000 7 . ~ . : ~;. . .

Claims (32)

WHAT IS CLAIMED IS:

1. A method for optimizing the gripping strength of a collet of the type having a plurality of gripping jaws spaced around a common axis with resilient material between the gripping jaws, said method comprising the steps of:
determining the radial force of the gripping jaws upon a bar disposed through the collet, the radial force being dependent upon an axial force applied to the collet;
determining the torque developed on the bar from the radial forces of the gripping jaws just prior to a toggle condition between the gripping jaws and the bar;
determining the total moment force generated between the gripping jaws and the bar at toggle condition for a given toggle angle;
varying the toggle angle until the total moment force between the gripping jaws and bar at toggle condition reaches a maximum; and determining the total torque on the bar by summing the torque prior to toggle and the maximum total moment force at toggle condition;
whereby an optimum design for a given collet configuration can be determined by varying parameters of the collet design and determining the total torque on the bar until a maximum torque is determined for a given collet configuration.

2. The method as in claim 1, further including the step of varying the thickness of the gripping jaws for a given collet to determine the thickness of gripping jaw generating maximum total torque for a given collet configuration.

3. The method as in claim 1, further including the step of varying the number of collet jaws to determine the number of gripping jaws generating maximum total torque for a given collet configuration.

4. The method as in claim 1, further including the step of varying the collet jaw material to determine the type material generating maximum total torque for a given collet configuration.

5. The method as in claim 1, further including the step of varying the thickness and number of gripping jaws, to determine the combination of thickness and number of gripping jaws generating maximum torque for a given collet configuration.

6. The method as in claim 1, further including the step of varying the collet jaw thickness, number of collet jaws, and collet jaw material to determine the combination of thickness, number, and material of gripping jaws generating maximum torque for a given collet configuration.

7. The method as in claim 1, wherein said determining the radial force of each gripping jaw includes determining the axial force imparted to the gripping jaws from engagement of the collet with a collet holder and collet nut and calculating the radial force from the applied axial force.

8. The method as in claim 7, wherein the axial force imparted by the collet nut and collet holder is calculated using known values for the parameters of the collet nut threaded surface.

9. The method as in claim 1, wherein said determining the torque just prior to toggle includes segmenting a gripping jaw into a predetermined number of segments along the length thereof, calculating the torque prior to toggle for each segment, summing the torques for all segments of the gripping jaw, and multiplying the summed torque for the segment by the number of gripping jaws in the collet.

10. The method as in claim 1, wherein said determining the total moment at toggle condition includes segmenting a gripping jaw into a predetermined number of segments along the length thereof, calculating the toggle moment for each segment due to elastic deformation of the segment and the moment due to frictional force between the segment and bar, summing the toggle moments and frictional force moments for all segments along the gripping jaw, and multiplying the summed moment for all segments by the number of gripping jaws in the collet.

11. The method as in claim 1, further including predicting if slip will occur between the collet gripping jaws and bar for the particular geometry parameters of the gripping jaws.

12. A method for determining the optimum design for a given collet configuration for a collet having a plurality of gripping jaws spaced around a common axis with resilient material between the gripping jaws, said method comprising the steps of:
calculating the total torque generated on a bar passing through the collet for a given collet configuration having predetermined design parameters, the total torque including torque generated just prior to toggle condition between the gripping jaws and the bar and the maximum moment force generated between the gripping jaws and the bar at toggle condition; and varying at least one design parameter of the collet and recalculating the total torque generated until the total torque generated reaches a maximum value for the given collet configuration.

13. The method as in claim 12, including varying the gripping jaw thickness to determine the optimum gripping jaw thickness for a given collet configuration.

14. The method as in claim 10, including varying the number of gripping jaws to determine the optimum number of gripping jaws for a given collet configuration.

15. The method as in claim 12, including varying the collet jaw material to determine the optimum jaw material for a given collet configuration.

16. A method for determining maximum collet torque for a collet configuration having predetermined design parameters, said method comprising:
calculating radial force of the collet gripping jaws upon a bar disposed through the collet, the radial force being dependent upon an axial force imparted to the collet from nut torque between a collet nut and collet holder;
calculating torque developed on the bar from the radial forces of the gripping jaws just prior to toggle between the gripping jaws and the bar;
calculating moment due to toggle between the gripping jaws and the bar at a presumed toggle angle;
incrementing the toggle angle and recalculating the total moment due to toggle in a repetitive loop until the total moment due to toggle reaches a maximum; and summing torque developed from the radial forces of the gripping jaws just prior to toggle and the maximum moment due to toggle.

17. A system for optimizing collet design parameters for a type collet having a plurality of gripping jaws spaced around a common axis with resilient material between the gripping jaws, whereby a bar passing through the collet is securely held by the gripping jaws, said system comprising:
means for variably inputting design parameters of the collet of a given configuration;
means for calculating the radial force of the collet gripping jaws upon the bar, said radial force being dependent upon an axial force applied to the collet through a collet holder and collet nut;
means for calculating the torque developed on the bar from said radial forces of the gripping jaws just prior to toggle between the gripping jaws and the bar;
means for calculating the maximum moment at toggle condition between the gripping jaws and the bar; and means for summing the maximum moment at toggle condition and torque developed just prior to toggle to give a total torque developed on the bar by the gripping jaws for the inputted design parameters of the collet, whereby the total torque developed on the bar can be maximized by varying at least one design parameter through said design parameter inputting means so that an optimum set of design parameters can be determined.

18. The system as in claim 17, further comprising a computer, and said radial force calculating means, said torque calculating means, said moment calculating means, said toggle angle varying means, and said summing means comprising respective software executed by said computer.

19. The system as in claim 18, further comprising a library of known design parameters for various collet configurations for use by said software, said means for variably inputting design parameters being interfaced with said computer so that at least one of the design parameters can be varied.

20. The system as in claim 18, further comprising a library of known parameters for various collet nut geometries, said radial force calculating means using the collet nut geometry parameters to compute axial force imparted to the collet.

21. A collet torque slippage analysis method for calculating torque developed by a collet held by a collet nut and collet holder, comprising the steps of:
calculating the maximum number of gripping jaws which can be disposed around the inner radius of the collet;
defining the thread geometry of the collet nut;
calculating the axial force per gripping jaw imparted from the collet nut being tightened onto the collet holder using the collet nut thread geometry;
deriving the radial force per gripping jaw from the axial force per gripping jaw;

calculating the total torque due to frictional force between the gripping jaws and a bar disposed through the collet without slippage between the jaws and bar, the total torque due to frictional force being dependent upon the radial force per gripping jaw, the coefficient of friction, and the number of gripping jaws;
determining if slip occurs between the gripping jaws and the bar based upon the geometry of the gripping jaws and the coefficient of friction between the gripping jaws and the bar;
calculating the total torque developed between the gripping jaws and the bar just prior to a toggle condition between the gripping jaws and the bar, comprising the following steps:
determining the engagement length between a gripping jaw and the bar;
dividing the gripping jaw into a number of segments along the engagement length thereof;
determining the torque per segment by summing the forces generated in the radial and tangential direction and summing moments about the center of the bar for each segment;
determining the torque per gripping jaw by summing the torques per segment; and multiplying the torque per gripping jaw by the number of gripping jaws in the collet;
calculating the total torque developed between the gripping jaws and bar at toggle condition between the gripping jaws and the bar at a first incremental toggle angle, comprising following steps;
dividing a gripping jaw into a number of segments along the length thereof;
calculating the moment generated for each segment due to the degree of elastic deformation of each section of the gripping jaw, and summing the moments for the segments along the gripping jaw;

calculating the moment generated for each segment due to the Coulomb friction force between the segment of gripping jaw and bar, and summing the moments for the segments along the gripping jaw;
summing the total moment due to elastic deformation and total moment due to Coulomb friction force for the gripping jaw to give total torque at toggle for the gripping jaw; and calculating the total torque at toggle for all gripping jaws by multiplying the total torque at toggle for the one gripping jaw by the number of gripping jaws in the collet;
repetitively incrementing the toggle angle and recalculating the total torque at toggle for all gripping jaws until the total torque at toggle reaches a maximum value; and summing the maximum total torque at toggle with the total torque developed just prior to toggle to give a value of total torque with toggle.

22. The method as in claim 21, further comprising the step of varying at least one of the design parameters of the collet and re-executing said program so as to determine the optimum value of the particular design parameter which maximizes the gripping strength of the collet, the gripping strength being directly proportional to the total torque toggle calculated by said program.

23. The method as in claim 22, comprising varying the number of collet gripping jaws in the collet.

24. The method as in claim 22, comprising varying the thickness of the collet gripping jaws.

25. The method as in claim 22, comprising varying the collet jaw material.

26. A machine tool collet which is actuated by engagement with a conical surface of a collet holder and collet nut, said collet comprising:

a resilient material for holding a plurality of gripping jaws in a desired spaced relation;
gripping means for optimally holding a machine tool within said collet, said gripping means comprising a plurality of gripping jaws held by said resilient material in a desired longitudinally and angularly spaced relation about the longitudinal centerline axis through said collet, said gripping jaws having an exposed inner face parallel to the centerline axis whereby said plurality of gripping jaws define an inner radius of said collet, said gripping jaws having an angled exposed outer face whereby said plurality of gripping jaws defines a conical outer surface to engage the collet holder conical surface, and said gripping jaws comprising at least one structural characteristic optimized for maximizing the gripping strength of said collet.

27. The machine tool collet as in claim 26, wherein said gripping jaws have a thickness optimized to maximize the gripping strength of said collet.

28. The machine tool collet as in claim 26, wherein said gripping jaws are of a precise number optimized to maximize the gripping strength of said collet.

29. The machine tool collet as in claim 26, wherein said gripping jaws are formed of a material optimized to maximize the gripping strength of said collet.

30. The machine tool collet as in claim 26, wherein said gripping jaws have a thickness and are of a number optimized to maximize the gripping strength of said collet.

31. The machine tool collet as in claim 26, wherein said gripping jaws are formed of a plastic resilient material.

32. A machine tool collet comprising a plurality of independent longitudinally disposed gripping jaws molded in resilient material around the longitudinal centerline axis through said collet, said collet comprising an angular space between each said gripping jaw optimized for maximizing the gripping strength of said collet, said resilient material occupying at least a portion of said angular space.