BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to an improved method and apparatus for determining a position trim for a shear pro- cess controller while the speed of the material is changing, particularly during acceleration of the shear knife in positioning the shear knife to a shearing operation.

2. Description of the Prior Art

In hot strip mills, a rotary crop shear is in- stalled at the finishing end of a table so that the front and back ends of the material can be squared off before finishing. In order to prevent damage to the shear, the shear knife speed must be synchronized to the strip speed. Generally, this synchronization in speeds for the strip and shear knife is achieved by using a correction signal referred to as a "position trim" on che knife speed reference where the actual knife position is compared to a desired position and the resultant error signal is used to trim the knife speed reference to compensate for the error in the knife position during the acceleration of the shear knife.

This method of knife trimming in order to produce a desired cut of the strip by the shear knife is a function of strip position and strip speed prior to the acceleration of the shear knife. However, these known "position trim" methods do not take into account the fact that the speed of the strip changes or may change during the acceleration of the shear knife prior to the time the shear knife cuts the strip, invariably resulting in an inaccurate cut of the

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strip. Methods other than a "position trim" on the knife speed reference in order to obtain a desired knife cut while the strip speed is changing are also known. But these systems are complicated and oftentimes do not result in an accurate, desired cut in the strip.

Ideally, therefore, in order to make an accurate cut of the strip with the crop shear while the strip speed is changing after the acceleration of the shear knife has occurred, requires a different type of correction signal to adjust the knife speed during the acceleration of the shear knife and, therefore, the position of the shear knife to compensate for this change in the strip speed during the acceleration phase of the shear knife in the shearing cycle. Therefore, there remains a very real and sub- stantial need for an improved method and apparatus for determining a "position trim" which provides a nearly correct position trim signal, particularly when the strip speed changes during acceleration of the shear knife to the time the knife cuts the strip which, in turn, improves the accuracy of the cut.

SUMMARY OF THE INVENTION The present invention has met the above-described need. The present invention provides for the fact that during the acceleration of the shear knife to a speed for the cutting or shearing of a worspiece, the speed of the workpiece may change or, in fact, does change. The invention employs an improved method and apparatus for providing a correction value to adjust the speed and, therefore, the position of a shear knife to compensate for a change in the speed of the workpiece after acceleration of the shear knife has occurred in order to improve the accuracy of the cut of the workpiece by the crop shear. This correction value of the present invention involves an

improved "position trim" value on the knife speed reference, which improved "position trim" value is added to a newly instantaneous calculated acceleration value which is based on the change in the speed of the workpiece after the acceleration of the shear knife has occurred, and which resultant value is used as a speed reference value to the shear knife speed controller.

Additionally, this improved "position trim" value, per se, is based on the newly calculated instantaneous acceleration value. Through the teachings of the present invention, a simple and easy algorithm can be implemented in a microcomputer program of the main control or microproces¬ sor for operation of the crop shear.

It is, therefore, an object of the present in- vention to provide an improved method and apparatus for determining a position trim speed reference for a control for a crop shear knife which results in a more accurate cut of a workpiece.

It is another object of the present invention to provide a method and apparatus for determining a position trim speed reference which compensates for changes in the speed of the workpiece occurring prior to and during accel¬ eration of the crop shear knife in assuming its positioning for the shearing operation. A further object of the present invention is to provide a method and apparatus for producing a more accurate cut of the workpiece by a speed reference signal to the shear knife controller which is based on a position trim reference which has been augmented by a newly calculated acceleration value which, in turn, is based on the set speed for the shear knife for the shearing operation which is a function of the workpiece speed prior to the detection of the change in the speed of the workpiece before the

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acceleration of the shear knife, and on the instantaneous change in speed of the workpiece during the acceleration phase of the crop shear knife.

A further object of the present invention is to provide a method and apparatus for producing a more accurate cut of the workpiece based on a position trim reference which, in turn, is based on a constant velocity and an instantaneous velocity of the workpiece before and during the acceleration phase of the crop shear, which terms are used in a newly calculated instantaneous acceleration value for the shear knife.

These and other objects of the present invention will be more fully appreciated and understood from the following description of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a schematic of a typical rotary crop shear control system employing the present invention;

Figure 2 is a schematic showing several rotational angles of the shear knives from a starting position to a position for the cutting operation;

Figure 3 is a graph pertaining to the present invention showing a speed reference ω_ to a shear drive speed controller vs. the time when the speed of the workpiece is detected; and indicating the angular velocities for the speed reference at certain time intervals;

Figure 4 is a schematic of the present invention illustrating part of a drive control which generates an acceleration signal used to determine the speed reference signal to a shear drive speed controller;

Figure 5 is a graph pertaining to the present invention showing the distances a workpiece travels from a position sensor vs. time for the shearing cycle, and

indicating velocities υ of the strip at certain time intervals; and

Figure 6 is a graph pertaining to the present invention showing a speed reference ω_ to a shear drive speed controller vs. time where a time delay t^ is calculated from the area under the curve; and

Figures 7A and 7B are logic flow diagrams of a subroutine employing the equations of the present invention for determining the new acceleration, a\' and the instantaneous knife travel value, θ„.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is directed, but not limited, to controlling a shear process controller for shearing or cutting the head end and/or the tail end of a workpiece, such as a strip, in a hot strip mill as the strip exits from a roughing mill so that the workpiece is squared off before proceeding to the finishing mill.

Referring first to Figure 1, there is shown a schematic of a typical rotary crop shear control system 10- The strip 11 travels horizontally on roller tables (not shown) in a direction indicated by the arrow to a crop shear 12.

A reference value indicated along line 16 from a shear process controller 14 is a speed reference signal (SRS) to control the crop shear 12 through a shear drive speed controller 18. Rotary crop shear 12 has two rotational drums 20, 22. Drum 20 rotates in a counter¬ clockwise direction for the shearing operation and carries knife set 24. The positioning of knives 24 and 26 in Figure 1 represent a "start" positioning for the rotation of drums 20, 22. Drum 22 rotates in a clockwise direction for the shearing operation and carries knife set 26. Drums 20, 22 are driven by a drive motor 28, a pulse tachometer 30, and a

gearbox 32 in a known-manner. Feedback from the motor 28 and tachometer 30 is fed to shear drive speed controller 18 as indicated along line 19 and to shear process controller 14 as indicated along line 21. The speed of crop shear 12 has to be the same or substantially the same speed as strip 11 in order to prevent damage to the equipment and/or the strip. A safe cut, one in which there is little or no possibility of damage to or the degradation of crop shear 12, must be within limits specified for the application, which typically is about 0.5 meters/second to about 1.9 meters/second. Accordingly, for cuts with a strip speed within the specified limits, the speed of shear knives 24, 26 must be synchronized to the speed of strip 11. Still referring to Figure 1, the components to the top left of shear 12 are used for a head cut for strip 11. The components to the top right of shear 12 are used for a tail cut of strip 11. Hot metal detectors or sensors 34 and 36 are located upstream of crop shear 12. The length of the head cut of strip 11 is controlled by these metal sensors 34 and 36 where metal detector 34 signals the shear drive speed controller 18 of crop shear 12 to rotate shear knives 24, 26 to a start position for the shearing operation, and detector 36 controls the cut by initiating the calculation of the speed reference signal (SRS) along line 16 to the shear drive speed controller 18 to accelerate, after a time delay ^ shear knives 24, 26 to a cut speed. The cut speed is reached when the knives 24, 26 of shear 12 first contact the strip 11. Figure 2 illustrates the starting position for knives 24, 26 as represented by point A and the cutting position as represented by point B. In Figure 2, the start of rotation for shear knives 24, 26 is indicated at point "A", and the position for shear knives 24, 26 relative to

strip 11 for the shearing operation is indicated at point

"B" whereby knives 24, 26 touch strip 11.

The several angles for the rotation of shear knives 24, 26 are represented by θ, θ . and θ*; where θ is the actual distance shear knives 24, 26 have travelled, since knives 24, 26 commenced rotation; θ is the total distance shear knives 24, 26 must travel from point "A" to point "B", and θo - θ , which is the difference between 0o.- and θ, and which represents the travel remaining for knives 24, 26.

It is to be appreciated that 0, 0 _o , and 0* are arbitrarily represented in Figure 2, and can represent any angle or amount of degrees for the rotation of knives 24, 26. The cut speed is defined as follows:

Cut speed = strip speed + lead speed (1) where the strip speed is determined by pulse tachometer 38, and measuring rolls 40, 42 and fed to controller 14 along line 41, and the lead speed is set by speed rheostat 43 (Figure 1) which lead speed is generally from about zero to 30% of the strip speed.

At time t, knives 24, 26 must be at cut speed, which is point 3 in Figure 2. At constant strip speed, the value for the time t is determined by the following relationship: = (dd + 1 - (dia. x sin 3))/strio soeed (for a head cut) (2)

2 where dd is the distance from metal detector 36 to the center line of crop shear 12; 1 is the cut length set by the cut length rheostat (not shown), which generally ranges from about

0 to 50 centimeters; dia. is the diameter of shear knives 24, 26 respectively; 3 is shown in Figure 2 and is the angle from point B (Figure 2) which is when knives 24, 26 first touch strip 11 until knives 24, 26 are at a vertical dead center position during the cut (typically, 3 is about 14 to about 18

degrees, depending on the thickness of strip 11); and t is the time from when strip 11 is at the detector 36 to the start of the cut, which is point B in Figure 2.

The length of the tail cut for strip 11 is controlled similarly to the length of the head cut, except that the strip speed is detected by a set of pinch rolls 44 and 46 and a pulse tachometer 48. The sensed speed of strip 11 is fed along 49 to controller 14. At constant strip speed, t is determined for a tail cut by the following relationship: t = (dd-l-(dia. x sin 3 ))/strio speed (for a tail cut) (3)

2 where these terms are the same as those in the expression (2) for the head cut.

Rotary crop shear 12 follows the physics of rotational kinematics for a particle on a circle where the angle 9 is the angular position of the particle with respect to a reference position. A positive sense of rotation may be chosen so that θ increases for counterclockwise rotation and decreases for clockwise rotation. If shear 12 is rotating counterclockwise, at time t, the angular position of a particle or location on the shear , a its angular position is 9,. The angular displacement for this location then is 9,b - 9a = 9 during ³ the time interval t^- _a = t. The average angular speed ω of the particle or location in this time interval is defined as

ω = 3 _a - 3 _fa = Δθ (4) b ^{" =} a Δt

The instantaneous angular speed _. is defined as the limit approached by this ratio as Δt approaches zero.

_j = im _A „ ,„

_ΔΘ_ = dθ ( D) t -o Δ t dt The average angular acceleration a of the particle or locati r. is defined as:

_ , b ω — ω a = Δω . _c

^{01 "} . D - t a Δt ^{( 6 )}

The instantaneous angular acceleration is the limit of this ratio as Δt approaches zero, or α = Lim Δω _ dω t *o Δt dt ( 7 ) These principles and the operation of a rotary crop shear 12 are well known to those skilled in the art.

The present invention will now be discussed with further reference to Figures 1 and 2, and to Figures 3-7b, which pertain particularly to the present invention. Referring now to Figure 3, there is shown a graph depicting along the vertical axis the angular speed ω_ which is the reference to the shear drive speed controller 18 of Figure 1, and which has a linear relationship with respect to time which is along the horizontal axis. Line A of the graph of Figure 2 depicts the calculated acceleration of shear knife

12 to its angular speed ω in order to reach its cutting position (point B of Figure 2). This cut speed _oc at t •_— is based on the speed of strip 11, and is calculated according to the well-known principles in the art. During this acceleration, at some point (ω ,t) indicated along line A, the strip speed changes. The time at which the change in strip speed occurs is indicated at t along the x-axis. The change in strip speed is detected and in accordance with the teachings of the present invention, new values for the angular speed of the shear knife 24, 26 at the shearing position and for the time to cut, which is represente in Figure 3, as being .. \' , t _c \' are calculated based on the strip position and the changed value of the speed of strip 11, more about which will be discussed hereinafter. Line B in Figure 3 represents in a linear fashion the new values _J \' ,

.0 -

t _c \' for the acceleration for shear knives 24, 26 from the point (ω,t).

In view of the change in speed of strip 11, a new acceleration for the rotation of shear 12 is calculated based on the point (ω ,t) which represents when the change of the speed in strip 11 while the shear knife is accelerating occurs. The system in the mill which calculates the values for ω at t _c prior to the change in the strip speed now calculates during the acceleration of shear knives 24, 26 new values ωc\' at -\' for the desired angular velocity for the shear knives for cutting strip 11. A new acceleration a\' for the shear 12 is calculated based on ωc\' , t\'"—., ω, and t.

Specifically, the new acceleration a ¹ is derived according to the following expression: a\' = to \' - ω (8)

- t where a ¹ is the instantaneous acceleration, ω \' is the desired angular speed for knives 24, 26 for the shearing operation of strip 11 in view of the change in the speed of strip 11 during the accelerating of shear knives 24, 26, ω is che calculated angular speed reference to shear drive speed controller 18 of Figure 1 when the change in the speed of strip

11 actually occurs, t\' *~ is the time factor for ω\' c, and t is the time factor for ω.

Figure 4 shows the manner in which the new acceleration a\' value derived according to the teachings of the present invention is employed in the control circuit for shear 12. This new acceleration value a\', which is always greater than zero, is added to a "position trim" signal, which position trim signal is identified at numeral 50, by a summing device 52 which device 52 generates an acceleration reference signal, ARS. This resultant acceleration reference signal, ARS goes into a speed reference calculator 53 which calculates the speed reference signal SRS, based on the signal ARS, and a scan time of a microprocessor. As shown in Figure 1, the SRS signal is

the signal from shear process controller 14 to control shear drive speed controller 18.

Still referring to Figure 4, a further explanation a to the manner in which the position trim signal 50 is derived will now be given.

A summing device 54 receives two signals. One signa is represented to the left of Figure 4 as being θ* which as discussed hereinbefore with reference to Figure 2 is the amoun of travel remaining for shear knives 24, 26 to reach the cutting position at point B. A second signal to summing devic 54 is represented in Figure 4 as being θ,, which is a calculated instantaneous knife travel value based on the terms used in calculating the new acceleration value, a\'. More specifically, θ, is determined according to the following expression: θ = (t _c \' - t) (ω _c \' + ω) ₍₉₎

2 where 9, is a calculated instantaneous amount of travel shea knives 24, 26 have to travel in view of the change in the spee of strip 11 after acceleration of the shear knives 24, 26; !_> \' and t \' represent the desired angular velocity and time, respectively, for shear knives 24, 26 in order to attain the cutting position at point 3 in view of the change in the speed of strip 11 during acceleration of the shear knives 24, 26; and ω and t represent the calculated angular speed reference to the shear drive speed controller 18 and the time, respectively, at the moment in time when the strip speed cnanges during acceleration of shear knives 24, 26, as discussed hereinbefore.

The values for 9* and <_J,, are algebraically summe in summing device 54 to produce an error signal indicated at 56. This error signal 56 is modified by an adjustable gain term "Kp" identified at number 58 to produce the position trim signal 50, which is then algebraically added to the newly calculated acceleration value a\' as discussed hereinbefore.

The gain term "K " is a constant and is set up for the positioning of knives 24, 26 during the start up of shear 12.

The speed reference signal (SRS) to the shear drive speed controller 18 is determined from the acceleration output signal (ARS) of summing device 52.

Referring to Figure 5, the new values for the angular velocity and time, ωc\', t\'- \' , respectively, for shear knives

24, 26 in view of the change in speed of strip 11 are calculated. The value for ωc\' is derived from the following ^~ exDression; _u ^■ = ( ¹ + v ) x _2_ x _1 (10) ^{c *J} (dia. ) cos β where v\' is the instantaneous speed of strip 11 after the detection of the change in the speed of strip 11; v _L is the lead speed which, as discussed hereinbefore, is set by the speed rheostat 43 of Figure 1 which is generally from about zero to 30% of the strip speed; dia. is the diameter of knives 24, 26; s is the angle from when knives 24, 26 first touch strip 11 until knives 24, 26 are at their vertical dead center position during the cut, wnich typically is about 14 to about 18 degrees, depending on tne strip thicxness.

The calculation for t _c \' is based on the following expression: t ^Z c\' = t-- + ⁺ So* - S-1. (11) v\' where t is the time when tne change in the speed of strip 11 is detected; S ₀ * is the distance strip 11 travels from detector 36 of Figure 1 to the instance wnen knives 24, 26 first toucn strip 11; S _T is the distance strip 11 travels from sensor 36 when the change in the speed of strip 11 is detected, and v\' is

SUBST

the velocity or speed of strip 11 after the change in the speed of the strip 11 is detected.

Figure 5 shows the terms for the above calculations of expression Nos. 10 and 11. The vertical axis represents S which is the distance strip 11 travels from sensor 36. The horizontal axis represents time in which the strip 11 travels from sensor 36. As can be seen, the velocity v of the speed of strip 11 prior to the detection in the change in the speed of strip 11 is along line A, and the speed v\' of strip 11 after the detection of the change in the speed of the strip 11 is indicated along line B. Line B of Figure 5 for the speed of strip 11 at different time intervals correspond to Line B of Figure 3 for the angular velocity of shear knives 24, 26. Figure 6 depicts the speed reference along the vertical axis and the time along the horizontal axis. A time delay t < _j from when the head (or tailO of strip 11 is at sensor 36 until the start of the acceleration of shear knives 24, 26 can be calculated from the area under the curve where

9 ₀ = ( ) (t _c -t _d ) (12)

where these terms have been defined hereinbefore. A time delay t^ can be algebraically solved from expression No. 12, resulting in _td = tc - 222_ ₍₁₃₎

-c

Figures 7A and 7B show block diagrams for the logic involved in calculating a* and 9. of expression Nos. 8 and 9. The start symbol 60 represents the detection by sensor 36 of a head end or a tail end of strip 11. The logic of the subroutine of Figures 7A and 7B asks, as shown in bloc 62, whether knives 24, 26 are at their cut position, that is, the position when knives 24, 26 first touch strip 11. If the answer is yes, then the subroutine ends, as indicated by the

word "END" along line 64 in Figure 7A. If the answer is no, then the routine proceeds to block 66 as indicated by line 68.

The step of block 66 determines the strip speed, v\' by measuring rolls 40, 42 for a head end cut and pinch rolls 44, 46 for a tail end cut. If the strip speed has not changed then v\' = v. From this step in block 66, the subroutine proceeds to block 70 along line 72. The step in block 70 is to determine the distance the strip 11 travels from sensor 36. From this step in block 70, the subroutine proceeds along line 74 to the next step in block 76 identified as "calculate t _c \' per Eq. (11)". This step calculates t _c \' according to expression or equation No. 11. If the strip speed has not changed then t\' _c = t _c .

The subroutine proceeds from the step in block 76 along line 78 to the next step represented in block 80. This step in block 80 entitled "calculate ω \' per Eq. (10)" calculates ω \' ^* according to equation No. 10. If the strip speed has not changed then ω ¹ = ω . The method of the invention proceeds along line 82 to the next step in block 84. The step in block 84 calculates the time delay t^ required to start the acceleration of knives 24, 26. The time delay t^ is shown in Figure 6 and was discussed hereinbefore. The steps continue from block 84 along line 86 to block 90 which step includes asking whether the time delay t^ has expired. If the answer is no, the subroutine along line 92 returns to the step in block 66. If the time delay t^ has expired, then the subroutine along line 94 proceeds to the next step in block 96, which calculates a\' according to expression or equation No. 8. If the strip speed has not changed at this time, then a\' = a, whereby a was the acceleration of shear knives 24, 26 prior to the change in the strip speed.

SUBSTITUTE SHEET

The subroutine proceeds to the next step of block 100 along line 98 which is shown in Figure 7B. This step deter¬ mines θ, which is the actual position of knives 24, 26 from point A of Figure 2, as discussed hereinbefore. The next step, as indicated along line 101 is that shown in block 103 which is to calculate θ* based on the difference between θ , and θ as discussed hereinbefore. From the step in block 103, the routine proceeds along line 102 to block 104. The step in block 104 calculates 9- which is done by expression No. 9. The next step as indicated along line 106 in block

108 is to determine the position trim signal 50 of Figure 4. As indicated along 110 the next step in block 112 is to calculate the signal ARS of Figure 4. From this step in block 112 the subroutine continues along line 114 to the step of block 115 which calculates the speed reference signal SRS as discussed hereinbefore with reference to Figure 4.

Preferably, the calculations involved in the present invention are implemented in a microprocessor controller (not shown) by an algorithm or algorithms which are simple and easy to devise for the shear process controller 14 of Figure 1 and which are based on the several steps illustrated in Figures 7A and 7B.

The change in the strip speed is detected near the beginning of the microprocessor scan, and during the same scan, the new values for __c\' and t> ^■» \' are calculated, in addition to calculating the new values for the acceleration a\' and the amount of knife travel 9. based on the acceleration a\', as discussed hereinbefore.

The scan of a microcomputer controller is initiated by a timer interrupt routine which is typical for controllers of the type used for calculating the acceleration of shear knives 24, 26. The timer interrupt routine is driven by an internal clock which is programmed to provide an interrupt

every "x" counts of the clock. The scan time is determined by presetting "x" in a software routine. A scan is initiated each time an interrupt occurs. A microprocessor controller maintains the accuracy of the cut of strip 11 by the shear knives 24, 26 when the speed of strip 11 is changing linearly or non-linearly with respect to time.

It is desirable to update the calculation of a\' and the position trim signal 50 soon after a change in strip speed is detected to reduce the time to respond to a change in strip speed. Detecting a change in strip speed near the beginning of the microcomputer scan and updating the acceleration a\' and the position trim signal 50 before the end of the scan meets this objective. Reducing the time to respond to changes in strip speed improves the accuracy of the cut. A microprocessor controller maintains the accuracy of the cut of strip 11 by knives 24, 26 when the speed of strip II is changing linearly or non-linearly with respect to time. The reason being*• that the values for __\' c and t\'c are recalculated during every scan of the microprocessor controller and corresponding updates of the acceleration a\' and the position trim signal 50 are performed in the same scan based on the recalculated values. Thus, the corrections required by a change in the strip speed are updated every scan. The scan time is short with respect to how fast the strip speed changes. Therefore, whether the change is linear or non-linear with respect to time, the required corrections are updated fast enough so that the calculations follow any change in the strip speed.

The fact that the method of the present invention maintains the accuracy of the cut of the strip 11 when the strip speed is changing either linearly or non-linearly is significant. In cases where the change in strip speed with respect to time is expected or required, the anticipated change

is expected to be linear. However, as the strip is driven toward the crop shear 12 by table rollers (not shown) which rollers may not have a good mechanical coupling with strip 11, the strip speed may change non-linearly with respect to time in view of slippage of table rollers. Therefore, it is desirable to have the capability to make an accurate cut whether the strip speed is changing linearly or non-linearly or not changing with respect to time.

It is to be noted that Figures 3, 5, and 6 depict calculations made during one scan of the microprocessor controller. During the next scan, the calculations are repeated except that new values for ω\' C and t\' - are calculated based on the strip speed and stripi distance travelled from the sensor, both updated at the start of the scan. The calculations for an updated a\' and a new position trim signal 50 are made in the same scan .based on the new values for ω\' _c and t\' _c and on the updated values of ω, t, and θ. This iteration begins when the head (or tail of strip 11 is at sensor 36 and continues until knives 24, 26 first touch strip 11. If there is no change in the strip spee during this iteration, then there is no change in __■ C and t„ ^y - , and the values calculated for ω \' and t\' _c are equal to the values calculated in the previous scans for ωc and tc_, as discussed hereinbefore. It is further noted that once the acceleration begins, the value of td (Figure 2) is held fixed at its value, calculated in the scan just prior to the start o the acceleration.

The invention is based on the assumption that shear knives 24, 26 are controlled such that they are accelerating a the start of the cut of strip 11, that is, shear knives 24, 26 are being driven into the cut for shearing strip 11.

It is to be noted that the present invention results in good accuracies of cut length for both constant and changin strip speeds.

Under normal operating conditions, without the incorporation of the invention, a torque step is usually applied to the motor of the shear in order to attempt to reduce the position error of the shear knife caused by the speed of the shear motor lagging behind the speed reference at the startup of acceleration of the shear knife for both constant and changing strip speed. The invention eliminates or reduces this need for implementing this torque step at the start of acceleration. The present invention has been described in the environment of a shear having one knife set. For shears having two knife sets, that is, one knife set for cutting the head end of the strip and another knife set for cutting the tail end of the strip, it is generally required that during a head cut, the knife set for the tail cut clear the tip of the strip before the head cut is made. The present invention improves this clearance between the tip of the strip and the knife set for tail cut.

While the present invention has been discussed in connection with the embodiment thereof, and its designated use, it should be understood that there may be other embodiments and uses which fall within the spirit and scope of the invention as defined by the following claims.

In accordance with the provisions of the statutes, I have explained the principles and operation of my invention and have illustrated and described what I consider to represent the best embodiment thereof.