I need to make two steel shafts to mate to a female splined coupler. The diameter is about an half an inch. I will need to be able to machine these shafts on a small lathe and a 2hp bench mill. I will have to spline the shafts as well. I will be putting 4 hp thru the shaft which will be under 12 inches long. I need something reasonably easy to machine, but strong enough to last. I will be more then likely ordring the steel from mcmaster carr. I understand the problems with cutting a spline vs hobbing, but I am hoping that since this is a low hp motor it will not be a problem.
I do not know your application but you might consider two sprockets, one mounted on either end of the shaft, coupled with double roller chain.This would require just two keyways to be machined. This setup also allows for some misalignment. Steve
Really have to know more about the specific application. That shaft can easily handle 200 horsepower. Or it might twist with 1/4 horse. All depends on the speed.
Tau = K * T * c / J (T is torque, found above. Tau is the max shear stress due to T. c is the max radius (D/2), and J is Pi*c^4 / 2 for a solid shaft. K is a stress concentration factor and varies from ~1.1 for a shaft that gently radiuses into a larger dia. spline, to 2, 3+ for steps, keyways, etc. Another K should also account for fatigue losses, if this is a high cycle app. Roughly speaking you can throw in another K of 2 for infinite life.)
Yield Strength depends a lot on the heat treatment, as you probably know.
Simplifying: T = HP * 63024 / RPM Tau = 16 * K * T / ( Pi * D^3) = .58 * YS / SF
Combining and solving for YS, I get (check this)... YS = 553,000 * K * FS * HP / (D^3 * RPM) (where D is in inches and YS is in psi)
E.g., if K=3 (some fatigue plus stress conc.), FS=2, HP=4.0, D=.5, RPM=1600 YS = 66,360psi
So, IF those RPM and HP numbers are the same as yours, D is .5 or greater, and your splines don't have severe stress risers, then you need a material with that YS, or greater. 4140-Normalized is around
95kpsi YS and machines ok. 4140-annealed is around 60kpsi, and would machine easier. 1045-Cold Drawn is around 85kpsi, would be cheaper, machines ok, but is not as ductile as either 4140.
Some cautions: Motors can give ~1.5x their full load torque. Inertia or braking torques can be many times the running torque. Strength is very sensitive to D ( 1 / D^3). If shaft failure could cause human injury, FS=2 may not be enough. Keyways have big stress risers. If your spline od is the same as the shaft od, you need to be working with the diameter of the spline root, or use a larger K.
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