Modified Beam Bending Equations
Modified Beam Bending Equations
(OP)
Hi everyone,
I am attempting to model the stiffness of a gearbox using none FEA methods, and the way I have approached it so far is to break down the gear into a load of separate elements to analyse each element's contribution to the stiffness, e.g. torsional stiffness of the bulk of the gear, contact stiffness (hertzian contact)
Anyway, as part of this I am thinking of modelling the gear teeth as simple beams, with a load applied at some point along the beam (at PCD). However, the formula that I was going to use:
Y_max = (Wa^3/6EI)((3L/a) - 1))
is not valid for such 'stubby' beams as would be found on gear teeth - my data book tells me the equation is only valid for lengths twice that of the depth
Do any of you know of a formula that may be more appropriate? or even a modification of the above formula?
Thanks for your help
I am attempting to model the stiffness of a gearbox using none FEA methods, and the way I have approached it so far is to break down the gear into a load of separate elements to analyse each element's contribution to the stiffness, e.g. torsional stiffness of the bulk of the gear, contact stiffness (hertzian contact)
Anyway, as part of this I am thinking of modelling the gear teeth as simple beams, with a load applied at some point along the beam (at PCD). However, the formula that I was going to use:
Y_max = (Wa^3/6EI)((3L/a) - 1))
is not valid for such 'stubby' beams as would be found on gear teeth - my data book tells me the equation is only valid for lengths twice that of the depth
Do any of you know of a formula that may be more appropriate? or even a modification of the above formula?
Thanks for your help





RE: Modified Beam Bending Equations
RE: Modified Beam Bending Equations
RE: Modified Beam Bending Equations
rb1957, you are right - the bending of the teeth is insignificant compared to other factors - I think that the stiffness of the gearbox is mostly affected by the hertzian contact of the teeth. I just wanted to cover all bases in my model to start off with really. Once I have some experimental data I may simplify it all (or perhaps more likely just scrap it and try FEA!)
btrueblood: Used Roark's book - pretty helpful although sometimes confusing to navigate... ending up using a modified lewis equation for bending stress to find the deflection under load of a gear tooth
thanks