United States Patent: 3558073

[US Patent & Trademark Office, Patent Full Text and Image Database]

( 6622 of 6622 )

United States Patent	3,558,073
Mukai	January 26, 1971

DIFFERENTIAL WINDING UP SYSTEM

Abstract

A differential winding up system which achieves automatic control during the winding operation with a substantially constant speed characteristic and a gradually reducing tension characteristic. The system includes a supply roll, a winding roll, and delivery means for delivering the material to be unwound from the supply roll and wound on to the winding roll, and has differential transmission means for imparting a plurality of differentially divided outputs from a single drive power source to the delivery means and to the driving means for the winding roll. The differential transmission means includes a plurality of motors connected in parallel with a single pump and either a fluid transmission or differential gear system. The winding roll may be driven concurrently from both its center shaft and the surface thereof.

Inventors:	Mukai; Hideo (Kyoto, JA)
Assignee:	Nishimura Seisakusho Co., Ltd. (Kyoto, JA)
Appl. No.:	04/716,118
Filed:	March 26, 1968

Foreign Application Priority Data


Nov 19, 1965 [JA]			40/71,308

Current U.S. Class: 242/412.1 ; 242/414; 242/415; 242/541.1

Current International Class: B65H 23/195 (20060101); B65h 077/00 ()

Field of Search: 242/75.53,75.5 60/53,(Inquired)

References Cited [Referenced By]

U.S. Patent Documents


2903852	September 1959	Bottoms
2164599	July 1939	Tyler
2181049	November 1939	Douglas
2469004	May 1949	Rosebrough
2753128	July 1956	Thomas et al.
2924869	February 1960	Klein

Primary Examiner: Mintz; Nathan L.

Parent Case Text

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation-in-part application of my copending application Ser. No. 538,648 filed Mar. 30, 1966, now abandoned, under the same title as the present invention.

Claims

I claim:

1. A differential winding up system comprising a supply roll, a plurality of delivering means for the material to be wound from said supply roll, a winding roll, winding roll shaft driving means, winding roll surface driving means and differential transmission means, said differential transmission means including motor means connected in parallel with a single drive power source to thereby impart differential outputs from said single drive power source to each of said plurality of delivering means, said winding roll shaft driving means and said winding roll surface driving means, whereby a winding operation may be automatically controlled so as to have a substantially constant speed characteristic and a gradually reducing tension characteristic.

2. A differential winding up system as defined in claim 1, including brake means in the transmission system of said delivering means for the material to be wound.

3. A differential winding up system as defined in claim 1, in which said differential means comprises a hydraulic drive source and a hydraulic differential output network.

4. A differential winding up system as defined in claim 1, wherein said differential transmission means includes gear reduction means for each of said delivering means, said winding roll shaft driving means and said winding roll surface driving means, and at least one of the transmission ratios of said gear reduction means being set at a preselected value prior to operation of said differential winding up system.

5. A differential winding up system as defined in claim 1, wherein said differential transmission means includes a fluid transmission system for each of said delivering means, said winding roll shaft driving means and said winding roll surface driving means, and at least one of the transmission capacities of said fluid transmission system being set at a preselected value prior to operation of said differential winding up system.

Description

GENERAL BACKGROUND AND OBJECTS OF THE INVENTION

This invention relates to a differential winding up system for winders, especially for winders in which the winding roll is driven both from its shaft and from its surface.

The term "differential drive" or "differential winding up" refers to a drive system in general in which one driving power is divided by differential transmission means to two or more torques of any desired magnitude which are transmitted to different loads such as an unwinding shaft, delivery roller, surface drive roller and winding shaft, whereby the feeding and winding of a material is carried out.

It is among the advantages of the differential winding up system that it produces a performance which is intermediate between the nature of a combined negative delivering and positive winding and the nature of a combined positive delivering and negative winding, so that as the winding diameter is increased, the number of revolutions and the magnitude of torque in each part are varied automatically or, stated more adequately, spontaneously, thus allowing to obtain properties as desired without requiring any external adjustment or control. Moreover, irrespective of the transmission ratio, reduction ratio, etc. of the transmission line, at any value of the roller diameter and winding diameter, the number of revolutions becomes spontaneously matched to assure agreement in peripheral speed for driving, so that a variable speed gear or the like can freely be inserted in the transmission line to optionally change the various values of the transmission line or control them at values having no direct connection with the winding diameter, thereby to create desired variable characteristics.

Further, if such differential transmission means are increased in number, the division into any desired number of desired torques is possible. If the driving force is divided into two equal torques, the winding operation on two winding rolls can be effected with correctness and uniform strength without regard to minor variations in diameter. Thus, if it is divided into more parts to drive individual winding bobbins, a performance of perfect individual drive can be obtained for each bobbin.

Further, a more pronounced advantage of this system is that if a fluid transmission (hydraulic transmission and pneumatic drive method) is used, the whole system can be completed with a very simple circuit structure. In a mechanical case, use may be made of a differential gear system, but this is complicated and requires a large space and hardly provides smooth rotation and allows only two outputs to be obtained from a single apparatus, so that in order to obtain a large number of outputs many differential gear systems are required. As contrasted thereto, with fluid, merely by tapping the piping to provide branches, it is possible to obtain the function of differential transmission means from which any desired number of outputs can be obtained at will. In addition there is no irregularity in transmission and thus the rotation is smooth and the torque is divided with correctness in accordance with the capacity ratio of the motor used. Further, if the motor used is of the variable capacity type, the transmission can be optionally controlled to change the torque characteristics. If the prime mover pump used is also of the variable capacity type, the speed of the whole machine can be adjusted over the range from full stop to maximum speed, without causing any variation in torque and tension. Moreover, even at very low speed, positive and stabilized driving is possible, and also during stop the same magnitude of torque as that during running can be maintained. Besides these merits, there are various additional merits such as absorption of shocks, prevention of overload, applying quick brake, and high transmission efficiency.

The primary object of the invention is to provide an improved and useful differential winding up system for winders in which the above mentioned advantages are obtained.

Another object of the invention is to provide an improved and useful differential winding up system for winders of such type that the winding roll is driven both from its central shaft and from its surface, whereby an automatic control without any adjustment from the outside during a winding operation can be achieved with a substantially constant speed characteristic and a gradually reducing tension characteristic.

A further object of the invention is to provide an improved and useful differential winding up system for winders of such the type that the winding roll is driven both from its central shaft and from its surface, in which the winding operation can be carried out along any gradually reducing tension characteristic as desired at will.

The other objects and advantages of the invention will become apparent from the following detailed description in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a differential winding up system embodying the present invention;

FIG. 2 is a diagrammatic illustration of a hydraulic transmission circuit for a differential winding up system embodying the invention, illustrating an application of the invention to a roll slitting machine which draws a web of material from a first roll, slits it into four strips, and winds the strips onto four winding rolls;

FIG. 3 is a diagrammatic illustration in elevation of the roller arrangement of FIG. 2; and

FIGS. 4 and 5 are graphical representations illustrating the variation in tension and torque as the diameter D of the winding rolls is varied, for the application illustrated in FIGS. 2 and 3.

DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

Referring to the drawings in general, and to the symbols applied thereto, in the case of a hydraulic transmission M denotes a prime mover motor; P a hydraulic pump driven by the prime mover motor M; and M.sub.I, M.sub.II and M.sub.III denote hydraulic motors connected in parallel to the hydraulic pump P and adapted to rotate by center drive a delivery roller R.sub.1, winding roll R.sub.2 and intermediate delivery roller R.sub.3 through reduction gears G.sub.I, G.sub.II, G.sub.III, respectively. A material F to be wound such as yarn, cloth, paper, film or foil supplied from a supply or unwinding roll S is wound onto a winding roll R.sub.2 via the delivery roll R.sub.1 and intermediate delivery roll R.sub.3. B denotes a brake acting on the shaft of the delivery roller R.sub.1.

A mechanical transmission as compared with the hydraulic transmission differs therefrom in that in place of the hydraulic pump P and the hydraulic motors M.sub.I, M.sub.II and M.sub.III connected in parallel thereto there is used a differential gear system (not shown), the remaining arrangements being the same.

The number of the revolutions of the motor M is represented by N, the transmission ratios, the diameters of the rolls or rollers R.sub.1, R.sub.2 and R.sub.3 by d.sub.1, D and d.sub.3 (in meters), respectively, the numbers of revolutions of the rolls or rollers R.sub.1, R.sub.2 and R.sub.3 by n.sub.1, n.sub.2 and n.sub.3 (in r.p.m.), respectively the torques of the rolls or rollers R.sub.1, R.sub.2 and R.sub.3 by m.sub.1, m.sub.2 and m.sub.3 (in K g-m), respectively, the brake torque of the brake by the reference B (in Kg-m), the tension on the material pulled out from the unwinding roll S by T.sub.5, the forces exerted on the surfaces of the rollers R.sub.1 and R.sub.3 owing to the torques m.sub.1 and m.sub.3 transmitted thereto by T.sub.1 and T.sub.3, respectively, the tension appearing after coming out of the delivery roller by T.sub.4, and the winding tension at the winding roll R.sub.2 by T.sub.2 (each in K g). Further, referring particularly to FIG. 2 in the case of the hydraulic transmission, the capacity of the hydraulic pump is represented by Q (in 1/rev.), the capacities of the hydraulic motors M.sub.I, M.sub.II, M.sub.III by Q.sub.1, Q.sub.2 and Q.sub.3 (each in 1/rev.), the numbers of revolutions of the hydraulic motors M.sub.1, M.sub.II and M.sub.III by N.sub.1, N.sub.2 and N.sub.3 (in r.p.m.), and the generated torques of the hydraulic motors by M.sub.1, M.sub.2 and M.sub.3 (in K g-m). In the case of the mechanical transmission (not shown), Q'.sub.1, Q'.sub.2 and Q'.sub.3 would represent the output torque ratios or gear ratios, and N'.sub.1, N'.sub.2 and N'.sub.3 and M'.sub.1, M'.sub.2, and M'.sub.3 would represent the numbers of revolutions and output torques of the respective differential outputs, respectively.

In the above, assuming that the material F is to be wound at a speed v (m/min.), then in the case of the hydraulic transmission since the quantity of flow is constant,

Qn = q.sub.1n.sub.1 + q.sub.2n.sub.2 + q.sub.3n.sub.3 (1)

on the other hand, in the case of the mechanical transmission, it follows from the differential characteristics that

(Q'.sub.1 + Q'.sub.2 + Q'.sub.3) N = Q'.sub.1N'.sub.1 + Q'.sub.2N'.sub.2 + Q'.sub.3N'.sub.3 (1') where if Q'.sub.1 + Q'.sub.2 + Q'.sub.3 = Q', the formula (1) holds here as in the case of the hydraulic transmission. Accordingly, in the remainder of the specification reference is made only to the capacities Q.sub.1, Q.sub.2 and Q.sub.3 of the hydraulic motors, it being understood that these capacities are equivalent to the capacities Q'.sub.1, Q'.sub.2, Q'.sub.3 of the output torque ratios or gear ratios of a mechanical transmission system.

The fundamental principle of differential transmission means is that the torque ratio at which the rotation is divided is constant.

That is, Q.sub.1 : Q.sub.2 : Q.sub.3 = M.sub.1 : M.sub.2 : M.sub.3 = constant (2)

Further, m.sub.1 : m.sub.2 : m.sub.3 = M.sub.1 e : M.sub.2 f : M.sub.3 g = Q.sub.1 e : Q.sub.2 f : Q.sub.3 g = constant, where 1/e, 1/f and 1/g are the transmission ratios of the reduction gears G.sub.I, G.sub.II and G.sub.III, respectively.

In this case, even when the three are regarded as being united into one, the condition of positive driving is, of course, maintained. Accordingly, tensions and torques depend solely on the loads. The loads in this case are the unwinding tension T.sub.5 and brake B.

Thus, since the loads are constant,

T.sub.1 + t.sub.2 + t.sub.3 = t.sub.5 + .sup.2b = constant (3)

Now, the present invention makes use of the above mentioned differential drive means as a combined surface drive and center drive winding transmission. In FIG. 11, a winding roll R.sub.2 is in a light contact with a surface contact roller R.sub.3 at the top thereof while a tension T.sub.2 for center drive and a tension T.sub.3 for surface drive act in cooperation with each other, providing an actual winding tension T.sub.4 = T.sub.2 + T.sub.3.

The capacity ratio of the differential drive Ym, is expressed as follows: ##SPC1##

The quantity which has connection with the change is D, while d.sub.3 and d.sub.1 are constant.

Therefore, the capacity ratio Ymv in connection with the speed and the number of revolutions may be expressed as

Further, the quantities having connection with the winding tension are T.sub.2 and T.sub.3 and the quantity having connection with the waste horse power T.sub.1 alone.

Therefore, the capacity ratio Ymt in connection with tension and torque may be expressed as

However, there are various kinds of materials to be wound, some having a high degree of elasticity such as resilient bodies with lasting restorability, some on the contrary being hard with less elasticity, so that it is not always possible (horsepower) given gradually decreasing tension characteristic to obtain optimum wound products for all materials.

The purpose of obtaining any desired gradually decreasing tension characteristics can be attained by changing the capacity ratio in the differential drive for three drive parts.

That is, in the formula,

the quantities Q.sub.1, Q.sub.2, Q.sub.3 or e, f, g may be changed. In case that a hydraulic motor is used, the use of a variable capacity type hydraulic motor will allow continuous change of Q.sub.1, Q.sub.2 and Q.sub.3. In a mechanical case, a continuous variable speed gear or change gear system is effective to change the reduction ratios e, f and g. When the characteristic is to be changed, it is not always necessary to change all the three transmission capacities, it being sufficient to change one or two so as to change the ratios thereof. However, if the sum of the three, i.e., the total transmission capacity is changed, the absolute value of the speed is changed.

A system, shown only by way of example of particular application thereof, which provides a particularly excellent characteristic will now be described. If of the three capacity ratios, the transmission capacity Q.sub.3 g .sup.1 of the surface drive part of the winding roll and the transmission capacity Q.sub.1 e .sup.1 of the material delivering roller part are relatively and associatively adjusted in mutually opposite directions so as to make their sum always constant, then, the curves for n.sub.1, n.sub.2, n.sub.3, v, T.sub.2 and m.sub.2 all remain unchanged, only that T.sub.1, m.sub.1 and T.sub.3, m.sub.3 are changed in mutually opposite directions in proportion to the changes of said two. The winding tension (T.sub.4) is the sum of T.sub.2 and T.sub.3 or, in other words, the constant total load (T.sub.5 + .sup.2B ) minus T.sub.1. Further, the characteristic curves for T.sub.1 and T.sub.3 are the same shape as that of the curve for v and, while maintaining the same shape of curve, are changed in proportion to the whole.

That is, the transmission capacity of the material delivering roller part is changed from zero to the maximum and the transmission capacity of the surface winding drive roller is changed from the maximum to zero so as to make the sum of the two always constant, whereby without producing any influence on the number of revolutions and speed for all parts. It is made possible to change only the winding tension over a wide range covering from a perfectly constant tension characteristic to a gradually decreasing tension characteristic. Moreover, a change of the degree of the gradual decrease of tension in proportion to the above mentioned adjusting amount can be obtained where

The above formula shows that in order to change the winding tension characteristic without producing any influence on the speeds for all parts, the share ratio Q.sub.1 e .sup.1 of the drive power transmitted to the delivering means and the share ratio Q.sub.3 g .sup.1 of the drive power transmitted to the winding roll surface drive means should be selected interrelatively to each other in such a manner that the ratio of the drive power transmitted to the winding roll shaft driving means to total drive power transmitted to the delivering means and the winding roll surface driving means take a predetermined value with respect to a certain selected diameter of the wound roll. It will be understood that the ratio expressed by the above formula represents the winding up characteristic of the system and this ratio is given with respect to a certain selected diameter of the wound roll, for example, an average diameter which is selected at a predetermined value throughout various winding up systems having different winding up characteristics.

In case that the system described is applied to a slitter in which the winding operation is carried out after the longitudinal and continuous slitting operation, through the utilization of oil pressure transmission, it is possible to install any desired number of small size motors for driving winding rolls, and if the winding arms for winding the respective slitted tapes are made independent for each winding, there can be obtained the same performance as that of a perfectly individual, independent friction drive and it is possible to effect the perfectly independent control of the contact pressure between each winding roll and pressure roll, whereby in cooperation with surface drive it is made possible to perfectly slit and wind any materials such as very thin films, slippery articles, laminated paper, worked paper, and foils. Since there is no need of providing a single continuous long winding shaft, it is possible to design and manufacture a large size slitter having a very large machine width, yet allowing very easy handling of such slitters.

Referring now more particularly to FIGS. 2 and 3, there is shown an application of the present invention to a roll slitting machine which draws a material F from an unwinding roll S, slits it by razor blades RB into four strips, and winds them on four winding rolls R.sub.2-1', R.sub.2-2', R.sub.2-3 and R.sub.2-4. This is an embodiment in which a hydraulic transmission system is utilized, and moreover, winding is effected by dividing the material into four differential outputs. As is apparent from FIG. 2, the differential drive described is a very simple drive which effects driving simply by diverting oil from a single pump P to all hydraulic motors M.sub.I, M.sub.III, M.sub.II-1, M.sub.II-2, M.sub.II-3 and M.sub.II-4.

While the winding roll has previously been described as comprising only a single roll R.sub.2, it will be understood that the winding characteristics do not vary whether the material extending over the entire width be wound on a single shaft or divided into several strips and then wound, and conversely, when the latter embodiment is present, the four windings may be calculated as one.

Therefore, the winding rolls R.sub.2-1, R.sub.2-2, R.sub.2-3, R.sub.2-4 have the same diameter D, and the hydraulic motors M.sub.II-1, M.sub.II-2, M.sub.II-3, M.sub.II-4 for driving their central shafts are of the same size and their capacities Q.sub.2-1, Q.sub.2-2, Q.sub.2-3 and Q.sub.2-4 are the same, the total of which may be taken as Q.sub.2. Further, the transmission ratio 1/f of the reduction gear G.sub.II is the same for the four components.

Thus, the diameter of winding roller R.sub.2 is D. Assuming the service or working maximum winding diameter of the machine to be 0.4 m., let

its mean diameter, D.sub.m = 0.4/2 = 0.2 m.;

diameter of roller R.sub.1 be d.sub.1 = 0.25 m.;

diameter of roller R.sub.3 be d.sub.3 = 0.3 m.;

the capacity of the hydraulic motor M.sub.I be

Q.sub.1 = 0.05 liter/rev., and M.sub.III be

Q.sub.3 = 0.015 liter/rev.;

the total of capacities of winding:

While the transmission ratio 1/e for the system of FIG. 2, extending from M.sub.I to R.sub.1 is as described above, if the transmission ratio for the system extending from the brake B to roller R.sub.1 is 1:1, then the numbers of revolutions of the brake B and R.sub.1 are always equal to each other.

If the brake torque on the brake is assumed to be B = 2.5Kg-m, then the load tension applied by the brake B to the material F on the roller R.sub.1 is calculated as follows:

Load tension by brake B is .sup.2B = .sup.2 .times. 2.5 =20 Kg. If the unwinding tension caused by the brake applied to the unwinding roll S is assumed to be T.sub.5 = 40 Kg, then the total load tension is T.sub.5 + .sup.2B = 40 + 20 = 60 Kg.

Then, Q.sub.1 e .sup.1 = 0.015 .times. 2.5 .times. .sub.0.25 = 0.15

Q.sub.2 f .sup.1 0.02 .times. 1.5 .times..sup.1 = .sup.0.03

where, when D = Dm, Q.sub.2 f .sub.Dm = 0.15,

Q.sub.3 g .sup.1 = 0.015 .times. 3 .times. .sub.0.3 = 0.15,

Qn = 0.03 liter/rev. .times. 1432 r.p.m. = 42.96 liter/min.,

It will be seen that the numerical values when D is varied, are shown in FIGS. 4 and 5.

It will be understood that n.sub.1, n.sub.3, v, T.sub.1, T.sub.3, m.sub.1, m.sub.2 and m.sub.3 are different in actual units and are also different in numerical values because the numbers of revolutions and torques are evaluated with different roller diameters. However, they can be shown in curves of the same type, n.sub.2 and T.sub.2 being the same curves having reversed forms.

In the numerical values in this exemplary embodiment, the capacity ratios of the respective differential drives are the same, as shown by,

Q.sub.1 e .sup.1 : Q.sub.2 f .sup.1 : Q.sub.3 g .sup.1

or, 0.15 : 0.15 : 0.15

or 1 : 1 : 1

Therefore, in FIG. 4, when D = 200 mm, T.sub.1 = T.sub.2 = T.sub.3.

As also described before, this capacity ratio is proportional to the driving tensions T.sub.1, T.sub.2, T.sub.3 on the respective rollers as described above, and in addition, it is proportional to the ratio of distribution of the driving power (horse power) of the differential drive and also to the ratio of distribution of the flow quantity of oil from the hydraulic drive. Therefore, for the horsepower and the flow quantity of oil, the changes in the values as they are distributed into three are entirely the same curves and the same proportions.

Ymv and Ymt, described before, are now as follows:

With Ymv = .sup.1, unchanged, if one of Q.sub.3 g .sup.1 and Q.sub.1 e .sup.1 is increased with the other decreased, Y mt will greatly vary, through Ymv remains constant.

n.sub.1 is expressed as follows:

n.sub.1 will maintain an unchanging curve if Q.sub.1 e .sup.1 = Q.sub.3 g .sup.1 is maintained constant and the respective values are varied. The same holds true for n.sub.2, n.sub.3 and v.

However, as to T.sub.1, T.sub.2, T.sub.3, m.sub.1, m.sub.2 and m.sub.3, if Q.sub.1 e .sup.1 is increased and Q.sub.3 g .sup.1 decreased, T.sub.1 and m.sub.1 increased while maintaining the same curve as a whole, and T.sub.3 and m.sub.3 similarly decrease.

Thus, as is apparent from FIG. 4, since the winding tension T.sub.4 is the sum of tension T.sub.2, due to the central drive, and tension T.sub.3, due to the surface drive, or T.sub.4 = T.sub.2 + T.sub.3, and since T.sub.1 + T.sub.2 + T.sub.3 = T.sub.5 + .sup.2B = (total load tension), it also follows that T.sub.4 = (T.sub.5 + .sup.2B ) - T.sub.1.

Therefore, without changing Q.sub.2 f .sub.Dm , if Q.sub.1 e .sup.1 is reduced to zero and Q.sub.3 g .sup.1 is doubled, then T.sub.2 will not change and T.sub.1 = 0. Hence, T.sub.3 becomes a doubled or "two-times" curve, and T.sub.4 = T.sub.2 + T.sub.3 = T.sub.5 + .sup.2B = constant, thus providing a constant tension characteristic. Similarly, if Q.sub.1 e .sup.1 is doubled and Q.sub.3 g 1 is reduced to zero, then T.sub.2 will not change and T.sub.1 becomes a doubled curve and T.sub.3 becomes zero. Thus, T.sub.4 = T.sub.2 + T.sub.3 = T.sub.2 = (T.sub.5 + .sup.2B ) = T.sub.1, so that the winding tension T.sub.4 sharply decreases as the winding diameter D increases.

As a result, when Ymv, i.e., the ratio of Q.sub.3 g .sup.1 + Q.sub.1 e .sup.1 to Q.sub.2 g .sub.Dm , is maintained constant and Q.sub.3 g .sup.1 and Q.sub.1 e .sup.1 are respectively changed, it is possible to change only the winding tension characteristics without introducing any changes to the curves for speed and number of revolutions, more specifically previously described herein.

In order to change either Q.sub.3 g .sup.1 or Q.sub.1 e .sup.1 , variable capacity types are used for the respective hydraulic motors to change the capacity Q.sub.3 or Q.sub.1, or alternatively, the transmission ratio g or e may be changed.

Further, since the winding diameter D is a variable quantity, Q.sub.2 f .sup.1 decreases as D increases. As a result,

has no definite value. Thus,

Yv = 0 .about. .infin. as D changes.

Therefore, if D is set at a certain definite real number (e.g., mean dia.Dm) by which D can be represented, there will be obtained a definite value for

at that diameter. It is thus necessary to maintain constant the ratio of Q.sub.1 e .sup.1 + Q.sub.3 g .sup.1 to said certain optional definite diameter. The value of D m itself, however, may be any value.

Finally, the powers transmitted respectively to the material delivering mechanism and surface driving mechanism are (n.sub.1).times.(m.sub.1) or (T.sub.1).times.(v) and (n.sub.3).times.(m.sub.3) or (T.sub.3).times.(v) and since n.sub.1, m.sub.1, n.sub.3, T.sub.1, T.sub.3 and v all increase as D increases, these powers also sharply increase. Therefore, the sum of these two powers also sharply increases.

* * * * *

Current U.S. Class:	242/412.1 ; 242/414; 242/415; 242/541.1
Current International Class:	B65H 23/195 (20060101); B65h 077/00 ()
Field of Search:	242/75.53,75.5 60/53,(Inquired)