EP1368575A1 - Rotationally elastic shaft coupling - Google Patents

Rotationally elastic shaft coupling

Info

Publication number
EP1368575A1
EP1368575A1 EP02750545A EP02750545A EP1368575A1 EP 1368575 A1 EP1368575 A1 EP 1368575A1 EP 02750545 A EP02750545 A EP 02750545A EP 02750545 A EP02750545 A EP 02750545A EP 1368575 A1 EP1368575 A1 EP 1368575A1
Authority
EP
European Patent Office
Prior art keywords
flange
joint
shaft coupling
shaped
joint body
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP02750545A
Other languages
German (de)
French (fr)
Inventor
Rainer ANDRÄ
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
SGF Sueddeutsche Gelenkscheibenfabrik GmbH and Co KG
Original Assignee
SGF Sueddeutsche Gelenkscheibenfabrik GmbH and Co KG
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by SGF Sueddeutsche Gelenkscheibenfabrik GmbH and Co KG filed Critical SGF Sueddeutsche Gelenkscheibenfabrik GmbH and Co KG
Publication of EP1368575A1 publication Critical patent/EP1368575A1/en
Withdrawn legal-status Critical Current

Links

Classifications

    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16DCOUPLINGS FOR TRANSMITTING ROTATION; CLUTCHES; BRAKES
    • F16D3/00Yielding couplings, i.e. with means permitting movement between the connected parts during the drive
    • F16D3/16Universal joints in which flexibility is produced by means of pivots or sliding or rolling connecting parts
    • F16D3/20Universal joints in which flexibility is produced by means of pivots or sliding or rolling connecting parts one coupling part entering a sleeve of the other coupling part and connected thereto by sliding or rolling members
    • F16D3/202Universal joints in which flexibility is produced by means of pivots or sliding or rolling connecting parts one coupling part entering a sleeve of the other coupling part and connected thereto by sliding or rolling members one coupling part having radially projecting pins, e.g. tripod joints
    • F16D3/205Universal joints in which flexibility is produced by means of pivots or sliding or rolling connecting parts one coupling part entering a sleeve of the other coupling part and connected thereto by sliding or rolling members one coupling part having radially projecting pins, e.g. tripod joints the pins extending radially outwardly from the coupling part
    • F16D3/2055Universal joints in which flexibility is produced by means of pivots or sliding or rolling connecting parts one coupling part entering a sleeve of the other coupling part and connected thereto by sliding or rolling members one coupling part having radially projecting pins, e.g. tripod joints the pins extending radially outwardly from the coupling part having three pins, i.e. true tripod joints
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16DCOUPLINGS FOR TRANSMITTING ROTATION; CLUTCHES; BRAKES
    • F16D3/00Yielding couplings, i.e. with means permitting movement between the connected parts during the drive
    • F16D3/50Yielding couplings, i.e. with means permitting movement between the connected parts during the drive with the coupling parts connected by one or more intermediate members
    • F16D3/78Yielding couplings, i.e. with means permitting movement between the connected parts during the drive with the coupling parts connected by one or more intermediate members shaped as an elastic disc or flat ring, arranged perpendicular to the axis of the coupling parts, different sets of spots of the disc or ring being attached to each coupling part, e.g. Hardy couplings
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10STECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10S464/00Rotary shafts, gudgeons, housings, and flexible couplings for rotary shafts
    • Y10S464/904Homokinetic coupling
    • Y10S464/905Torque transmitted via radially extending pin

Definitions

  • ⁇ o ⁇ P LQ ⁇ ⁇ 0 P ⁇ tr ⁇ P. ⁇ F 1 J CQ ⁇ ⁇ LQ P F- Hj P F- F- rt
  • the invention is therefore based on the object of providing a rotary-type shaft coupling which is particularly suitable for front-wheel drives of motor vehicles and which, given the torque to be transmitted, takes up a small amount of space and runs essentially unbalanced even at high speeds.
  • a torsionally flexible shaft coupling according to the invention can be composed of a universal joint of conventional design, in particular of a standard cross-pin joint, tripod joint or cage-controlled constant velocity joint, on the one hand, and a number of likewise conventional elastic coupling elements, including associated fittings, on the other hand. It is therefore possible to consistently use components which have proven themselves in series vehicles and which are low-cost. are adjustable. With the invention it is achieved, among other things, that the first flange is centered in relation to one another with respect to the counterflange, and thus two rotating bodies, in particular shafts, connected by a shaft coupling according to the invention for the transmission of torques, and yet remain acoustically decoupled from one another. also with regard to radial vibrations of high frequency. In addition, the elastic coupling elements are not significantly stressed on bending, but essentially only on tension, even when large torques are transmitted.
  • the sliding blocks provided in accordance with claim 2 ensure that the mutual centering of the two flanges remains essentially wear-free even if the shafts or other rotating bodies connected by the shaft coupling according to the invention execute torsional vibrations of large amplitude and / or high frequency with respect to one another.
  • the tube section of the first joint body is used twice in a particularly space-saving manner, namely inside as a component of the universal joint, which is essentially rigid with respect to the angle of rotation, and outside as a component of the centering described.
  • the features of claim 5 also serve the purpose of keeping a sufficiently large installation space within the ring of elastic coupling elements for accommodating a highly resilient universal joint.
  • PJ PJ LQ Pi 3 F "P.> d ⁇ P ⁇ P rt 0 P CQ P CQ P F- rt LO 0 Hi ⁇ ⁇
  • Wreath 40 made of elastic Kup lungselerne 42 held with its right end face in Fig. 3 on the two flanges 22 and 34.

Landscapes

  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Shafts, Cranks, Connecting Bars, And Related Bearings (AREA)
  • Motor Power Transmission Devices (AREA)

Abstract

A collar (40) consisting of loop-type elastic coupling elements (42) which each loop round a first moulded part (50) and a second moulded part (52) is arranged around a universal joint (12) comprising a first and a second essentially rigid joint body (14, 28). The first moulded parts (50) are rigidly connected to the first joint body (14) by means of a flange (22) and are arranged between the second moulded parts (52). The second moulded parts (52) are connected to a counter-flange (34) in a fixed manner, said counter-flange pertaining to a rotating body (62). Said rotating body forms an end of a torque transmission chain, the other end thereof representing the second joint body (28). The first joint body (14) comprises a tubular part (16) enveloping the second joint body (28), said tubular part comprising an outer generated surface (18) having a circular cross-section and supporting the elastic coupling elements (42) in the radial direction.

Description

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lenks mit hohen Drehmomenten nicht genügend lang standhalten, sofern sie aus einem Elastomer bestehen, das weich genug ist, um eine ausreichende Schwingungsentkopplung zu bewirken.Steers with high torques do not withstand long enough if they consist of an elastomer that is soft enough to provide sufficient vibration decoupling.
Für Vorderradantriebe von Kraftfahrzeugen sind Wellenkupplungen erforderlich, die große Winkelausschläge von 30 Grad und mehr ermöglichen und zugleich wenig Bauraum, vor allem in radialer Richtung, benötigen. Diesen Anforderungen entsprechen bekannte starre Kreuzzapfengelenke, Tripodegelenke und käfig- gesteuerte Gleichlaufdrehgelenke, die jedoch sämtlich denFor front wheel drives of motor vehicles, shaft couplings are required which allow large angular deflections of 30 degrees and more and at the same time require little installation space, especially in the radial direction. Known rigid cross-pin joints, tripod joints and cage-controlled constant velocity joints meet these requirements, but they all do
Nachteil haben, Schwingungen nahezu ungedämpft zu übertragen. Um störende Schwingungen zu eliminieren, hat man deshalb versucht, solche Gelenke und elastische Gelenkscheiben axial in Reihe anzuordnen. Dadurch ergeben sich jedoch Doppelgelen- kanordnungen, bei denen ein drehmomentübertragendes Bauteil, beispielsweise Wellenstück, zwischen dem starren Universalgelenk und der elastischen Gelenkscheibe nicht ausreichend geführt ist und infolgedessen eine Unwucht hervorrufen kann, die ihrerseits störende Schwingungen erzeugt .The disadvantage is that vibrations are transmitted almost undamped. In order to eliminate disturbing vibrations, attempts have therefore been made to arrange such joints and elastic joint disks axially in series. However, this results in double joint arrangements in which a torque-transmitting component, for example a shaft piece, is not adequately guided between the rigid universal joint and the elastic joint disk and, as a result, can cause an imbalance, which in turn generates disruptive vibrations.
Der Erfindung liegt deshalb die Aufgabe zugrunde, eine insbesondere für Vorderradantriebe von Kraftfahrzeugen geeignete dreheleastische Wellenkupplung zu schaffen, die bei gegebenem zu übertragenden Drehmoment einen geringen Bauraum bean- sprucht und auch bei hohen Drehzahlen im wesentlichen unwuchtfrei läuft.The invention is therefore based on the object of providing a rotary-type shaft coupling which is particularly suitable for front-wheel drives of motor vehicles and which, given the torque to be transmitted, takes up a small amount of space and runs essentially unbalanced even at high speeds.
Die Aufgabe ist erfindungsgemäß mit den Merkmalen des Patentanspruchs 1 gelöst .The object is achieved with the features of claim 1.
Eine erfindungsgemäße drehelestische Wellenkupplung kann aus einem Universalgelenk üblicher Bauart, insbesondere aus einem serienmäßigen Kreuzzapfengelenk, Tripodegelenk oder käfiggesteuerten Gleichlaufdrehgelenk einerseits und aus einer An- zahl ebenfalls üblicher elastischer Kupplungselemente samt zugehörigen Formstücken andererseits zusammengesetzt sein. Es lassen sich also durchwegs Bauteile verwenden, die sich in Serienfahrzeugen bewährt haben und mit geringen Kosten her- stellbar sind. Mit der Erfindung wird unter anderem erreicht, dass der erste Flansch in Bezug auf den Gegenflansch, und somit zwei durch eine erfindungsgemäße Wellenkupplung zur Übertragung von Drehmomenten miteinander verbundene Rotationskör- per, insbesondere Wellen, in Bezug zueinander zentriert werden und dennoch akustisch voneinander entkoppelt bleiben, auch bezüglich Radialschwingungen hoher Frequenz. Außerdem werden die elastischen Kupplungselemente selbst bei Übertragung großer Drehmomente nicht nennenswert auf Biegung, son- dern im wesentlichen nur auf Zug, belastet.A torsionally flexible shaft coupling according to the invention can be composed of a universal joint of conventional design, in particular of a standard cross-pin joint, tripod joint or cage-controlled constant velocity joint, on the one hand, and a number of likewise conventional elastic coupling elements, including associated fittings, on the other hand. It is therefore possible to consistently use components which have proven themselves in series vehicles and which are low-cost. are adjustable. With the invention it is achieved, among other things, that the first flange is centered in relation to one another with respect to the counterflange, and thus two rotating bodies, in particular shafts, connected by a shaft coupling according to the invention for the transmission of torques, and yet remain acoustically decoupled from one another. also with regard to radial vibrations of high frequency. In addition, the elastic coupling elements are not significantly stressed on bending, but essentially only on tension, even when large torques are transmitted.
Bei den aus Fig.2 und 4 der EP 0 563 940 A bekannten Wellenkupplungen ist zwar auch schon dafür gesorgt, dass die miteinander verbundenen Wellen in Bezug zueinander zentriert werden, doch geschieht dies durch eine metallische Mittenzentrierung an den einander kreuzenden Gelenkbolzen; diese Mittenzentrierung ist für eine akustische Entkopplung nicht geeignet .In the case of the shaft couplings known from FIGS. 2 and 4 of EP 0 563 940 A, it is already ensured that the shafts connected to one another are centered in relation to one another, but this is done by means of a metallic centering on the joint pins crossing one another; this centering is not suitable for acoustic decoupling.
Norteilhafte Weiterbildungen der Erfindung ergeben sich aus den Unteransprüchen:Advantageous developments of the invention result from the subclaims:
Die gemäß Anspruch 2 vorgesehenen Gleitsteine bieten Gewähr dafür, dass die gegenseitige Zentrierung der beiden Flansche auch dann im wesentlichen verschleißfrei bleibt, wenn die durch die erfindungsgemäße Wellenkupplung miteinander verbundenen Wellen oder sonstigen Rotationskörper in Bezug zueinander Drehschwingungen großer Amplitude und/oder hoher Frequenz ausführen.The sliding blocks provided in accordance with claim 2 ensure that the mutual centering of the two flanges remains essentially wear-free even if the shafts or other rotating bodies connected by the shaft coupling according to the invention execute torsional vibrations of large amplitude and / or high frequency with respect to one another.
Bei der im Anspruch 3 beschriebenen Weiterbildung ist das Rohrstück des ersten Gelenkkörpers in besonders raumsparender Weise zweifach genutzt, nämlich innen als Bestandteil des - im wesentlichen drehwinkelstarren - Universalgelenks, und au- ßen als Bestandteil der beschriebenen Zentrierung.In the development described in claim 3, the tube section of the first joint body is used twice in a particularly space-saving manner, namely inside as a component of the universal joint, which is essentially rigid with respect to the angle of rotation, and outside as a component of the centering described.
Während bei der aus EP 0 563 940 A bekannten Wellenkupplung mit einem modifizierten Kreuzzapfengelenk der Kranz aus ela- stischen Kupplungselementen nur vier solche in Umfangsrich- tung hintereinander angeordnete Elemente enthält, ist gemäß Anspruch 4 eine größere Anzahl elastischer Kupplungselemente in der erfindungsgemäßen Anordnung vorgesehen. Dadurch wird radial innerhalb der elastischen Kupplungselemente ein verhältnismäßig großer Bauraum für ein entsprechend hoch belastbares Universalgelenk freigehalten.While in the shaft coupling known from EP 0 563 940 A with a modified cross-pin joint, the ring made of elastic tical coupling elements contains only four such elements arranged one behind the other in the circumferential direction, a larger number of elastic coupling elements is provided in the arrangement according to the invention. As a result, a relatively large installation space for a correspondingly highly resilient universal joint is kept free radially within the elastic coupling elements.
Auch die Merkmale des Anspruchs 5 dienen dem Zweck, innerhalb des Kranzes elastischer Kupplungselemente einen ausreichend großen Bauraum zur Unterbringung eines hoch belastbaren Universalgelenks freizuhalten.The features of claim 5 also serve the purpose of keeping a sufficiently large installation space within the ring of elastic coupling elements for accommodating a highly resilient universal joint.
Die Weiterbildung gemäß Anspruch 6 garantiert, dass sämtliche elastischen Kupplungselemente mit der wünschenswerten Genauigkeit symmetrisch zu der gemeinsamen, zur Gelenkachse normalen Mittelebene des Universalgelenks und des Kranzes aus elastischen Kupplungselementen angeordnet werden und bleiben. Bei der aus EP 0 563 940 A bekannten Wellenkupplung ist dies wegen nicht immer vermeidbarer Formungenauigkeiten und im Betrieb auftretender Formänderungen der elastischen Kupplungs- elemente nicht gewährleistet.The development according to claim 6 guarantees that all elastic coupling elements with the desired accuracy are and remain symmetrical to the common central plane normal to the joint axis of the universal joint and the ring of elastic coupling elements. In the shaft coupling known from EP 0 563 940 A, this is not guaranteed because of inaccuracies in shape which cannot always be avoided and changes in shape of the elastic coupling elements which occur during operation.
Die Gestaltung der Formstücke gemäß Anspruch 7 und Vorzugs- weise auch Anspruch 8 erleichtert die Herstellung und Montage des Kranzes aus schlingenförmigen elastischen Kupplungselementen.The design of the fittings according to claim 7 and preferably also claim 8 facilitates the manufacture and assembly of the ring from loop-shaped elastic coupling elements.
Schließlich hat sich die in den Ansprüchen 9 und 10 beschrie- bene Gestaltung und Anordnung der Flansche als besonders montagefreundlich und raumsparend erwiesen.Finally, the design and arrangement of the flanges described in claims 9 and 10 has proven to be particularly easy to install and space-saving.
Zwei Ausführungsbeispiele der Erfindung werden im folgenden mit weiteren Einzelheiten anhand schematischer Zeichnungen beschrieben. Darin ist: L»J > t t F F1 Two exemplary embodiments of the invention are described in more detail below with the aid of schematic drawings. In it is: L »J> tt FF 1
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Pi F- P φ H Φ LQ rt F- VD LQ Φ CQ rt rt <J φ Φ P) P F- Φ Φ CQ tr ^ 0 Ω LQ rtPi F- P φ H Φ LQ rt F- VD LQ Φ CQ rt rt <J φ Φ P ) P F- Φ Φ CQ tr ^ 0 Ω LQ rt
PJ= PJ LQ Pi 3 F" P. >d Φ P Φ P rt 0 P CQ P CQ P F- rt LO 0 Hi Φ ΦPJ = PJ LQ Pi 3 F "P.> d Φ P Φ P rt 0 P CQ P CQ P F- rt LO 0 Hi Φ Φ
P tr Φ φ Φ Φ PJ F1 rt P CQ X Φ φ ) α Hj Pi rt LQ rt P= P Φ oo - P) Hi Z P F-P tr Φ φ Φ Φ PJ F 1 rt P CQ X Φ φ ) α Hj Pi rt LQ rt P = P Φ oo - P ) Hi ZP F-
P Q P LΠ F- CQ Hj ) - Φ P rt PJ LQ F- P F- P φ P 0 CQ tr Φ 1 Hj P 0= F- P= Ω φ Φ to P Φ PJ P Hj rt φ Ω P CQ Φ φ F- d 3 Φ Φ Φ Hi rt P P CQ Hi P tr trPQP LΠ F- CQ Hj ) - Φ P rt PJ LQ F- P F- P φ P 0 CQ tr Φ 1 Hj P 0 = F- P = Ω φ Φ to P Φ PJ P Hj rt φ Ω P CQ Φ φ F- d 3 Φ Φ Φ Hi rt PP CQ Hi P tr tr
Hi z J CQ CQ P F1 LQ P CQ Φ F" tr rf- Φ tr P »d Φ F- Hi Φ P Ω 3 P. Φ φ J P)= CQ PJ φ LQ F- rt Hi F1 CQ 00 H Φ ISl Hi Φ P . P L_I. CQ LQ tr F- φ Hj PHi z J CQ CQ PF 1 LQ P CQ Φ F "tr rf- Φ tr P» d Φ F- Hi Φ P Ω 3 P. Φ φ JP ) = CQ PJ φ LQ F- rt Hi F 1 CQ 00 H Φ ISl Hi Φ P. P L_I. CQ LQ tr F- φ Hj P
P) P P F- 3 ö Hj Φ φ Φ Φ tr rt Φ 0 Φ Φ Hj Φ P 3 Φ Φ Φ LQ trP ) PP F- 3 ö Hj Φ φ Φ Φ tr rt Φ 0 Φ Φ Hj Φ P 3 Φ Φ Φ LQ tr
P P. P P φ P F1 CQ CQ Hj - PJ < X Hj Φ F" P tt-. φ Pi Hj p. Ω P to Φ o LQP P. PP φ PF 1 CQ CQ Hj - PJ <X Hj Φ F "P tt-. Φ Pi Hj p. Ω P to Φ o LQ
Hl rt φ P CQ Hj >τj rt tr 0 P P) rt CQ F- P LQ (I-. P Hj Φ φ isj tr P. F1 Hl rt φ P CQ Hj> τj rt tr 0 PP ) rt CQ F- P LQ (I-. P Hj Φ φ isj tr P. F 1
Hi Ω 0 N Hj Φ w Ω P CQ F1 F- rt P CQ rt J CQ IQ t > Hj Φ Φ ι_ι. CQ LQ tr Hi P φ F- o tr P Hj φ F1 P>= tr Φ φ Φ P P Φ φ. P P P Hj F-Hi Ω 0 N Hj Φ w Ω P CQ F 1 F- rt P CQ rt J CQ IQ t> Hj Φ Φ ι_ι. CQ LQ tr Hi P φ F- o tr P Hj φ F 1 P> = tr Φ φ Φ PP Φ φ. PPP Hj F-
Φ F- F- φ 3 P LQ 3 Hj Ω P Hj Φ Hi PJ td tr Hj P φ F1 F- P ISl CQ frJ P 3 CQ P ΩΦ F- F- φ 3 P LQ 3 Hj Ω P Hj Φ Hi PJ td tr Hj P φ F 1 F- P ISl CQ f rJ P 3 CQ P Ω
P P 3 •d PJ CQ X Φ 3 P Ω P PJ X P Hj Φ P CQ PJ Hl P CQ LQ Ω p-P P 3 • d PJ CQ X Φ 3 P Ω P PJ X P Hj Φ P CQ PJ Hl P CQ LQ Ω p-
Φ P P)= >d P rt 3 rt CQ tr F- P) 0 P P Hj LQ 3 LQ *. rf- O PJ F1 Φ φ> >d Φ φΦ PP ) => d P rt 3 rt CQ tr F- P ) 0 PP Hj LQ 3 LQ *. rf- O PJ F 1 Φ φ>> d Φ φ
F- C! (Λ) LQ P= F- Φ F- rt CQ PJ CD Hj P P Ω φ φ φ to o PJ H ) CQ cπ J P LQ PJF- C! (Λ) LQ P = F- Φ F- rt CQ PJ CD Hj PP Ω φ φ φ to o PJ H ) CQ cπ JP LQ PJ
P P 3 P CQ Ω rt P P= φ Φ rt 3 LQ ' 1 P tr Hj P Hj φ PP P 3 P CQ Ω rt P P = φ Φ rt 3 LQ '1 P tr Hj P Hj φ P
Φ P 1 tl P F" X rt Ω F- F- 0 o CQ rt φ P) P) P Ω 1 Φ Ω P LO P CQΦ P 1 tl PF "X rt Ω F- F- 0 o CQ rt φ P ) P ) P Ω 1 Φ Ω P LO P CQ
3 P. F- LQ o Φ Φ Φ X P P Φ 3 P P. 1 P. Φ rt P P P Φ Hj Hj P σ\ LQ LQ CQ Ω 1 F- Φ Hi φ P Φ P) I CQ 1 1 1 J 1 Φ tr 1 Hj P Hj CQ P 1 3 P. F- LQ o Φ Φ Φ XPP Φ 3 P P. 1 P. Φ rt PPP Φ Hj Hj P σ \ LQ LQ CQ Ω 1 F- Φ Hi φ P Φ P) I CQ 1 1 1 J 1 Φ tr 1 Hj P Hj CQ P 1
LO LO to to F1 F1 LO LO to to F 1 F 1
Lπ O LΠ o LΠ O LΠLπ O LΠ o LΠ O LΠ
TJ Φ -i CQ H P α CQ p JTJ Φ -i CQ H P α CQ p J
0 Hj Φ Ω Hj Φ Φ Ω Φ J0 Hj Φ Ω Hj Φ Φ Ω Φ J
Hj CQ P. tr Φ Hi Ω tr CQ P.Hj CQ P. tr Φ Hi Ω tr CQ P.
3 F- Φ Φ F- X F-3 F- Φ Φ F- X F-
CQ Ω CQ PJ Φ F- tr P rt tr t tr tr φ φ CQCQ Ω CQ PJ Φ F- tr P rt tr t tr tr φ φ CQ
P= rt P. t F1 LQ Λ rtP = rt P. t F 1 LQ Λ rt
Ω Φ Φ Φ LΠ Φ Hj F-Ω Φ Φ Φ LΠ Φ Hj F-
X F- Hj P F- tr σi P Φ PX F- Hj P F- tr σi P Φ P
Φ Ω P tr F- Hi tr Pi P. rt M P Hl trΦ Ω P tr F- Hi tr Pi P. rt M P Hl tr
LΠ P - P P φ φ to •d O φ P P ISlLΠ P - P P φ φ to • d O φ P P ISl
F- *d Φ> P rt P PF- * d Φ> P rt P P
P. 3 F1 Φ Φ P. φ LQP. 3 F 1 Φ Φ P. φ LQ
P P F- Hj P Φ PP P F- Hj P Φ P
Hj cd P P P ISlHj cd P P P ISl
Ω φ LQ P J Pi P tr Hj CQ cd F- P tr P Hj φ Φ Φ Φ tr Φ 3Ω φ LQ P J Pi P tr Hj CQ cd F- P tr P Hj φ Φ Φ Φ tr Φ 3
Φ F- F1 tsi Φ F- •d ΩΦ F- F 1 tsi Φ F- • d Ω
F- Ω Φ P LQ F1 P. F> φF- Ω Φ P LQ F 1 P. F> φ
P tr 3 LQ Hj P> φ PP tr 3 LQ Hj P> φ P
Φ Φ 0= LQ P P φΦ Φ 0 = LQ P P φ
P Hi P t i CΛ> Φ LQ PP Hi P t i CΛ> Φ LQ P
P) rt P rt tr CQ XP ) rt P rt tr CQ X
Ω p. Φ 3 P Φ φ JΩ p. Φ 3 P Φ φ J
F" F- φ 0= Φ P F1 ΩF "F- φ 0 = Φ PF 1 Ω
Φ PJ Φ> F- LQ Hi P) φ trΦ PJ Φ> F- LQ Hi P ) φ tr
F- t P Ω 3 CQ rt P) F- s! tr φ φF- t P Ω 3 CQ rt P ) F- s! tr φ φ
CQ F- F- P Ω φ tr P rt P CQ Pi tr F1 ) rtCQ F- F- P Ω φ tr P rt P CQ Pi tr F 1) rt
Φ P rt φ Φ F1 Hj CQΦ P rt φ Φ F 1 Hj CQ
F- Φ - Hi Φ rt F1 F- Φ - Hi Φ rt F 1
P Hi s! P φ φ. F- tr Z tr F- X P to Φ σι PJ F- Φ P P LQ o Φ CQ X »d tsi N Φ tr rt φ •d Z z PP Hi s! P φ φ. F- tr Z tr F- X P to Φ σι PJ F- Φ P P LQ o Φ CQ X »d tsi N Φ tr rt φ • d Z z P
F- Φ F- F1 Φ F-F- Φ F- F 1 Φ F-
P l_l. tr 3 P) P F- CQ P φ Φ 3 P P rt Ω PP l_l. tr 3 P ) P F- CQ P φ Φ 3 PP rt Ω P
HJ P P rt CQ LQ Φ tr PHJ P P rt CQ LQ Φ tr P
PJ φ Hl • F1 P φPJ φ Hl • F 1 P φ
P- CQ P) Φ L-I. P PP- CQ P ) Φ LI. PP
F- F" P Φ α φ J TJ F1 X Φ CQ PF- F "P Φ α φ J TJ F 1 X Φ CQ P
PJ CQ P Φ Ω F-PJ CQ P Φ Ω F-
Φ p) P F- X Ω lOΦ p ) P F- X Ω lO
Hj H! P) LQ P φ tr PHj H! P ) LQ P φ tr P
CQ P F1 φ J CQ P P Φ HjCQ PF 1 φ J CQ PP Φ Hj
F- N Φ & F- CQF- N Φ & F- CQ
Ω z TJ Hj CQ LΠ P rt tr Φ F- rt σι 1 Φ rt F- LQ TJ PJ LQΩ z TJ Hj CQ LΠ P rt tr Φ F- rt σι 1 Φ rt F- LQ TJ PJ LQ
P rt P F-P rt P F-
P Φ P) P. P φ. Q Hj LO P 00P Φ P ) P. P φ. Q Hj LO P 00
Φ Φ
LO LO t CO F FLO LO t CO F F
Lπ o LΠ O LΠ O LΠLπ o LΠ O LΠ O LΠ
φ Pi F- ö μ_i |_,. F1 φ Pi F- ö μ_i | _ ,. F 1
P φ P P) PJ P Φ rt P CQ LQ P Q 3 Φ Φ Φ F"P φ PP ) PJ P Φ rt P CQ LQ PQ 3 Φ Φ Φ F "
Φ F- Hj J Hj F- PJ Q rt tr 0 rt p LQΦ F- Hj J Hj F- PJ Q rt tr 0 rt p LQ
Φ rt PJ tr Φ ΦP rt PJ tr Φ Φ
P Φ F1 Hi 3 H Q F" tr CQ PP Φ F 1 Hi 3 HQF "tr CQ P
Φ CQ rt ΩΦ CQ rt Ω
CQ p. P= Φ lCQ p. P = Φ l
Φ Φ Φ Ω rt CTi rt F- CQ X Hi -Φ Φ Φ Ω rt CTi rt F- CQ X Hi -
IS! P F- rt Φ LQ F1 Φ <!IS! P F- rt Φ LQ F 1 Φ <!
Φ Hj F1 CTl tr 0Φ Hj F 1 CTl tr 0
P O Φ PP O Φ P
: ! Ω P. LQ td P) X Φ Φ P:! Ω P. LQ td P ) X Φ Φ P
P ^ Φ CQ tr ΦP ^ Φ CQ tr Φ
P •d P P)= PP • d PP ) = P
Φ Φ Hl Φ P Φ o= H CQ PΦ Φ Hl Φ P Φ o = H CQ P
3 00 Hj CQ Φ3 00 Hj CQ Φ
F- o 3 rt P rt F- Φ -J P rt P) LQ P 00 HjF- o 3 rt P rt F- Φ -JP rt P ) LQ P 00 Hj
Φ tr ΦΦ tr Φ
LQ P Ω P φLQ P Ω P φ
CQ Φ Φ 3 F-CQ Φ Φ 3 F-
CD α F1 PCD α F 1 P
Φ Ω Hj Φ P. φΦ Ω Hj Φ P. φ
F- tr Φ P F- CQF- tr Φ P F- CQ
P F" tr X Φ φ o X X F-P F "tr X Φ φ o X X F-
CQ CQ 0= 0= Ω PCQ CQ 0 = 0 = Ω P
CQ Hj Hj ΦCQ Hj Hj Φ
»xj Φ >d * F1 TJ»Xj Φ> d * F 1 TJ
PJ P φ φ Φ F-PJ P φ φ Φ F-
Hj Hi P LQ rt P CQ CQ X • φ P P) Hj Hi P LQ rt P CQ CQ X • φ PP )
P P. σi F1 Ω F tr t Φ> trP P. σi F 1 Ω F tr t Φ> tr
P> F- 01 PP> F- 01 P
CQ PJ F- φ PJ Q rt P CQ Hi φ LQ rt LQCQ PJ F- φ PJ Q rt P CQ Hi φ LQ rt LQ
CQ PJ Φ ΦCQ PJ Φ Φ
P 0 P) P CQP 0 P ) P CQ
00 Hj P Hj rt to CQ P. Φ φ00 Hj P Hj rt to CQ P. Φ φ
Φ P CQ P; F1 Φ P CQ P; F 1
Pi F- φ Φ tr F"Pi F- φ Φ tr F "
F- P rt F- PJ rtF- P rt F- PJ rt
Ω Φ Φ P Hj tr 3 P Φ F- rf 3 LQ CQ td Φ rt P 1 Ω Φ Φ P Hj tr 3 P Φ F- rf 3 LQ CQ td Φ rt P 1
LO O co co F1 FLO O co co F 1 F
LΠ O LΠ o σι O LΠLΠ O LΠ o σι O LΠ
X Ω P. σ P1 LQ CQ φ CQ CQ P 00 Hj P P- CQ td tr tr CQ tr Ω td Z LQ l_I. CQ CQ 3 'xj ISl 3 φ tr Φ P F- Φ φ rt F- O rt Φ CTi F- φ J rt F- Φ φ Ω Φ Φ tr Φ φ Φ rt rt PJ= F- P F-X Ω P. σ P 1 LQ CQ φ CQ CQ P 00 Hj P P- CQ td tr tr CQ tr Ω td Z LQ l_I. CQ CQ 3 'xj ISl 3 φ tr Φ P F- Φ φ rt F- O rt Φ CTi F- φ J rt F- Φ φ Ω Φ Φ tr Φ φ Φ rt rt PJ = F- P F-
Φ F1 Hj Φ Hj CD F- P 3 F- CQ LQ 3 CQ Φ P LQ F- tr F LQ Φ CQ P Φ φ CΛ> LQ LQ rtΦ F 1 Hj Φ Hj CD F- P 3 F- CQ LQ 3 CQ Φ P LQ F- tr F LQ Φ CQ P Φ φ CΛ> LQ LQ rt
LΠ Hj Φ Ω LQ rt LQ F- CQ N Φ CQ F" Hi Φ φ φ P Φ hh Φ F1 Φ • φ o P tr CO φ Φ φ Ω rt Ω Pi P Hj Φ φ P CQ F- P Φ P F" F- •xj F1 P φ- 0 P. Ω CQ F" P Φ tr Hj CQ Hi -J- rt z φ P φ Ω Hl rt PJ P rt Hj Φ r tr f p. tr rt Z •d Φ PJ PJ N CQ φ Φ F- ISJ 3 I tr F1 P φ PJ φ S! P P HiLΠ Hj Φ Ω LQ rt LQ F- CQ N Φ CQ F "Hi Φ φ φ P Φ hh Φ F 1 Φ • φ o P tr CO φ Φ φ Ω rt Ω Pi P Hj Φ φ P CQ F- P Φ PF "F- • xj F 1 P φ- 0 P. Ω CQ F" P Φ tr Hj CQ Hi -J- rt z φ P φ Ω Hl rt PJ P rt Hj Φ r tr f p. Tr rt Z • d Φ PJ PJ N CQ φ Φ F- ISJ 3 I tr F 1 P φ PJ φ S! PP Hi
N F- 0= F- Hj Φ rt PJ F- PJ rt O P) F- F- CQ z P P 3 P P P Φ P PN F- 0 = F- Hj Φ rt PJ F- PJ rt OP ) F- F- CQ z PP 3 PPP Φ PP
P Ω Φ P) z rt P. P rtP Ω Φ P ) z rt P. P rt
F1 Φ 3 P PJ N 3 φ Φ φ Φ F- -. PJ P Φ Ω Ω CQ F1 P φ s;F 1 Φ 3 P PJ N 3 φ Φ φ Φ F- -. PJ P Φ Ω Ω CQ F 1 P φ s;
P. tr P F1 P P. Hj Pi Φ φ F- P CQ Hj <! P F1 CQ LQ tr tr φ Ω d F" rt ΦP. tr PF 1 P P. Hj Pi Φ φ F- P CQ Hj <! PF 1 CQ LQ tr tr φ Ω d F "rt Φ
P Φ F- tr rt Φ φ Z P CQ P rt P Φ Φ F- CQ Ω Φ φ Φ P tr Φ Φ in F1 P Φ F- tr rt Φ φ ZP CQ P rt P Φ Φ F- CQ Ω Φ φ Φ P tr Φ Φ in F 1
LΠ Hj Hj P Φ Cd Hi Φ •d LQ Φ cj TJ CQ Hj Hj • j P tr P P CQ rt F- P F- co Ω P P Φ CQ 0 F- >d Φ- Φ Hj 1 PJ Hl P. F- Hi P. Φ • CQ to CQ X N CQ Φ tr co P. P F- rt Ω CQ M O Hi Hl PJ P= c| Hj LQ 0 F- CQ F- LO O co >d P Φ rt φ LQ Φ- Φ LΠ P- CQ Φ tr Φ P PJ •xj 0= Hj tr P Φ Φ P φ. i F- • • F- • LOLΠ Hj Hj P Φ Cd Hi Φ • d LQ Φ cj TJ CQ Hj Hj • j P tr PP CQ rt F- P F- co Ω PP Φ CQ 0 F-> d Φ- Φ Hj 1 PJ Hl P. F- Hi P. Φ • CQ to CQ XN CQ Φ tr co P. P F- rt Ω CQ MO Hi Hl PJ P = c | Hj LQ 0 F- CQ F- LO O co> d P Φ rt φ LQ Φ- Φ LΠ P- CQ Φ tr Φ P PJ • xj 0 = Hj tr P Φ Φ P φ. i F- • • F- • LO
F- Φ P φ. O P P PJ CQ 0 Hi Hi rt tr H LQ LO Φ φ F- Φ •d LQ coF- Φ P φ. O P P PJ CQ 0 Hi Hi rt tr H LQ LO Φ φ F- Φ • d LQ co
P CQ tr CQ F- 00 ISl LQ P CQ Hi 3 ISl P Φ tr Φ PJ Φ- P. φ ) Ω P F1 φ Q rt N >xj Z F- Φ »xj oo P CQ CQ rt 3 F- P P Hj P) tr P. P φ F- P tr P P <P CQ tr CQ F- 00 ISl LQ P CQ Hi 3 ISl P Φ tr Φ PJ Φ- P. φ ) Ω PF 1 φ Q rt N> xj Z F- Φ »xj oo P CQ CQ rt 3 F- PP Hj P ) tr P. P φ F- P tr PP <
Φ φ Z F1 Φ P F1 F" CQ Φ CQ LQ CQ LQ CQ Hj F- φ Hi Φ Hj P Hi Φ CQ <! P ΦΦ φ ZF 1 Φ PF 1 F "CQ Φ CQ LQ CQ LQ CQ Hj F- φ Hi Φ Hj P Hi Φ CQ <! P Φ
CQ Ω P) Hi P PJ Hi J F" 1 CQ rt Φ PJ CQ Ω • CQ CQ P Hj φ P P Φ 0 LQ φ nCQ Ω P ) Hi P PJ Hi JF "1 CQ rt Φ PJ CQ Ω • CQ CQ P Hj φ PP Φ 0 LQ φ n
Ω X P P. CQ P P= 3 Φ F- P= P 3 tr tr CQ φ CQ Pi Hj F- P F- Hj F- tr tr rt CO CQ Φ φ F- CQ Hi 3 3 LO Φ tr rt φΩ X P P. CQ P P = 3 Φ F- P = P 3 tr tr CQ φ CQ Pi Hj F- P F- Hj F- tr tr rt CO CQ Φ φ F- CQ Hi 3 3 LO Φ tr rt φ
•- 3 P P P• - 3 P P P
Hj σι Ω P z P Ω 3 Φ F-Hj σι Ω P z P Ω 3 Φ F-
F- P Ω φ φ F- P X cd φ F- φ P 3 ti Hj LQF- P Ω φ φ F- P X cd φ F- φ P 3 ti Hj LQ
- 3 X Φ J P. P- 3 X Φ J P. P
P) tr P P. tr P. P P Φ Φ P= P CQ P P. φ Φ Φ rt Hj P F1 J PP ) tr P P. tr P. PP Φ Φ P = P CQ P P. φ Φ Φ rt Hj PF 1 JP
P F- Φ LQ PJ F- LQ rt P. LQ LQ Ό PJ CQ P Ω X 3 - φ CQ φ z Φ tr P F- P Φ P CQ co Φ Φ Φ φ Z Lπ Φ Φ F- LQ Hi F- P. X Hj φ F- X Φ F- P rt P 3 P PJ= to Hl P Hj 0 to F1 tr Φ φ LQ P φ rt Φ F- CQ CQ Hj 3 CQ rt "*P F- Φ LQ PJ F- LQ rt P. LQ LQ Ό PJ CQ P Ω X 3 - φ CQ φ z Φ tr P F- P Φ P CQ co Φ Φ Φ φ Z Lπ Φ Φ F- LQ Hi F- P. X Hj φ F- X Φ F- P rt P 3 P PJ = to Hl P Hj 0 to F 1 tr Φ φ LQ P φ rt Φ F- CQ CQ Hj 3 CQ rt "*
P. co PJ= Φ 3 ISl J P P. 0= LQ Φ P F- P o CQ φ F- ΦP. co PJ = Φ 3 ISl J P P. 0 = LQ Φ P F- P o CQ φ F- Φ
P F- P co CΛ) Hj rt tr P CQ Φ. 3 P F- 00 Hj φ CQ CQ CQ CQ Φ F- P. Ω Hi PP F- P co CΛ) Hj rt tr P CQ Φ. 3 P F- 00 Hj φ CQ CQ CQ CQ Φ F- P. Ω Hi P
P Φ F- F1 N LQ CQ t Hj P φ> F- tr P rt P. P F- cn P) P. X CQ P) tr φ F-P Φ F- F 1 N LQ CQ t Hj P φ> F- tr P rt P. P F- cn P ) P. X CQ P ) tr φ F-
P. Φ P 1xj <! F- Z Φ rt P) Ω - LQ Φ P= φ F- CQ Ω φ 3 ) rt CQ Hj CQ ΦP. Φ P 1 xj <! F- Z Φ rt P ) Ω - LQ Φ P = φ F- CQ Ω φ 3 ) rt CQ Hj CQ Φ
Ω CQ P F- 0= Ω tr Φ Φ Ω tr Φ Φ CQ tr F1 Φ CQ tr X Φ CQ 0 Φ F- <Ω CQ P F- 0 = Ω tr Φ Φ Ω tr Φ Φ CQ tr F 1 Φ CQ tr X Φ CQ 0 Φ F- <
Hh Φ Φ P LQ tr 0= P Hj tr F- P Hj rt φ CQ >d rt P CQ Hi X P 0 cd P.Hh Φ Φ P LQ tr 0 = P Hj tr F- P Hj rt φ CQ> d rt P CQ Hi X P 0 cd P.
Φ Z 3 • φ PJ H et Pi P P Φ Hj rt Φ J 0 O hh rt P φ φΦ Z 3 • φ PJ H et Pi P P Φ Hj rt Φ J 0 O hh rt P φ φ
CQ F- LO F- 3 F- * ] Φ F- Φ p. Φ tr φ H r Hi tr 0= O P F- 3 rt P >xj Φ> φ. LQ cd LQ 0 F- 1 Φ 3 Hj rt P P tr P Φ hh t i Φ li Hj P P CQ Q P. P) P= Ω Φ Hi Ω L_I. CQ φ Φ P Hi 0= P F- 3 Hi rt φ > ISlCQ F- LO F- 3 F- *] Φ F- Φ p. Φ tr φ H r Hi tr 0 = OP F- 3 rt P> xj Φ> φ. LQ cd LQ 0 F- 1 Φ 3 Hj rt PP tr P Φ hh ti Φ li Hj PP CQ Q P. P ) P = Ω Φ Hi Ω L_I. CQ φ Φ P Hi 0 = P F- 3 Hi rt φ> ISl
Φ φ F1 PJ <! LQ LQ Φ 3 tr CQ tu N Φ rt LQ 3 cd F- LQ Hj Hj P. F- 0= Φ 3 F- ZΦ φ F 1 PJ <! LQ LQ Φ 3 tr CQ tu N Φ rt LQ 3 cd F- LQ Hj Hj P. F- 0 = Φ 3 F- Z
ISl F1 P 0 Φ LQ CO CQ rt Ω φ φ P. φ 3 φ LQ Hj Hj Φ ΦISl F 1 P 0 Φ LQ CO CQ rt Ω φ φ P. φ 3 φ LQ Hj Hj Φ Φ
O o= CQ P z P φ ΦO o = CQ P z P φ Φ
Φ F" Φ Ω rt Φ tr Hi φ φ Hj 3 F- F- Φ co F- F- Ω Φ 3 CQ F- F1 F- Q Ω CQ LQ F- P tr P= Hi F" CQ F- CQ PJ= P CQ P σi P LQ Φ TJ P F- Ω P rtΦ F "Φ Ω rt Φ tr Hi φ φ Hj 3 F- F- Φ co F- F- Ω Φ 3 CQ F- F 1 F- Q Ω CQ LQ F- P tr P = Hi F" CQ F- CQ PJ = P CQ P σi P LQ Φ TJ P F- Ω P rt
Φ tr F- Φ Hj Ω 00 Hl Hj Ω rt F- rt rt !XJ CΛJ •d Φ Φ F1 F1 LQ tr Φ ΦΦ tr F- Φ Hj Ω 00 Hl Hj Ω rt F- rt rt ! XJ CΛJ • d Φ Φ F 1 F 1 LQ tr Φ Φ
P Φ P tr Φ tr φ. P) X P Φ Φ fτj 0 >χj F- >χj P P P φ P) Φ Φ >χj F- PP Φ P tr Φ tr φ. P ) XP Φ Φ f τj 0> χ j F-> χ j PPP φ P ) Φ Φ> χ j F- P
Hj P F- Ω • PJ P Φ Z LQ P PJ Hj >χj F- Φ F1 Φ P P P F- F- P H tr P P tr F- Φ F" P) 3 F- LQ F1 P) CQ X X CQ B CQ P LQ Φ Ω ü oo Φ P rt P CQ Φ Lπ Hj P P α Hj CQ LQ • P F" rX PJ Ω Ω Φ Hj Φ J 00 CQ φ CQ P- Ω o Pi Hh P 1 rt . F1 LQ CQ Φ Φ CQ Ω tr tr P rt F MHj P F- Ω • PJ P Φ Z LQ P PJ Hj> χ j F- Φ F 1 Φ PPP F- F- PH tr PP tr F- Φ F "P ) 3 F- LQ F 1 P ) CQ XX CQ B CQ P LQ Φ Ω ü oo Φ P rt P CQ Φ Lπ Hj PP α Hj CQ LQ • PF "rX PJ Ω Ω Φ Hj Φ J 00 CQ φ CQ P- Ω o Pi Hh P 1 rt. F 1 LQ CQ Φ Φ CQ Ω tr tr P rt FM
P. rt tr LΠ 0= LQ Hl ISl P= φ. Φ Ω Hj F- Ω tr Φ P CQ - Φ ΦP. rt tr LΠ 0 = LQ Hl ISl P = φ. Φ Ω Hj F- Ω tr Φ P CQ - Φ Φ
P P. α Φ P 00 φ. P Hi 0= P Ω tr LQ tr CQ P tr CQ F- CQ tr Hj PP P. α Φ P 00 φ. P Hi 0 = P Ω tr LQ tr CQ P tr CQ F- CQ tr Hj P
Hj Φ P P ) Ti LO P 3 P Hi CQ X P F- Φ Φ rt Φ P Φ to rt "d P. F- hh XHj Φ PP ) Ti LO P 3 P Hi CQ XP F- Φ Φ rt Φ P Φ to rt "d P. F- hh X
Ω Hj Hj Ω Φ> N P Φ F- P 3 PJ Φ P CQ P Φ Hj F- t rt PJ PJ CQ F- X tr Ω P) tr P) • P P LQ P. F- 3 P. φ Φ P Φ rt Hj CQ P 0=Ω Hj Hj Ω Φ> NP Φ F- P 3 PJ Φ P CQ P Φ Hj F- t rt PJ PJ CQ F- X tr Ω P ) tr P ) • PP LQ P. F- 3 P. φ Φ P Φ rt Hj CQ P 0 =
>XJ tr Ω P 3 LΠ Φ Φ LQ 3 LΠ LO F- tr P rt P P. P CQ LO P Hj> XJ tr Ω P 3 LΠ Φ Φ LQ 3 LΠ LO F- tr P rt P P. P CQ LO P Hj
Z o CQ tr F1 CQ Fl to CQ P 2 Φ φ o LΠ P Φ fxj Φ P P Φ P P >dZ o CQ tr F 1 CQ Fl to CQ P 2 Φ φ o LΠ P Φ f xj Φ PP Φ PP> d
F- HJ PJ CQ F- 3 Cd O P P P PJ P Sl o P CQ LQ P. P P φF- HJ PJ CQ F- 3 Cd O P P P PJ P Sl o P CQ LQ P. P P φ
Hj 3 P t5 P co Φ tr P. Φ P LQ F- P PJ P CQ PJ F- P. Hi Φ Φ J LQ HjHj 3 P t5 P co Φ tr P. Φ P LQ F- P PJ P CQ PJ F- P. Hi Φ Φ J LQ Hj
P CQ LQ PJ X rt P. Hh PJ Φ F1 rt Cd Φ P P) Hj Pi 0 P P Φ 3 LO Ω P Hj Hj cn rt CQ Hi CQ PJ J Φ rt Hj P) PJ P= tr Hi LQ Φ X CQ PJ φ. Φ LQ LQ COP CQ LQ PJ X rt P. Hh PJ Φ F 1 rt Cd Φ PP ) Hj Pi 0 PP Φ 3 LO Ω P Hj Hj cn rt CQ Hi CQ PJ J Φ rt Hj P ) PJ P = tr Hi LQ Φ X CQ PJ φ. Φ LQ LQ CO
P. 0 F1 P) tr Hj 1 1 LQ LQ 0= Φ F- Φ Hi 1 co Φ Φ φ coP. 0 F 1 P ) tr Hj 1 1 LQ LQ 0 = Φ F- Φ Hi 1 co Φ Φ φ co
Φ X 0= F1 F" 1 Φ Φ - F1 φ F- CΛ Hj 1Φ X 0 = F 1 F "1 Φ Φ - F 1 φ F- CΛ Hj 1
Hj 1 1 1 1 F- P I z φ F"Hj 1 1 1 1 F- PI z φ F "
F I Φ 1 P 3 1 FI Φ 1 P 3 1
Kranz 40 aus elastischen Kup lungselerne ten 42 mit seiner in Fig. 3 rechten Stirnseite an den beiden Flanschen 22 und 34 anliegend gehalten. Wreath 40 made of elastic Kup lungselerne 42 held with its right end face in Fig. 3 on the two flanges 22 and 34.

Claims

Patentansprüche claims
1. Drehelastische Wellenkupplung (10) mit1. Torsionally flexible shaft coupling (10) with
- einem zentral angeordneten Universalgelenk (12) , das einen ersten und einen zweiten im wesentlichen starren Gelenkkörper (14,28) aufweist,a centrally arranged universal joint (12) which has a first and a second essentially rigid joint body (14, 28),
- einem rings um das Universalgelenk (12) angeordneten Kranz (40) aus schlingenförmigen elastischen Kupplungselementen (42) , die je ein erstes Formstück (50) und je ein zweites Formstück (52) umschlingen, wobei- A ring (40) made of loop-shaped elastic coupling elements (42) arranged around the universal joint (12), each of which wraps around a first shaped piece (50) and a second shaped piece (52), whereby
- die ersten Formstücke (50) mit dem ersten Gelenkkörper (14) im wesentlichen starr verbunden und zwischen zweiten Form- stücken (52) angeordnet sind, und- The first shaped pieces (50) with the first joint body (14) are essentially rigidly connected and arranged between second shaped pieces (52), and
- die Gelenkkörper (14,28) sowie die Kupplungselemente (42) im wesentlichen rotationssymmetrisch in Bezug auf eine gemeinsame Gelenkachse (A) sowie im wesentlichen symmetrisch in Bezug auf eine gemeinsame, zur Gelenkachse (A) normale Mitte- lebene (B) angeordnet und zur Übertragung von Drehmomenten in- The joint bodies (14, 28) and the coupling elements (42) are arranged essentially rotationally symmetrically with respect to a common joint axis (A) and essentially symmetrically with respect to a common center plane (B) normal to the joint axis (A) and for the transmission of torques in
Reihe geschaltet sind, dadurch gekennzeichnet, dassSeries are connected, characterized in that
- der erste Gelenkkörper (14) einen ersten Flansch (22) aufweist, mit dem die ersten Formstücke (50) fest verbunden sind und von dem aus sie sich parallel zur Gelenkachse (A) erstrecken,- The first joint body (14) has a first flange (22) with which the first shaped pieces (50) are firmly connected and from which they extend parallel to the joint axis (A),
- die zweiten Formstücke (52) mit einem Gegenflansch (34) fest verbunden sind und sich von ihm aus parallel zur Gelenkachse (A) erstrecken, - der Gegenflansch (34) zu einem Drehkörper (62) gehört, der ein Ende einer Drehmomentübertragungskette bildet, deren anderes Ende der zweite Gelenkkörper (28) darstellt, und- The second fittings (52) are fixedly connected to a counter flange (34) and extend from it parallel to the hinge axis (A), - The counter flange (34) belongs to a rotating body (62) which forms one end of a torque transmission chain, the other end of which represents the second joint body (28), and
- der erste Gelenkkörper (14) ein den zweiten Gelenkkörper (28) umhüllendes Rohrstück (16) mit einer äußeren Mantelflä- ehe (18) von kreisförmigem Querschnitt aufweist, an der sich die elastischen Kupplungselerne te (42) in radialer Richtung abstützen. - The first joint body (14) has a pipe section (16) enveloping the second joint body (28) with an outer lateral surface (18) of circular cross-section, on which the elastic coupling elements (42) are supported in the radial direction.
2. Wellenkupplung nach Anspruch 1, dadurch gekennzeichnet, dass die elastischen Kupplungselemente (42) sich im Bereich der zweiten Formstücke (52) über je einen Gleitstein (60) an der Mantelfläche (18) des Rohr- Stücks (16) des ersten Gelenkkörpers (14) abstützen.2. Shaft coupling according to claim 1, characterized in that the elastic coupling elements (42) in the area of the second shaped pieces (52) each via a sliding block (60) on the lateral surface (18) of the tubular piece (16) of the first joint body ( 14) support.
3. Wellenkupplung nach Anspruch 1 oder 2, dadurch gekennzeichnet, dass das Rohrstück (16) an seiner Innenseite Laufbahnen (20) für Wälzkörper (30) aufweist, die zu dem als Multipode- oder Gleichlaufgelenk ausgebildeten Universalgelenk (12) gehören.3. Shaft coupling according to claim 1 or 2, characterized in that the tube piece (16) has on its inside raceways (20) for rolling elements (30) which belong to the universal joint (12) designed as a multipode or constant velocity joint.
4. Wellenkupplung nach einem der Ansprüche 1 bis 3, dadurch gekennzeichnet, dass rings um das Rohrstück (16) des ersten Gelenkkörpers (14) mindestens sechs Kupplungselemente (42) in Umfangsrichtung hintereinander angeordnet sind.4. Shaft coupling according to one of claims 1 to 3, characterized in that around the pipe section (16) of the first joint body (14) at least six coupling elements (42) are arranged one behind the other in the circumferential direction.
5. Wellenkupplung nach einem der Ansprüche 1 bis 4, dadurch gekennzeichnet, dass - die ersten Formstücke (50) am ersten Flansch (22) , und die zweiten Formstücke (52) am Gegenflansch (34) jeweils paarweise angeordnet sind und5. Shaft coupling according to one of claims 1 to 4, characterized in that - the first fittings (50) on the first flange (22), and the second fittings (52) on the counter flange (34) are each arranged in pairs and
- jedes Formstück (50,52) nur mit einem einzigen anderen Formstück (52,50) durch ein elastisches Kupplungselement (42) verbunden ist, so dass- Each shaped piece (50, 52) is only connected to a single other shaped piece (52, 50) by an elastic coupling element (42), so that
- sämtliche Kupplungselemente (42) überlappungsfrei miteinander verkettet sind.- All coupling elements (42) are chained together without overlap.
6. Wellenkupplung nach Anspruch 5, dadurch gekennzeichnet, dass6. Shaft coupling according to claim 5, characterized in that
- die ersten Formstücke (50) zwischen je zwei ersten Deckeln (56) , und die zweiten Formstücke (52) zwischen je zwei zweiten Deckeln (58) am zugehörigen Flansch (22,34) befestigt sind, wobei - sämtliche Deckel (56,58) parallel zur Mittelebene (B) angeordnet sind, und- The first shaped pieces (50) are fastened between two first covers (56), and the second shaped pieces (52) between two second covers (58) on the associated flange (22, 34), with - all covers (56, 58 ) are arranged parallel to the central plane (B), and
- paarweise zusammengehörige Deckel (56,58) gleiche Abstände (d) von der Mittelebene (B) haben. - Lids (56, 58) belonging together in pairs have the same distances (d) from the central plane (B).
7. Wellenkupplung nach Anspruch 5, dadurch gekennzeichnet, dass jedes Paar erster Formstücke (50) einen U-förmigen ersten Bügel (84) bildet, und jedes 5 Paar zweiter Formstücke (52) einen U-förmigen zweiten Bügel (86) bildet.7. Shaft coupling according to claim 5, characterized in that each pair of first fittings (50) forms a U-shaped first bracket (84), and each 5 pairs of second fittings (52) forms a U-shaped second bracket (86).
8. Wellenkupplung nach Anspruch 7, dadurch gekennzeichnet, dass jedes der Formstücke (50,52) ein .0 Gewindeloch (88) zum Befestigen am zugehörigen Flansch (22) bzw. Gegenflansch (34) aufweist.8. Shaft coupling according to claim 7, characterized in that each of the shaped pieces (50, 52) has a .0 threaded hole (88) for fastening to the associated flange (22) or counter flange (34).
9. Wellenkupplung nach einem der Ansprüche 1 bis 8, dadurch gekennzeichnet, dass der erste Flansch (22) und der9. Shaft coupling according to one of claims 1 to 8, characterized in that the first flange (22) and the
.5 Gegenflansch (34) kreisringsektorförmige Aussparungen (26,38) aufweisen, von denen die Aussparungen (26) des ersten Flansches (22) gegen die Aussparungen (38) des Gegenflansches (34) drehwinkelversetzt sind..5 have counter-flange (34) annular sector-shaped recesses (26,38), of which the recesses (26) of the first flange (22) against the recesses (38) of the counter flange (34) are offset in rotation.
!0 10. Wellenkupplung nach Anspruch 9, dadurch gekennzeichnet, dass der erste Flansch (22) mit Drehspiel in die Aussparungen (38) des Gegenflansches (34) eingreift, und umgekehrt, so dass beide Flansche (22,34) in einer gemeinsamen Ebene liegen.! 0 10. Shaft coupling according to claim 9, characterized in that the first flange (22) engages with play in the recesses (38) of the counter flange (34), and vice versa, so that both flanges (22,34) in a common plane lie.
15 15
EP02750545A 2001-03-14 2002-03-14 Rotationally elastic shaft coupling Withdrawn EP1368575A1 (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
DE10112260A DE10112260C1 (en) 2001-03-14 2001-03-14 Torsionally flexible shaft coupling
DE10112260 2001-03-14
PCT/EP2002/002871 WO2002073056A1 (en) 2001-03-14 2002-03-14 Rotationally elastic shaft coupling

Publications (1)

Publication Number Publication Date
EP1368575A1 true EP1368575A1 (en) 2003-12-10

Family

ID=7677432

Family Applications (1)

Application Number Title Priority Date Filing Date
EP02750545A Withdrawn EP1368575A1 (en) 2001-03-14 2002-03-14 Rotationally elastic shaft coupling

Country Status (4)

Country Link
US (1) US6846240B2 (en)
EP (1) EP1368575A1 (en)
DE (1) DE10112260C1 (en)
WO (1) WO2002073056A1 (en)

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BR112012009299A2 (en) * 2009-10-20 2016-05-31 Gkn Driveline North America constant speed joint and shock absorber assembly
CN104421347B (en) * 2013-08-23 2018-01-09 常州长青交通科技股份有限公司 Elastic coupling
CN111911545A (en) * 2019-05-27 2020-11-10 中车大同电力机车有限公司 Transmission mechanism and drive coupling
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Also Published As

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US20040058736A1 (en) 2004-03-25
WO2002073056A1 (en) 2002-09-19
DE10112260C1 (en) 2003-01-16
US6846240B2 (en) 2005-01-25

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