Gear web strength and thickness - how to determine? 2

[pakgears]

Imagine a HyVo sprocket, driven from the inner diameter (perhaps via a spline or keyway). The difference between the outer diameter and inner diameter is large, and the width of the outer sprocket and inner hub need to be the same. There is a requirement to make the part as light as possible, and to do so you have to add face grooves to the sprocket, equidistant from either side. Also assume that the lower and upper diameters of the face groove are far enough away from the stresses induced by the sprocket teeth and inner coupling that they can be ignored.

For argument sake, let's say the width is 2 inches (inner hub and sprocket teeth), the inner diameter is 1 inch, the outer diameter is 6 inches, and the face groove is going in between the diameters of 2.5 inches and 4.5 inches. The torque you need to carry is 6000 lb-in, and the sprocket material is 4340 steel hardened to a UTS of 180 ksi.

How does one determine the minimum thickness of the remaining "web" of material? What fundamental equations are employed in this calculation?

 

[israelkk]

FEA

 

[rb1957]

does "groove" = "slot" ? if not, why only "groove" ?

what does the drive (pedal) gear on a bicycle look like ?

the gear transfers the torque from the ID to the OD, so the internal structure of the gear needs to do this. plus centrifugal acceleration. remeber there are other loadcases to consider (not just when the device is running smoothly).

if minimising weight is the objective i think partial thickness "grooves" won't get you there. for my money, triangular shaped slots would be more effective.

 

[pakgears]

Thanks for your responses thus far.

Really hoping for someone to provide an example, or insight into methodology behind analytically determining how thick that web can be. Maybe a link to an example on the internet or in a textbook? (I haven't found any)

Not really interested in alternative shapes, even though they may be superior - that is just outside the scope of this inquiry. Basically looking to know how to calculate how much torque can be transferred by a given thickness of that web at a given diameter. Really hoping FEA is not the only method of evaluating this problem...

Thanks again.

 

[drawoh]

pakgears,

What are you doing to the gear? Are there any side loads?

What is your failure mode? If the gear does not break outright, can it bend a little?

Can you heat shrink a steel rim round and press it a steel hum into some lightweight material?

JHG

 

[MintJulep]

I guess I would start by looking at the sheer stress at the step between the web and the hub.

 

[drawoh]

Let's try that last sentence again.

Can you heat shrink a steel rim around the outside and press a steel hub into some lightweight material?

What can your fabricator do? If you are machining your gear, lightening holes tend to be an extra setup. I try to design machined wall less than 2mm thick.

JHG

 

[pakgears]

drawoh: for this example, I wish to keep the part a single piece. I am trying to understand what analytical methodology (if any) can be used to determine the thickness of the web.

MintJulep: this sounds promising, can you elaborate or point to an example which I can use? I have not been able to recall any shear stress examples, or find any in say Peterson's, where the torque is applied in a hub and carried to the outside diameter like in my example...

 

[rb1957]

the web is transmitting torque, yes?

shear flow = torque/(pi*d)
shear stress = shear flow/t

and there's radial (normal) stress to consider.

 

[drawoh]

pakgears,

I seem to be having trouble writing complete, coherent sentences in this discussion. Let's try that last one again.

I try to not design machined walls less than 2mm thick. This is a manufacturing issue. Thinner than that might cause warping, and may make things more difficult and expensive in the machine shop.

A thin web between the hub and sprocket can be fabricated as part of your lathe setup. A set of ribbed pockets, which might work better, requires a setup on a CNC mill, probably an additional and more expensive operation for you.

You may be able to analyze it, but someone has to fabricate it, and hold your tolerances.

JHG

 

[Cockroach]

The spokes of a gear act merely to keep the rim in place and synchonous to the shaft during power transmission. Therefore the spokes see bending from the resisting torque at startup, shear from the transverse loading about the driveshaft, radial compression and a tensile load depending on the centrifugal forces acting at the rim in response to dynamic loading.

There are several good references on the subject, but gear manufacturers are perhaps the best. I would use their websites as a start, look around to see technical bookstore information or get to the publishers and search on gear dynamics and design.

Hope this helps.

Regards,
Cockroach