- 1 -
`
`Pro-Dex v. Intelligent Automation
`U.S. Patent 7,091,683
`Pro-Dex Ex. 1023
`
`

`

`US. Patent
`
`Jan. 16, 1990
`
`Sheet 1 of 8
`
`4,894,767
`
`Fig. !
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`TORQUE
`
`|
`TORQUE
`
`- 2 -
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`

`

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`US. Patent—Jan. 16, 1990 Sheet 2 of 8 4,894,767
`
`
`
`Fig. 3
`
`TORQUE
`|
`
`
`
`
`
`Fig. 4
`
`
`
`TORQUE
`1!
`=dT
`n/2
`
`dT
`
`(n/2)+ |
`2dT
`n
`
`ANGLE
`
`- 3 -
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`

`

`Sheet 3 of 8
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`4,894,767
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`US. Patent
`
`Jan. 16, 1990
`
`
`TORQUE
`
`Fig.6
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`- 4 -
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`

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`US. Patent
`
`Jan. 16, 1990
`
`Sheet 4 of 8
`
`4,894,767
`
`TORQUE
`
`Fig. 7
`[ S47
`aan
`per
`
`1 pg
`pe
`
`dA —-|'=—
`Pi
`
`
`
`
`
`
`Allin) Aa&n) A3in)
`
`Fig.8
`
`TORQUE
`
`P2
`
`Pn
`
`
`
`- 5 -
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`

`

`US. Patent
`
`Sheet 5 of 8
`
`Jan. 16, 1990
`
`4,894,767 PI
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`P2
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`P3
`
`ag—-— a3 _.
`
`P4
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`
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`- 6 -
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`

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`4,894,767
`
`US.Patent
`
`Sheet6 of 8
`
`Jan. 16, 1990
`1
`Fig. /
`v8
`—— PA
`TORQUE
`
`
`"RQ"
`
`
`
`TORQUE
`
`Fig. l2
`
`PI
`
`
`
`ANGLE
`
`- 7 -
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`

`

`US. Patent
`
`Jan. 16, 1990
`
`Sheet 7 of 8
`
`4,894,767
`
`Fig.13
`30 (MAIN CONTROLLER)
`
`TO
`PRINTER
`
`ro
`DATA
`ANALYZER
`
`
`
`a
`
`af
`
`SO(DATA BUS)
`
`
`
`
`ASSEMBLY
`MACHINE
`
`
`
`PPS]befe
`———,
`
`
`
`: —
`
`
`
`SCREW arp|FesissonDRIVING MOTOR ry
`—
`
`
`(WRENCH
`CONTROLLER)
`
`I/
`
`OR'
`TORQUE
`AMP.
`
`(POWER WRENCH)
`
`
`
`TORQUE TRANSDUCER
`
`ANGLE ENCODER
`
`- 8 -
`
`

`

`
`
`US. Patent—Jan. 16, 1990 Sheet 8 of 8 4,894,767
`
`
`
`TORQUE
`
`14
`
`Fig. 14
`
`aT
`
`
`
`
`
`- 9 -
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`

`

`1
`
`4,894,767
`
`METHODFOR YIELD TIGHTENING OF SCREWS
`
`BACKGROUND OF THE INVENTION
`
`The present invention relates to a method for yield
`tightening of screws to tighten a screw up to the maxi-
`mum ofelastic stress of the screw.
`In the field of screw tightening, attention is now
`being focused on what is called a yield tightening
`method which tightens a screw up to the maximum of
`elastic stress of the screwitself, and thereis also a grow-
`ing tendency toward wide application of the method in
`the actual productionline.
`A physical phenomenon commonly called yield re-
`fers to a phenomenon that as external tensile force is
`applied to, for example, a rodlike object of metal, the
`external force and the elongation of the object are pro-
`portional to each other in the elastic area but in the
`plastic area only the elongation of the object increases
`although the external force does not substantially in-
`crease. In graphical terms, letting the external tensile
`force be represented on the ordinate and the elongation
`of the rod-like object on the abscissa, the externaltensile
`force showsa linear locusat a fixed angle ofinclination
`to the abscissa in the elastic area but in the plastic area
`it shows a locus almost parallel to the abscissa at a very
`small angle thereto. The same phenomenonis observed
`in screw tightening as well. Letting the angle of rotation
`of the screw be represented on the abscissa and the
`tightening torque on the ordinate, the torque locus is
`very close to the locus of the external tensile force
`mentioned above. This phenomenon has long been
`known in the art and a variety of methods have been
`proposed for its application to screw tightening in the
`actual production process.
`Since the yield tightening method permits tightening
`screws with tension maximal to their elastic stress, as
`referred to above, the method is advantageous over a
`conventional method which tightens screws within a
`sufficiently safe range in the elastic area, such as a so-
`called torque tightening method, in that screws of a
`smaller cross-sectional area could be used if they are
`tightened with the same tension as in the above method
`and that the numberof screws used could be reducedif
`their cross-sectional area is the same as in the above
`method. Since almost all
`industrial products have
`blocks or parts assembled together through screwtight-
`ening, it would bring about a considerable advantage in
`practice if the screw size or the number of screws used
`could be decreased by use of the yield tightening
`method.
`However, manydifficulties are encountered in actual
`applications of this yield tightening method. Theoreti-
`cally, a point of refraction on the torque locusis surely
`a yield point, but it is very difficult to correctly find it
`out on an actual torque curve.
`SUMMARYOF THE INVENTION
`
`The present inventionis intended to fulfil the above
`most important requirement for yield tightening and
`hance ensure the detection of the actual yield point
`including unknownfactors, on the basis of a novel con-
`ceptbasically different from the prior art and through
`use of novel logical expressions and methods ofanalysis.
`An object of the present invention is to provide a
`method of analysis for detecting the actual yield point
`which is the prime essential to the yield tightening.
`
`10
`
`40
`
`35
`
`60
`
`65
`
`2
`To attain the above object of the present invention, a
`method is proposed for yield tightening of screws by
`use of a wrenchincluding a device for detecting a tight-
`ening torque in the actual tightening process, a device
`for detecting a tightening angle and an electric motor
`for applying a torque to each screw,a device for driv-
`ing the wrench, and a controller including a device for
`communication with an external device. After the ac-
`tual tightening torque reaches a certain value, an aver-
`age torquerate is obtained by an integration using four
`or more pieces of torque data and is compared with a
`preset target torque rate, judging a yield point. The
`integration is performed for each minimum angle for
`which new torque data can be obtained. The tightening
`process is stopped when the judgement of the yield
`point has been given in succession a larger number of
`times than 4 of the number of torque data used for the
`integration. Further, a value obtained by substrating a
`certain value from the actual tightening angle is inte-
`grated and the area of a right triangle inscribed in the
`area of the integrated value is obtained. Thetightening
`process is stopped also when the difference between the
`integrated value and the area of the right triangle is
`greater than an area calculated using a preset target
`angle.
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`The present invention will be described in detail
`below with reference to the accompanying drawings, in
`which:
`FIG.1 is a graph of an example of an actual fluctu-
`ated torque curve obtained in screw tightening;
`FIG. 2 is a graph which illustrates actual torque
`curves explanatory of the boundary region between the
`elastic area and the plastic area in screw tightening;
`FIG. 3 is a graph which illustrates actual torque
`curves explanatory of obtaining an average torque rate
`using an integration method;
`FIG.4 illustrates a torque/angle graph explanatory
`of obtaining a torque rate in accordancewiththe princi-
`ple of the present invention;
`FIG.5 illustrates a torque/angle graph explanatory
`of differences between the present invention and prior
`art;
`FIG.6 illustrates a graph explanatory of an accept-
`able area enclosed by torque limits and angle limits on
`an actual torque curve;
`FIG.7 is a graph of a torque/angle curve explanatory
`of integration operations according to prior art;
`FIG.8 is a graph of a torque/angle curve explanatory
`of sequences of integration calculations according to
`the present invention;
`FIG.9 is a side view including a section explanatory
`of mutual states of tightening screws;
`FIG.10 is a graph of a torque/angle curve explana-
`tory of a result of tightening screwsin the state shown
`in FIG.9;
`FIG.11 is a graph which illustrates tightening torque
`curves of two screwsin the same application by prior
`art;
`FIG.12 is a graph of a torque/angle curve obtained
`in accordance with the present invention for the same
`application enclosed with reference to FIG.11,
`FIG.13 is a block diagram illustrating and example of
`an apparatus for performing the method ofthe present
`invention; and
`
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`

`

`3
`FIG.14 is a graph of a characteristic curve explana-
`tory of a screw tightening process carried out by the use
`of the apparatus shown in FIG.13.
`DETAILED DESCRIPTION
`
`4,894,767
`
`4
`cated by a curve “B”. It is very difficult to find out
`actual yield points on such curves, with accuracy and
`with certainty. With a view to over-coming the defect
`of the above-mentioned method of calculation, some
`yield tightening methods have been proposed, accord-
`ing to which high and low torque limits are set to the
`actual tightening torque, high and low angle limits are
`set to the actual tightening angle, an acceptable area
`called a green area is set using these limits, and at the
`end of the actual tightening process check is made to
`determine whether the two tightening values stay
`within the acceptable area, thereby preventing an erro-
`neous detection of the yield point.
`However, the actual tightening torque and the actual
`tightening angle are not directly related to the yield
`point and the limits to these values are totally auxiliary
`and merely expedient measures. The first basic require-
`ment of the yield tightening method is to detect the
`actual yield point as accurately as possible. Accord-
`ingly, if little importance is attached to this, then no
`reliable yield tightening could not be achieved, what-
`ever indirect methods may be used for remedying the
`above-mentioned drawback.
`In view of the above principle of the actual screw
`tightening process, the present invention will now be
`described.
`As referred to previously, the actual torque curve
`inevitably takes a complex wavy form undertheinflu-
`ences of various factors. The measurementof the angle
`of inclination of the torque locus between two point
`thereon,i.e. the calculation of the torque rate, for judg-
`ing the inclination of the locus will not only suffer an
`error between the calculated torque rate and the actual
`average one but also lead to a misjudgement”
`In the torque rate calculating technique according to
`the present inventionit is a first requirement to obtain
`the average torque rate from four or more pieces of
`torque data.
`In the screw tightening process the torque curve in
`the elastic area is almost straight and its angle of inclina-
`tion, Le. its torque rate is dependent on the configura-
`tions and physical properties of the screw used and the
`memberto be tightened. In the plastic area the torque
`curveis nearly parallel to the abscissa, and accordingly
`the torque rate is close to zero. In the boundary region
`between theelastic and plastic areas may vary gently in
`some cases and may changeso abruptly in some cases
`that points of refraction can clearly be discerned. More-
`over, a known method proposes a technique which
`detects the yield point by determining how much the
`torque rate and the actual torque rate have changed in
`the elastic area. According to this method, however,if
`the rate used as the criterion for the yield pointis se-
`lected small, then there will be a fear of stopping the
`tightening process before the final yield point
`is
`reached, whereas whentherate is selected large, if the
`torque rate in the elastic area is small, the torque rate
`which is used as the criterion in the plastic area will
`becomenegative, introducing the possibility of tighten-
`ing the screw to the end ofthe plastic area. This method
`is incompatible with the concept of quality control
`regarded as important in recent years.
`Theultimate object of the present invention residesin
`quality control of yield tightening of screws. To attain
`this object, the present invention offers a reliable yield
`tightening method which is free from unstability and
`uncertainty in the detection of the yield point which has
`
`To readily understand the present invention, the prin-
`ciple of an actual screw tightening will first be de-
`scribed. To lookfor the yield pointcalls for two dimen-
`sions of the tightening torque applied to the screw and
`the tightening angle thereof. As is well-known in the
`art, a torque transducer for detecting the tightening
`torque applied to the screw and an angle encoder for
`detecting the tightening angle of the screw are mounted
`on a wrench which applies the tightening torque, and
`these devices convert detected values into electric sig-
`nals for application to electronic circuits.
`In the actual screw tightening process, the actual
`torque curve will be produced in such a complicated
`‘wavy form as shown in FIG. 1 underthe influence of
`surface roughnesses of the contact surfaces of screw
`threads and the contactsurface of the screw head with
`a memberto be tightened, the influence of a dynamic
`vibration which is produced when the wrench applies
`the tightening torque to the screw,and the influence of
`electric noise which is generated when the above-men-
`tioned devices output the detected values after amplify-
`ing them. For implementing the yield tightening, it is
`necessary to find out the point of refraction where the
`actual torque curve leavestheelastic area and enters the
`plastic area. This means the necessity of obtaining the
`angle of inclination of the actual torque curve.
`Generally speaking, two points on the torque locus
`are joined by a straight line and then the angle ofincli-
`nation of the straight line is obtained.
`In FIG.1, letting the angle of inclination between
`points P1 and P2 and the increment torque and the
`increment angle between them be represented by a1,
`dT1 and dA1, respectively, the angle al is given as
`follows:
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`al=dT1/dAl
`
`This angle a1 is commonly referred to as the torque
`rate.
`In a case where the actual torque curve has such a
`complicated wavy form as depicted in FIG. 1, how-
`ever, a seriouserror will occur between the actual aver-
`age torque and the calculated torque rate “a1” accord-
`ing to the sample position where to obtain the angle of
`inclination. To reduce this error, the increment angle
`“dA”on the abscissa mustbe selected large. However,
`where the incrementangle is selected extremely large as
`indicated by “dA2”, evenif the torque rate at terminat-
`ing end portion of the actual torque curve is so small
`that this portion is almost parallel to the abscissa, the
`calculated torque rate “a2” will not become so small
`compared with that “a”, as shown in FIG. 1. Therefore,
`the increment angle cannot be chosen so small nor can
`it be selected so large.
`Theangle ofinclination is usually obtained by the use
`of what is called a differentiation method, but this
`method ofcalculation is not suitable for use in connec-
`tion with such a complicated curve as depicted in FIG.
`1.
`
`45
`
`30
`
`55
`
`60
`
`Furthermore, the locus of the actual torque curve in
`the boundary region between the elastic and plastic
`areas may sometimes be gentle over a wide range, as
`indicated by a curve “A” in FIG. 2, and in some cases
`it may have such a complicated refraction area as indi- .
`
`65
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`4,894,767
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`5
`limited wide application of yield tightening although it
`superiority has been recognized in the art. To this end,
`the refractive index of the torque curve is not used as
`the criterion for the yield point but a preset yield torque
`tate is employed as a target value of the criterion. This
`is based on a theory that the torque curvein the plastic
`area becomesnearly horizontal regardless of the torque
`tate in the elastic area. This is a second requirement of
`the present invention.
`In the calculating process according to the present
`invention, after the actual tightening process has pro-
`ceeded to the rotation angle where the next new piece
`of torque data can be obtained, the new torque data is
`included in the calculation and the oldest torque data is
`removed from the calculation. By this, the calculating
`process can proceed while exchanging torque data one
`by one no matter how many pieces of data may be
`included in the calculation. This is a third requirement
`of the present invention.
`In this iristance,if the whole torque data is exchanged
`for each calculation, no judgement can be made during
`the tightening process until a rotation angle is reached
`wherethe next whole torque data to be calculated can
`be obtained; namely, a dead zone is provided. Since the
`accuracy of stoppageof the tightening process is main-
`tained by stopping the process upon issuance of a stop
`command, the presence of the dead zoneitself impairs
`the accuracyof stopping the process. The third require-
`ment of the present invention is aimed at obviating this
`showtcoming.
`In general, single screw tightening is extremely rare
`and multiple screw tightening takes place in almostall
`cases. In case of tightening a plurality of screws to
`fasten one member to another, the torque curve of the
`respective screw often contains spike-shaped undula-
`tions superimposed on its peculiar wavy locus under the
`influence of tightening of the other screws. The occur-
`rence of this abnormal undulation provides the same
`result of calculation as if the yield point has been
`reached. When this phenomenon occursrelatively early
`in the tightening process, the final tightening angle and
`tightening torque go out of the aforementioned accept-
`able area referred to as a green area, and consequently
`this phenomenon can be dealt with as an error. How-
`ever, when this phenomenon occurs near the actual
`yield point, it is impossible, with the above-said tech-
`nique alone, to detect.the actual yield point. To avoid
`this, the torque rate is calculated by a predetermined
`numberof times and only when the AND operation of
`the results of calculations is YES,it is judged that the
`actual yield point has been reached. The number of
`calculations necessary for this judgement needs to be
`larger than .4 of the number of data to be calculated.
`This is a fourth requirement of the present invention.
`In the basic theory the torque curvein the plastic area
`is nearly horizontal orflat, but this is seen only when the
`coefficient of friction inherent to the screw is always
`constant.In practice, the torque locus in the plastic area
`may remain extremely flat in some cases and tendto rise
`at a certain angle of inclination in some cases. Thelatter
`indicates that the coefficient of friction increases little
`by little as the tightening angle increases. In this in-
`stance,it is feared that the actual torque rate will not
`become smaller than the preset target torque rate, intro-
`ducing the possibility of misjudging that the calculating
`process has not reached the yield point yet; namely, the
`tightening process cannot be stopped. A reliable device
`is needed for preventing this over-tightening. Accord-
`
`— 3
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`30
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`40
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`45
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`wv0
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`55
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`60
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`65
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`6
`ing to a method whichis used in the present invention
`therefor, after the actual tightening process has reached
`one preset torque limit, a value obtained by substracting
`the preset torque value from the actual torque valueis
`integrated as the tightening process proceeds, the area
`of a rightangles triangle inscribed in the integrated area
`is obtained, and when the difference area has exceeded
`a certain value, the tightening process is brought to an
`emergency stop.
`The emergencystop of the tightening process by this
`method is approximately equivalent
`to stopping the
`process when the screw is tightened a certain angle
`after the actual yield point was reached. This is a fifth
`requirement of the present invention.
`The above-described requirements are indispenable
`for establishing quality control of the yield tightening
`procedure. Byfulfilling these five requirements in paral-
`lel with the progress of the tightening process, reliable
`quality control of the yield tightening can be achieved.
`The ultimate object of the present invention residesin
`highly reliable quality control of the yield tightening,
`with a view to promoting the introduction of the yield
`tightening technique into the wide field of screw tight-
`ening.
`A detailed description will be given first of the first
`requirement of the present invention. The defect of the
`conventional calculating method using torque data at
`two points on an unsmooth torque locus, for obtaining
`accurate average torque data, has been described previ-
`ously in connection with FIG. 1. To clarify the superi-
`ority of the calculating technique of the present inven-
`tion over the prior art method, an analysis will be made
`of an effect which would be produced by further inclu-
`sion of the differentiation of torque data between the
`above-said two points on the torque locus. Since this
`method includes torque data at many points on the
`torque locus as shown in FIG.3, it seems that an aver-
`age value very close to the true value can be obtained.
`In FIG.3, letting the average torque rate be repre-
`sented by a, it can be obtained as follows:
`
`a=2(dT/dA)/n
`
`Further, the above can be modified as follows:
`
`[(2dT)/dA/n
`ZdT/dA +n
`
`(1)
`
`(2)
`
`In FIG. 1, however, since it can be defined that
`2dT=T and dA-n, substitution of these values into equa-
`tion (2) gives
`
`a=T/A
`
`Thus, the result of calculation in this case is the same as
`in the case of merely calculating torque data atthe start
`point and the end point on the torque locus, and the
`both methodssuffer the same calculation error for such
`a torque locus as depicted in FIG.1.
`Since thefirst requirement of the present invention is
`to use a method of obtaining the average torque rate by
`integrating four or more pieces of torque data, a value
`approximately close to the actual average torque value
`can be obtained. An equation for obtaining the average
`torque valueis as follows:
`
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`

`7
`
`4,894,767
`
`a=s{° Qt) or 3 ar|e
`
`f2)+1
`n
`
`1
`n/2
`
`(3)
`
`Theprinciple of this equation will be described with
`reference to FIG. 4. The ordinate represents the actual
`tightening torque,
`the torque value at each point
`thereon being represented by dT, and the abscissa rep-
`resents the tightening angle. The torque value is pro-
`cessed for each minimum resolution of the tightening
`angle. Let the number of torque value data to be preset
`be represented by n. The number n needsto be an even
`numbernotless than 4. Dividing a region containing n
`pieces of torque data into two, respective integrated
`values of their areas are such as indicated in FIG. 4. In
`order to obtain the average torque value, the torque
`locus in this region must be regarded as linear. A differ-
`ence in area between the right-and left-hand regionsis
`equal to the sum total of the areas of the hatched por-
`tions. Quadrupling the total area and dividing it by the
`number n, an increment t of the torque is obtained.
`Further dividing it by the number n, the average torque
`rate in this region can be obtained. This is the logical
`contents of equation (3). When the direction ofinclina-
`tion of the locus is reverse from the direction in FIG.4,
`the answer of equation (3) is negative.
`Turning now to FIG.5, it will be described that the
`method using equation (3) is‘superior to the conven-
`tional differentiation method. A value obtainable with
`the differentiation method is as follows:
`
`a=t/A =5/7=0,.7142857.
`
`This value has an error of about 30% because the actual
`torque rate aA is 1. According to equation (3),
`
`a=4[(15-+14417+ 16) —(11-+ 10-4 13-412)//32=4¢-
`62—46)/64=1
`
`This is a correct answer. Since equation (3) uses all data
`in the area of calculation, a value close to the true one
`can be obtained regardless of the shape of the actual
`torque curve.
`Next, the second requirementof the present invention
`will be described in detail. A description will be given
`first of the relationship between the tightening angle
`and the tightening torque.
`Letting the tightening torque, the tightening angle,
`the coefficient of friction of the screw and thestress of
`the screw be represented by T, 6, 4 and o,, respectively,
`the tightening torque T can be given by the following
`approximate expression:
`
`o = K1-0
`T =~ Kl-«p-eo
`
`(4)
`
`where K1 and K2 are constants.
`Tf the constant K2 andthe coefficientoffriction yz are
`constant, then the tightening torque T and the stress of
`the screw or are in direct proportion to each other and
`the stress of the screw o is in direct proportion to the
`tightening angle @ as well. This meansthat the tighten-
`ing torque T and the tightening angle 6 are in direct
`proportion to each. other. However, the stress of the
`screw o has a limit and does not exceeda certain value.
`
`10
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`15
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`20
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`30
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`35
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`45
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`50
`
`55
`
`60
`
`8
`This is called to have entered theplastic area or yielded
`area.
`Whenthe stress of the screw o does not increase after
`having reached its limit, it becomes unrelated to the
`tightening angle 9, and consequently the tightening
`torque T will not increase no matter how much the
`tightening angle @ increase. However, this is a theoreti-
`cal conclusion, and in practice the torque rate in the
`plastic area may somewhatincrease in some cases, as
`indicated by yA and yB in FIG. 2. Judging from the
`relations between aA and yA and between aB and yB
`in FIG.2, it seems as if the torquerate in the elastic area
`and the torque rate in the plastic area are in proportion
`to each other. An analysis of a large quantity of actually
`sample data shows
`
`a(A) = yA, yB a(B) = yA/ad, yB/oB
`
`wherea is a standard deviation of the torquerate.
`The value «(A) is apparently smaller than the value
`a(B). This indicates that the yielded torque rate in the
`plastic area is not in proportion to the torquerate in the
`elastic area and has a fixed deviation independently of
`the latter.
`In many known methods, however, the torque rate in
`the elastic area is used as a reference value for judging
`the yield torque rate.
`This is based on the fact that the yield torque rateis
`always smaller than the torque rate in the elastic area,
`and is intended to prevent erroneous presentting of the
`target value for judging the yield torque rate. In prac-
`tice, however, the torque locusin the elastic area is not
`only smooth as shownin FIG.2 but also complicated as
`shown in FIG. 6. A region “A” on the curve in FIG. 6
`showsa process in which unparallel contact surfaces of
`members to be fastened together are brought close to
`each other by bending moment, and a region “B” oc-
`curs in a case where very small protrusions of the
`contact surfaces or chips of metal still
`remaining
`thereon after cutting undergo plastic deformation by
`plastic stress applied thereto during the tightening pro-
`cess. It is extremely difficult to accurately calculate the
`torque rate between points T1 and T2 on the torque
`curve containing these regions. The torque curveis not
`rare but often seen in the actual production line. Work-
`ing tolerances are always defined for every work-piece
`and errors in its surface roughness and parallelism are
`never zero; therefore, such a torque curve as shownin
`FIG.6, though in varying degrees, naturally exists. The
`conceptofutilizing the torque rate in the elastic area for
`judging the yield torque rate is based on the assumption
`that the torque curve in theelastic area is straight, but
`this concept is apparently wrong because a curve from
`which an accurate torque rate cannot be calculated is
`inevitably involved in the judgementofthe yield torque
`Tate.
`The portion “B” in FIG.6 is a false yielding condi-
`tion, and if the judgement of the yield torque rate is
`started at the point T1, then the portion “B” will be
`judged as the yield point.
`Accordingly, in order to judge the yield torque rate
`with certainty, it is necessary to start the judgement at
`a point wherethe torqueis as high as possible, for exam-
`ple, at the point T2 in FIG. 6, and the target torque
`value must bea fixed preset value in view of the afore-
`mentioned theoretical and statistic conclusions.
`
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`-13 -
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`

`

`4,894,767
`
`5
`
`9
`Next, the third requirement of the present invention
`will be described in detail.
`The first requirement of the present invention is to
`obtain the average torque rate by the integration using
`at least four pieces of torque data, as referred to previ-
`ously. Each torque data are stored for each angle corre-
`sponding to the minimum resolution of the tightening
`angle. Accordingly, the spacing of the individual pieces
`of torque data is the minimum unit of the tightening
`angle. Letting the number ofpieces of data to be inte-
`grated be represented by n, the minimum unit of the
`tightening angle is n—1. If the numberofpieces of data
`for each integration is n, then the angle range by each
`calculation is n—1. If each calculation is performed
`using entirely new data different from that used in the
`previous calculation, then the calculation becomes pos-
`sible after the tightening angle proceeds through n—1.
`Thatis, the integration is performed only at points P1 to
`Pé4at intervals n—1 in FIG. 7. Assuming that the mini-
`mum resolution of the angle is 1° and the number of
`pieces of data is 20, the integration is performedatinter-
`vals n—1=19° alone.
`The third requirement of the present invention is
`intended to obviate the above defect. According to the
`present invention, the actual average torque rate a is
`calculated at the time point where the actual tightening
`process has reached the point P2, and if the calculated
`actual average torquerate is not smaller than the preset
`target torquerate, then the actual average torquerateis
`calculated again for the region “S1” immediately after
`the actual tightening process has proceeded by the mini-
`mum resolution dA of the angle. Thereafter the actual
`average torque rate is calculated for regions “S2” to
`“S4”one after another until the afore-mentioned condi-
`tion is fulfilled.
`Theactual calculating process will be described with
`reference to FIG.8. Atfirst, the actual average torque
`rate is calculated in a region of the angle n—1 from the
`point “P1”to ““P2”. If the calculated value is not smaller
`than the preset target torque rate, then torque data T1 is
`omitted from a data area of a microprocessor for the
`calculation, and when the tightening process has
`reached a point “Pn”, new torque data “Tn”is added to
`the data area of the microprocessor andthe actual aver-
`age torque rate a is newly calculated. In this way, the
`calculating process is repeated for each resolution unit
`d@ of angle regardless of the numbern of pieces of the
`torque data.
`Next, the fourth requirementof the present invention
`will be described in detail. As referred to previously,
`screw tightening is multiple screw tightening in almost
`all cases. In these cases, the torque and tension of each
`screw are always subject to the influenceofthetighten-
`ing condition of other screws disposed adjacentthereto.
`To clearly explaing this influence, an example of 55
`tightening two screws is shown in FIG. 9. During the
`tightening of a screw #1 the other screw #2 is sub-
`jected to an upward or downward external force “F1”
`or “F2” due to the unparallel contact surfaces of a mem-
`ber “A” to be fastened. The external force “F1” applied
`to the screw produces a positive spike-like torque locus
`“S1” and the external force “F2” produces a negative
`spike-like torque locus “S2” as shownin FIG. 10. Dur-
`ing the actual tightening process proceeding from the
`point “P1” to the point “P2” while performing the
`calculation for each minimum unit “dA”ofthe tighten-
`ing angle, the spike-shaped torque locus “S1” stays in
`the right-handhalf portion “al” of a calculation region
`
`65
`
`20
`
`25
`
`35
`
`10
`“Al”. Accordingly, the area of the portion “al” con-
`taining the spike-shaped torque locus “Si” is large.
`Since the torque rate is obtained by subtracting the area
`of the left-hand half portion from the area of the right-
`hand haif portion, the calculated torque rate “a” is
`larger than in a case where the spike-shaped torque
`locus is not contained. On the other hand,in the actual
`tightening process from the point “P2” to the point
`“P3” the spike-shaped torque locus “S1” lies in the
`left-hand half portion of a calculation region “A2”, so
`that the calculated torque rate “a” is apparently small.
`Also in the actual tightening process from the point
`“P3” to the point “P4”,
`the negative spike-shaped
`torque locus “S2”lies in the left-hand half portion of a
`calculation region “‘A3”, and accordingly the calcu-
`lated torque rate “a” is apparently small. In such a case,
`if the values of the spike-shaped torque loci “S1’’ and
`“S2” are large, the calculated torque rate “a” will be-
`come smaller than the preset target torquerate, leading
`to such a misjudgementas if the yield point has been
`reached.
`Such a misjudgement can be avoided by making a
`rule that the judgement on the yield point is not re-
`garded as valid unless the judgement has been passed in
`succession a plurality of times more than 4 the number
`of data to be calculated. This is the object of the fourth
`requirement of the present invention.
`Finally, the fifth requirement of the present invention
`will be described in detail. FIG. 11 shows tightening
`torque curves of two screws in the same application.
`Even if the screws are identical in shape and used for
`fastening the same member,a difference between their
`inherent coefficients of friction makes a large difference
`in the shape of the torque curve. Whenindividual yield
`torque rates “yA” and “yB”of the two torque curves
`“A” and “B”in FIG.11 are greater than a certain