Basically you can determine the transmission error if you know the mesh stiffness. Some classic literature (in German) on this for spur gears:

Weber, C.; Banaschek, K.: Formänderung und Profilrücknahme bei gerad- und schrägverzahnten Rädern; Schriftenreihe Antriebstechnik 11, 2. Auflage, Braunschweig, 1955

Schmidt, G.: Berechnung der Wälzpressung schrägverzahnter Stirnräder unter Berücksichtigung der Lastverteilung; Dissertation FZG-Nr. 50, Fakultät für Maschinenwesen und Elektrotechnik, TU München, 1973

The gear mesh compliance is composed of several portions in these approaches, like Hertzian contact, tooth bending, shear and the the compliance of the support of the tooth in the wheel. Weber-Banaschek use a beam model for the bending and shear part and Schmidt a plate model.

There are many more approaches, but these are among the most commonly used ones.

Hi, I've worked on a method employing wavelet transform. I hope it can result useful!

https://www.researchgate.net/publication/257361292_Analysis_of_gear_rattle_by_means_of_a_wavelet-based_signal_processing_procedure?ev=prf_pub

https://www.researchgate.net/publication/257362476_GEAR_RATTLE_ANALISYS_BASED_ON_WAVELET_SIGNAL_DECOMPOSITION?ev=prf_pub

Article Analysis of gear rattle by means of a wavelet-based signal p...

Conference Paper Gear Rattle Analysis Based on Wavelet Signal Decomposition

You may find the answer in the paper: Calculation of transmission errors, actual path of contact and actual contact ratio of non-conjugate gears, published in VDI-Berichte 03/2002; , 1665:981-994, of C. Spitas, Th. Costopoulos, V. Spitas, as shown in my ResearchGate section, page 6.

hey  Vahid Dabbagh 

I have started working on transmission error.

Will you suggest some papers or topics on how to calculate TE

Meshing of gears and the calculation of the involved parameters may be found in my ResearchGate section, where several papers produced during my carrier of four decades are posted for free use by the researchers.

Dear  Theodore Costopoulos

Thanks for the input

 Will you tell me the name of the all the papers or relevant literature on TE calculation

I hope you will solve the problem of gear stiffness in the way we did.

1. Analytical investigation of gear tooth stiffness variation due to vibration and their effect on the chaotic response of gear power transmission.2. Calculation of transmission errors, actual path of contact and actual contact ratio of nonconjugate gears. 3. A new theory for the determination of the actual characteristics of loaded spur gears in mesh. 4. Elasticity problems and stresses in involute gears. 5, Recent advances in solving gear modelling problems. Minimization of spur gear loading through the generalized theory of gearing. 6. Fillet compliance and loading of spur gears. Good luck with your research.

Dear costopoulos

I am not able to download the papers from research gate.

please let me know what to do?

or will you please mail me the relevant papers at [email protected]

Thanks once again

Dear Paras,

If you have problem in downloading from here then try other places under my name.

T.C.

Dear Theodore

will you tell me how to calculate the mesh stiffness variation in case of helical gears?

how the stiffness varies on the contact line in case of helical gears?

I am doing static loaded TE calculation. Is there any function to calculate the mesh stiffness variation as a function of mesh cycle.

Thanks and Regards

PARAS GUPTA

The following papers may be found in my Researchgate section. They all examine spur gears.

Effect of progressive tooth engagement on the dynamic response of spur gears in action

Study of transient phenomena and response spectra in spur gear mechanisms

Kinematical simulation of tip relieved spur gears to compare performance

Calculation of transmission errors, actual path of contact and actual contact ratio of non-conjugate gears

A new model of improved accuracy for the dynamic behavior of gears.

A new theory for the determination of the actual characteristics of loaded spur gears in mesh

A novel full-scale model for the dynamic simulation of a spur gear pair

Minimization of spur gear dynamic loading through the generalized theory of gearing

Effect of rack geometry on tooth stress of gears

Design of gear flank and calculation of tooth compliance and stresses

Elasticity problems and stresses in involute gears

Recent advances in solving gear modelling problems

Tooth compliance and load distribution of spur gears

Fillet compliance and loading of spur gears

Spur gears as well as Helical gears have not a line as a path of contact. They have a plane. In spur gears this plane is swept by a line parallel to the smaller side, from one side to the end (and this is why we talk about a line of contact). In helical gears this plane is swept by a line from one corner to the diagonally opposite thus changing in length and inclination due to the way the teeth of helical gears start and finish their meshing. Simultaneously, the number of teeth in mesh changes in the same way the teeth of spur gears during their cooperation while their contact sweeps this plane. Thererfore, you have to understand the geometry of spur gears first and then start thinking about the meshing process of helical gears and the pertinent stiffness.

A work by Delft Univ. some thirty years ago is a nice piece of work to this direction

Good luck.  

Hello Costopoulos

Thanks for your input.

I have gone through most of the papers that you suggested.

Now, for helical gears how the load varies along the line of action is clear to me.

but how the load varies along the line of contact is not clear for spur and helical gears.

Will you let me know this part.

Thanks

Paras