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Tehnica mecanica

Tehnica mecanica


Index » inginerie » Tehnica mecanica
Variante de asamblare


Variante de asamblare




Variante de asamblare

Pentru a atasa transmisiile cardanice la mecanisme de transmisie si osii sunt necesare diferite tipuri de asamblǎri. Sunt disponibile urmǎtoarele tipuri de flanse (standard ISO): XS

http://www.gwb-essen.de/fahrzeugbau/images/seite_08a.gif

http://www.gwb-essen.de/images/blauerpunkt.gif

Flansǎ cu angrenare pozitivǎ (Positive engagement)
- XS (danturǎ in x)(x-serration), conform standardului
http://www.gwb-essen.de/images/leer.gifISO 8667 referitor la flanse pentru cutia de viteze;
http://www.gwb-essen.de/images/leer.gifISO 12667 referitor la flanse pentru arborii de transmisie





http://www.gwb-essen.de/images/blauerpunkt.gif


Flansǎ de frictiune (Friction type)
- dupǎ standardul DIN, corespunzǎtor standardului ISO 7646
- dupǎ standardul SAE, corespunzǎtor standardului ISO 7647

DIN http://www.gwb-essen.de/fahrzeugbau/images/seite_08b.gifSAE http://www.gwb-essen.de/fahrzeugbau/images/seite_08c.gif

Flansa cu danturǎ in x (XS) este utilizatǎ tot mai mult datoritǎ avantajelor sale tehnice si economice si va fi preferatǎ in viitor.

Avantajele acestui tip de flansǎ sunt:
http://www.gwb-essen.de/images/blauerpunkt.gif(Positive engagement of serrations) Angrenarea pozitivǎ a danturii
http://www.gwb-essen.de/images/blauerpunkt.gifNecesitǎ un timp mai scurt de montare
http://www.gwb-essen.de/images/blauerpunkt.gifSistemul de fixare cu suruburi este simplificat
http://www.gwb-essen.de/images/blauerpunkt.gifSe utilizeazǎ mai putine suruburi
http://www.gwb-essen.de/images/blauerpunkt.gifComplexitate redusǎ a . (Reduced stock complexity)
http://www.gwb-essen.de/images/blauerpunkt.gifPozitia de asamblare este clar definitǎ
http://www.gwb-essen.de/images/blauerpunkt.gifSe utilizeazǎ piulite cu blocare automatǎ Use of self-locking nuts


Numǎrul variantelor de flanse

10 Flanse DIN

4 Flanse cu danturǎ in x ISO 12667

12 Flanse SAE

http://www.gwb-essen.de/fahrzeugbau/images/seite_09a_1a.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_09a_1be.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_09a_1c.gif
http://www.gwb-essen.de/fahrzeugbau/images/seite_09a_2a.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_09a_2be.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_09a_2c.gif

Variante si combinatii de transmisii cardanice Variantele principale sunt:



http://www.gwb-essen.de/fahrzeugbau/images/seite_10a.gif


Transmisie cardanicǎ cu compensare axialǎ
(fixǎ si mobilǎ) http://www.gwb-essen.de/fahrzeugbau/images/seite_10b.gif


Transmisie cardanicǎ fǎrǎ compensare

axialǎ, cu cuplu maestru/imbunǎtǎtit (Cardan shaft without length compensation with midship)
(fixǎ si de mijloc) http://www.gwb-essen.de/fahrzeugbau/images/seite_10c.gif


Transmisie cardanicǎ cu cuplu scurt / intermediarǎ si compensare axialǎ (Short coupled cardan shaft with length compensation)
variants with
sleeve yoke/sleeve muff

sleeve= manson, bucsa, mufa, tambur, cilindru, stut, niplu, cuzinet]

yoke = furca, travee, etrier, colier, brida

muff = cuplaj, manson, bucsa
Designul liniei de transmisie cardanicǎ poate varia in functie de utilizare, de exemplu:


http://www.gwb-essen.de/fahrzeugbau/images/seite_10d.gif


Ansamblu de arbori cu ax central de lungime fixǎ

si transmisie cardanicǎ cu compensare axialǎ Shaft assembly with fixed-length midship shaft and cardan shaft with length compensation

http://www.gwb-essen.de/fahrzeugbau/images/seite_10e_neu.gif


Ansamblu de arbori cu compensare axialǎ

si suprafatǎ de reazem centralǎ Alte variante disponibile la cerere. Shaft assembly with
length compensationin midship bearing area
Additional variants on request.


Variante speciale- ex:

Nu necesitǎ intretinere, temperaturǎ crescutǎ/scǎzutǎ, constructie cu izolatie fonicǎ etc. la cerere.


Arbori cardanici cu compensare axialǎ

http://www.gwb-essen.de/fahrzeugbau/images/seite_12a.gif

Arbori cardanici fǎrǎ compensare axialǎ cu cuplu central Cardan shaft without length compensation with midship
http://www.gwb-essen.de/fahrzeugbau/images/seite_13a.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_13b.gif

Ansamblu de arbori cu compensare axialǎ in suprafata de reazem centralǎ Shaft assembly with length compensation in midship bearing area

http://www.gwb-essen.de/fahrzeugbau/images/seite_13c.gif


http://www.gwb-essen.de/fahrzeugbau/images/seite_13d.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_13e.gif

Arbore cardanic intermediar cu compensare axialǎ Short coupled cardan shaft with length compensation
Design Cilindru - Furcǎ Sleeve-Yoke-Design

http://www.gwb-essen.de/fahrzeugbau/images/seite_14a.gif

Arbore cardanic intermediar cu compensare axialǎ Short coupled cardan shaft with length compensation
Design Cilindru Bucsǎ Sleeve-Muff-Design

http://www.gwb-essen.de/fahrzeugbau/images/seite_15a.gif


Arbore cardanic cu compensare axialǎ si articulatie dublǎ pe ambele pǎrti Cardan shaft with length compensation and centred double joint on both sides

http://www.gwb-essen.de/fahrzeugbau/images/006.gif


Arbore cardanic cu compensare axialǎ si articulatie dublǎ pe o singurǎ parte Cardan shaft with length compensation and centered double joint on one side

http://www.gwb-essen.de/fahrzeugbau/images/008.gif


Flanse de asamblare - model X Serration flange fittings (XS)

http://www.gwb-essen.de/fahrzeugbau/images/seite_16a.gif


Flanse de asamblare - model DIN

http://www.gwb-essen.de/fahrzeugbau/images/seite_17a.gif

Flanse de asamblare - model SAE

http://www.gwb-essen.de/fahrzeugbau/images/seite_18a.gif

Rulmenti intermediari

http://www.gwb-essen.de/fahrzeugbau/images/seite_19a.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_19be.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_19ce.gif


Cinematica articulatiilor Hooke

1. Articulatiile
In cadrul teoriei mecanicii articulatia cardanicǎ, numitǎ si articulatia Hooke, este definitǎ ca fiind o unitate de actionare spatialǎ sau sfericǎ cu raport de transmisie neuniform. Modul de transmisie al acestei articulatii este descries prin ecuatia urmǎtoare:

the theory of mechanics the cardan joint or Hooke's joint is defined as a spatial or spherical drive unit with a non-uniform gear ratio or transmission. The transmission behaviour of this joint is described by the equation.

http://www.gwb-essen.de/fahrzeugbau/images/seite_20a.gif


http://www.gwb-essen.de/fahrzeugbau/images/seite_20b.gif
In aceastǎ ecuatie http://www.gwb-essen.de/images/zeichen_alpha2.gifreprezintǎ momentul unghiului de rotatie al axului 2. Miscarea capetelor antrenante si a celor antrenate este descrisǎ in diagrama de mai jos. Miscarea asincronǎ si / sau omocinematicǎ a axului 2 este descrisǎ prin oscilarea periodicǎ a liniei asincronice http://www.gwb-essen.de/images/zeichen_alpha2.gifin jurul liniei sincronice http://www.gwb-essen.de/images/zeichen_alpha1.gif(linia intreruptǎ).

In this equation http://www.gwb-essen.de/images/zeichen_alpha2.gifthe momentary rotation angle of the driven shaft 2. The motion behaviour of the driving and the driven ends is shown in the following diagram. The asynchronous and / or non-homokinematic running of the shaft 2 is shown in the periodical oscilation of the asynchronous line http://www.gwb-essen.de/images/zeichen_alpha2.gifround the synchronous line http://www.gwb-essen.de/images/zeichen_alpha1.gif(dotted line).

http://www.gwb-essen.de/fahrzeugbau/images/seite_20c.gif


O valoare a neuniformitǎtii este datǎ de diferenta dintre unghiurile de rotatie http://www.gwb-essen.de/images/zeichen_alpha2.gifsi http://www.gwb-essen.de/images/zeichen_alpha1.gifsau raportul de transmisie dintre vitezele unghiulare http://www.gwb-essen.de/images/zeichen_omega2.gifsi http://www.gwb-essen.de/images/zeichen_omega1.gif.





A measure for the non-uniformity is the difference of the rotation angles http://www.gwb-essen.de/images/zeichen_alpha2.gifand http://www.gwb-essen.de/images/zeichen_alpha1.gifor the transmission ratio of the angular speeds http://www.gwb-essen.de/images/zeichen_omega2.gifand http://www.gwb-essen.de/images/zeichen_omega1.gif.

Pusǎ in ecuatie, inseamnǎ: a) diferenta unghiului de rotatie

Expressed by an equation, that means: http://www.gwb-essen.de/images/leer.gifhttp://www.gwb-essen.de/images/zeichen_linie.gifa) rotation angle difference

http://www.gwb-essen.de/fahrzeugbau/images/seite_20d.gif


(numitǎ si eroare cardanicǎ)

http://www.gwb-essen.de/fahrzeugbau/images/seite_20e.gif


b) Raportul de transmisie

http://www.gwb-essen.de/fahrzeugbau/images/seite_20f.gif




2. Arborele universal
Diferenta unghiului de rotatie http://www.gwb-essen.de/images/zeichen_phik.gifsau eroarea cardanicǎ a unui arbore universal curbat

poate fi compensatǎ in anumite conditii de instalare cu ajutorul altui arbore universal. Solutiile constructive sunt urmǎtoarele:

The rotation angle difference http://www.gwb-essen.de/images/zeichen_phik.gifor the gimbal error of a deflected universal joint can be offset under certain installation conditions with a second universal joint. The constructive solutions are the following:

1) Unghiurile de curbare ale ambilor arbori trebuie sǎ fie egale, adicǎ:

The deflection angles of both joints must be equal, i.e.

http://www.gwb-essen.de/fahrzeugbau/images/seite_21c.gif


Existǎ douǎ posibiliǎti de montare: Two arrangements are possible:

http://www.gwb-essen.de/fahrzeugbau/images/seite_21de.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_21ee.gif

2) Cei doi arbori trebuie sǎ se afle in relatie unghiularǎ cinematicǎ de 90 (http://www.gwb-essen.de/images/zeichen_pi.gif / 2), adicǎ furcile arborelui de legǎturǎ sǎ se afle in acelasi plan.

The two joints must have a kinematic angular relationship of 90 (http://www.gwb-essen.de/images/zeichen_pi.gif / 2), i.e. the yokes of the connecting shaft are in one plane.

Pentru un studiu mai amǎnuntit al cinematicii arborilor universali puteti consulta recomandarea 2722 a VDI (Asociatia Inginerilor Germani), literatura tehnicǎ relevantǎ si mai ales cartea ,,Kardangelenkgetriebe und ihre Anwendung' (Actionǎrile arborilor cardanici si aplicatiile acestora) scrisǎ de Florian Duditza si publicatǎ de VDI.

For a more intensive study of universal shaft kinematics we refer you to the VDI-recommendation 2722 to the relevant technical literature and especially to the book ,,Kardangelenkgetriebe und ihre Anwendung' (Cardan joint drives and their application) by Florian Duditza, published by VDI.

Elemente care influenteaza folosirea arborilor

General technical terms of propshaft application

Pentru a utiliza arborii din seria Compact 2000 s-au creat o metodǎ de calcul si un software speciale. Aceastǎ metodǎ de calcul se bazeazǎ pe termeni fizici generali si mǎsurǎtori effectuate pe vehicule reale.

For the application of propshafts of the series Compact 2000 a special calculation method and software has been developed. This calculation method is based on general physical terms and additional experiences of real vehicle measurements.

Termenii fundamentali ai metodei "VAMP" (Metodǎ de aplicare a arborilor la vehicule) se referǎ la:

The fundamental items of the 'VAMP-method' (Vehicle Application Method for Propshafts) reflect to:

http://www.gwb-essen.de/images/blauerpunkt.gifparametrii vehiculului
http://www.gwb-essen.de/images/blauerpunkt.gifconditiile de operare
http://www.gwb-essen.de/images/blauerpunkt.gifvalorile caracteristice ale arborilor din seria Compact 2000
http://www.gwb-essen.de/images/blauerpunkt.gifcerintele speciale ale clientilor


Astfel, se verificǎ urmǎtorii parametrii:

  • Rezistenta la obosealǎ
    Criteriul pentru rezistenta la obosealǎ este efortul de torsiune maxim generat in/de transmisie in conditii normale de operare. Este determinat de:

Criteria for fatigue strength is the maximum generated torque in the driveline under normal operating conditions.

a) cuplul motor maxim

b) momentul maxim de aderentǎ the maximum adhesion torque

  • In functie de criteriul relevant se poate detrmina mǎrimea arborelui cu capacitate staticǎ suficientǎ Tcs. Panǎ la aceastǎ limitǎ a efortului de torsiune un arbore poate fi incǎrcat fǎrǎ a denatura functionarea transmisiei.

In relation to the relevant criterion the size of propshaft with the sufficient static capacity Tcs is determined. Up to this torque limit a shaft can be loaded without disturbing the function of the driveline.

  • Rezistenta structuralǎ
    Rezistenta structuralǎ se bazeazǎ pe efortul de torsiune maxim care poate apǎrea in conditii extreme sau in urma utilizǎrii necorespunzǎtoare. Trebuie luate in considerare si limitǎrile referitoare la momentul / cuplul de aderentǎ.

The structural strength is based on the maximum torque which can occur under extreme conditions or misuse. Limitations which refer to the adhesion torque are also taken into account.

  • Durata de viatǎ a unei unitǎti
    Durata de viatǎ a unei unitǎti se calculeazǎ utilizand distribuiri specifice de icǎrcare furnizate de clienti sau parametrii obtinuti in urma mǎsurǎtorilor si expeientelor proprii. me of a unit pack is calculated by use of specific load distributions from the customer or parameters of general inhouse measurements and experiences.
  • Vitezǎ, unghi de lucru, lungime
    Criteriile sunt:

-

Relatia de vitezǎ maximǎ din timpul utilizǎrii ? the relation of the maximum speed during

-

Excitarea vibratiilor de torsiune generate de viteza arborelui si unghiul de lucru the excitation of torsional vibrations generated by propshaft speed and working angle


In cele din urmǎ se va recomanda mǎrimea optimǎ a arborelui.

Pentru a identifica valorile caracteristice specifice, de exemplu comportamentul dinamic special al tansmisiilor, putem sprijini clientii prin efectuarea de simulǎri si mǎsurǎtori ale vehiculului.
To identify specific characteristical values of e.g. special dynamic behaviour of drivelines we can support the customers with simulation calculations and vehicle measurements.

Vǎ rugǎm sǎ contactati expertii nostri in aplicatii pentru orice alte probleme.

Cum se pot solicita informatii sau depune comenzi

Procesarea solicitǎrilor de informatii si a comenzilor de arbori cu articulatii universale va fi mai usoarǎ si mai rapidǎ dacǎ ne oferiti informatii referitoare la:

  1. Tipul si descrierea fabricii sau a unitǎtii
  2. Conditiile de operare
  3. Date despre motor
  4. Date despre transmisie
  5. Conditii de instalare
  6. Dimensiunile unitǎtilor conectate

Conditii de instalare
In timp ce se roteste articulatia universalǎ are While rotating, the universal joint has a sinuslike, fluctuating angular speed depending on the deflection angle. As described in detail in the chapter ,,General fundamental theory', this system-linked fault can be offset for a driving line equipped with two or more joints by choosing special joint arrangements.

When dimensioning the drive or the auxlliarv drive, the following rules must be observed in practice:

Angle conditions of the universal shaft

1. Ax cu douǎ articulatii Shaft with two joints


'Z-arrangement'
http://www.gwb-essen.de/fahrzeugbau/images/seite_22a.gif


'W-arrangement'
http://www.gwb-essen.de/fahrzeugbau/images/seite_22b.gif


http://www.gwb-essen.de/images/blauerpunkt.gifThe deflection angles of the joints must be equal: http://www.gwb-essen.de/images/leer.gifhttp://www.gwb-essen.de/images/zeichen_beta1.gif= http://www.gwb-essen.de/images/zeichen_beta2.gif
http://www.gwb-essen.de/images/leer.gifThis rule is also applicable to front view and top view pictures.
http://www.gwb-essen.de/images/blauerpunkt.gifThe joint yokes of the connecting shaft must be in one plane.
http://www.gwb-essen.de/images/blauerpunkt.gifAll three shafts must be in one plane.

Note: All these three rules must be observed simultaneously.

A joint arrangement in two planes must be avoided if possible. lt is always given when the driving and driven shafts are not in the same plane. If this arrangement is unavoidable and rigid on the installation side, this ,,fault' can be kinematically compensated by a joint misalignment.





Front view: http://www.gwb-essen.de/images/zeichen_betav.gif
http://www.gwb-essen.de/fahrzeugbau/images/seite_22c.gif


Top view: http://www.gwb-essen.de/images/zeichen_betah.gif
http://www.gwb-essen.de/fahrzeugbau/images/seite_22d.gif


For the resulting deflection angles the following equations are applicable:

http://www.gwb-essen.de/fahrzeugbau/images/seite_22e.gif



2. Shaft with three joints
In cases where greater distances between units have to be bridged, the universal shaft must be supported by an additional, mostly elastic, bearing.

http://www.gwb-essen.de/fahrzeugbau/images/seite_23ae.gif



In order to keep the remaining irregularity in the drive (joint 3) as small as possible, the sum of all irregulanties of the individualjoints must be equal to or almost equal to zero.

http://www.gwb-essen.de/fahrzeugbau/images/seite_23b.gif


(See 'Kinematics of Hooke's joints')

The signs must be entered according to the following sign rule. Here the sign rule is:

http://www.gwb-essen.de/images/zeichen_plus.giffor the joint position

http://www.gwb-essen.de/fahrzeugbau/images/seite_23c.gif



http://www.gwb-essen.de/images/zeichen_minus.giffor the joint position

http://www.gwb-essen.de/fahrzeugbau/images/seite_23d.gif



The remaining non-uniformity if any should not be greater than:

http://www.gwb-essen.de/fahrzeugbau/images/seite_23e.gif

The minimization of the remaining non-uniformity can also be achieved by the so-called equivalent deflection angle http://www.gwb-essen.de/images/zeichen_betae.giferfolgen.

http://www.gwb-essen.de/fahrzeugbau/images/seite_23f.gif

The sign rule is also applicable here.

The equivalent deflection angle http://www.gwb-essen.de/images/zeichen_betae.gif= 3 is the equivalent deflection angle of a single joint which corresponds with a degree of non-uniformity U = 0,0027.


3. Shafts with several joints
In case of an arrangement with more than three joints proceed as described above.

General recommendations for lorry drives:

http://www.gwb-essen.de/images/blauerpunkt.gif

For fast-running drive shafts observe the instructions on the transverse whirling speeds for installation length.
(See 'Influence of speed and deflection angle')

http://www.gwb-essen.de/images/blauerpunkt.gif

Choose small resulting deflection angles for the main drive range:
(See also (n x )perm. 'Influence of speed and deflection angle')

http://www.gwb-essen.de/images/blauerpunkt.gif

Minimize the angular difference between the joints and the remaining inequaltity


If these recommendations are not observed, one must reckon with vibrations and noises and with a reduced driving comfort as well as with a reduced lifetime of the units.

Deflection of joints in two planes
If a 'classic shaft arrangement' cannot be realized and the joint deflection cannot be changed, this can be offset by turning the joints. For this shaft arrangement the Installation rule that the resulting deflections of the joints must be equal remains in force, i.e.

http://www.gwb-essen.de/images/zeichen_betares.gif

Plane 1 formed by the driving shaft 1 and the connecting shaft 2 on the one hand and Plane II formed by the connecting shaft 2 and the driven shaft 3 on the other hand form the angle http://www.gwb-essen.de/images/zeichen_phi.gifwhich is offset by turning the joints correspondingly.

The torsion angle http://www.gwb-essen.de/images/zeichen_phi.gifis determined as follows:

http://www.gwb-essen.de/fahrzeugbau/images/seite_24ae.gif


Yoke=furcǎ
The rotation direction results ifom the side view, i.e. joint 1 must be turned to plane 1 by the angle http://www.gwb-essen.de/images/zeichen_phi.gif.

The shaft must be mounted according to these statements and this before a possible balancing. This position of the joints must be marked with arrows.


http://www.gwb-essen.de/fahrzeugbau/images/seite_24be.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_24c.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_24d.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_24e.gif


http://www.gwb-essen.de/fahrzeugbau/images/seite_24fe.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_24g.gif

lnfluence of speed and deflection angle

Speed
The permissible speed of the universal joint shaft is influenced by the following parameters:
http://www.gwb-essen.de/images/blauerpunkt.gifsize of the shaft
http://www.gwb-essen.de/images/blauerpunkt.gifwidening of the yokes due to centrifugal force
http://www.gwb-essen.de/images/blauerpunkt.gifquality of balancing
http://www.gwb-essen.de/images/blauerpunkt.giftrue running of the connected flanges
http://www.gwb-essen.de/images/blauerpunkt.gifdeflection angle during operation
http://www.gwb-essen.de/images/blauerpunkt.giflength of the shaft

Speed x deflection angle
Theoretical considerations and observations of various applications have shown that certain mass acceleration moments of the centre part of the shaft must not be exceeded if a quiet running of the shaft drives is to be achieved. This mass acceleration moment depends on the speed n, the deflection angle and the mass moment of inertia of the centre part of the shaft.

The mechanically possible deflection angle for each joint depends on the size of the shaft. Owing to the kinematic conditions of the universal joint described before, the practical deflection angle must be limited in relation to the rotational speed.

The following table shows the max. speeds and the max. permissible values for the product

http://www.gwb-essen.de/fahrzeugbau/images/seite_25a.gif

of the various shaft sizes for a moment of inertia of the centre part according to a shaft length of approx. 1500 mm.
When approaching the critical rotational speed and in the light of the demand of maintenance of balance quality (see Balancing of Propeller shafts ) , it may be necessary to reduce the rotational speed.


Since the quiet running of the universal shaft in practice also largely depends on the installation conditions, the n x values shown in the table can only be regarded as a guidance. Slightly higher values are possible. In case of favourable spring and mass conditions the values may be exceeded by up to 50 %.

Transverse whirling speed
Universal shafts are flexible elastic units, which must be calculated considering the bending vibrations and the transverse whirling speed.
For reasons of safety the max. perm. operating speed must be sufficiently below the transverse whirling speed.

The diagram on the end of this page shows the transverse whirling speeds of the varbus shaft sizes depending on the operating lengths and the tube dimensions shown in the catalogue.

The diagram values apply to normal installation conditions with a supposed distance of the centre point of the joint shaft from the adjacent bearing equal to 3 x M and a rigid suspension of the connected units.

In order to achieve a safe and quiet running behaviour the max. perm. operating speed, i.e. including a possible excess speed, must not exceed 80 % of the transverse whirling speed shown in the diagram.

http://www.gwb-essen.de/fahrzeugbau/images/seite_26ae.gif

If the permissible speed is exceeded, the length of the universal shaft must be reduced or an intermediate bearing must be provided.

The following diagrams only refer to universal shafts of the standard design. For special designs with greater length compensations than normal or with other alterations reducing the flexural strength a special calculation of the critical speed is required. In this case please ask our advice.


Transverse whirling speed of cardan shafts dependent on operating length http://www.gwb-essen.de/images/zeichen_lb.gif

Load on connection bearings

The bearings of the driving and the driven shafts are strained by statle and dynamic forces and moments.


These bearing forces result from:

Static bad due to
http://www.gwb-essen.de/images/blauerpunkt.gifthe weight of the universal shaft
http://www.gwb-essen.de/images/blauerpunkt.gifthe length compensation under torque
http://www.gwb-essen.de/images/blauerpunkt.gifthe torque deviation in case of deflected universal shafts

Dynamic bad due to
http://www.gwb-essen.de/images/blauerpunkt.gifthe remaining unbalance of the shafts
http://www.gwb-essen.de/images/blauerpunkt.gifthe aperiodical length compensation (axle movement) under torque
http://www.gwb-essen.de/images/blauerpunkt.gifthe torque deviation in case of rotating, deflected shafts and
http://www.gwb-essen.de/images/blauerpunkt.gifcentrifugal forces in case of untrue running of the connected units


Bearing forces due to torque deviation
The torque equation for a deflected joint is:
http://www.gwb-essen.de/fahrzeugbau/images/seite_27be.gif
(See 'General fundamental theory ')

If the transmitted power (N) is taken as constant (no friction losses), the torque relation can also be es follows:



http://www.gwb-essen.de/fahrzeugbau/images/seite_28a.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_28b.gif
http://www.gwb-essen.de/fahrzeugbau/images/seite_28ce.gif
The extremes of the transmission i are:
http://www.gwb-essen.de/fahrzeugbau/images/seite_28de.gif
Thus also:
http://www.gwb-essen.de/fahrzeugbau/images/seite_28e.gif

Bearing forces due to Iengh alteration

http://www.gwb-essen.de/fahrzeugbau/images/seite_28f.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_28g.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_28h.gif

With a constant drive capacity resp. with a constant drive torque http://www.gwb-essen.de/images/zeichen_m1.gifand a constant angular drive velocity http://www.gwb-essen.de/images/zeichen_omega1.gifan irregular torque behaviour is obtained in the drive. Since the torque is only transmitted in the journal cross plane, the cross, however, has a horizontal position with regard to the drive shaft at one moment and a vertical position with regard to the driven shaft at another moment, depending on the position of the yoke, there is, in the former case, a bending torque http://www.gwb-essen.de/images/zeichen_mb2.gifon the yoke of the driven shaft and, in the latter case, a bending torque http://www.gwb-essen.de/images/zeichen_mb1.gifon the yoke of the driving shaft.

Thus the driven torque http://www.gwb-essen.de/images/zeichen_m2.giffluctuates twice per rotation between the extreme values

http://www.gwb-essen.de/images/zeichen_m1.gif/ cos and http://www.gwb-essen.de/images/zeichen_m1.gif* cos



http://www.gwb-essen.de/images/zeichen_alpha1.gif= 0; 180

http://www.gwb-essen.de/fahrzeugbau/images/seite_28i.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_28j.gif



http://www.gwb-essen.de/images/zeichen_alpha1.gif= 90; 270

http://www.gwb-essen.de/fahrzeugbau/images/seite_28k.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_28l.gif



The universal shaft with two joints in the Z-arrangement shown is Ioaded with the following moments. Here, as for the single joint, only the two extreme positions are shown.

http://www.gwb-essen.de/images/zeichen_alpha.gif= 90; 270
http://www.gwb-essen.de/images/zeichen_beta2.gif= http://www.gwb-essen.de/images/zeichen_beta1.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_29a.gif
http://www.gwb-essen.de/fahrzeugbau/images/seite_29b.gif



http://www.gwb-essen.de/images/zeichen_alpha.gif= 0; 180
http://www.gwb-essen.de/images/zeichen_beta2.gif= http://www.gwb-essen.de/images/zeichen_beta1.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_29c.gif
http://www.gwb-essen.de/fahrzeugbau/images/seite_29d.gif


In general:

http://www.gwb-essen.de/fahrzeugbau/images/seite_29e.gif



Radial forces on connecting bearings
For universal shafts with two joints mounted normally while observing the installation instructions it is usually enough to know the greatest reaction forces in the bearings of the driving and driven shafts, which occur two times per rotation. The following calculation scheme may be helpful. (See 'Calculation scheme')



Axial forces on connecting bearings

Axial forces on connecting bearings are encountered in the form of reaction forces due to:
http://www.gwb-essen.de/images/blauerpunkt.gifdisplacement of the engine / transmission and / or transfer box units
http://www.gwb-essen.de/images/blauerpunkt.gifaxle displacements

These axial forces are a function of:
http://www.gwb-essen.de/images/blauerpunkt.gifthe amounts of torque to be transmitted
http://www.gwb-essen.de/images/blauerpunkt.gifthe sectional dimensions of Ion gitudinal compensating elements
http://www.gwb-essen.de/images/blauerpunkt.gifthe friction coefficient in Ion gitudinal compensating elements
http://www.gwb-essen.de/images/blauerpunkt.gifthe deflection angles of the cardan shaft under operating conditions
http://www.gwb-essen.de/images/blauerpunkt.gifthe relative dynamic displacement of engine and transmission units
http://www.gwb-essen.de/images/blauerpunkt.gifadditional loads due to hydraulic effects arising when the grease
http://www.gwb-essen.de/images/leer.gifchamber in the Ion gitudinal displacement system is filled beyond capacity


Calculation scheme of radial forces on connecting bearings

Universal shaft in Z-arrangement

Position 0 flange yoke right-angled to drawing plane
Position http://www.gwb-essen.de/images/zeichen_pi.gif/2 flange yoke in drawing plane

Universal shaft in W-arrangement

Position 0 flange yoke right-angled to drawing plane
Position http://www.gwb-essen.de/images/zeichen_pi.gif/2 flange yoke in drawing plane

http://www.gwb-essen.de/fahrzeugbau/images/seite_30la.gif

http://www.gwb-essen.de/fahrzeugbau/images/seite_30ra.gif

Length dimesions

The operating length of a universal shaft is determined by:
http://www.gwb-essen.de/images/blauerpunkt.gifthe distance between the driving and the driven units
http://www.gwb-essen.de/images/blauerpunkt.gifthe length compensation during operation


The following abbreviations are used:

Lz = Compressed length

This is the shortest length of the shaft. A further compression is not possible.

La = Length compensation

The universal shaft can be expanded by this factor La is a constant factor for each universal shaft. An expansion beyond that factor is not permissible.

Lz + La = Max. perm. operating length LBmax.

http://www.gwb-essen.de/fahrzeugbau/images/seite_31a.gifhttp://www.gwb-essen.de/fahrzeugbau/images/seite_31b.gif


During operation the universal shaft can be expanded up to this length. The optimum working length LB of a universal shaft is achieved if the length compensation is extracted by one-third of its length.

http://www.gwb-essen.de/fahrzeugbau/images/seite_31c.gif

This rough rule appiles to most of the arrangements. For applications where larger length alterations are expected the operating Iength should be chosen in such a way that the movement will be within the limit of the permissible length compensation.



Arrangements of cardan shafts

A tandem arrangement of universal shafts could become necessary
http://www.gwb-essen.de/images/blauerpunkt.gifto cope with greater installation lengths
http://www.gwb-essen.de/images/blauerpunkt.gifto by-pass construction units


Basic forms of shaft combinations:

Universal shaft with intermediate shaft
http://www.gwb-essen.de/fahrzeugbau/images/seite_31d.gif
Universal shaft with two intermediate shafts
http://www.gwb-essen.de/fahrzeugbau/images/seite_31e.gif
2 universal shafts with double intermediate bearing
http://www.gwb-essen.de/fahrzeugbau/images/seite_31f.gif









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