U-joint connection

[TeoAlfa]

I am in the process of designing an agricultural machine which uses the power from the tractor to give rotation and torque to an inclinable tiller head.
During the process i have reviewed several designs. One of them made me sceptical. They connected the transmission (just to let you know that the tractor connects to a transmission box which then give rotation to the tiller head at 90 deg. angle) to the tiller head by using just one u-joint. Do you think this solution will cause vibrations and lastly bearing failure at the end?
As a solution it's simple but i would like your views on that. I know that a universal joint system includes two seperate u-joints. Have you ever seen a system with only one u-joint? Thanks!

 

[desertfox]

Hi
Any chance of a picture?

 

[TeoAlfa]

I attach a CAD image of my design to better understand the concept.

 

[TeoAlfa]

And here is the design that features only one u-joint.
Notice how close the transmission is to the tiller head.

 

[desertfox]

Hi

Thanks for the information, vibration normally comes from misalignment or out of balance rotating parts.
Universal joints are usually provided in pairs when two parallel shafts are not aligned, I cannot see a problem with the set up assuming all the calculations for the bearing etc have been analysed

 

[TeoAlfa]

In this case we need to connect 2 unparallel shafts. So are we going to get any vinrations by using a single u-joint?
Will it be better and more smooth if we use a pair of u-joints?
Thanks!

 

[FeX32]

Yes you will experience vibrations only if the input shaft angle is significantly different from the output. With 2 U- joints, this sinus vibration is canceled out.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian

 

[FeX32]

Here is some more information. I remember deriving the equations for this actually.
If I find them (or have a chance to re-derive them) I will post them for your analysis.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian

 

[3DDave]

The problem is that u-joints are not uniform transmitters of rotation. See

http://www.cs.cmu.edu/~rapidproto/mechanisms/chpt8.html#universal3fig.

The reason they are usually used in sets with the input and output parallel is to undo at the final joint the non-uniform acceleration introduced at the first joint. CV joints are called constant velocity to distinguish them from u-joints.

The design team should have presented the expected loading from the non-uniform effect.

I also see in the CAD image that the input shaft is not parallel to the output shaft. If the angle change between input and output in the new design is the same as that in the old design, the load on the u-joints because of misalignment will be the same. Further examination indicates the CAD design is to allow the tiller to tilt relative to the fixed motor, which would vary the amount of non-uniformity. At least the new design is constant.

 

[FeX32]

I found some of the derivations. I attached just the results of the kinematic derivations.

Notably, the results indicate a sinus vibration that is directly proportional to the differences in shaft angle.

I have also derived the inertial torque. If you are interested let me know.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian

 

[TeoAlfa]

@3DDave
By telling "new design" you mean the picture and "old design" you mean the CAD image?
If so, in the new design (picture) the tiller is allowed to tilt, although not apparent in first view. And i assume that the axis of tilt should be the same as the axis of the u-joint cross to be able to tilt.

By definition, the tiller head should be able to tilt. This is a given. So we must find a way to eliminate the vibrations caused by misalignments.
In my design (CAD image) i tried to cancel out the vibrations caused by misalignment (which will always be present as the head should be able to tilt) by using a shaft with 2 u-points featuring opposite angles (see image below).

The 2 shafts will never be perfectly aligned because the tiller head will be able to tilt and the operator (theoretically) will not be able to tilt the head perfectly to align it with the angle of the transmission shaft. The question is: Will we have less vibrations with the double u-joint design?

 

[3DDave]

The vibration is only proportional to angle for cases where theta is approximately equal to sin(theta).

The ratio varies from cos(theta) to 1/cos(theta) for theta is the angle between the shafts over each rotation.
For 5 degrees this is .996 to 1.004.
At 15 degrees this is .966 to 1.035, too much for most drivelines, probably OK for low RPMs.
30 degrees is .866 to 1.155, which is very noticeable.

 

[FeX32]

"The question is: Will we have less vibrations with the double u-joint design?"

Depends on how much misalignment there is. But in general, assuming similar angles between the single and double u-joint arrangements, there will be less in the double arrangement. This can be easily proven with the kinematics I provided.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian

 

[TeoAlfa]

@ FeX32
In the single u-joint design the misalignment angle (between transmission and tiller shafts) will always be greater.
Could you please make a sample of calculations for me? Whatever you need please ask me. Thanks a lot!

 

[FeX32]

Dave, that link you provided is useful. However, it's analysis assumes the angle between the input and output (beta) is the same. This is not likely a good assumption for the OP's application.
Consequently, the analysis is inaccurate.
Although, the conclusions (in general) drawn are for sure valid.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian

 

[3DDave]

If you make the tilt axis the same as the gearbox input shaft axis then the tilt of the tiller will not change relative to the output of the gearbox. You can move the gearbox by adding a double-pulley (at least that's what the input looks like now) and a belt from there to the gearbox. Costs more, more finger catchers, but eliminates u-joint vibrations.

I thought you were reviewing in-house designs with old-costly-two u-joints vs new-cost-saving-one u-joint. It's early.

 

[TeoAlfa]

I made a modification to the initial design. I made the 2 shafts parallel. And given that the tiller head will most of the times be working horixzontally i think that this is the best solution. As i have told before, we will always have a bit of vibrations for the reason that the tiller head is designed to tilt.
I attach an image of the new setup at the bottom of the post.

If we use a single u-joint, even with the tiller head in horizontal position the misalignment will be high. There is no way to cancel the vibrations out.
What do you think?

 

[FeX32]

I agree with Dave's statement.

Also, here is what you asked for. The kinematics of a single u-joint. I coded it in Matlab.

https://dl.dropboxusercontent.com/u/18923918/u_joint_kine1.m

You can change the angle of Beta at the top and re-run the code to compare.

If you don't use Matlab let me know and I can save the plots.


"Simplicity is the ultimate sophistication." L. da Vinci
- Gian

 

[TeoAlfa]

@FeX32
No, i don't use Matlab unfortunately.

 

[GregLocock]

Have you considered using a double cardan joint? These give almost perfect CV behaviour and allow large articulation angles.

Cheers

Greg Locock


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