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Cardan Error Eq.
2

Cardan Error Eq.

Cardan Error Eq.

(OP)
Hi,

What is the equation for cardan error (relation between the input/output angles and the input/output speed). I'm trying to establish the misalignment tolerance for u-joint but before that, I need to know how the input/output angles of the u-joint affects the speed.

Thanks
KL

RE: Cardan Error Eq.

This topic was covered in the Transmission and Driveline engineering Forum (Forum78) in the thread Compound U-Joint Angles (Thread78-53988). Is this what you are talking about?

A link to a resource I have found helpful in looking at U-Joint angles is here:

http://www1.mn.man.de/manted/aufbaurichtlinien/gb_f4.html#Anchor-21683

Best regards,

Matthew Ian Loew
"Luck is the residue of design."
Branch Rickey


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RE: Cardan Error Eq.

TKL8,

The equation you seek for a single Cardan joint for the input shaft/output shaft speed is

Woutput/Winput = cosB/(1-sin^2[B]sin^2[A])

where

B = angle between the shafts

A = rotational angle of the input shaft

RE: Cardan Error Eq.

(OP)
thanks matthew and sreid for your replies.
sreid, actually the equation i seek for a double cardan joint. is the equation the same?

Rgds
KL

RE: Cardan Error Eq.

(OP)
thanks matthew and sreid for your replies.
sreid, actually i'm seeking for the equation for a double cardan joint. is the equation the same?

Rgds
KL

RE: Cardan Error Eq.

TKL8,

U-Joints are often used in pairs with a shaft between them.  If the input and output shafts are at the same angle and the forks are oriented corrrectly, the output shaft speed will be constant.  The shaft between the u-joints still has a speed variation as stated in the equation but the speed variation is cancelled at the output shaft u-joint.

RE: Cardan Error Eq.

tkl8,

You are in an automotive forum, so can I assume yours is an automotive application, yes, good.

The reason so well stated by sreid is why you will see the engine, tran, and dif, as well as any in between gadgets, (such as retarders or aux gear boxes in large vehicles) all set on the same angle.

To minimize drive line angles, and hence u joint stress, the engine is set on an angle so as to "look" down towards the diff, which is on a lower elevation.  If the engine were to be set level, with the tran attached, the angle to the dif would be horrendous, in u joint parlance, with miminal tolerance for suspension motion.

Therefore, if whatever you are doing that prompted your question involves automotive drivetrains, measure and maintain the design inclination of the drive train components to prevent u joint stress, and/or harmonics.  If you get some component rotating with the angular acceleration/deceleration that the intermediate shaft between two u joints has, you will get harmonics, and/or vibration.  That is what is created, and then cancelled out as so aptly noted by sreid.

With all the angles set correctly, your u joint still has a maximum angularity that it can operate at for the speed which you are trying to run it.  You have to find that out from the vendor.

rmw

RE: Cardan Error Eq.

Referring to sreid's post:
"The equation you seek for a single Cardan joint for the input shaft/output shaft speed is Woutput/Winput = cosB/(1-sin^2[B]sin^2[A]) where B = angle between the shafts A = rotational angle of the input shaft"

When I plot this, I get a sine wave from +1 to -1 as the ratio of input to output. I plotted cos(b)/(1-(sin(b))^2*(sin(a))^2) VS b for 2pi revs. This doesn't seem correct. What did I do wrong?
Monkeywrench

RE: Cardan Error Eq.

You should have plotted against A

HTH

Cheers

Greg Locock

RE: Cardan Error Eq.

Sorry, my mistake; I meant to say A (I used beta = 2*pi angle of rotation in Mathcad). Can't figure this out yet.
Any idea? -Monkeywrench

RE: Cardan Error Eq.

If you are converting degrees to radians the conversion is 2 x pi x angle/360

RE: Cardan Error Eq.

I don't know what you are doing wrong. I get two cycles of a sine-like wave when I cut and paste your equation into Excel, for b=.01 and a is 0 to 6.3 in .1 steps

Cheers

Greg Locock

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