Is there any way of finding force on gears through torque?

1. Feb 15, 2015

knight92

1. The problem statement, all variables and given/known data
I have an assignment which is asking me to calculate the minimum diameter of a shaft. Shaft length is 300 mm.
The shaft is held between two bearings with one on the left hand side and one on the right 220 mm away. At 143 mm there is a spur gear and at 300 mm(at the end) is a keyway. I know how to find the minimum diameter using DET or MSST but the problem I am facing is I need to find the reactions on the bearings first and there are no forces given at all. All I know is that 40 kW of power is transmitted at 7000 RPM which gives a torque of 55 Nm. I have posted an example (Fig.1) my lecturer has given me but the forces at the gear(G) and pulley(P) in z and y direction are already given in the example. A and B are bearings.

2. Relevant equations
See Fig.1

3. The attempt at a solution
My attempt at the solution is to first find out what the forces on the spur gear are in the z and y direction. Can I use the torque transmitted by the shaft to calculate these forces assuming the shaft is driven by the gear?

Thanks for the help!

I have attached the generic data I have been given for the shaft in my assignment as Fig2.

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Last edited: Feb 15, 2015
2. Feb 15, 2015

SteamKing

Staff Emeritus
What's the definition of torque? How would you use this definition to calculate the force acting on a gear, for example?

3. Feb 15, 2015

knight92

Torque = Force * Radius. I have the Pitch circle diameter(d) of the gear.

I have tried this before but how do I split the force into z and y direction?

4. Feb 15, 2015

SteamKing

Staff Emeritus
Isn't this why you are given the pressure angle of the gear teeth?

5. Feb 15, 2015

knight92

so basically am I right in thinking the two components are:

Force*cos(Pressure Angle)
Force*Sin(Pressure Angle) ?

6. Feb 15, 2015

SteamKing

Staff Emeritus
It's a start.

7. Feb 15, 2015

knight92

I can draw the SFD and BMD from those figures. As the keyway is part of the shaft which is not connected to anything (question doesnt say) can I ignore it? I don't really see how else the keyway would affect the forces on the shaft

8. Feb 15, 2015

SteamKing

Staff Emeritus
The key is used to keep the gear (or whatever is keyed) from slipping around the shaft under the application of the torque being transmitted. Due to the need to machine a keyway (essentially a notch) into the shaft to fit the key, a stress concentration is created there.

Since the point of this problem is to design the shaft to minimum diameter given the stress constraints on the material, the stresses created by the presence of the keyway should be considered, in addition to the other stresses creating in bending or shear from the gears or the bearings, for example.