Analysing FEA Gear Box Housing 1

[morris9791]

Dear Experts,

I need to analyse the structural strength of a helical gear box housing which contains an input, idler and output gear. I have all the relevant torques and forces acting on each gear.

I have having difficulty applying the loads in the correct direction in order for the system to be balanced which is requirement of a FEA static analysis.

I feel stupid asking this question but does an FEA model ‘ALWAYS’ have to include moments ‘AND’ forces if such loads occur in reality. I know this is the case when one is doing hand calcs, i.e., both summation of moments and forces must sum to 0 for a balanced system.

The reason I ask is because I am confused as to whether it is sufficient to apply forces only at mesh points. Note, that I do not include the teeth geometry, just the cylindrical shapes. The tangential component of the force will provide the torque automatically. Or do I need to apply the resulting torques as well.

Perhaps there are sources explaining how such a problem is modelled?

Any information will be appreciated.
Best Regards
Ed

 

[gurmeet2003]

morris,

This is information that has to be considered for every analysis; deciding the extant of the model and the loads to be applied. I think that the concept of a thermodynamic system may be relevent. Identify the boundaries of your system. What is the extant of the model? It appears that you are including the gear assemblies in your model. Next question is about the shaft bearings. Do you need to include the bearings?

How does one include the effect of parts that are not included in the assembly? This has to be done by calculating the reaction between the part that is removed and the remaining assembly. The reaction should be applied to the remaining assembly at the correct location.

If you do not model the teeth, you have to make sure that the forces applied at the interface reflect the actual forces between the teeth. The contact will not do this, becuase the contact will not represent the actual geometry. Therefore if you plan to use circular gears, leave a gap between two adjoining gears and apply the correct calculated tangential and radial forces on both shafts.

An input and output torque should be applied on input and outoput shafts.

No moment need be applied on the gearbox housing, as the bearings can not transfer a moment. Gearbox will have to be fixed somewhere at the base and there may be a moment transferred through these constraints. However reactions at the constraints are automatically calculated by the software.

If I was to do this analysis. I would first start with the gear box housing alone. I may or may not include the bearings. I would fix the base of the housing. Do a force balance for the shafts (assuming rigid shafts) and calculate the reactions at the housing bores (using free body diagrams). Apply these reactions on the housing and run the analysis. Then looking at the results I may decide whether to add the bearings.

I feel it is improbable that additon of gears and shafts would be required. However that could be decided by looking at the result of last analysis mentioned above.

For your information I have never done analysis of a gear box housing. But I have done many similar analyses.


Gurmeet

 

[gwolf2]

I have done a gearbox housing and agree with Gurmeet - that's exactly how I did it, the basis is a free body diagram for each component (Shafts, gears, and housing).

I would add that for some gearboxes, like the one I did for a helicopter tail rotor, the stiffness of the shafts has an influence on the deflection of the housing. This happens with big HP shafts and thin optimised housings. This is really bloody awkward but it does sometimes happen.

Enjoy - I'd happily do another.

 

[morris9791]

Dear gwolf2 and gurmeet,

Thanks for your great replies. It is really appreciated.

>>> I feel it is improbable that addition of gears and shafts would be required.>>>>>

1) I also feel this way too. My understanding is that the torques applied on the gears will develop forces at the mesh points. These forces will be reacted by the radial loads on the bearings and finally by the housing. I drew a FBD for the gear, shaft, bearing and housing and I can only see radial loads acting on the housing.

Therefore, I understand that the housing will react the torques ‘indirectly’ by reacting the forces developed at the teeth.
Therefore in my case, I do not think it is necessary to include the gears or shaft. Of course, excluding these components will have an effect on the stiffness/ deflection. For me, this would be an assumption I have to contend with.

I have obtained the radial reaction and thrust loads acting on the bearings due to the torques acting on the helical gears (Timken program). I have applied these directly to the housing bores. I think this is a reasonably accurate way of determining the stress at the housing mounts which is the goal of my analysis.

Do you guys agree with my above approach?

2) Finally, if one had to include the gears and shafts etc, how would one model the cylindrical gears without the teeth to transfer the torque using appropriate boundary conditions? The gears are not 1:1 ratios so how do you balance the torques if the input is not the same as the output, not to mention the idler thrown in to complicate things!
It is easy balance the forces at the gears since they are opposite and equal.

Looking forward to hearing from you!

Best Regards
Ed

 

[gurmeet2003]

morris,

Giving pointwise answer to your questions:

1. Yes, radial loads would be transmitted to the housing. Tangential gear loads will blance the external torque. However these loads also have to be balanced by the housing.
If the tangential loads are not transmitted to the housing the shaft will not be in force balance.

Since there is a gear ratio involved, the input and the output torques will not be equal. Difference in torque will have be transmitted to the housing through the housing reactions to the tangential gear loads. Since the gears are helical there will also be a thrust load transmitted to the housing (bearings).

Calculating the value of the tangential gear load is very simple. It will be torqu/radius. Therefore your approach is ok, except that you need to add the tangential force also to the housing.

2. As I have mentioned above the torques are not balanced. The difference in torques is transmitted to the housing mounts. Forces transmitted to mating gears teeth have to be equal and opposite. Therefore the torque is proportional to the gear diameter.

You have to make sure that when you eliminate the gear teeth, the force system is not altered. In normal gear operation there will be a force normal to the teeth and another tangential to the teeth surface. As long as this force system is replaced by an equivalent system of radial force and tangential forec (tangential to cirucular gear without teeth), the reactions at the housing should not be altered.

Hope this helps.

Gurmeet

 

[morris9791]

Dear Gurmeet,

>>>>>Yes, radial loads would be transmitted to the housing. Tangential gear loads will blance the external torque. However these loads also have to be balanced by the housing.>>>>

I think you were referring to the ‘radial’ loads as the separating loads on the gears. I am referring to the radial loads on the bearings as the resultant of the tangential and separating forces from the gears. So I believe I have included all necessary forces that are to be reacted by the bearings.


It think it would interesting if I could compare the bearings loads for the following 2 FEA models
1) Only the housing is included and the bearing loads are loaded onto the housing bores which I have done already. The results behave as I would expect.
2) Include the bearings, shaft and gears (without teeth) and apply the forces and torques onto each gear. Measure the reaction forces at the housing bores. This leads onto my next question to which I have uploaded a schematic.

I am not really sure how to correctly model the real condition in the FEA model.
My approach would the schematic shown to the right. Instead of having the torque going ACW on the output, I would reverse this because the system has to be ‘locked’ in order to prevent rotation. The idler is constrained from rotating about its own axis. This will cause the input and output to roll off the idler to the left and therefore putting forces onto the shaft and bearing in the left direction.

What are your opinions on this?
I appreciated and look forward to your suggestions. Have a nice weekend.

Best regards
Ed

 

[gurmeet2003]

Ed,

I think that you have this baby taken care of. Fix the end of the output shaft. It will generate the reaction in the correct direction.

Gurmeet

 

[morris9791]

Gurmeet,

you say fix the output shaft, however I put the torque on this shaft in the opposite direction to the input shaft simulate the gear train being locked.

Unfortunately, I am not getting good comparison between the applied bearing loads in model A and the reactions measured at the housing bores in model B.
The reactions in model B are less by approx 40% to 60%. I am not sure why, I doubt the error is purely due to the absence of the shaft and bearing deflections etc.
Perhaps my method shown in the attachment is not correct, I will be glad to receive other suggestions.

Anyhow, I think I have more confidence using model A which does not have the gears. I believe that that applying the bearing forces directly to the housing is sufficient in this case.

Best regards
Ed