- #1
TomBanks
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Hello everyone. The physics forum is a great online community, and I used to spend a lot of time browsing the philosophy pages. But now I've had to register and post, because I've got a very specific problem with regards mechanical engineering.
My problem is relating to torque transmission through a press fit connection. Basically, I have a design that works and transmits the torque required of it; the design is, however, over-engineered and I wish to optimise it. I wish to be able to specify a torque (say 60Nm) and from that be able to mathematically determine a length of press fit required to transmit that torque.
Step 1.
I believe there are three steps required to reach to get there. The first step requires to determine the contact pressure at the press fit connection. Because there are tolerances on the components, there will be a maximum and minimum pressure. Currently the tolerances on the components are fixed, and I can not change them. The formula I'm using to calculate the pressure is one I've seen referenced in several books and on several websites. The formula I'm using is:
Where:
Vo = Poisson’s ratio of hub = 0.292
Vi = Poisson’s ratio of shaft = 0.292
Dhi = Hub inner diameter = 108.5mm
Dho = Hub outer diameter = 113.0mm
Dsi = Shaft inner diameter = 62.0mm
Dso = Shaft outer diameter = 108.5mm
Eh = Hub elastic modulus = 210000 mpa
Es = Shaft elastic modulus = 210000 mpa
Delta = Size of interferance = 0.119
There is also an excel based online calculator that uses the same equation at:
http://www.meadinfo.org/2009/07/press-fit-pressure-calculator-optimize.html
Using the above formula and values I calculate the pressure (P) to be: 8.475 N/mm^2. Which is also the same answer -- minus rounding errors -- that the excel based calculator gives me.
This leads me to believe that step 1. is the correct approach. Any input would be apprecaited.Step 2.
Now that I know the pressure at the press fit, I can specify the desired amount of torque I wish to transmit and from that determine the force acting on the press fit.
I wish to transmit = 60 N/m of Torque = 60000 N/mm = T
Shaft Diameter = 108.5mm = D
T = Force x (D/2)
Rearranged to isolate the Force (F):
F = T / (D/2)
F = 60000 / (108.5 / 2)
F = 1106 N
If my thinking is correct, the force exerted on the shaft (and press fit) by transmitting 60Nm of torque is 1106N. From this, and knowing the pressure, I can calculate the length of the press fit required to transmit the torque.
Step 3.
To calculate the length of the press fit required, I'm using the following equation and transposing it to make Length the subject:
F = P x D x pi x L x u
L= F / pi x D x P x u
Where:
u = steel on steel coefficient = 0.4
So:
L = 1106 / pi x 108.5 x 8.475 x 0.4
L = 0,92mm
The required length of press fit necessary to transmit 60Nm of torque I calculate to be 0.92mm, which I feel is well too liberal (I'd expect between 5mm and 10mm). Is there anything that jumps out at anyone as being an obvious error? Perhaps I'm using the wrong equation(s) in step 2 and 3? Perhaps it is a unit error? Or a mistake transposing the equation? Or perhaps it is simply correct. Any input would be appreciated. I've been looking at the problem for a week now and I can't work out where I am going wrong.
Thank you everyone in advance,
Tom
My problem is relating to torque transmission through a press fit connection. Basically, I have a design that works and transmits the torque required of it; the design is, however, over-engineered and I wish to optimise it. I wish to be able to specify a torque (say 60Nm) and from that be able to mathematically determine a length of press fit required to transmit that torque.
Step 1.
I believe there are three steps required to reach to get there. The first step requires to determine the contact pressure at the press fit connection. Because there are tolerances on the components, there will be a maximum and minimum pressure. Currently the tolerances on the components are fixed, and I can not change them. The formula I'm using to calculate the pressure is one I've seen referenced in several books and on several websites. The formula I'm using is:
Where:
Vo = Poisson’s ratio of hub = 0.292
Vi = Poisson’s ratio of shaft = 0.292
Dhi = Hub inner diameter = 108.5mm
Dho = Hub outer diameter = 113.0mm
Dsi = Shaft inner diameter = 62.0mm
Dso = Shaft outer diameter = 108.5mm
Eh = Hub elastic modulus = 210000 mpa
Es = Shaft elastic modulus = 210000 mpa
Delta = Size of interferance = 0.119
There is also an excel based online calculator that uses the same equation at:
http://www.meadinfo.org/2009/07/press-fit-pressure-calculator-optimize.html
Using the above formula and values I calculate the pressure (P) to be: 8.475 N/mm^2. Which is also the same answer -- minus rounding errors -- that the excel based calculator gives me.
This leads me to believe that step 1. is the correct approach. Any input would be apprecaited.Step 2.
Now that I know the pressure at the press fit, I can specify the desired amount of torque I wish to transmit and from that determine the force acting on the press fit.
I wish to transmit = 60 N/m of Torque = 60000 N/mm = T
Shaft Diameter = 108.5mm = D
T = Force x (D/2)
Rearranged to isolate the Force (F):
F = T / (D/2)
F = 60000 / (108.5 / 2)
F = 1106 N
If my thinking is correct, the force exerted on the shaft (and press fit) by transmitting 60Nm of torque is 1106N. From this, and knowing the pressure, I can calculate the length of the press fit required to transmit the torque.
Step 3.
To calculate the length of the press fit required, I'm using the following equation and transposing it to make Length the subject:
F = P x D x pi x L x u
L= F / pi x D x P x u
Where:
u = steel on steel coefficient = 0.4
So:
L = 1106 / pi x 108.5 x 8.475 x 0.4
L = 0,92mm
The required length of press fit necessary to transmit 60Nm of torque I calculate to be 0.92mm, which I feel is well too liberal (I'd expect between 5mm and 10mm). Is there anything that jumps out at anyone as being an obvious error? Perhaps I'm using the wrong equation(s) in step 2 and 3? Perhaps it is a unit error? Or a mistake transposing the equation? Or perhaps it is simply correct. Any input would be appreciated. I've been looking at the problem for a week now and I can't work out where I am going wrong.
Thank you everyone in advance,
Tom
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