EP1461169A1

EP1461169A1 - Device and method for bending profiles

Info

Publication number: EP1461169A1
Application number: EP02750952A
Authority: EP
Inventors: Peter SCHÜLE
Original assignee: Individual
Current assignee: Individual
Priority date: 2001-05-21
Filing date: 2002-05-18
Publication date: 2004-09-29
Anticipated expiration: 2022-05-18
Also published as: EP1461169B9; WO2002094470A1; WO2002094469A1; US20040244453A1; US7159432B2; ATE421393T1; DE50213246D1; EP1461169B1

Abstract

In a device and in a process for bending a tube 72 , the tube 72 is guided through a bending tool 71 , which rotates around a section guide housing 81, 82 and also around a cam unit formed by two tubes 83, 84 . Rollers 86 serve as pressing elements, and a mandrel 73 serves as an abutment; as the tube 72 is pushed through the section guide housing 81, 82 between the rollers 86 and the mandrel 73 , it is squeezed to different degrees in different areas of its wall cross section, so that, as a result of the stretching and squeezing of the tube 72 , a bend is produced. The size of the bending radius of the tube 72 to be bent is determined by the eccentricity adjusted via the cam unit and/or by the axial feed of the rollers 86 toward the section guide housing 81, 82 . By means of the bending tool 71 according to the invention, it is possible to produce different bending radii in one and the same bending device in a tube 72 to be bent by changing the feed, that is, the distance between the rollers 86 and the mandrel 73 . No uncontrolled cracks or deformations occur. The bending tool 71 used imposes only minimal limitations on how the tube 72 can be bent in any of 3 dimensions, which means that a section can be bent into any desired shape.

Description

Device and method for bending profiles

The invention relates to a device and method for bending profiles with a profile wall which has wall cross-sectional areas at different distances from the axis of the bend to be carried out, comprising a bending tool with at least one pressure element assigned to the outside of the profile wall, the bending tool being assigned at least one at least one pressure element Has counter pressure element, and wherein at least one pressure element and at least one counter pressure element associated therewith can be moved in relation to one another in the cross-sectional direction thereof by squeezing at least one wall cross-sectional area of the profile wall that is external to the axis of the bend. Such a bending device has become known from DE 689 018.

Various bending devices are known for bending profiles, in which a force above the yield strength of the material is introduced into the workpiece, which then results in a partial stretching of the workpiece on the outside and a compression on the inside and thus a bending due to the dimensional stability of the workpieces causes. This bending process is limited by the structural strength, since if the structural strength is exceeded, the material will crack, dent or buckle. At the same time, the number of degrees of freedom is limited. Machines that use this method particularly in pipes are known as mandrel bending machines, bending presses and multi-roller bending machines. The mandrel bending machines and presses only allow bends whose radii are predetermined by the tool shapes. Multi-roll machines enable variable radii with a helical course, but a relatively large radius / tube diameter ratio (5 to 10) is required here.

In the case of roll stretch bending or round bending, the shape-related design is generated by rotating a core roll while at the same time generating bending moments by pressing the profile onto the core roll. In the case of roll stretch bending, there is an additional superimposition of an axial tensile stress.

A bending machine is known from DE 689 018, in which a tool which interacts with an impact-generating object (for example a pneumatic hammer) is used to bend by driving profile rails. An anvil is assigned two or more movable hammers, which are under the Influence of the impact-generating device and in each case due to their shape and spacing from the anvil designed according to the rail profile act on two adjacent legs of the rail profile in such a way that the rail is stretched according to the desired curvature.

The present invention has for its object to provide a bending device and a bending method that dispenses with axial tensile stresses when bending profiles and allows the bending of any shape.

This object is achieved with respect to the device in that the pressure element (s), as seen in cross-section, are delivered to the counter-pressure element (s) while maintaining a gap with a gap width that is at least in a cross-sectional area smaller than a wall cross-sectional area of the profile to be bent, which is caused by the Gap is transported through.

The device according to the invention thus has the advantage that profiles can be produced in one and the same bending device with different bending radii. A counter pressure element adapted to the profile to be bent, such as jaws, rollers, rollers, mandrel, is fixed in position on the inner walls of the profile to be bent and is arranged in such a way that the counter pressure element is opposite a pressure element that can be delivered to the counter pressure element at different distances. Infeed can also take place from the counter-pressure element to the pressure element, always in such a way that a gap remains between the pressure element and the counter-pressure element, through which the profile to be bent is transported. When transported through the gap the profile or a section of profile is squeezed until the desired bend occurs. By squeezing, the profile wall becomes thinner at the pinched point or over a length section on the profile, and the profile can be compressed at the profile section opposite the pinched profile section. The profile to be bent can still be rotated during a bending process, so that the bending direction of the profile to be bent can also be influenced.

According to the invention, the profile provided for bending is squeezed to different extents by a radially directed application of force to the profile in different wall cross-sectional areas, so that a bending occurs on the profile due to material expansion and compression. The force can be applied via a stamp, roller or roller against a counter pressure element attached to the profile and the material of the profile between stamp, roller or roller and counter pressure element is squeezed to a predetermined extent over the circumference or contour of the profile , During a bending process, the profile to be bent can be pushed in sections or continuously in the axial direction of the profile more or less strongly and / or step by step or at different speeds through the bending device according to the invention, as required.

According to the method designed according to the invention, in the case of a profile, the wall that forms the outer dimension between two tools is compressed, that is, squeezed, in sections by advancing the workpiece (profile) to be bent. The stretching required for bending by compressing (crushing) the wall on one side of the workpiece is thus acts. The material is compressed (squeezed) in the radial direction and consequently causes an expansion in the axial direction, so that a bend occurs in a profile. As a result, compression on the opposite side, for example a pipe wall, can likewise occur in the axial direction of the profile to be bent. With this method, the degree of bending can be set relatively precisely by the corresponding application of force, no striking movements having to be applied in comparison with the prior art and the risk of overstretching being avoided. Pressure elements and counter-pressure elements are fed as close to each other as desired and the bend cross-section allows the bending to be effected as desired. During a bending process, the pressure element and counter-pressure element or elements can be moved in the radial direction in such a way that the gap size and / or the gap shape changes. As a result, the material surface is also in an optically better condition, and no additional tools such as, for example, anti-wrinkle smoothers are required to keep the surface in an optically good condition. By turning the profile to be bent and then compressing it, any bending shapes can be produced. By adjusting the feed and thus the size of the sections, the bend, ie the amount of bend or the bend direction, can also be influenced in a simple manner. The feed is not only intermittent, but can also be continuous. Higher quality surfaces are achieved with profiles to be bent if the force is applied across an upper and / or a lower roller. In order to be able to give the profile any shape, various bends can be achieved in that, according to a preferred embodiment, the force is introduced via the roller surface is different. Due to the one-sided compression (crushing) of the profile, for example on the upper side, the compression (crushing) of the material and thus the change in length in this area occurs only in an edge area, so that a corresponding curvature of the profile can be brought about.

A mandrel is arranged in the profile to be bent, for example a pipe, and the material is compressed between the mandrel and the punch by means of a stamp, i.e. crushed. The stamp is designed so that it is adapted to the outer shape of the profile to be bent and the force is transmitted accordingly. In the case of a continuous bending, the force can also be applied via a roller or a punch in a varying way. The counter-pressure element in the interior of the profile is a mandrel which at least partially abuts the inner surface of the profile and which absorbs the pressure of the movable plunger or the roller.

A correspondingly designed device with which the method can be carried out has a die for guiding the material to be bent, wherein a force-introducing tool (pressure element), for example a stamp, can be moved laterally on the die in the direction of the workpiece and the die also has a counter bearing for the stamp on the underside. Furthermore, a mandrel that can be inserted (inserted) into the workpiece is provided, against which the stamp can be moved (predetermined infeed) in order to compress (squeeze) the workpiece material between the mandrel and the stamp and cause it to stretch in the axial direction. A device for bending profiles has at least one roller instead of the stamp, roller as a force-introducing tool. The force applied to the roller surface can be different.

In preferred different embodiments of the bending device according to the invention, the at least one pressure element is designed as a movable stamp or movable stamp and / or as a movable roller or movable rollers and the counter-pressure element as a mandrel opposite the one or more stamps or the rollers, which at least in sections on the inner circumference of the hollow profile is positionable.

According to the invention, the size and / or cross-sectional shape of the gap can be adjusted. Through a different infeed of the pressure element or elements to the counter pressure element or elements, any gap shapes and sizes can be set, which can cause a wide variety of crushing on the profile wall sections passed through the gap. Bending radii in a wide range and also various bending shapes can be generated.

The profile to be bent can be pushed through and / or pulled through the gap. This has the advantage that, depending on the profile size, material thickness of the profile to be bent and / or profile contour, a wide variety of transport modes can be selected in order to guide the profile to be bent through the gap delimited by pressure and counter pressure elements. It goes without saying that the bending tool (pressure and counter pressure elements) can also be moved axially relative to the profile to be bent, in order to achieve the desired bending on the profile to be bent. The pressure elements can be designed as stamps, rollers and / or rollers, and mandrel shapes, support jaws, anvil configurations, rollers, rollers, etc. are suitable as counter-pressure elements. The counter-pressure elements rest on the inner wall cross-sectional areas of the profile wall to be bent, and it goes without saying that the outer contours of the pressure elements and the counter-pressure elements are adapted to the profile shape to be bent.

In a further embodiment of the bending device according to the invention, one or more rollers are rotatably mounted parallel to the axial course of the profile to be bent or with a roll axis of rotation extending transversely to the axial course of the profile to be bent.

The stamp or stamps or the one or more rollers can be pressurized to different extents over their extent transversely to the axial profile of the profile to be bent, so that different bending directions can be generated on a profile to be bent with this pressure setting.

Furthermore, the bending direction of a profile to be bent can be influenced in that the profile is held stationary, axially displaced and / or rotated about an axis of the profile in the bending direction by means of holding means, such as a chuck, during a bending process.

In a preferred embodiment of the bending device according to the invention, the bending device has a stationary profile guide housing. An eccentric unit is rotatably arranged around the profile guide housing and, independently of the eccentric unit, the one or more pressure elements are rotatably mounted on the eccentric unit. The assignment of the pressure element (s) to the profile guide housing can be adjusted independently of the eccentric unit. The eccentric unit can be formed from a first and a second, viewed in cross-section, one above the other, circular tubes rotatable relative to one another. In one embodiment, the circular tubes can be fixed in any rotational position.

In a further embodiment of the bending device according to the invention, the assignment of the pressure element (s) to the profile guide housing can be adjusted via one or more wedge bars or one or more cone sleeves.

If the pressure elements are arranged rotatably around the profile guide housing, then the material can be squeezed relatively evenly over the circumference of a profile.

It is also advantageous if the eccentric unit can be adjusted hydraulically or via a gear.

With regard to the method according to the invention for bending profiles, the object is achieved in that the profiles are bent by applying a wall cross-sectional area of the profile wall that is external to the axis of the bending in the cross-sectional direction and squeezing and elongating in the longitudinal direction of the profile and by referring to the The axis of the bend of the inner wall cross-sectional area of the profile wall remains unstressed in the cross-sectional direction or is acted upon on both sides and thereby squeezed and lengthened to a lesser extent in the longitudinal direction of the profile than the outer wall cross-sectional area. With these procedural steps, that is Process for bending profiles with a profile wall which has wall cross-sectional areas at different distances from the axis of the bend to be carried out. At least one profile wall section of a profile to be bent or profiles to be bent are transported through a gap which causes the pinch.

In further process configurations, one or more wall cross-sectional areas of the profile wall are acted upon and squeezed by one or more movable punches or one or more rotatable rollers, which are moved more or less far from the longitudinal axis of the hollow profile to be bent via an eccentric unit and / or by means of delivery devices.

Both with the device according to the invention and with the method according to the invention, profiles with any cross-sectional shapes and also profiles which are closed in the circumferential direction, such as circular tubes, with a wide variety of bend radii and bends of the profiles in different directions can be produced with high shape and repeat accuracy. Cracks and uncontrolled deformations on the profiles to be bent are avoided. The spatial course of the bending of a profile is only minimally limited by the bending tools, so that any shapes can be produced with one and the same bending device on the profile to be bent.

Likewise, the features mentioned above and those listed further can be used individually or in any combination with one another. The mentioned embodiments are not to be understood as an exhaustive list, but rather have an exemplary character. The individual figures of the drawing show functional principles and an embodiment of the bending device according to the invention in a highly schematic manner. The individual drawn features are not to be understood to scale. Features of the bending device according to the invention are shown so that their construction according to the invention can be clearly shown.

It shows :

Figure 1 shows the bending principle of a bending device according to the invention in longitudinal section.

FIG. 2 shows a section according to II-II of FIG. 1;

3 shows the principle of a bending device according to the invention in longitudinal section with pressure elements designed as rollers;

FIG. 4 shows a section IV-IV according to FIG. 3;

5 shows a bending principle according to the invention in longitudinal section with rollers as pressure elements and a mandrel as counter pressure element;

Fig. 6 is a view VI-VI of Fig. 5;

7 shows a bending principle according to the invention in side view with an H profile to be bent; ^■

8 is a view VIII-VIII of Fig. 7, *

9 shows a bending principle according to the invention in a side view with rollers as a pressure and counter pressure element; Fig. 10 is a view XX of Fig. 9;

11 shows a bending principle according to the invention in a front view with a U-profile to be bent;

12 shows a side view of an embodiment of a bending device according to the invention;

13 shows a longitudinal section through a bending tool of the bending device of FIG. 12;

14 shows a detailed view of pressure elements of a bending device according to the invention in longitudinal section;

FIG. 15 shows a view XV-XV according to FIG. 14;

16 shows a detailed view of pressure elements of a bending device according to the invention with conical sleeves;

Fig. 17 is a view XVII -XVII of Fig. 16;

18 shows a further section through a bending tool according to the invention of a bending device in the area of the pressure elements;

19a shows a basic illustration of an eccentric unit of a bending device according to the invention in a neutral position; and

19b shows a basic illustration of an eccentric unit of a bending device according to the invention, utilizing the maximum eccentricity. 1 shows at 10 a bending principle for a bending device according to the invention with a die 11, through which a circular tube 12 can be pushed. The die 11 holds and stabilizes the tube 12 in its orientation. The die 11 is arranged in a stationary manner. A mandrel 13 is arranged in the tube 12, which bears against the inner circumference of the tube 12 and is as large in diameter as the free tube diameter of the tube 12. The mandrel 13 is fixedly connected to a mandrel rod 14, via which the mandrel 13 is fixed in position and is immovably arranged in the tube 12 during a bending process. The tube 12 can be moved in the direction of the arrow 15 through the die 11 and over the mandrel 13. A plunger 17 movable in the direction of the arrow 16 is arranged at the end of the die 11 in such a way that when pressure is exerted on the pipe 12 it also presses on the mandrel 13, which forms a counter bearing designed for the plunger 17. In the embodiment of FIG. 1, the stamp 17 comprises half the outer circumference of the tube. The punch 17 can be pressed onto the outer circumferential surface of the pipe so strongly that the pipe 12 is squeezed in the area of the punch 17 and thus elongated. This creates a bend on the tube 12. It goes without saying that the tube 12 can be squeezed with a plurality of movable punches arranged around the circumference of the tube 12. If the tube 12 is not circular in cross-section, movable punches can be used, which cover different outer peripheral surfaces of the tube, and the cross-sectional shape of a mandrel is always adapted to the inner periphery of a tube to be bent, so that the mandrel is effective Can form counter bearing to the movable stamp. 4J φ

1 ε XI 1

1 a cn ß ß a CJ 4-1 ^ X! N

Λ ß Φ Φ rl 4H rH ß rH Φ υ Di 1

Φ a X ^• H »a φ rl ⁽ Ö -H Φ Φ Q ε ß r- -rö 1 ß ß -H

Xi Di x: -H rH rö 4-1 X, ^ rö φ Φ ε TJ φ φ • rl -H -H Φ 4-> φ rH o ü ß φ rH H TJ ß 4-) Φ 4J TJ Φ TJ CN CQ i X CQ - ^• H TJ α. CQ ω a Ω Cn H CQ ß φ = (Ö Φ TJ CQ 4H 4 Di rH Φ ß rö Dl rl 4-> Φ X rl X! Φ rH Φ ß Di ri TJ Φ ε cn ß X! -H a ß. φ rH .. = rö

H Φ Φ s Φ Φ ε ß O n ß CQ σ> rl CQ rö υ Di JH TJ X! ß CÖ rH X ß r S U> a TJ Φ N α. Q * x: rö Λ ß Φ a rö 0 Φ -H ß x; ü -H -M H CQ = a -rl CN Φ rö ß Λ 4-> ε Φ M Φ Φ X! rö rH M-l TJ Φ ε φ CÖ 0 rl CQ ε Φ MH φ Di

<- 4-) Φ -H Φ ß Dl 4J CJ rl TJ rl UH PS φ 4-) rö fl OQ ε ^ 4-> a CN rH φ 4J o TJ Φ DI a CN 0 ⁾ Φ ß 4-> ß ß φ ε X! Φ rH N -HH 4H rl

-H Φ 4-) Ui NH ε rö ε rH CQ ß ß Φ CQ a CQ = aa φ 4-) Φ CN rö 0 4 <! φ -H TJ rö 4H rl Cn D. ε ^• H CQ a ß 03 ß (Ö σ CQ TJ -H Ω CQ rö ß rH S CQ a CQ 0 CQ -H CQ 5 Φ rH Φ a ε φ TJ TJ Φ ß SH ε Φ W -H

-H X! ß Φ ύ Φ Cn ß 4 4 a ε rH 5 << -H C3 ß - Φ 4 rl N rl ß φ υ Φ j Tj -rl ß CQ -H CN X! = a a 4-> a Dl X Dl rö 0 4J SH φ SH

-H CQ x: ^• H 4-> X! ß φ Φ Φ N rH o Ml. ß CN ro 05 ß 0 φ 2 UH -H Φ 4- ⁾ ro

Φ xi ß u Ω Λ 4H 0 Φ Λ ß rl CQ 4J Φ H Φ »a S -H CQ rl 4J Φ Λ u rö CQ ri rö es 4-> XI Φ -H rl aa Φ TJ X! -H CQ i rH JH Dl 4 ß ß rl ε -H • rö rl xi J -rl Dl rl X! Ω ^• 4 rl 0 rH cn υ CQ SH Φ ß rö a TJ Φ

Φ a 13 5 4-> Xi CQ u 0 TJ ß α 0 CQ 4H Xi PS 3 ß a Φ Φ TJ a S rl -H sπ J ß N Φ H Φ CQ ß a φ PS Φ Φ -H a 0 u rö ⁽ Ö TJ Λ 4-) X! 0 X a 4-) Φ φ TJ ß j cn Di -rl ß Φ rö es ε CQ H 4-> = a ß rH Φ U φ -H ß Ό TJ ^• H 4-J 4-> = a X! u Φ φ CQ TJ Φ rH CÖ

I ε ε cn Dl ß -H rö ß a Di 4-1 ß SH Cn ß Φ ß X! Λ s u u -H -H rö ε ^ J CQ a ΪD ß Φ 4 -H rö ß

H ^• H ß ⁽ Ö Λ a O a Φ aa PQ CQ Ω TJ ε X! Rl rö r- Φ a Dl 4-) CQ w rö 4-)

5 a 5 rl trj XI Cn Ω ß 0 = rö CÖ J rH r- CQ ß ß φ Dl φ CN CQ ß j-) rl rö SH U CJ φ CQ. x: a M 5 4-> iH Φ -H X! Dl Φ Di. CN CN Φ

Φ _* . Jß Φ φ Λ CQ ß rl • 4 Φ Φ CQ CQ CQ TJ Φ φ -H CQ O CN 4H

CQ 4 u 0 Λ cn Φ rl φ Φ ß XJ ^• σ »r- \ Dl CQ rH rH Ω r- rH a CN CQ

CQ CQ -H PS <ö Di 0 TJ -H Φ o 1 ß 0 0 rö φ Φ Φ rH rH: X 4

Φ -H PJ m r- 4-1> ß xi TJ CQ cn H Φ> ß CQ TJ a a 4J Φ Φ CN CQ 0 X rl

TJ rl rH ß a φ ß ß M 4-> ß H

4-) SH Φ φ ⁽ Ö ß xi ß Φ = aa rH Φ ⁽ Ö VD _* . Φ ε ε Φ rH a ß rH H φ a es 0 0 ε -H Φ rl -H es ß Φ φ ß ß Dl Φ υ ß s- 5 ß 4 rö -H TJ rH T3 4-> 4 = CÖ Φ Φ a CQ φ N CQ

-H ß rH ^• H rl φ r- CQ Φ (Ö Φ TJ Λ X! TJ u cn cn K 4 ε Φ 4-> ß Φ ε CN

TJ ⁽ Ö Φ 0 CD H • rl rl 4 DU Φ £ ß ^• H cn TJ Φ rl -H -H Di -H

»-HP φ Ctl N 0 -H cn Λ u Φ 5 CQ rl ß 4J Λ Φ rl -H Φ rH o TJ Cn CQ rH Ö s CQ CQ 4-> Φ ß CQ and others Dl Φ Φ a rl a cn 0 ^< : a

Φ ⁽ ß ε rH Φ CQ 4-> rH Φ -H ε ß n ß H rl CÖ ß 4-) TJ Ω N φ es φ rl -H ß

• Di a rö & 4J ß rH CQ TJ H a a ΛJ TJ Di ε Φ Dl = 0 Φ rö

CD ß 4- ⁾ T ε 4 Φ rö Φ Φ TJ CQ 4-) u Φ _* CQ ß Φ ß φ φ 4H 4

-H ro ß X TJ Φ ^• H 4H Di TJ -H Φ X! ^• a Dl TJ -H 4-> a J Φ -H -H CQ TJ CQ n -HU Tj ß 4-> ß rl ß ß TJ Φ N TJ φ u! H rö Λ M 4 TJ Φ CQ -H ß ß m -H ß a cn Xi φ φ -H -rl ß 4- ⁾ rl CQ ^• H TJ rH -H Xi φ ß Φ ß H a es a U TJ ß Φ 5 4-> ^• H • H -H CQ rl φ ß s ß -H u ^• H φ 4- ⁾ ß SH 0

0 cn Di ε CQ φ Di Φ 5H 5 Φ rH Di rö Φ 5 -H Ω Dl Cn φ S .. Ω ß ß J-H r- ß Φ Λ ß X! X! Tue -H 4y

-H Φ u ß Φ ε -H CQ 4 X! Φ OS φ -H 3 rH

SH a Φ rH a TJ (Ö ß CÖ CN Xi φ CN Dl Xi ü Λ • -H Φ -cö CQ -H Φ

Sπ 0 I rH SH Di -H a N ^• HH ß ü -H rH 4-> s rH υ 4-1 rl Di Λ ESI ε φ Λ ß

X! Q u rö rH! ß ß CN Φ u ft a CQ rH X φ ß Φ TJ CÖ -H

0 ω • rl Φ = a 0 Φ rH Ü N -HO] H CQ oa CQ rl 4 4 υ rH aam Di ß 4-> Φ os SH 4-> X &Cn> rH 4 Φ φ Φ TJ ß φ X! Φ ß -H rö 4-) N CQ Φ CQ o Φ Φ rö ε rö • ^{* (} rH •. TJ rl -H rl = aa Φ φ -HX! • Cn Dl CQ rl

CQ Sπ a rl Φ -HX ß CQ ß Dl Di X! xi Λ JH & ¹ CQ TJ J CQ Dl ß φ X φ O rö ⁽ TJ σ ß 4-> Φ ^• HX 0 Φ a -H * H -H ß 0 0 0 Φ Φ Φ Φ CÖ -H Φ * H a -H υ Λ

Q Λ -H cn TJ TJ rö PS TJ N Φ fo Cn -H PS ei H OS CQ Di & CQ rl es TJ Cd TJ Λ rö = a

1 Tue 1

C5 ß ß

1 -H 4H 1 a X! IΛ a Φ N J 1 CQ

Dl x: X! a ß ß XI TJ rl rl X! -H CQ a ß Φ φ

© ß • u CÖ φ φ ß u φ CN X! u SH φ a SH 1 N Φ Di TJ o (TJ ^• 5 -H CN 3 ß Φ CQ ß ß CN 1 0 -H Φ N CÖ = a SH Dl ß α.4H N SH CN Xi a ß TJ 4J -H -H SH es rH TJ Φ 4H Φ CQ 4J ^• H rö ß ω ε Λ r- CJ = 0 Φ φ CQ Φ TJ Φ 4J Di r- 4J rö -H ε φ

H a -H CQ -H x 4H aa CQ Φ 4-> ε Φ CQ ß CN Φ ß TJ ε SH m DU ß SH Φ Φ CQ Φ ao -H rl ß rö -H -H -H -H a ß ^• or φ α. Φ Φ 4H SH -H r- rö N ß X! ax: ß Φ ß TJ 4H o ^• H 4H -H

03 CQ ft, ß ß TJ C rl ß ^• H o Dl J ^• H ^• f Φ 4J an CQ ß CQ a CQ 0 Φ X Φ -H es co ß CQ r- rH 4J 4H CÖ ε -H SH CQ

^• Φ ß es Xi ß ß 4-) rl m CN a X! , CN rH -H rö a Φ Φ O ε rö ε -H φ CÖ φ CÖ ß a CM CQ Dl Φ U n 0 ε SH ß -H ß SH Ω a Ω ß Xi CQ SH rH 4J a φ φ ß Φ 4J ^• H -H ß es rö «φ N -HXN

Φ U: φ TJ Φ rH CQ Dl ß J Φ -H ß CQ Cn Φ TJ X! • ß Φ ß •

TJ SH υ TJ -rl O 4-1 φ rl X CQ a rH SH Φ Φ ß ^• H ß -H Φ J a ^• HV £> TJ es X -H -H 0 Cn J TJ SH rH Φ - Di CQ ß rl TJ Φ Φ ß SH

4H Tj rH Di CN J ε CQ Ω ß -rö Φ ß ß Φ 0 TJ ß -H φ rö a ß ß -H ^• H a SH ri ß ~ Φ -H rö rö rH 4-) Φ a TJ es Φ TJ Di M Φ a -rl 4-> Φ 3ϊ rö Xi Φ a D) r- -H rH TJ φ ß 4H 4H X ß φ a ß Di φ CQ

0 ^• H Di ß CN Ω TJ 4J Φ ε ß ü ß ß ß SH CQ a Φ Φ ß φ rH -H ß ß

Dl S a Φ a Φ TJ rH TJ a Φ CQ ^• o φ φ X! -H 5 Xi Φ -H n CD ^• H Φ ß ß -H 4- ⁾ ß • -H ß rH ß rH ß XJ TJ ü X 4J CJ TJ CQ ⁽ Ö CN Λ a SH -H CQ X! Φ TJ XI a φ Φ rH = a rl. ö 0 = rö rl φ J m ^• * O

X Φ -P u rH ß u 4J Φ 03 0 £ t Φ ß φ Xi a ß r- φ CQ N m Λ

Xi ß SH -rl rH ^• H CQ ß CQ Λ a es Φ CN 5 Φ CQ Φ N 4H 5 φ -H - SH ü

-H U 0 a 0 CQ SH Φ • Φ = a Dl X! xi SH CQ ß 03 SH CN X! Φ CQ

IT) 5 -H; tsi -i OS Φ ΛS ß Dl Φ ß ß Φ CJ Ω Φ rH φ 4J 4J ( ^* • ^* ) O Dl φ ß rH • -H 4J 4J U Φ rl 4J ß SH Φ Φ Φ SH rö Di -H rH Φ ε cö OS ß Dl

-H Dl TJ ß H φ CN CQ ß = a D ⁾ rö CQ Φ X! ß rH Λ TJ X! Φ cö 4H rH 4-> φ 2 SH as

Φ ß SH ß CN 4-1 CN CQ a SH Φ J ^• H TJ -H ^• H - {0 Φ -HJO 0 -H Di X! ε 4-> ß

4-> = a ^• H ⁽ Ö 0- Ö TJ -H Φ 0 Λ VD SH TJ SH es Φ CQ ß 0 Φ CQ 0

4H rl 5 S Φ CQ a oo Λ cn CN 4H SH OS J CN Ω ß a r-t Dl Φ OS TJ ß -H

⁽ Ö a N ß Φ Φ CN CN CN a Φ CQ CQ • Φ rH Φ Φ ß 4 SH 4->

SH CQ 4-> CN 4-> SH Dl CN CN • rö Λ CQ φ SH Dl Φ X 4 Xi -H Di a Φ ß ß O -H

^ rl SH CN • rl Xi ß ß CN Dl rl = a rö ^• H Φ ß -H υ Dl O TJ ß TJ ß Φ Ω CQ a Φ • 0 Ö Φ CQ ^• H XI TJ TJ Ω> a TJ -H - H ffi -H ß TJ 4-> 0

SH TJ SH 4-) ß es X Φ SH Cn 0 ß r- 4-> rH Φ SH Φ -H SH SH Φ PJ

Φ ß ß X! (Ö Φ CN J rl X! OtS a N 0. A X! X! Di N CQ Φ 4H 0 X 4J ß

4 Φ -cö 0 2 TJ CQ CN: (Ö XI 0 ß CQ ß N u CJ = 0 Φ Φ Λ rH rl Φ = a CQ ^• H Φ ß CQ SH PS SH φ rH 0 es -H ω .. ß ß -H o ε Di ß = a -H Φ Dl 4H ^• H Φ 4-1 a C Φ Φ Φ TJ CQ 4H PS (TJ 4J Φ .. ⁽ Ö SH SH ß ^• H 4H ß Φ Φ Φ

Φ> Φ -H 2 Φ ß Φ CQ Ω SH rH XX Φ rH X! SH Φ X 0 ß (T Di ΞΪ SH ß xi TJ Dl TJ Dl SH Φ CQ Di rö Φ rH TJ ^• H 4-) U a SH -H 4H Φ Dl u 4-) -H ß ß X! rH φ -H TJ • -H 0 rö ß ß Φ SH a Dl D ⁾ CÖ a Φ 4-> H a Λ -H a CN X ε Xi Φ ö 0 rH TJ ε> CQ OS 4J φ rö 4-1 Φ CÖ -H ß 4-> rH CQ m rö = a Φ rö CN ü SH ü Λ 4H OS O SH 4- ⁾ ^• H CQ TJ ß C -H Cn a CQ X! 4-> Φ Φ

-H = 0 rl 0 ε es Dl = 0 Dl 1 rH φ SH -H 4J 4-> Xi o Di 4H Φ 4-> SH Dl

CQ CQ ß 4H a XI a CQ ß 4H -rl> -H -HX! Φ Φ ß X CQ rl JXX ^• H CO N 4-> Φ

CQ Φ CQ TJ o ß φ Φ Ö CQ φ Λ TJ υ S 4H -H ß • H Φ CQ υ Φ 4J -H ^• H TJ CN rö SH ε -rl CQ Φ TJ SH 4H -HN rö -H aa TJ 4 -> -H φ N SH SH ß rn

TJ X! SH Φ tn Φ 03 Xi ε Φ 4-) 4J ß rH 4J CÖ Di a CQ Φ rH TJ 0 4 X! .. o 0 0 rl CN Dl a SH -H a SH ^• tf X! CQ Φ TJ Dl ß X! ω ß a TJ ß in (β ü 4-1 CQ es 4H X XI <a ß XU: Φ oa S a J ^• H σ φ φ SH 2 CQ Φ φ

4-> SH Di J 4-> rl φ • -H ε υ ^• H Φ SH ß -H. ^• H Di • Φ SH ß SH O Φ CQ XI CQ ß rl ε ß Φ 03 CQ Oil CQ SH = a X! N (Ö TJ SH 4-> SH Φ X! Φ D) ß SH Φ TJ X!

4- ⁾ Φ 0 Ö aa Φ 0 Λ a rö -rl ß 0 ^ CJ rl 4J rl 4J Φ Φ ^• H CJ -H • l -H Φ a SH O

CQ TJ PS Ω 4- ⁾ TJ TJ X = a <TJ Cn Cn TJ CQ φ CQ 0 CQ ß TJ TJ CQ Λ Cn Φ TJ a O es

TJ ß

1 1

C5 ε 1 a Φ 1

X ε -H ß -f Φ r- 1 Φ Φ o ß rH rl IΛ 1 J φ φ ε SH 1 CQ XD ⁾ cn ^• H ß 4J C ö 1 ... Φ rH Φ rö

2 SH -H a ß 0 0 SH X rH ß a N Φ CJ a TJ ß ß CD a SH φ 5 Φ PS CQ

H TJ rH Φ Φ ß TJ Φ 4-) Φ 0 ro cö X! sa -H Φ -H CN TJ rö Φ 3 = Φ Φ Φ rH U rö XI H TJ -H ß TJ CQ ε CD OS a Φ SH SH -H ß * vf TJ Di a -H 4-) rH α. in ro Φ φ CÖ Dl cn SH Di SH a X Φ 03 X! r- D ¹ TJ ß Φ ro r- CQ 4H J Dl ^• H TJ CQ CQ SH ß Φ 0 φ 4J CQ ^• cö TJ u ^ Φ a 4-) ro CQ Φ a ß Φ Φ Φ φ φ a ß TJ Φ > Dl a -H rH ε SH SH D 4J CQ

Dl rö N rö -H -H XI ß Dl> ^• H 4- ⁾ -H -H SH Φ N Φ -H φ -H a ß CQ Φ a ß ß TJ -H CQ XO φ ^• HX! X! Φ -. J Φ -H cn 4H Di 3- TJ Φ CN -H -H IS) a Φ SH CN 3- SH ß 4J υ 4-> xi CQ ß 0 CQ ß rH "* TJ

4 rH «. 4J ro a Φ φ X .. ^• H XI X 4J -H ß SH Dl in -H rH Dl φ

X! rH 4-) rö m N - ß TJ Φ ß SH u -H rH D) CQ Φ φ PI ß ^* xP xi 0 CQ ß CQ ß J 0 rH 2 SH in ß 4H Φ rH 0 Φ Ifl ß φ T 1 a it r- a rH • H

-H OS rH X ß CQ M SH 4H 4J ^• H ß rH aa 03 4J X TJ Di H • rl xi rö Φ rl Φ φ 0 Φ rö Φ Φ ß φ X <cn Di -rö CQ ß ß ß <-f ß 4H o, rH TJ 4-) ^• H es rH TJ Dl ε Φ 4H SH φ ε ^• H cö ß -H a 0 0 CQ 4->

-H ß CQ TJ rH -H CQ ß ε e- a Φ ß -H Φ Φ 4H 4J Φ> rl 4 rH 4-)

Φ ^• H Φ CQ 0 ε Cn CQ -H Φ ß> φ CQ Di H TJ TJ SH Xi N ft Φ rH Dl

4H CQ Di Xi CÖ es a • cö Φ rH ß TJ n ^• Φ ß ß Φ J -H VO 1 a Φ rH ft au TJ CQ 4-1 TJ Φ ^• H CQ r- φ Di a Φ -H SH X σ 4-) 0

C £> N SH φ X! a X 0 X CQ ro X 4J ß Φ Dl Φ SH 4J ω 4H

I ß cn a » ^• HU Ö J - CQ J ß cö u xi a N 4-> Φ ^• H rH CÖ Dl ß Φ φ rl

^• H 0 J ro Ω -H φ 4-) a Φ TJ ß SH CJ TJ -H SH -HJ -H 2 ß φ 4J Di φ

D) CQ ro CQ H TJ φ TJ SH TJ Φ a CQ ß SH X XI Φ a TJ rH a

4J ß CN •> SH ß ß Ω rl _^ rH TJ ß -H 4-> ^• a • 4H φ 4-) ß rH N CQ

4H a Di cn CQ TJ H Φ TJ a φ 4-> rH 4H cö 4H a 4-) O * -H Φ Φ φ a 4J ß ß Φ> SH ß 5 rt 0 CN 5 SH 2 Φ N Dl TJ ü Dl 4-) ro Dl

: CÖ Xi a CQ SH -H TJ> 0 4J Φ rH es ro Φ Φ Dl φ ß -H Φ CQ ^• v ß rH υ TJ φ 0 S r- Φ rH T3 r Φ n SH CQ rH HX! SH -H Φ Ö

Xi -H ß rl Ω - 4J cn Dl rH ro 4-> ß CQ CQ Φ J Φ Φ υ rH X ⁾ Dl ß Di ü ⁽ Ö XI 4-) 4J .ß ß = aa CQ Φ Φ Φ Φ ß J TJ Tue SH ^• H rl Φ SH

SH 5 o CQ X! υ ß cö 4H N ß Φ J SH -H SH -H -H ß ß a Φ a cö X 0 a -H ß es Φ U Φ -H Φ CQ Φ Dl X J Φ Φ rH D cö Φ TJ 4H N TJ υ

TJ Φ φ TJ CQ Di CQ rH 0 a 4-> rH a TJ O 4- ⁾ X Φ TJ Oj cö Φ

4H 03 CD 4J CÖ ß rH CQ CÖ ß rH N ß PS 4-) -H ß φ 4-> ro r- \ CN CQ CQ cn

CN 0- a Φ Φ Φ rH> 0 Φ 0 a ^• H Φ H -H cn ^• ^ • H -tf ß Φ a φ ro nj TJ Di a Φ es cn CN ε es 4-> CQ ε SSX! -H TJ Dl ß -H

! H SH (Tj J ¹ Di Φ cn cn Φ -H ro φ rö • ü ε ß rH ^• H φ 0

SH Φ X! ß J Φ ß Φ rH Φ Φ ro TJ TJ ß 4-> CQ Φ Φ -H Di ß Cn TJ

X! XI 0 φ Di ∞. -H -H ß Q Φ -H S -H X! SH J X 4-) 4H ß Φ CQ

0 = a es X) rl cn ß Φ TJ SH Φ X Ω 0 ß ß J Φ CJ Φ U ß 0 a X! SH rl Φ es φ Φ Φ ß 0 SH υ CQ SH φ ß -H> ß ⁽ Ö Φ SH rH υ Φ φ TJ

TJ SH -H 4 X! CÖ 4-> 00 Ω X a. 0 SH a 4-J CQ rö CQ ε Pu rH = CÖ TJ X

Φ ß Φ X! rl J Φ X Di cn 0 SH ß ro Ω X! Di ß CN Φ 1 Φ rH = (0 TJ

TJ a J ü φ -rö Dl -H SH es TJ ß ro = a Di -H rö J Cn rH X 4-) 4H ß ß ß ß CQ -H rH ß Φ Φ ß cö ε 4H ß Φ ß ß -H Φ CQ ß -H Φ

Φ H Φ Xi ß 4H SH Φ N Φ TJ CQ Φ X ß Φ XI a N Φ rH a 4- ⁾ X Φ a Φ r-- SH D ⁾

Dl ro 4J υ 0 CQ 4J X Di Φ Di rl TJ u Xi 4J -H -H υ TJ N 03 Φ • X ß

-H Φ Φ a 4J ß φ SH CQ Ü Φ Ω ß

X! N ε TJ -H rö rH J • 4J ^• H ε TJ φ TJ 4J • cn SH Dl TJ TJ Dl Φ rH Φ O -H Φ ß CQ 4H r- Dl ß a J rH ß xi ß φ D) 0 ^* ß ^• H ß Φ 4-> Φ rH ^• TJ a SH rH -H 0 ε 0 CM -rl Φ CN CÖ ß -H Φ ü ^• H a -H ß 1 a Φ Φ -H ß • H = a 0 r ~ ß

N 4J Φ X aa es cn fr rH cn SH a) TJ CQ X σ Cn -HW TJ X cn XI a T Cn es ^• ^ - <τj

TJ SH

C5 ß CQ CQ r- Φ Φ CQ ^• H IΛ aaa ^• =} * Dl Ü φ

X! , ö rö Di ß ö 4Y TJ

4J SH a ß CN Φ a Φ ß -H rH

Φ Φ ß r-l CQ o φ CÖ φ Φ.

H X!

N CN X! φ πJ rH U es s SH CD Di CN 4- ⁾ = rö α. Φ ^• ^ Di S -H SH X in N s

Di Φ φ 4-1 Φ CQ Di 4-)

CQ ß -H CQ 0 Φ> CQ rH a rH Φ in r- rH φ X rH TJ rH rö Φ -H CQ in

-H XI rö CM SH Ö N 4H Φ

• 4H φ a Di Φ f- X 0 cn Di

Dl 0 ß N X X ß 4J r- * -F u SH ß ß

-H SH φ υ a ß ^• ^ φ CM ^• H

Cn CM a

XI m a CQ rH a Φ 2 Φ 4J

CJ rö CÖ Φ rH Φ rH cn X! ß cd -H TJ TJ Φ a rH rH CQ ro U

O φ Φ 4-) -H rH 0 Φ ß in ^• H

> ß tNl Di ^• H Di CQ NO OS TJ Φ SH

Φ -rl TJ ß a ß PS ß TJ ß rH

H TJ SH J atl -H ß Φ ß Φ ^• H

H ß Φ ^• H - Dl SH ß Φ 4J φ N φ

H Φ TJ Φ r- Φ Φ rH 4H

I a Φ SH -H Dl

> Di CQ • * ^• H -H Φ SH Φ Φ Φ CÖ CM φ CQ TJ CQ TJ D) Φ 4-> rH -H 3-

H -H a -H ß Φ X) ß ß X ß

X! rö Φ φ Φ 4-> -H O a -H ß -H H XI rH -H CQ CQ Φ -) rH a Φ

> a 4 TJ -H • SH rl 4J IM rH TJ

N Dl ß 0 4-> CQ Φ φ 4H rH rl

4J rH Φ OS TJ U) Φ CÖ ß ß rö ε 0 ^• H

Xi Cfl 0 SH SH 4J TJ ^• H -H SH Φ es 3t u φ 4H Φ φ ^• H a Φ Φ X ß

-HT SH -H ^• H 5 φ Φ 4-1 ^• H ß CN

CQ Φ CQ TJ rH TJ CQ 4-> TJ CQ Φ φ in ß 2 ¹ -rl - -H Φ -H -H ß rl TJ ß Dl rH SH ß Φ Di ε a cö 4-1 u rH a ß -H Φ Φ 4H ß oo ^• H Φ -H

Φ 4J a X! X) ß CM rö CM Di CQ ε 5 4H ß Xi 4-> Ö = a ß TJ ^• * a rH 0

-H υ X! 4-> = 0 Φ ro ß Φ r-H 4J Φ SH

Φ -H <J CQ TJ X ^• H a CQ N rö Xi 4- ⁾ e.

SH -H ß TJ r-t X 4H u ß

4-) 4J S-i ro a ß ß t -H rl ß -H Φ ffi

CQ SH - F -H SH Φ 4H φ Φ CQ

-H ε

0 0 CN φ Φ X • 0 3: X! ß Φ φ a> ß ^• Ψ CQ XI 0 Di SH Φ rö rH T

∞ CQ Φ Φ = 0 » ⁽ ύ -H Cn CQ ß Φ ß ß D) X rH 4- ⁾ CQ Cn Φ SH Φ

• X φ cö Φ υ -H Φ • X TJ Φ 4- ⁾ ü Dl

-H a

EH CQ CQ 0 rH CQ Φ Φ CQ φ O Φ rl ^• H

M TJ TJ Ω X n Di NH Φ rH a -H Di N

Φ

-H

Ω

, ß

Φ

TJ

SH

Φ

5

4 years old

Xi

= a

4H φ

di

XI u

SH a

TJ

CN

<£> rH

-H

4H

0

SH

CM

D ε cö

Dl ß a

dl

Φ

-H

CQ

Φ

4-)

Xi

U

CQ ß

§

Φ di

4-1 CD 1

C5 J φ ß ß -H φ -ri f rö a φ ß XI IΛ Φ -rl Xi ß -H x: ß ß. Φ TJ φ 4J N CQ φ Φ ß 0 o ^• H o

-H CQ CJ -H ß U -i cö cö ß i 0 Xi -H Xi -ri

©> co XI 4H es X! •

X! -H ß 4J Φ CQ ^• H ß i X φ ß φ φ ß os CQ CJ CQ CQ φ φ SH CJ ß υ Φ rH o 0 CQ CD ß Φ Φ Φ SH -H Di CQ M φ cö 4-1 Dl 4J rH cö CD -H φ

H Φ ß ε Cn Dl CN TJ Φ: CQ 4J Φ CQ rö ß TJ φ 0 TJ ß XI CQ i Di CQ Dl = 0 U 4-1 Φ ß ß r- Dl ß υ ε -HO 4-1 CD ß CQ -H i ^• i => ß a Dl Φ X α. ß TO aa -H CQ Φ SH ß CD Dl cτj 4J i 4- ⁾ 4J u SH -H φ -H ß -rl a φ • X ⁾ 4-1 Di rl ß SH Φ ß ß Φ Ö ß X CQ u CÖ X CQ. Φ Φ N Φ a CQ ß

-H xi φ Xi Φ Φ ß Dl -H Φ CN N J = CÖ -H Ö 4-1 U SH CN J X! X X Xi Φ ß i a u -H o XI ß ß i Φ TJ C-- X Xi ß CD 0 = a Φ r- a Φ Φ J

Φ J -H -rl CQ es 0 -rl CÖ CJ ß m SH Φ O Di OS SH a ß X! φ ß SH X! SH

X! CQ N SH i φ X 4-1 a SH Φ U TJ r- ß TJ D ¹ CQ ^• HO 3ϊ ß Ω ü Φ

Φ SH ß rl SH Φ υ a -H X! Xi Φ TJ Φ SH = CÖ φ J φ CQ φ rö -H 3-

CD φ -rl 0 a Dl CD ß CN TJ ε SH O ß TJ Φ σi J -HO ß SH CN SH D) X SH ri φ> SH N -H Φ -H r- ß Φ PS -rl 4-1 3s ß J CQ ⁽ Ö XI C- 0 Φ Φ TJ 4-1

Di a Φ ε Di ^• H SH> φ -H CD a rl: 0> -H ß Φ XI

CD Φ Di rH! H ß O SH Xi Φ φ ε a ß 4J Φ J _^ OS SH SH CQ 1> -H -H ü

Φ CD Dl Φ r- = 0 -H r- Xi TJ rH Dl rl cö Φ XI TJ SH ß 4H Xi X! Φ XI -H

Xi CÖ Φ -H 4H φ 0 r- r- -ri = a »X) υ -H Φ a ß 0 0 CQ U Φ

CJ TJ ^• H CQ Cn CQ Di es t - ε 4H 4-1 Φ 0 ^• H 4J 3 = XI rö φ es PS Ö Φ 4-> CQ SH

-rö CQ a -H ß ß VD σi SH Φ CD s rl -H 0 TJ TJ 4J -H rl SH ri 0 Φ Φ Φ SH a CQ Dl r- a = 0 Dl ß xi u rl ε • xi X ß Φ Φ 4-1 ε φ Φ

4H CQ ß 03 N rl O 4J Ö

I a Φ 4H ß Xi υ CD 0 Xi CJ SH φ TJ ß X! a 4J ß Φ: CÖ ΛS X Ω X! Ω Φ ß N CQ a J CÖ> rH CJ CQ cö Dl ß -H u 4H CD ß CN φ .. 03 0-1 ε SH u N Φ X -H 4-1 -H CD φ Φ l • H SH 4 -1 Φ Φ Φ ß CQ ar ^» ri ß -rö Φ Φ CQ ß -H • X ε Φ XI Φ ß> Dl Φ Φ CQ -ri Dl a ß rö ri Φ ε Di 3- CÖ -H SH 4-1 rl Φ φ SH u N 0 CQ Φ CQ rH> X Φ rl TJ rö TJ σ> CQ

0 TJ Φ CQ Φ TJ Φ SH CD φ ^• H 3- X -H Φ -H a -H Φ Dl XI -H φ ar ^» φ es SH Di Dl Di 0 -rl 3- SH Φ SH D) 4J rö CQ Di CQ CN CJ a X XI CN cn 0 SH

Φ CD ß Φ ß CN> φ CQ Di CD rl ß CÖ! H a Di r- -H N = a E- CQ X

Φ S Dl a -HM r- Φ SH Di XI Φ cö 0 ^• H 4J Φ SH φ ß rH a CD φ 0 rl ß TJ CQ Dl cö Φ φ -H TJ> Φ 0 Xi Φ N a CQ TJ CQ N TJ ö »4J OS xi 4J a ß • CQ Φ XI ^• ri -H CQ rH es TJ X, * Φ Φ Φ ß X Ω ß 4J

-H Φ TJ -H ε CN Φ -H SH CQ SH ε rH O CN u J SH ^• H TJ tD ao φ a ß

4-1 ß 4H Φ CQ Φ 4-1 C a Φ r- SH r- Dl φ φ Xi X ⁽ Ö es • TJ 4H Φ

SH CQ -H SH ß X -H CQ ß Ö 4-1 φ ß s J 0 CJ TJ TJ _^ ß SH ß TJ

Φ CÖ 4H Φ -H ß 0 SH X CÖ <J H CQ Dl ß CD a Φ es CQ ß ß Φ φ Φ ß ß

XI rH SH Φ Φ PS Φ ^• HJ r- rl ß ^• H Φ rH Dl CN SH Ö TJ Φ J TJ S (TJ φ

= a Φ Φ Φ SH TJ 4H ß SH φ a φ SH rH Φ f- CQ φ S SH 4J ß SH a Dl

X ß 4-1 X! CD Φ X Φ = a Di> 4J CD Xi φ -H φ 4J rH ^• H ri Φ Φ 4-> cn Φ ß X ε -H -HO Φ ß Dl u ß 4-1 a Xi 0 4-) CQ CQ TJ ß -H Ξ rö cn 5 xi ^• H φ CJ Φ Φ ε es TJ cö CÖ SH ^• H Φ φ CJ 4J OS cn Φ a 4H X! Φ Φ CD X ß a TJ rH a Φ r- N ß -H • ri CQ SH φ 0 σ Φ ^• H ß SH cö ß SH 4J 4J ß Di ^• * TJ P ^» X -ri SH B ß ß Φ X! CQ r SH r- Dl XI Φ J TJ a

= 0 TJ 4-) D) Xi Φ ß r Di SH φ SH Φ φ J 0 xi r- CM XI Φ N

X ^• H -H CJ Dl a ß in Φ Sπ φ 0 ri Dl rH OS ü SH oa 0 Dl SH

X ε Φ -H -H 4J Φ at XI 0 3: 4J>t> -H Ö Φ cö Di SH Φ r- N Xi Φ CQ r- N CD ε s D ⁾ rH O 4-1 Φ CQ Φ ε rl CQ ß CQ a Φ 4- ⁾ ü CQ XI Φ o cö ß ß SH u ß rH Di 0 Di -H Di Di rl 4-1 xi Φ Dl Φ TJ 4J Di CD CD rH = a TJ

4J Φ CM CÖ = 0 -H cö Φ ß • ε Φ Φ a = 0 a J TJ ß N a ß Ö φ r-i

Φ SH Φ CQ CD CQ cn 4-1 Φ X CQ f ^* * CQ N CQ ß D Φ J SH X ß 4-3 XI 4H f ^» Φ

© N Xi 0 TJ • 4-1 ^• H Di ß X TJ Φ X -H ß Di Φ ü ß X ß U ß Di O rH CJ 4H ß D> • rl Φ ß SH ß CJ SH -H CQ 4J SH Φ SH 0 Φ SH S ^• H CÖ υ ß SH φ CQ ß Ö -H φ -H • rl Φ SH = CÖ O Φ -H Φ SH rö -H Φ φ rl Φ -ri -ri a Φ Φ a -ri cö a Xi Φ a

12 rH cn CD Cn cn X Ω 4-) SH 5 4J TJ 2 TJ 5; ß 4J XN Dl SH cn X TJ φ SH 4-1

a 1 <tf Φ CN. ε ß Dl ß tN NX! r ^» φ SH ^• H SH r- IΛ ε co 4-1 a 1 Φ 1 Q ri CD a ^• H

Φ ß -H ß »Φ TJ Φ 4J a φ Φ C φ 1

= cö. CQ SH SH 4-> CQ Φ 3- SH SH Di Xi SH CD o -ri ^• H a 4-1 Φ Φ Φ co Φ ε 5 Φ -H

H ε 4- ⁾ a Φ XI CQ O XS ß • N Dl X TJ Φ Xi es φ SH SH ß Di N 5 ^• H a φ rH XU Φ 4J: CÖ> 0 ß C = a TJ 4J ß 0 SH SH 3 : υ SH 4 Φ Φ ß 0 N ß Ω ß Dl rH α. Tue ^• HX! PS SH Cn SH CQ ε cö es Φ cö Φ <ß Φ ß Di N as SH Φ Φ Φ 0 a

CQ ß Φ rH O ß 0 -ri Φ 4H> X TJ Φ 4J Φ rö X a TJ rH 03 ^• H OS N

Dl XI Dl -H φ Ω Φ rH Φ ß ε Φ X ß Φ Dl ß NX) w in Φ ß ri TJ a CQ ß u CQ XI TJ 4J -H Dl rl -HP -HX Φ CD ß -rl -ri φ X co Di a 0 ß <Φ CQ a cn Dl rö ß Φ s 4-1 ß Ö Φ Ω SH a rö TJ ε N Φ Φ SH Φ es -H CQ -H Ö

TJ ß 4-1 φ -ri CJ O cö XI ß cö TJ cö X SH X -H Φ ß '-ri ß CQ Φ CÖ TJ J ß ε a CD Dl J CQ SH xi TJ Φ • 4-1 TJ = o 4-1 Ω TJ φ PQ Φ Φ -ri TJ

-H -H SH Φ Φ ß PJ 4-1 φ ß SH ß CQ 4J X ß ß 4H rl X! 4J 4-1 4J J ß ß

4H XI Di -H SH = a -rl SH ai Φ ^• H Φ -H CD rl φ. ^• J CQ CO ß SH 4-1 φ Φ

SH H = a rö XI Φ 5 ß φ TJ -ri CO SH Φ cö TJ CD -H φ -H CN co ^• H φ Φ Φ 4-1 SH XX

Φ r- Cn rH X! φ Φ Xi rl ß -H Φ X 4-1 SH φ TJ 4-> IrΦ ß φ ε D ⁾ a Φ CJ J a = a Di 4J ß Φ Φ Φ Di ß CQ Φ 0 SH 0 SH N -H Φ cö rö ^• H CQ -H

SH Di rH CN N CQ -H> 4J φ 3 = -H ^• H 3 = CD X 4H rl en X CO Φ ε ri ri 4J 4J Φ

Φ a -H r- SH SH Φ Φ CQ X 4H ß Φ SH a φ 0 Dl Φ Φ Φ 00 0 Φ rl

TJ φ 4H CQ Φ Φ 4H SH CN SH = aa Φ Φ ß »ß cö H SH OS a TJ TJ XD ⁾ co es a Φ

N 0 rl Ö TJ ß CQ Φ CO Φ CÖ 3: φ Dl Φ 4J Φ E- * X! N ß u J ¹ X) ß X SH Xi TJ -H 4J 4J - 4-1 ^• H XI X TJ CQ 0 ß Φ Φ co a SH ß CQ

0 CM 0 _^ Φ rl ß ~ ε CQ ß SH ß ß 0 φ ß Ö Dl OS Φ CQ rl a SH cö Φ CM 0 4-1

> φ es TJ 4-1 0 Φ rH Φ rH φ Φ Φ Φ X! Φ TJ a 4J Xi rö Ω X) i CQ 4-1 o 3- ß SH SH ß N CO ß -rl X TJ N 5 o TJ Di Φ ß -rl

CN ε = CÖ XI u ^• H

4-> φ -H Φ -H Φ ^• H ε X -H φ 0 X CQ SH Φ TJ N φ Φ Φ 3- TJ CQ Φ -rö CQ *. ß

4-1 Di Φ TJ 5 -H φ w Φ Φ 5 -cö ω SH SH Φ ^• H ß X TJ 3- TJ ß rH SH rH Φ CN Xi

-H Φ ß CD CQ TJ CQ φ 4J SH Φ Φ> XI a ß N CD Φ CÖ TJ 4H SH E- ^* CJ ß -H 4J Φ ß -H Φ Φ a CQ CQ Xi J> Φ Φ 4-1 CÖ XI ß i CQ

Xi CQ 4H Dl SH r-i CQ 4H -H - ö a TJ Φ Φ 0 CQ SH a .. 3- Dl ε -H TJ Φ TJ r- Φ 0 rl rl

CJ a φ Φ • H CQ a TJ XI ö φ ß ε TJ a Φ N X! Φ Φ ε 4-> ß co r-i OS XI φ

CQ ε -cö -H ß X Φ <φ -H CÖ SH cö TJ CJ Dl ^• H TJ ~ CD ^• H ri 0 a

CQ Φ rH X ß Ö N 4-) Dl 4-1 TJ S SH 4H X SH ß CO ^• H Φ XI • τ-i Φ CQ ß o ß OS Ö ¹ a J XI H 4-> 0 • CQ CO CO Φ a Φ Φ ö Φ φ ^• H 4H Di E- XI Φ es Φ TJ υ a CD SH 4-1 ^• H Dl -ri - Φ TJ cö ε Xi ß TJ rH CQ aa -H - DJ φ ß

4-1 SH N ε a CD ß 4-1 i ß -H Dl N rö Cn σi - 4-) xi φ ß J rO ß ^• H a H ro φ -H CN a 4J Φ u cö CQ rH CN Φ TJ CQ Φ a 4J SH CJ SH φ ß:

Φ ε TJ CQ r ^» cn CO SH -H TJ ^• H ß CÖ r ^» r ß ß CD 4-1 CQ H SH Φ -H Φ X! Dl φ ß Ö • Φ ß XI Φ -i rH -H TJ Φ a ß rl Φ f ^» Φ N Φ -H -ri Φ Dl ß

^• H Dl CN TJ 4-> ß -H Φ -. = a X! -H TJ Φ Di CQ Di a φ J TJ XX! 4-> ß -H Φ Φ

Φ ß r- CQ rl CQ 4-1 rH Cn ß XI φ ß CQ a φ Φ 4-1 XD ⁾ CO ß 0 -HX • H xi a ε ^• H 0 rH 00 -rl Φ -rl Φ CQ φ SH Di -HJ öS Φ Φ ß Φ -H SH φ XI υ

4-1 4-> Sπ Φ Ω CQ ⁽ Ö ri Φ Dl Xi Di rö N Xi φ Φ ri CD Di -H 5 Φ Φ XI a -H

Di Xi Xi TJ 4-> φ X! Φ -H SH J Φ TJ X 0 xi TJ Φ Xi a Φ SH - -ri = a N a rH

^• HJ 0 SH ß ß φ CQ 4H Φ ^• -Φ CO Dl SH OS co ß Di J Φ 4-1 Di Φ ^• ^ TJ N TJ

Φ -H es ß Xi Φ -ri Dl a 0 4J CO SH 0 Φ ^• H rl rö N CQ Φ 4J co ß CQ φ

N SH -H = a ß φ = CÖ U ß Φ ß CD 3- CQ .. φ X! co X ^• H -H ß »Φ Φ CQ -H

SH Φ 4H -H 4- ⁾ XI CM Φ .. 4-1 Φ Φ φ ro SH φ rö Dl CQ Φ - 4-1 X TJ CÖ Xi ro 0 TJ .. Φ Φ TJ CQ Φ N ro

H> ß CN Di ß Φ Di ε X CO a ß ß Φ 4J: CÖ 5 -H ε X co J = a Φ CQ

• ε

Dl Di XI ü SH CD Di TJ SH .. X TJ CQ CQ SH φ xi -ri Di Xi TJ SH -H TJ J a Φ O D) Φ Φ - CJ SH XI 4-1 ß φ XI ß SH x; X N u 4J φ Φ ß Φ X! X! -cö 4->

-H ^• H ^• HH ^• H a = CÖ rl aa • rl 0 Φ - Φ Φ CJ 0 X -H 0 -H -H -H ß • rl 0 Φ V £> rH H ß

Cd CQ X 00 ri J 3- 0 SH N Ω es xi CO 2 4- ⁾ CÖ OS ω ß SH TJ CQ Φ H TJ es Dl co 4H O a

1 1 1 co 1 TJ SH CQ 1 CQ X 1 X 4J σi X φ

IΛ 4J ß Φ Φ 1 rH CQ CJ SH ω o 4-1 ∞ = a TJ Dl _^ CQ

4H

CÖ 1 1 • = a 4H <£> -H Φ φ cn S CQ TJ SH 5 SH ß ß 1 4J -H r -H

SH SH ß 4-1 Φ a co φ TJ rH -H ^• H ^• H

SH ß φ a SH Dl φ Φ φ SH = 0 TJ X Φ -i ß Di r-i as 0 4H • H

H ß Φ

Φ U a -ri rö Φ ß ß rH X! TJ> ^• a 4H TJ C Φ CN ß O ε 4-1 TTJ cö SH α. CD X 4 φ a rH Φ 4H CQ ß ß SH CQ r- a OS -H co Cn CD 4-1 Φ

Φ ß CD CD rH rH 0 CD φ 0 -ri φ Φ Φ Dl O rH rH Φ i CQ TJ

-H H a Φ rö rH rH es CQ ß φ TJ J 3- ß CÖ SH rH rl Di -H CQ CJ ß ß

TJ N Dl TJ 0 Φ ε X ß a r-i Xi Φ φ ß φ ö - SH SH rö

• es 4J Φ -H .. öS X .. Φ 4J 4-1 0 4-> J a «Ω 4-1 a 0

CQ 4-) CQ • X! CQ -H 4J ß XX Dl SH X Dl OS CQ rH Φ TJ P 4-1 a Di CÖ 3- υ φ a Ω CQ CQ Φ 4H φ CJ Φ Φ υ ß rl Di rH SH • 4-1 ß ö rH TN SH -HN CÖ -HX) a TJ a -H Di -H a CD φ ß • Φ Φ J a Di Φ Φ

0 X! a TJ. TJ 0 CÖ ß SH X ß SH 4-) φ> a ß 4-> Λ ß Φ ß -rl -H co 4-1 TJ TJ rl ß 4J X rH φ Ω -H ri i Dl rH Φ CQ = a - H TJ a TJ TJ

CD SH SH 4J ß Φ φ ~ rl J ε Dl a SH -rl CJ -rl φ rH X rl CQ φ XI

CÖ Φ -H Di φ φ SH TJ 4-1 φ CD a φ SH N SH Φ -H ε 4-1 Φ φ Ö Ό Dl Φ SH TJ

TJ 3- ß -H ß Xi SH SH Dl SH ß -H Φ Φ 4H SH SH φ 4-1 Dl Ω co H ß -H Φ ß

CN -cö TJ ß -H Φ Φ ⁽ Ö Φ Φ X TJ CQ> CM SH = 0 ß CD SH E ö XI XI a

0 c- * ß r-i = 0 5 Dl r-i> rH Φ 0 4H Di SH 0 ß ß CJ = a

CQ Φ Φ _^ X ß rö φ rH a ß TJ X SH> CQ -ri φ> φ φ CQ. CQ SH

CD X! Di 4-1 -H ß rH Dl rH 0 N ß υ Φ Φ -H φ>4-> rH Φ D ⁾ SH ß

"A φ J ^• H". Φ Φ er, es cö Φ SH TJ Dl Φ φ rl i -i D -H Φ Φ 4->

X rl -ri X Φ TJ cn XI Di X! CQ X Xi a Φ SH Di φ Φ CJ 0 a Cn> 4-1 ß

Xi φ Xi SH co o ü Di SH rö υ TJ ß -ri X • H TJ rö es Φ rH 0

CN ö 0 rl ö ß -H XI o ^• H ß Φ TJ CQ --rö rö Φ CQ Φ TJ ß 4H N SH SH (Ö ^

4J es φ 4J -H 3: ß CJ σ> rH a ß r-i rH TJ Dl co ß öS ß rl S Φ Φ xi 1

I CD X! CQ Φ Φ CQ X! 4J -ri 4H ri 4H Φ ß φ -rl XI ß -H φ SH TJ ß Φ rH co CQ SH 4J D) SH φ Φ XI φ a Ö co - Di φ TJ Φ υ ^• H Φ J Φ -H Di - H

X φ 4J Xi Φ Φ ß Φ CQ -H u ö 4H Dl ß 4-1 4J ß SH φ rl 3- ß Φ 4H

CJ TJ 4J ü 4-1 TJ cö> a X -H rl ß ß φ ß Di φ SH a ß φ D Φ -ri CQ - 0

-H -H -H ß rH 4-) = CÖ υ SH φ X φ cö XI φ -H Dl Φ TJ 0> ß Di ro SH rH Di ß ri Φ -H CQ CN XI CQ ri CQ ü X 4H = a Φ Φ XI> a Φ 4J -H ιr- CM

TJ ß i JNX) ri r φ SH -ri CO aw ε CQ σ \ N -H = a xi SH rH • rl CQ Φ φ a J Φ X φ • rl Dl φ Φ Φ SH aa ∞ Φ XI CJ Dl Φ rl CQ-HX ß Φ

-H Di CQ -H w Di Φ SH ß> 4H ε Ω • ß rö Dl rH a -H ß Φ SH -H s φ XI X ii Xi φ CM X! 4J a ß a X! cö Di -H 4-1 CQ CN CN 0 TJ u -rl rö υ SH ^• sT 0 ri HJ SH XI 03 CN Φ CM N 0 ß Φ CQ Φ 00 r- Ω

CQ CQ TJ D Φ 00 Φ OS ri r- ß rl Φ = 0 a E- Di H 3ϊ Φ = rö SH TJ CD rl ß SH TJ SH 0 ^• H a TJ X! <ß ß 0 -H i ß Φ »SH SH 4J φ Φ cö Φ .. Φ φ es CQ Ω SH CQ cö • -H CD 5 XI -H> rH HX! Φ ^• H

4J ß 3: 4J ß ro SH TJ Φ σi TJ Φ Φ Φ 4J Cn Φ as -ri CO 0 Ω Φ ß -H ß 0 oo XI ß ε Dl co rl ß -ri SH CQ -H Φ 4-1 ß 4 -J Φ Φ OS CQ a Φ ß a> Φ φ Φ a φ a TJ TJ Xi rH Cn 4H 4J -H a. Dl ß 4-> Φ • rl

Φ SH ε Di ß Φ ß J SH 0 -H. a 4H Φ -H -H TJ CQ φ Dl Φ

CM Di X! CN Dl XS Φ -rl N φ - -H 4H es Φ 4J ß CÖ -erj Xi SH Φ Φ ß a J ß ß

C- ß υ f- -H 0 SH -ri φ X Cn XI c- ^■ 5 a XI -H SH ß Φ N rö = CÖ ß a -ri a -H Dl OS Φ X ß CJ ra Ö ß φ φ « -H TJ O 4J s Φ -U φ

SH 4-1 rH SH ß TJ ß Φ rö ^• H CN Φ Φ -H SH -H Φ ß rH CQ Φ D) X!

O Φ Φ 0 X 4J N Φ CQ Φ co -H TJ u TJ Φ φ ß ε CQ CQ ^• H • ri N

Φ -H ü φ ß S -H rö -H -H φ Φ 0 0 φ = 0 CÖ Φ -H -H Φ φ a • H 0 -H a a 0 4-1

TJ Φ CQ JPN Φ TJ CQ CQ ß SS rH 4H ε> 2 CD! NN Cn ß TJ SH N> CQ

Dl co ß SH 4J Di

<M rH H a TJ l φ co Φ ß Di rl φ ß ß IΛ ^• H E- * φ ε Φ ß Φ CQ cö XI CÖ X ß XI Dl 4J ß rö

N / A

4-1 i Di Φ u 4-1 CO X! Dl XI 4J -H Φ Φ H -H ω a 4-> J H a CJ ß Φ a 5 co Xi ε 4-1 0 ß r-i ß 4H CQ> Xi CO φ Di -rl O TJ -H SH H a O

H Φ SH Φ φ ^• H υ - 4-> PS aa ri Φ a CN CJ Φ 4-1 Φ SH rH ß CQ Φ N Ω ri U ε JN Dl SH co -H 4-1 N = a TJ rö 4- 1 oil σι -H Di ß -rl -ri Ω -ri α. Φ X Φ 4J 4J CD ß φ XI 4-1 Φ co ß aa CQ 0 Φ 4H TJ CO Φ φ rH o -H ß φ rH X TJ CJ CO Φ 4H ß Dl Φ> CO SH ß • rö • rl 4H

Φ σ> φ CQ Φ a rö CJ ß -H rö D) a cö TJ ß ß in N - CQ Φ a Φ a CN TJ TJ CM

X 5 NJ ¹ CD φ SH Ω CQ cö XI φ a rH X vo φ Dl: CÖ O

U Φ φ CQ X SH D ⁾ SH a XI 0 D) 4J 00 ß Φ Xi Φ 4J H TJ rl ß a CQ Di CÖ Φ TJ Φ Φ Φ 0 • Ö vo Φ φ ß X! , Φ ^• H -H Φ -HN ß φ ^• H ua Φ Ω ß X a ^• H><00 SH Di a J Di 3- ß Φ CQ Dl TJ 4J CQ a XI

Ω = CÖ -H ε a Ö ¹ XI Φ rH ro TJ ß 4 -ri • rl φ φ CQ = a Φ = a rH

XI CQ SH - s J D) r ß rö CD Cn Di r-i ε ß D) Xi 4J SH - o

Φ Φ 4J O CN 4-> ß a φ • Φ TJ rH r-i φ r-i rl Φ ß CJ CQ xi ß TJ H

-H Di CQ CQ Cn r- CO rö N -ri Di ß r-i ß o -H -H SH -H o O 03 a SH 0 Φ ß

TJ ß Φ -ri 3- m -H H rH -H C Φ Φ Φ CQ es 4H = rö SH a ro PS 4-> a Φ

Φ TJ ß C0 CN rH CD Cn 0 0 CQ W 4H TJ CQ ε Xi TJ o rH CQ

Φ rH X Φ Φ t -rl CÖ φ Ω es Φ C CD SH Di φ = a H ß rö ro 'a

-ri rH CQ CJ 4-> SH 4H Ω -H ß VO CD ß Φ Φ ß Dl Cn r-i φ X o: CÖ

TJ 0 Φ -H rH Xi SH O TJ 0 ε ß oo a Φ ß ^• H TJ -H a CQ -ri ß TJ Φ HX! it CD rH ri 0 X! rl> Φ Φ = CÖ X -HX! SH Dl rH X SH ß Di Φ

»A X Φ OS 0 CM 4-1 i TJ X ß X! = a Φ Φ XS ß -H rö 0 φ ß Di

CO ε = CÖ Φ 4-1 os Φ υ> CJ φ Φ ß -ri -i - -aa 4H 4-1 Ω Dl ^• ^ SH co

CM co Φ X! -H CD ß SH 4-1 SH X ß = a ri Dl X! ß Ω ^• H Φ • 4H TJ O CQ Φ o 0 D ⁾ CN ß φ S Φ φ Φ Φ aa 0 SH ri ß CJ CÖ Φ 4-1 ß CQ ß SH φ ß -H rH Ω ß ß ^• H CD J Dl TJ TJ ß Φ TJ>> TJ 0 Φ -HX • EH ß Φ a -H Cn Dl -ri XI a

Φ Φ CQ SH ß ß -H TJ X es rH CD ß Φ N 4H rö φ Φ ß rl rH CQ SH rö φ Φ Φ Φ in ß ß rH D) φ T ε 4J SH ß rH a Di Φ Xi rH ß φ φ TJ Di Di Dl r- 4J φ Φ 0 4J a SH ß Φ = a Φ Φ -ri TJ N ß J = a

0 -H TJ> Φ Φ 4-1 ß Xi φ xi ^• H es CO Φ Φ -H rH 4-1 SH w CN ß as Cn es r ^• H ^• H ^• H ö Di J ß υ Ω CQ N -ri CO Φ CO Φ SH oa CQ 4J SH

TJ XI cn XI X ε ß -H ß ε: CÖ; 4J X 4J Φ. H Φ CD Φ rH φ ß ri oo • a CO ri. Φ rH SH 0 Φ CJ TJ -H ß ß -. TJ ß XI ^• H

-H -H as Dl a a 4J rH 4-1 ß 4H CN TJ Φ rl rH a ß Φ -ri ß SH Dl SH = a 4H

TJ CQ X ß -H N N CO X <ε CQ f- O S -H SH a 3- φ rö i ß ε O O

Φ Cn -H • J -H Di ß cn Φ CN Φ Ω X 0 a SH Ω ß SH

SH CO Φ Di CQ CD Di -H Φ ß CQ -H Dl t 4-1 ß Φ ß es 4J O ß CM

= a co ß ß ß Φ CÖ CD ^• H SH ß 4J Ö Φ φ Φ a ß Φ ß -H ß XI 4H Φ rö

4H ß öS ^• H TJ TJ Φ Cn ri -H CQ 4H SH Φ CD -H SH cö Φ 4-1 -H Φ CQ CJ CQ • ri X CQ ß -rl 4-1 -H -ri Φ -H ε Xi ^• H a CQ XI CQ ß ri Φ 01 TJ φ -H 4-) J cö

SH Φ CQ SH Φ XI Ω SH Φ a 0 TJ: CÖ 0 r-i rö Ö rl TJ SH 4-1 CM TJ

Φ rH CQ rH Φ CQ CJ Φ 4H 4-1 CN ß es Xi CD OS ß Φ XI 4-1 TJ φ ß SH -H rl O

Dl rH CÖ ^• H TJ XI -rl • TJ Cn Di r- Φ - Φ rö Φ N ß Di 5 φ 0 ß Φ rH xi cö 0 TJ Φ υ φ Xi -H 03 CQ 4J D ⁾ Ω φ ß ß Φ - H - Dl> i XJ rH ei ß rö rl o ß ß Φ SH a φ SH ß TJ Φ -ri ε Φ o 4J φ Φ ü = a SH SH ß - -H co φ -H -rl -HN Xi <TJ Φ φ. ß X Φ ε N o N ^• HD ⁾ CQ Xi a

Φ Φ 4-1 Φ Di CQ φ • o Dl r-i ß φ φ cö rH 4-> X! Φ SH TJ O TJ

Dl -H ^• H 4J ß Di TJ ß in es Φ Di rö ri Φ Dl -H φ CD vo Φ -H φ rl PS

, rö SH -H ß 3- 0 • TJ 4H Dl ^• H XI υ • ⁾ D ⁾ Φ TJ H

CQ ß ri Φ 4-1 Φ Φ ß ß X Ö) ß 4H ε CD XI CD Φ SH Ö) a ß ß 03 Φ ro ß rH φ Φ X 0 ^• HX Φ = a CN CJ • H Φ aa cö CJ a Φ -H Φ - l φ -H -H -ai -H o φ Φ

CÖ J Di -a SH J 0 rl TJ t CO Cn Di cö ß co Ω ω NX! TJ TJ Cn N Φ Φ ε J rH Di Dl

1 1 1 1 SH • CD «. co 4-1 ß ß SH

^• ri Φ ß CÖ ε Φ fN SH SH 1 φ Φ 1 Dl N SH Φ Φ ß X Φ 4-1 IΛ 0 Φ rH -H φ XI Φ • xi TJ ß ß

> 0 ß = a XI 4J υ SH • H ^• H ε a 4-1 0 rH ß Φ Ό ß 4J X

©> TJ

Di SH Φ a Φ Φ Ω φ rH -H TJ -H -H ^• H CJ 1

PS φ Φ φ ε a Φ ß N CO -ri O Φ rH Φ ß -H Φ © vo ß rl X TJ ß -H -H Φ Φ α. a X! Φ NX Φ ß TJ PS SH TJ X! CQ Dl o ^• ri φ φ υ SH φ SH Φ ω TJ rl Di Φ -H Φ Φ X! CJ Φ φ -H = a TJ ß • ri 03 rH X --öS Φ TJ 4J N ß CQ Φ TJ

SH Φ Φ ß TJ ^• H Ö a Φ ß ß SH TJ Φ X -rl U co ß -H

H TJ = a ri X! <s -H • H = a ß X = a X! cö SH Φ PQ U ß 4H Φ Dl Di φ SH TJ a .. φ Φ Φ 4H ^• ri υ ß Φ CD α. Φ φ ß TJ co 4-1 5 ß ε • H 4J ö VO SH cn CQ CM .. CQ a CD CQ rH XI Φ ß Dl Dl Ö vo rH ε ^■ ? i ε ri o Φ Φ Dl i SH H co rl CN D ¹ Ö Φ

-P ß a ß -rl vo H 0 υ

0 a H TJ -rl ß CJ Φ in HH φ H CQ ri ß ß cö SH o Dl i ro CD Φ CQ a SH Di rH H 4-1 rH Dl ^• ri

PS • * o ß 4H TJ H ß • rH o 4J oo ß Dl 4-1

X Φ ε φ a Di rH rH φ o c ~ - a rö H SH ß ß CΛ φ ro Φ ß ß xi TJ r-i X! ß

TJ o TJ a • H a SH a rH ß XI -H 0 a H o rH a ^• H CJ ß Φ 0 φ X TJ H CQ ß ri a SH ß ß Φ ^• ri Cn> ß er -i rH 4J φ - H TJ Φ CQ S Di »0 ß φ

-H N Φ φ SH rH φ SH Φ ß 0 X! SH SH Dl

CQ ß 3- 03 Φ r- rl ß a ß ß es rO ß CQ ε 0 Di Φ Φ PS CJ X SH • ri Φ -as φ

SH SH a 0 4-1 0 a Φ S Φ a a Ω Di Di • ri. CJ 0 3 = CD X TJ 4J xi Φ SH Dl = πü

Φ O Φ 4-> <• PS 4H> (Tj CN ß ß SH PS CN> Φ ß xi Φ J X! Ss i

4J Ω TJ ri 3- CÖ SH ß O a ^• H Φ O a φ CN ß Dl φ o CQ ß O cö Φ ß ß ri Φ N ß X ß Φ H 4J SH TJ ß rH TJ Dl rH -H ß Dl • It's 4J CD

Φ SH cö Φ -ri X Φ H Φ TJ XI to -H Φ H Φ Φ Φ SH Dl Dl CQ ε Φ ß 4-1 TJ 4-1 rl> ß CJ a Di CQ 4-1 -H rH -ri rH Φ φ rH CD

Φ T -H CQ 4J rl φ X ß ß X ^• H ß ß .. Φ 4-> CQ SH Dl rH X • H CM -HX • H Φ rH Φ SH 4H Xi φ X 1 H φ 0 SH 0 a TJ SH ^• H Xi -H 0 Φ HX SH Φ J

Φ 4J 4H Φ a = 0 Di ro = a Dl PS rH i4 X ß Xi ß ß 0 4J PS

X ß a> cö xs cö a 4H ri öS «

CM ε Φ -H Φ -H 0 Xi Φ PS -H N Ct¬

CJ Φ rö rl rH r- a 4-1 X

> -H Di φ Φ Φ • ri CQ PS U 03 Φ H X φ Φ o X TJ 4H -H ε CQ N CQ SH r-i a -H S X cn: CÖ CD N Φ CQ rl Φ Φ CÖ

SH TJ r- Φ J D) rH 4-1 TJ ß CM Ω CJ 4-1 ß ε Φ Xi ß CÖ φ SH CQ Xi X Xi

Ω o J a CM 4J CQ ß Φ CQ SH Φ ß φ TJ CJ -rl TJ TJ X! CÖ CJ = P SH

SH H ß SH o SH ß Xi ^• H a Di SH. SH Φ TJ φ Dl ß -H Φ 0 TJ ^• ri Φ

CQ Φ rö Ω rH ö Φ J Φ Φ 4-) Φ Di ß SH CQ Φ Φ Φ SH PS ri • ß ri D ⁾ ß ß XI CQ -H CN - ^• H TJ SH> cö Φ Φ Dl Dl rH ß - ri Φ CQ TJ 4-) ß

<cö Φ -H SH CQ S rH CD O 4J XI Φ rH Dl TJ ß Φ CD H TJ ß ß CQ Φ CQ -ri • rH CΛ Φ Φ φ Φ = as rH ri rl ^• H Φ Φ Φ ß a -H -H Φ CÖ -H -H ß

• ß r-i a TJ rl SH i rH a Φ 4-1 X Dl -H rö TJ X SH. ". Φ TJ TJ xi Φ in φ ß Φ = a N Xi TJ CD SH N ß 0 φ -a XI ß Φ 4-1 4-1 ß J 5 H X

Dl Xi ß 0 a φ S 4H • ri SH öS SH ß -H Φ SH ß φ 0 co

TJ Φ CO J a TJ 4H rH φ ß PS Cn ß ß 0 Φ CQ Φ 4J ö ß rö -H 0 -H a Φ 4H N TJ Φ • H Di CQ SH a -H

SH CD a S Di CÖ CN CD XI N ß SH .. rH Dl Φ φ cö Φ Xi

Φ ß rö X ß 4H i S Φ o TJ ß o Xi -H Φ ß 4J • H öS D ⁾ -H .. 4-1 CD CJ

5 CQ 0 4-1 φ -cö Φ a -H H X Φ CQ Φ -H SH X! rH ß X! ß ß xi a CQ rH i S o Dl TJ fc-S SH 4J TJ rö O υ SH Φ SH Φ ß rö ω Φ a Φ au -cö SH a ß ß Φ CD ß o Di SH -H TJ TJ 4-1 Φ • ri Φ Dl

Φ a φ xs a XI -H Xi φ ε TJ -H Φ ro H a Xi rH Di TJ. CD 4-J Φ N CJ Di Φ Φ>

X TJ Φ rH Di Di o Φ 0 TJ Dl Φ • H ß -H ß SH SH co ß SH D)

0 ß TJ ε rH φ ß ß c-> Φ H ß N PS Φ -H X Φ • H ß rH Φ rö TJ CQ 4J rö Φ ß co

X a -H Φ -H • ri Φ H -H Φ X • ri 4H CJ N Φ rö • ri ε X CQ Φ Φ Dl XI Φ φ J ß 4-> X φ xi X ß rH Φ X = rö X) XX Φ X ß J Dl

CQ ß Φ vo CD Φ • SH ri a H Φ rH φ TJ CJ «rH ∞ CÖ rH Φ 0 CX ¹ 0 Dl rH

XI o rl a ß SH Ö) a 0 0 3ϊ ß co 4H H CQ ß 4J Φ -H Dl> Φ 0 Φ

Di XI φ rH φ N -H Ω -H N PS Φ

Φ υ Φ φ Φ -H cö ß CÖ Φ -rl -H ^• H ß -H CÖ -H • H Φ H SH H 0 ^• rl φ

H Di CD rH CQ ß H ε 4-1 -H ε

Ω TJ Ω TJ J CQ XI a Φ 4H Cn 3Ϊ ϊ rH Ω H PS P co CQ -H TJ 3ϊ

CQ Φ SH

Φ ß ß co • ri -H Φ • 4-J Φ Φ ß fN IΛ φ Φ ro ß CD TJ φ rH 03 • rl Φ ß CN

H ro o Φ ß ß SH -rl r-i vo - ö TJ J 0 r- φ

Φ a 0 ß 0 Di 3- 4-J Φ SH φ ß φ CQ

Dl Di rl ß SH Xi ß ß a CQ ß Dl CD Dl P Ω Φ rH ß ω Φ a TJ SH O υ Φ = cö 4-1 N φ φ CD Dl Φ ß SH CÖ Φ

-H Φ ß - O Ω CD xi J Di Dl rH Dl ß -H Φ •.

HX ε TJ U CQ N a ^• F Ω Φ J a ε ß rl ß a XI TJ 4-1 4H 0 -ri ß α. ΛS co ε Di -H Φ Φ Φ -HO a Dl SH a PS ß φ ε SH CN ß Φ Φ ß N ß Φ OS TJ Φ a. Φ as -H Di a Φ co - -ri TJ CN SH ^• H SH -H ß -HN XI TJ ß ε Φ

N 3-ro φ co Φ Φ Φ Φ 4 SH -H CQ ß 4J Φ -H

Φ - co J X -H Φ 4H ε TJ -cö X! TJ rl X ß Di H TJ ß - co Xi Dl ß Φ. Ό SH Φ Φ υ ß a

Φ Φ CO ß ß a H 4J CJ ß aS x; Φ X! ß - ro ^• ri φ ß a

SH ^• ri Φ a 00 4J SH a ß Dl CJ ^• H Dl r ß Dl N

X! CQ Φ SH vo -H a Di CD ^• ri ß ε ^• H Φ ß Φ H π5 CQ XI Φ co Φ ß T Φ Φ φ a Φ rH a ß ß -ri E- ^* ε

4H ß a 0 4-J CQ XS -H CQ rH TJ TJ ß rH SH Φ XI Φ rl ^• ri ^* CÖ es ß ß a υ CQ CQ CQ φ rH Φ cö ri O 4-1 Dl ß

Φ Φ s Φ φ: CÖ CQ CQ a 4-1 Φ 4J ^• ri Φ Ω Φ aa -H

> φ -H ε rH Xi SH rö Φ -H ß 4-J ^• HX Dl 4J SH N Φ Φ

Xi Dl φ Φ rH φ φ TJ ß J Φ CQ 2 ü ß CD ε 4-JN ε u CQ 3ϊ ri 0 Di a ^• H OS N a CD aa Φ CQ X ß φ rl Dl N Φ es CQ er 0 Φ SH XN. 4J N TJ ß Φ rl CÖ ß a ß X Di J CQ Φ w rH CN Φ Xi Φ ß φ

-H TJ a ß CJ ß ß ß CN Di CÖ co 4J υ φ TJ Dl -H 3- ß in φ SH oa Φ a cö - r- Φ φ -H ß ^• H -H ß ß Φ φ Φ

CN CN xi> SH TJ SH £ 4J ^• H -H - υ Φ ä a SH TJ aa Di ε

-H c- = a Ω XI X CD CQ TJ H rl ε Di Φ φ Cn 4-J ß = a ß 00 XI 0 ß vo SH ß -H 0

XI SH Φ co Φ Cn Φ co SH CQ SH Φ υ rö co 0 a PQ Cn

X! rH TJ rH X! 1 X! 4J XI φ Φ ß Φ -H Φ ε 4H Di •

TJ 0 -H rH Ö υ rH ü φ 0 ß XI -H CD CO Dl ß SH Φ ß Φ ß ß PS 4H ^• H CQ -H -H a OS -H = a Φ a Φ ε Φ Φ -H Φ Dl Φ a 0 XI ß -rl 4H rH r Φ ^• cö ß -H Φ rH> CQ 4J -H TJ

CQ SH φ Φ 5 o TJ Φ co Φ SH Xi Φ CQ TJ rH N XI SH

Dl rö Pu D ß N φ Di φ Φ -H Φ Φ CD ß 0 SH SH 4J φ Φ ß TJ Φ CM ^• H TJ 03 TJ TJ DI CD ß ^• H es Φ Φ Φ • ri 5 a ß »-H TJ X! X -o 0 CD CÖ Φ TJ TJ CQ rH

4-1 TJ ^• ri 4-J TJ ß CQ CJ Dl SH 4J -> - »» Dl rH X «. ß 0 Φ Φ 4y

Xi SH φ -H a cö CD cö ß CD CQ TJ ß r-i ß Φ 4H Dl XI r-i J -H Φ VO J SH 4-J a -H ß a -i Φ Φ TJ Φ a ß r-i

^• H 3. B xi co - Φ o XI Φ a r- CO TJ CQ ö -rl CQ Φ

SH a ß SH X! 4J υ -H CN X r-i ß co rH φ CQ 4J

CN ^• H ß Φ υ ß xi a TJ 4J = a Di Φ -ri φ -H SH rö CD

0 f- CQ Φ φ Di SH a υ ö ^• cö Cn a TJ XX os Φ ε TJ Φ

> Ö H rö a ^• H 4-J SH SH 4J φ CD u> Φ Dl co TJ φ rH rH TJ ß rH cn -a XI -H rH N TJ a CD φ TJ 0 SH

SH φ 4J o ß rö TJ 4H 0 N ^• HX ß rö • rl 4-J Φ CD Φ

Φ SH - ß es Φ CQ φ Φ es -H 4H a 5 SH X ß X! ß Xi 4-J Φ Dl cö CN • rl ß 03 SH 0 φ CN N Φ ü 0 ~

Φ φ Φ Φ ^• H ri • rl 0 Φ ß ^• H φ X a ^• H ß 0 4J rl = CÖ -H SH

CQ ß Di ß 4J rö 3- os 4J a ω Di ω N CQ ^• H OS CQ 4J SH 3- Dl CM

Claims

claims

Device for bending profiles with a profile wall, which has wall cross-sectional areas at different distances from the axis of the bend to be carried out, comprising a bending tool with at least one pressure element assigned to the outside of the profile wall, the bending tool having at least one counter pressure element assigned to a pressure element, and wherein at least a pressure element and at least one counterpressure element associated therewith, with squeezing at least one wall cross-sectional area of the profile wall that is external to the axis of the bend and can be moved relative to one another in the cross-sectional direction thereof,

characterized,

that the pressure element or elements (17; 27; 37; 47; 57; 67; 86; 106; 116) the counter pressure element or elements (13; 23; 33; 43; 53; 63; 73; 103; 113) seen in cross section while maintaining a gap with a gap width that is at least in a cross-sectional area smaller than a wall cross-sectional area of the profile to be bent, which is transported through the gap.

2. Device according to claim 1, characterized in that the gap is adjustable in size and / or cross-sectional shape.

3. Device according to claim 1 or 2, characterized in that the profile is pushed through and / or pulled through the gap.

4. Device according to one of claims 1 to 3, characterized in that the or the pressure elements as a stamp (17), rollers and / or rollers (27; 37; 47; 57; 67; 86; 106; 116) are formed.

5. Device according to one of claims 1 to 4, characterized in that the counter-pressure element or elements as a mandrel (13; 23; 33; 73; 103; 113), support jaws (43), anvil, rollers, rollers (53; 63) and the like are formed, which abut the inner wall cross-sectional areas of the profile wall.

6. The device according to claim 4 or 5, characterized in that the roller, roller or several rollers, rollers are rotatably mounted parallel to the axial course of the profile or with a roll axis of rotation transverse to the axial course of the profile.

7. The device according to claim 6, characterized in that the or the pressure elements (17; 27; 37; 47; 57; 67; 86; 106; 116) and / or the or the counter pressure elements (13; 23; 33; 43; 53; 63; 73; 103; 113) can be pressurized to different extents across their extent transversely to the axial profile.

8. Device according to one of claims 1 to 7, characterized in that the profile (72) during a bending process via holding means, such as a chuck (79), held stationary, axially displaceable and / or rotatable about an axis of the profile (72) is.

9. Device according to one of claims 1 to 8, characterized in that the device for bending has a stationary profile guide housing (81, 82) and an eccentric unit (83, 84) surrounding the profile guide housing (81, 82), on which, independently of the eccentric unit (83, 84), is rotatably mounted, the pressure element (s) (86) are arranged.

10. The device according to claim 6, characterized in that the or the pressure elements (86) are adjustable in their assignment to the profile guide housing (81,82) independently of the eccentric unit (83,84).

11. The device according to claim 9 or 10, characterized in that the eccentric unit is formed from a first and a second tube (83, 84), the tubes (83, 84), viewed in cross section, being arranged one above the other and being rotatable relative to one another, and Pipes (83, 84) have different wall thicknesses seen over the circumference.

12. The apparatus according to claim 11, characterized in that the circular tubes (83,84) can be fixed in any rotational position. co fN Xi Di Xi xi TJ ß -H TJ Di rl IΛ CJ SH ß ü CJ ß φ rl

SH 03 XI a φ φ 4-1 CD TJ a TJ ß a • a -. 3- Φ a ß rö -rl a -H Dl © TJ 0 TJ TJ TJ TJ X! rH α. ε 4H 3- CÖ -H TJ TJ rH σ Φ ß CQ rö SH rö ö ß cö co -rl ω Φ a SH ß CQ: CÖ rH

TJ - ~. 0 XI TJ -H J, -. φ 4H xi rö ß Dl TJ TJ • ri Φ ß TJ r-i cö

H Φ σi a rH Φ ri CQ - xi 0 o φ ß ß ß 3- ß ^• ri -H ri U »4-J co tsl rH - 4J ^• ri oo υ SH -H Dl Dl a rö a ß Φ -ri J α. CN ß - Φ ro ß 4H 4J ^• ^ CD Cn rH ß 0 Di 3- 4-1 ^• H TJ X 4H SH rH Φ SH 4-J rH Φ 0 Φ H ro ^• H TJ a X Φ ri 4-J Dl ß 0 -rl ε ß φ CD ε u ß co ß SH Φ Dl Φ -H -H Di ß Dl CÖ SH SH 2Ϊ

CQ Φ Φ SH SH CQ Φ Cn TJ CQ cö Φ -H Φ Dl CQ 4H rö: CÖ ß S Φ Cn

^• H rH Di XS φ -H rH) H -H xi ß XS ^• H 0 rH rH a rH TJ 4-J

XI Φ ß -H> X Φ φ 0 X 4-J CJ -H ü CQ Φ SH XI Φ • ri 0 ß Di

X rö X TJ Φ -H φ Φ CD r-i Φ C u Di Φ 4H -ri ß

E- u 4-J ß rH CJ ß Dl σi Φ ε SH ß -rl J CQ ^• H o 4-J = CÖ a CD ^• HH a φ ß X! 4J Φ Φ 4H 4H Di CQ SH XI TJ rH X! φ SH rH o Φ SH i CÖ Φ ß ß -H 4J TJ 0 Φ Φ a ß Cn ^• H ß Φ CJ xs Ω -H _^ - H Xi Ω φ X! • ri ^• H ε ß ß SH co TJ CÖ

O u -H a φ a Di -rl o φ SH J φ φ a φ P ^ xi Φ 4-1 Φ SH r-i Φ

= a Φ ^ o CN = a Φ X ö = a ß SH ü XI XI Xi TJ Φ X 4J φ SH

SH -HH CO SH ^• HX φ SH Φ 4-1 X Φ> U CJ TJ Xi 03 φ a TJ φ - - a TJ aa 4-1 φ rH -HD SH H CD N = a -H -H Di ^• H Φ 4-1 ü rö XI

Φ CQ ß xi -H ε 4H J φ Φ ^• H SH CQ Xi Dl CD 2 CQ ß rl Φ ß 00 ß SH -H ß φ = a 4H a ^• H ^ H 4-1 CD Xi υ ö 4-J 4 -> φ SH Φ - <Φ CQ 4-1 <N 0 Φ N rl TJ Φ -H Di CJ -H ri Φ ß 4J

TJ i CO TJ rö 0 X SH SH xi CQ φ XI Φ ß Φ X

0-1 a Φ • ri

0 Φ rH Φ 0 TJ SH w Φ CM CJ SH ß CM Φ a TJ 4H CQ CQ ^• cö SH CJ er ε = a CO φ Φ TJ -rl cö oa 4J TJ rH φ Φ CQ Φ Φ i

TJ CD sa TJ o ε _^ - »TJ φ 0 ß φ a 4J -H rH -H XI 4H cn Di CJ

CÖ rl o: CÖ rö a CN • rl • 0 SH SH rH -H Φ ^• H TJ CQ a ß CQ ε TJ φ a X! ε TJ rH ε TJ Xi 4-1> Φ Φ ^• H ß ß XI 4H 4J et ^• H ^• H SH 4-J

Φ J ß φ Φ H Φ CJ CQ XI TJ 4H Φ i O 4H 4-J Φ Φ SH Φ φ ß CQ 0 0 Di ß CD vo • _^ ß CQ CD • ri ß CQ 0 Dl U Dl rl

^• H CD ^ CD -H CD H CN -H CD ^• H a -H XI X5 Φ a ß

Φ 4J Φ SH 0 CQ ß CM cö ß ß cö Di er XI

Φ CÖ φ Dl Φ CÖ rH O Φ CÖ 4-1 SH Di 4J CQ CM N SH

TJ a XI a TJ TJ u ß Φ ß TJ r-i TJ Ö ö Φ -ri Xi φ φ 4J ß ß υ ε ß -H

XI -H SH a X! vo Xi ε XI -H ß ü ß XI a XI ^• H φ CQ Dl TJ φ rö Φ J - Φ Φ SH CJ - o CN υ a ri CQ xi <-H er u Dl ß ß ß 3: N ö 4J Xi cö 4J rH r- a 4J φ ri υ Φ ß T ^• ri TJ o φ aa ^• H ß ß Φ SH X = a ß Φ • _^ ß Φ ß Φ ε CD -rl ß rl ß N a 4J φ φ ß ß Φ Φ Cn ß VO CM ß a 4J a SH φ ^• H φ aS CD a φ er s 4-J TJ Φ

D ⁾ X XI ε Di Xi co O Dl X! CD N Φ TJ Φ 3: 4J XI TJ CJ Di ß ß X ß J = a rH ß J • »... ß υ SH a XI B 4J 4-> ß -H rö ^• H φ φ a -H SH - H a -H r- CN a -ri XI φ ß er ß 0 φ SH ^• ri Xi ß rö SH ri Dl Dl

4-Y Φ -. Φ 4H 4J Φ ro ro 4J φ CJ> Φ J 0 s TJ Φ ß ü • ri 3: CQ X Di Φ i N vo TJ 0 XI N • - • ~ i N CD rl ß> ß TJ xi CQ φ 4- 1 υ ß -rl Xi

CJ ß o 0 SH CJ ß CN υ ß ^• H φ XS cö -H ß U 4-J SH 4J co

-H a ri ü ß rH CM -H ß CN CN ^• rl ß rH XI 3: TJ 4-1 Φ CQ Φ B Φ -ri 4H 4-1 ß

SH Φ • - Φ TJ SH Φ • ~ • »φ a Φ 4H ß CQ - Dl SH a φ TJ ß a X! Φ

SH a

X VO ß ε ß SH X r- CN X ö -H SH Φ rö -H ß Φ φ er TJ ß i ö ü 03 J

0 φ co ^• H a -H 0 φ H rH 0 φ SH SH Φ -H 4J Φ Φ -H

> Dl Φ>Di> Dl TJ 4-1> J CD 5 TJ rH σ CD -H Di CQ X) SH ⁽ Ö TJ

©

that at least one section wall section of a section to be bent or sections to be bent is transported through a gap formed by pressure and counter-pressure elements, which causes the pinching.

17. The method according to claim 16, characterized in that one or more wall cross-sectional areas of the profile wall are acted upon and squeezed by one or more movable punches (17) or one or more rotatable rollers (86), rollers which are connected via an eccentric unit (83, 84 ) and / or via infeed devices (89; 107) are moved more or less far from the longitudinal axis of the profile (12; 22; 72; 102; 112) to be bent.