Anti-roll bar help?

[Nbruno]

So the never ending saga of ARB calculations continues...Using the optimumG tutorial on swaybar calculations I came up with a required stiffness in the front of ~320 Nm/deg of roll and ~400 Nm/deg of roll. Moving on to the calculation for bar thickness I used the torsion formula

Phi=(TL)/(IpG)

Where Phi is the angle of twist in radians, L is the length of the bar in meters, Ip is the mass moment of inertia and G is the shear modulus. I solved for Ip so that

Ip=(TL)/(PhiG)

Assuming one degree (.0175 rad)of twist, a length of .475m, T= 320 N/m and G of 80Gpa (enetered as 80*10^9 Pa). Ip is the mass moment of inertia of a hollow tube:

Ip= (Pi/2)(Ro^4-Ri^4)

Where Ro is the outer radius and Ri is the inner radius. So,

Ri=4th root(Ro^4-(Ip/(Pi/2)))

But, when I enter an Ro of something that seems reasonable like .00635m (.25in), I get a negative value inside my 4th root parenthesis. If I take the abs value of that, I get Ri that is greater than my Ro. If I switch my Ri and Ro its a reasonably sized bar, but I'm 99% sure it is incorrect.

Any help at all would be greatly appreciated.

[Nbruno]

So the never ending saga of ARB calculations continues...Using the optimumG tutorial on swaybar calculations I came up with a required stiffness in the front of ~320 Nm/deg of roll and ~400 Nm/deg of roll. Moving on to the calculation for bar thickness I used the torsion formula

Phi=(TL)/(IpG)

Where Phi is the angle of twist in radians, L is the length of the bar in meters, Ip is the mass moment of inertia and G is the shear modulus. I solved for Ip so that

Ip=(TL)/(PhiG)

Assuming one degree (.0175 rad)of twist, a length of .475m, T= 320 N/m and G of 80Gpa (enetered as 80*10^9 Pa). Ip is the mass moment of inertia of a hollow tube:

Ip= (Pi/2)(Ro^4-Ri^4)

Where Ro is the outer radius and Ri is the inner radius. So,

Ri=4th root(Ro^4-(Ip/(Pi/2)))

But, when I enter an Ro of something that seems reasonable like .00635m (.25in), I get a negative value inside my 4th root parenthesis. If I take the abs value of that, I get Ri that is greater than my Ro. If I switch my Ri and Ro its a reasonably sized bar, but I'm 99% sure it is incorrect.

Any help at all would be greatly appreciated.

[Gruntguru]

What are the units for Ip you are using?

[Nbruno]

Everything is in meters, so it would be m^4

[Gruntguru]

You need to start with a bigger diameter. The diameter you have selected will not achieve the Ip you need - even if the bar is solid.

[RobbyObby]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Nbruno:
But, when I enter an Ro of something that seems reasonable like .00635m (.25in), I get a negative value inside my 4th root parenthesis. If I take the abs value of that, I get Ri that is greater than my Ro. If I switch my Ri and Ro its a reasonably sized bar, but I'm 99% sure it is incorrect.
</div></BLOCKQUOTE>

I agree with Gruntguru. 1/4" OD for an ARB is pretty small. Maybe that's what your calcs are trying to tell you. If youre Ri comes out negative, maybe it means youre Ro needs to be bigger. I would set youre Ri=0 (i.e. solid bar) and solve for your Ro. That would tell you the minimum bar diameter necessary. Than if you really want to use a tube, select a larger OD than your first calculation and solve for Ri until you find a reasonable solution.

[BillCobb]

I am puzzled by the thinking process here. As a chassis subsystem participant, I would expect that a specific front (or rear) roll moment is called for to achieve some designated total front and rear roll moment distribution, which has taken into account spring rates, roll axis location, tire OVTM, blah, blah, blah. Then a spreadsheet would be established to calculate the bar contribution to this party. The spreadsheet would be validated by inputing the textbook example (yes from a textbook) of a simple torsion bar (solid and then hollow, maybe steel vs aluminum vs. stainless ...). Once validated, you would then tell Solver to deliver xxx.y N-m by adjusting either the geometry (for fitment) or thickness (for weight), or both to deliver the required amount of roll moment. Since hollow and solid steel tubes come in discrete sizes, a continuous inner dimension variable is not a practical solution.

Meanwhile, the tire team has altered the tire pressure, so another round or two or three or n, has demanded another optimal roll bar requirement which the spreadsheet should be prepared to deliver really quick (perhaps as an outer loop in another optimization tool). Also, most bars have side arms which BEND instead of TWIST, so while all this is going on, the spreadsheet could have been improved by taking into account all the 2D and 3D implications, maybe even taking into account the frame mounting vertical stiffnesses.

But solving for an inner diameter would not get you any points from me if I were the chief engineer, unless you were going to use it to store extra fuel or cool engine oil. Especially if it takes Red Matter to make it happen.

[Nbruno]

BillCobb, you are correct in my process, I suppose solver would be the easy way to do it but I haven't used in a while...this works 100. Unfortunately we have zero data to go off of since we are a new team. I'm just trying to get a ballpark answer right now so we can tune.

Using Robby's suggestion I got a solid bar of diameter .0339m (~1.3in) which seems very thick to me (I'm basing this off of my own car and working around Formula Fords for a few years). Is this close to what anyone else is running?

[Charlie]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Nbruno:
Using Robby's suggestion I got a solid bar of diameter .0339m (~1.3in) which seems very thick to me (I'm basing this off of my own car and working around Formula Fords for a few years). Is this close to what anyone else is running? </div></BLOCKQUOTE>

It's completely irrelevant to compare bar diameters to other vehicles unless you are also comparing lever arm length and motion ratio at a MINIMUM.

[Nbruno]

Gotcha. Well I suppose I'll go with this for now. Thanks a lot guys! See you out there in 2013 =)