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# torque-roll-axis calculation

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## torque-roll-axis calculation

(OP)

Good Morning All,
I am trying to calculate the torque roll axis for a powertrain system. After some research I know that the the calculation is only dependent on the moment of inertia and also after further research I have come across multiple papers from Singh (and referenced by almost everyone) which is the photo listed above. I have created some matlab code in trying to calculate the TRA direction but don't seem to be obtaining the right values. I was wondering if anyone could tell me where I am going wrong or have any other reference that I could perhaps follow.

I have the following inertia matrix (M_theta):

I=[2.519 4.458 4.409 -.1678 .5385 -.0947];

and should receive TRA_Direction as: [0 0 0 .992113 .0347851 .120426] but I do not. Is there anything that I am missing here when normalizing the first column or taking the inverse?

function[TRA_Direction]= TRA_Direction(I)
% User Input
% I: Moment of Inertia Matrix expressed as [Ixx,Iyy,Izz,Ixy,Ixz,Iyz]
%
% Output
% TRA_Direction: The Direction of the TRA
%Mass Inertia Matrix
M_Theta=zeros(3,3);
M_Theta(1,1)=I(1);
M_Theta(1,2)=-I(4);
M_Theta(1,3)=-I(5);
M_Theta(2,1)=-I(4);
M_Theta(2,2)=I(2);
M_Theta(2,3)=-I(6);
M_Theta(3,1)=-I(5);
M_Theta(3,2)=-I(6);
M_Theta(3,3)=I(3);
Inv_M_Theta=inv(M_Theta);
a=norm([Inv_M_Theta(1,1) Inv_M_Theta(2,1) Inv_M_Theta(3,1)]);
Torque_Axis=[1 0 0];
Theta_TRA=a*Inv_M_Theta*Torque_Axis';
TRA_Direction=[0 0 0 Theta_TRA']';

### RE: torque-roll-axis calculation

Rather than jumping straight to a solution, have you checked that your script agrees with obvious cases of the M matrix, such as Ixy=Iyz=Izx=0, where the solution is obvious by inspection?

It seems to me there are four broad possibilities for error

1) Singh is wrong

2)your mental interpretation of Singh is wrong

3)your matlab interpretation of 2) is wrong

4)your example is wrong (I am confused to see both positive and -ve cross terms)

I'd add that in practice ignoring the contribution of the powertrain mounts is a bit odd.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: torque-roll-axis calculation

The usual approach would be to find the principal axes of the powertrain, and then resolve the torque into those, and then it is easy to establish the rotation axis.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

### RE: torque-roll-axis calculation

(OP)
Thank you GregLocok for responding to my thread. For your second reply I have broke the inertia tensor down into the principal moments and principal axis and have obtained the same values as from the above code. I will have to look more into everything still.
Thank you though,
Mel

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