I have a question regarding the transformation matrix
 How can I derivative the rotational matrix from Nacelle / Yaw Coordinate System (d1,d2,d3) to RotorFurl Coordinate System (rf1,rf2,rf3) ? Where is the origin location of RotorFurl Coordinate System (rf1,rf2,rf3)?
Please provide me with the required papers to understand this part
Thanks
RotorFurl Coordinate System
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Re: RotorFurl Coordinate System
Dear Mohamed,
I can't seem to find the derivation of the transformation matrix between the nacelle and rotorfurl coordinate system published in any report. However, the transformation can be derived by multiplying several simpler 3x3 matrices together i.e.
{rf} = [TransMat] * {d}
with
[TransMat] = [RFrlSkew]^T * [RFrlTilt]^T * [q_RFrl] * [RFrlTilt] * [RFrlSkew]
where,
{} represents a 3x1 vector
[] represents a 3x3 matrix
^T represents a matrix transpose
[RFrlSkew] represents the transformation matrix associated with the single rotation RFrlSkew
[RFrlTilt] represents the transformation matrix associated with the single rotation RFirlTilt
[q_RFrl] represents the transformation matrix associated with the single rotation of RFrlDOF
The origin of the rotorfurl coordinate system is not defined nor used in FAST.
I hope that helps.
Best regards,
I can't seem to find the derivation of the transformation matrix between the nacelle and rotorfurl coordinate system published in any report. However, the transformation can be derived by multiplying several simpler 3x3 matrices together i.e.
{rf} = [TransMat] * {d}
with
[TransMat] = [RFrlSkew]^T * [RFrlTilt]^T * [q_RFrl] * [RFrlTilt] * [RFrlSkew]
where,
{} represents a 3x1 vector
[] represents a 3x3 matrix
^T represents a matrix transpose
[RFrlSkew] represents the transformation matrix associated with the single rotation RFrlSkew
[RFrlTilt] represents the transformation matrix associated with the single rotation RFirlTilt
[q_RFrl] represents the transformation matrix associated with the single rotation of RFrlDOF
The origin of the rotorfurl coordinate system is not defined nor used in FAST.
I hope that helps.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 27
 Joined: Mon Dec 25, 2017 5:47 am
 Organization: Zagazig University
 Location: Egypt
Re: RotorFurl Coordinate System
Thank you for your explanation. However, I have a question
Why it is necessary to use Similarity Transformations and express the [q_RFrl] rotational matrix in Yaw frame?
It seems that the rotations [RFrlSkew] and [RFrlTilt] are made with respect to current frame concept (not fixed frame concept).
Why it is necessary to use Similarity Transformations and express the [q_RFrl] rotational matrix in Yaw frame?
It seems that the rotations [RFrlSkew] and [RFrlTilt] are made with respect to current frame concept (not fixed frame concept).

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Re: RotorFurl Coordinate System
Dear Mohamed,
I'm not sure I understand your question, but [TransMat] in this case is defined such that {d} and {rf} coordinate systems are parallel {rf} = {d} when q_RFrl = 0, i.e. when [q_RFrl] = the 3x3 identity matrix.
Best regards,
I'm not sure I understand your question, but [TransMat] in this case is defined such that {d} and {rf} coordinate systems are parallel {rf} = {d} when q_RFrl = 0, i.e. when [q_RFrl] = the 3x3 identity matrix.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov

 Posts: 27
 Joined: Mon Dec 25, 2017 5:47 am
 Organization: Zagazig University
 Location: Egypt
Re: RotorFurl Coordinate System
Thank you for kind consideration and clarification.
However, I mean that why the transformation between rotor furl frame {rf} and Yaw frame{d} was not like this
{rf} = [TransMat] * {d}
[TransMat] =[q_RFrl] * [RFrlTilt] * [RFrlSkew]
Also, I agree with you partially, {d} and {rf} coordinate systems are parallel {rf} = {d} only when q_RFrl = 0, RfrlSkew =0 and RfrlTilt=0
So, Why it is necessary to add( [RFrlSkew]^T * [RFrlTilt]^T ) to the [TransMat] ?
However, I mean that why the transformation between rotor furl frame {rf} and Yaw frame{d} was not like this
{rf} = [TransMat] * {d}
[TransMat] =[q_RFrl] * [RFrlTilt] * [RFrlSkew]
Also, I agree with you partially, {d} and {rf} coordinate systems are parallel {rf} = {d} only when q_RFrl = 0, RfrlSkew =0 and RfrlTilt=0
So, Why it is necessary to add( [RFrlSkew]^T * [RFrlTilt]^T ) to the [TransMat] ?

 Posts: 5428
 Joined: Thu Nov 03, 2005 4:38 pm
 Location: Boulder, CO
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Re: RotorFurl Coordinate System
Dear Mohammed,
[RFrlSkew]^T * [RFrlTilt]^T are included in [TransMat] so that {rf} = {d} for any value of RFrlSkew and RFrlTIlt, as long as q_RFrl = 0.
Best regards,
[RFrlSkew]^T * [RFrlTilt]^T are included in [TransMat] so that {rf} = {d} for any value of RFrlSkew and RFrlTIlt, as long as q_RFrl = 0.
Best regards,
Jason Jonkman, Ph.D.
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
Senior Engineer  National Wind Technology Center (NWTC)
National Renewable Energy Laboratory (NREL)
15013 Denver West Parkway  Golden, CO 80401
+1 (303) 384 – 7026  Fax: +1 (303) 384 – 6901
nwtc.nrel.gov
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