CN103559365B - A kind of parametric modeling method suitable for Generator Stator Winding Ends coil - Google Patents
A kind of parametric modeling method suitable for Generator Stator Winding Ends coil Download PDFInfo
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Abstract
The present invention relates to a kind of parametric modeling method suitable for Generator Stator Winding Ends coil, it is characterised in that step is：Step 1, input coil geometric parameter；Step 2, the cross sectional shape for defining coil；Step 3, the modeling of stator winding end coil launcher；Step 4, set up coil FEM model.It is an advantage of the invention that：Make stator winding end coil modeling parameters, and can simultaneously set up the FEM model of end coil, to be applied to the research of stator winding end vibration characteristics.
Description
Technical field
The present invention relates to a kind of parametric modeling method of Generator Stator Winding Ends coil, it is adaptable to which end coil is
Each model unit of involute expanded form, belongs to the dynamic characteristic calculation and improved skill of Generator Stator Winding Ends structure
Art field.
Background technology
Stator winding end coil carries the important function that induced-current is exported power network in generator.Its vibration feelings
Condition is always the problem being primarily upon during generator is researched and developed.Wherein stator winding end coil is due to the expansion using involute
Mode, the FEM model for hence setting up reasonable end coil has certain difficulty.
The modeling method of conventional end coil is to set up model using Three-dimensional Design Software, and its operating process is relatively
Complexity, and modification is difficult, while being not easily applicable to the finite element analysis of stator winding end structure.
The content of the invention
The technical problem to be solved in the present invention is to provide a kind of parametrization for Generator Stator Winding Ends coil and builds
Mould method, makes stator winding end coil modeling parameters, and can simultaneously set up the FEM model of end coil, so as to
It is applied to the research of stator winding end vibration characteristics.
In order to solve the above-mentioned technical problem, the technical scheme is that providing a kind of suitable for generator unit stator winding
The parametric modeling method of end coil, it is characterised in that step is：
Step 1, input coil geometric parameter, at least including coil section overall width ECBW, coil section total height ECBH,
Coil section copper cash partial width ECBCW, coil section copper cash Partial Height ECBCH, coil section hollow copper wire hole width
ECBCHW, coil section hollow copper string holes height ECBCHH, coil are to distance between center line TECRH unshakable in one's determination, coil base radius
TECRJ, coil straight line to the excessive chamfer radius TECRO of the conical surface, coil involute beginning chamfer radius TECR1, coil gradually
Burst at the seams chamfer radius TECR2 at end, coil goes out groove straight line portion length TECHZ, coil involute and starts preceding length of straigh line
TECBH1, coil involute terminate across angle TECBYY, P point of rear length of straigh line TECBH2, coil conical degree of conical surface CONTP, coil
The involute angle of spread and polar angle difference DEFAX, C point involute angle of spread DEFAY, wherein, P points were O points
The intersection point for gradually opening the tangent line with involute that terminate arc section after involute expansion of the coil under polar coordinates, O points exist for coil
The basic circle center of circle after involute expansion under polar coordinates, C points are the involute section after involute of the coil under polar coordinates launches
Terminal；
Step 2, the cross sectional shape for defining coil；
Step 3, the modeling of stator winding end coil launcher, including：
Step 3.1 solves coil key point coordinates：
The geometrical curve of coil is formed by connecting by multiple key points, and the coordinate of each key point is stored in aray variable KPCS
In (i, j), wherein i is coordinate components, i=1, and 2,3 represent the X-axis of key point, Y-axis and Z axis coordinate respectively, and j is that key point is compiled
Number, variable KPCS (m, n) of defining arrays, wherein m be coordinate components, m=1,2 respectively represent key point polar polar diameter R and
Polar angle φ, n are numbered for key point, and the formula for calculating crucial point coordinates at each section of coil is as follows：
Coil beginning straightway key point coordinates：
Starting point coordinate：KPCS (1,1)=0,
KPCS (2,1)=TECRH,
KPCS (3,1)=O；
Terminal point coordinate：KPCS (1,2)=0,
KPCS (2,2)=TECRH,
KPCS (3,2)=TECHZ；
The crucial point coordinates of coil cone angle transition circle section：
Starting point coordinate：KPCS (1,3)=O,
KPCS (2,3)=TECRH+TECRO-TECROcos (CONTP), KPCS (3,3)=TECRZ+TECROsin
(CONP)；
Terminal point coordinate：KPCS (Isosorbide-5-Nitrae)=0,
KPCS (2,4)=TECRH+TECRO-TECROcos (CONP)+TECBH1sin (CONTP),
KPCS (3,4)=TECRZ+TECROsin (CONP)+TECBH1cos (CONTP)；
The coordinate of the initial circular arc waypoint of involute：
1) A point coordinates, A points are the starting point of the initial arc section of involute：
A point polar diametersA point polar angles THTA=45；
A points rectangular co-ordinate X values XA=RAcos (THTA), A point rectangular co-ordinate Y value YA=RAsin (THTA), vertex of a cone Z sit
Mark OZ=KPCS (3,4)-RAcos (CONTP)；
2) coordinate of fillet center of circle O1 is sought according to A point coordinates, O1 is the center of circle of the initial arc section of involute：
O1 points rectangular co-ordinate X values XO1=XA+TECR1cos (THTA+90), O1 point rectangular co-ordinate Y value YO1=YA+
TECR1·sin(THTA+90)；
O1 point polar diametersD1 point polar angles
3) E points are coordinates, and E points are the point of contact of O1 points and basic circle tangent line：
E points rectangular co-ordinate X values XE=TECRJcos (THTE), E point rectangular co-ordinate Y value
YE=TECRJsin (THTE), wherein, THTE=THTO1+THTEOO1,
4) B point coordinates, B points are the starting point of involute section：
B points rectangular co-ordinate X values XB=XO1+TECR1cos (THTO1E), B point rectangular co-ordinate Y value YB=YO1+TECR1
Sin (THTO1E), wherein,
B point polar diametersB point polar angles
The involute angle of spread of B points：
5) angle of spread of the coil in sector：
TECBEA=TECBYY·sin(TECTP)；
After step 3.2, zero point of launching polar coordinates zero point and involute overlap, each point coordinates is solved again：
1) A point coordinates：
A point rectangular co-ordinate X values XA '=RAcos (THTA '), A point rectangular co-ordinatesYValue
YA '=RAsin (THTA '), wherein, THTA '=THTA+ANGB-THTB；
2) O1 point coordinates：
O1 point rectangular co-ordinate X values XO1 '=XA '+TECR1cos (THTA '+90), O1 point rectangular co-ordinate Y values YO1 '=YA '+
TECR1·sin(THTA′+90)；
O1 point polar angles
3) E point coordinates：
E point rectangular co-ordinate X values XE '=TECRJcos (THTE '),
E point rectangular co-ordinate Y values YE '=TECRJsin (THTE '), wherein,
THTE′=THTO1′+THTEOO1：
4) B point coordinates：
B point rectangular co-ordinate X values XB '=XO1 '+TECR1cos (THTO1E '),
B point rectangular co-ordinate Y values YB '=YO1 '+TECR1sin (THTO1E '),
Wherein,
B point polar anglesB point polar diameters
5) P point coordinates：
P point polar angle ANGP=DEFAX+THTP, wherein, THTP=TECBEA+THTA '；
6) C point coordinates：
C point rectangular co-ordinate X values
XC '=TECRJcos (ANGC)+TECRJANGC π/180sin (ANGC),
C point rectangular co-ordinate Y values
YC '=TECRJsin (ANGC)-TECRJANGC π/180cos (ANGC),
Wherein, ANGC=DEFAY；
C point polar diametersC point polar angles
7) O2 point coordinates, O2 points terminate the center of circle of arc section for involute：
O2 point rectangular co-ordinate X values：
XO2 '=TECRJcos (ANGC)+[TECRJANGC π/180SIN (ANGC)] sin (ANGC)；
O2 point rectangular co-ordinate Y values：
YO2 '=TECRJsin (ANGC)-[TECRJANGC π/180COS (ANGC)] cos (ANGC)；
8) D point coordinates, D points terminate the terminal of arc section for involute：
D point rectangular co-ordinate X values XD '=XO2 '+TECR2cos (THTP+90),
D point rectangular co-ordinate Y values YD '=XD ' tan (THTP),
D point polar diameters
Step 3.3, continuation solve each section of coordinate of key point of coil, and the key point number of the initial arc section of involute is
N1, the number of involute section key point is N2, and the key point number that involute terminates arc section is N3, then have：
1) cycle calculations obtain the coordinate of the initial each key point in arc section inside of involute respectively, wherein：
The N1 polar diameter of key point is RB ', and polar angle is THTB '-THTA ', the rectangular co-ordinate X of remaining k-th key point
Value, K=1,2 ... ..., (N1-1)：
XTEMP=XO1 '+TECR1cos (TEMPTHTA+TEMPTHTABK/N1),
The rectangular co-ordinate Y value of k-th key point：
YTEMP=YO1 '+TECR1sin (TEMPTHTA+TEMPTHTABK/N1)；
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA ' of k-th key point, wherein：
2) cycle calculations obtain the coordinate of each key point of involute intersegmental part respectively, wherein：
The N2 polar diameter of key point is RC ', and polar angle is THTC '-THTA ', the rectangular co-ordinate X of remaining k-th key point
Value, K=1,2 ... ..., (N2-1)：
XTEMP=TECRJcos (ANGB+TEMPBCK/N2)+
TECRJ (ANGB+TEMPBCK/N2) π/180sin (ANGB+TEMPBCK/N2) '
The rectangular co-ordinate Y value of k-th key point：
YTEMP=TECRJsin (ANGB+TEMPBCK/N2)-
TECRJ (ANGB+TEMPBCK/N2) π/180cos (ANGB+TEMPBCK/N2) '
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA ' of k-th key point, wherein：
TEMPBC=ANGC-ANGB：
3) cycle calculations obtain the coordinate that involute terminates each key point in arc section inside respectively, wherein：
The N3 polar diameter of key point is RD ', and polar angle is THTD '-THTA ', the rectangular co-ordinate X of remaining k-th key point
Value, K=1,2 ... ..., (N3-1)：
XTEMP=XO2 '+TECR2cos (TEMPTHTC-TEMPTHTCDK/N3)；
The rectangular co-ordinate Y value of k-th key point：
YTEMP=YO2 '+TECR2sin (TEMPTHTC-TEMPTHTCDK/N3)；
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA ' of k-th key point, wherein：
If negative value, then it is modified to
TEMPTHTCD=TEMPTHTC-TEMPTHTD：
If negative value, then it is modified to
Step 3.4, the polar coordinates of each key point of coil are converted into cartesian coordinate using cycle calculations, wherein, k-th
KPCS (Isosorbide-5-Nitrae+K)=TECITEMPRsin (TEMPTHT) of key point,
KPCS (2,4+K)=TEMPRcos (TEMPTHT),
KPCS (3,4+K)=ICS (1, K) cos (CONTP)+OZ, wherein：
TEMPR=ICS (1, K) sin (CONTP), ICS (1, K) are the polar diameter of k-th key point；TEMPTHT=ICS (2,
K)/sin (CONTP), ICS (2, K) are the polar angle of k-th key point；
Step 3.5, set up key point：According to each crucial point coordinates that draws is solved in step 3.4, each key point is set up；
Step 3.6, the SPL for setting up coil：The key point set up in Connection Step 3.5, that is, generate the batten of coil
Curve；
Step 4, set up coil FEM model.
It is an advantage of the invention that：Make stator winding end coil modeling parameters, and can simultaneously set up end coil
FEM model, to be applied to the research of stator winding end vibration characteristics.
Brief description of the drawings
Fig. 1 is the stator winding end coil involute expanded form figure in the present invention.
Specific embodiment
To become apparent the present invention, hereby with preferred embodiment, the present invention will be further described.
The invention provides a kind of parametric modeling method suitable for Generator Stator Winding Ends coil, its step
For：
Step 1, input coil geometric parameter, including coil section overall width ECBW, coil section total height ECBH, coil
Section copper cash partial width ECBCW, coil section copper cash Partial Height ECBCH, coil section hollow copper wire hole width ECBCHW,
Coil section hollow copper string holes height ECBCHH, coil are to distance between center line TECRH unshakable in one's determination, coil base radius TECRJ, coil
Straight line terminates place to the excessive chamfer radius TECR0 of the conical surface, coil involute beginning chamfer radius TECR1, coil involute
Chamfer radius TECR2, coil go out groove straight line portion length TECHZ, coil involute and start preceding length of straigh line TECBH1, coil
The involute that involute terminates across angle TECBYY, P point of rear length of straigh line TECBH2, coil conical degree of conical surface CONTP, coil launches
The involute angle of spread DEFAY of difference DEFAX, the C point of angle and polar angle, wherein, P points were the coil of O points in polar coordinates
Under involute launch after the intersection point for gradually opening the tangent line and the involute that terminate arc section, O points be coil under polar coordinates gradually
The basic circle center of circle burst at the seams after launching, C points are the terminal of the involute section after involute of the coil under polar coordinates launches；
Step 2, the cross sectional shape for defining coil, in the present embodiment, the rectangular cross-section of coil, mainly by two kinds of materials
Constitute, section inner side is copper product, and outside is insulating materials.Pair cross-section is needed when setting up section carries out subdivision, and different
Positions of materials specifies corresponding material parameter.Mesh generation is carried out to coil section, the coil section that will be defined is saved as
.sect file for coil finite element modeling below when use.Idiographic flow is as follows：
Step 2.1, the square-section for setting up coil；
Step 2.2, by the different by two parts of section subdivision copper cash and insulation of coil method；
Step 2.3, specified mesh generation size；
Step 2.4, specified material parameter；
Step 2.5, division section grid；
Step 2.6, preservation .sect custom cross section files.
Step 3, the modeling of stator winding end coil launcher, including：
Step 3.1 solves coil key point coordinates：
Involute expanded form of Fig. 1 coils under polar coordinates, wherein, the O points position basic circle center of circle, at the beginning of A points are involute
The starting point of beginning arc section, B points position terminal is also the starting point of involute section, and O1 is the center of circle of the initial arc section of involute, C points
It is the terminal of involute section, the starting point of arc section is also terminated for involute, D points position involute terminates the terminal of arc section, O2 points
Terminate the center of circle of arc section for involute, E points are the point of contact of O1 points and basic circle tangent line, P points were that O points gradually open end arc section
Tangent line and involute intersection point.
The geometrical curve of coil is formed by connecting by multiple key points, and the coordinate of each key point is stored in aray variable KPCS
In (i, j), wherein i is coordinate components, i=1, and 2,3 represent the X-axis of key point, Y-axis and Z axis coordinate respectively, and j is that key point is compiled
Number, variable KPCS (m, n) of defining arrays, wherein m be coordinate components, m=1,2 respectively represent key point polar polar diameter R and
Polar angle φ, n are numbered for key point, and the formula for calculating crucial point coordinates at each section of coil is as follows：
Coil beginning straightway key point coordinates：
Starting point coordinate：KPCS (1,1)=0,
KPCS (2,1)=TECRH,
KPCS (3,1)=0；
Terminal point coordinate：KPCS (1,2)=0,
KPCS (2,2)=TECRH,
KPCS (3,2)=TECHZ；
The crucial point coordinates of coil cone angle transition circle section：
Starting point coordinate：KPCS (1,3)=0,
KPCS (2,3)=TECRH+TECRO-TECROcos (CONTP),
KPCS (3,3)=TECRZ+TECROsin (CONP)；
Terminal point coordinate：KPCS (Isosorbide-5-Nitrae)=0,
KPCS (2,4)=TECRH+TECRO-TECROcos (CONP)+TECBH1sin (CONTP),
KPCS (3,4)=TECRZ+TECROsin (CONP)+TECBH1cos (CONTP)；
The coordinate of the initial circular arc waypoint of involute：
1) A point coordinates, A points are the starting point of the initial arc section of involute：
A point polar diametersA point polar angles THTA=45；
A points rectangular co-ordinate X values XA=RAcos (THTA), A point rectangular co-ordinate Y value YA=RAsin (THTA), vertex of a cone Z sit
Mark OZ=KPCS (3,4)-RAcos (CONTP)；
2) coordinate of fillet center of circle O1 is sought according to A point coordinates, O1 is the center of circle of the initial arc section of involute：
O1 points rectangular co-ordinate X values XO1=XA+TECR1cos (THTA+90), O1 point rectangular co-ordinate Y value YO1=YA+
TECR1·sin(THTA+90)；
O1 point polar diametersO1 point polar angles
3) E point coordinates, E points are the point of contact of O1 points and basic circle tangent line：
E points rectangular co-ordinate X values AE=TECRJcos (THTE), E point rectangular co-ordinate Y value YE=TECRJsin (THTE),
Wherein, THTE=THTO1+THTEOO1,
4) B point coordinates, B points are the starting point of involute section：
B points rectangular co-ordinate X values XB=XO1+TECR1cos (THTO1E), B point rectangular co-ordinate Y value YB=YO1+TECR1
Sin (THTO1E), wherein,
B point polar diametersB point polar angles
The involute angle of spread of B points：
5) angle of spread of the coil in sector：
TECBEA=TECBYY·sin(TECTP)；
After step 3.2, zero point of launching polar coordinates zero point and involute overlap, each point coordinates is solved again：
1) A point coordinates：
A point rectangular co-ordinate X values XA '=RAcos (THTA '), A point rectangular co-ordinate Y values
YA ' RAsin (THTA '), wherein, THTA '=THTA+ANGB-THTB；
2) O1 point coordinates：
O1 point rectangular co-ordinate X values XO1 '=XA '+TECR1cos (THTA '+90), O1 point rectangular co-ordinate Y values YO1 '=YA '+
TECR1·sin(THTA′+90)；
O1 point polar angles
3) E point coordinates：
E point rectangular co-ordinate X values XE '=TECRJcos (THTE '),
E point rectangular co-ordinate Y values YE '=TECRJsin (THTE '), wherein,
THTE′=THTO1′+THTEOO1：
4) B point coordinates：
B point rectangular co-ordinate X values XB '=XO1 '+TECR1cos (THTO1E '),
B point rectangular co-ordinate Y values YB '=YO1 '+TECR1sin (THTO1E '),
Wherein,
B point polar anglesB point polar diameters
5) P point coordinates：
P point polar angle ANGP=DEFAX+THTP, wherein, THTP=TECBEA+THTA '；
6) C point coordinates：
C point rectangular co-ordinate X values
XC '=TECRJcos (ANGC)+TECRJANGC π/180sin (ANGC),
C point rectangular co-ordinate Y values
YC '=TECRJsin (ANGC)-TECRJANGC π/180cos (ANGC),
Wherein, ANGC=DEFAY；
C point polar diametersC point polar angles
7) O2 point coordinates, O2 points terminate the center of circle of arc section for involute：
O2 point rectangular co-ordinate X values：
XO2 '=TECRJcos (ANGC)+[TECRJANGC π/180SIN (ANGC)] sin (ANGC)；
O2 point rectangular co-ordinate Y values：
YO2 '=TECRJsin (ANGC)-[TECRJANGC π/180COS (ANGC)] cos (ANGC)；
8) D point coordinates, D points terminate the terminal of arc section for involute：
D point rectangular co-ordinate X values XD '=XO2 '+TECR2cos (THTP+90),
D point rectangular co-ordinate Y values YD '=XD ' tan (THTP),
D point polar diameters
Step 3.3, continuation solve each section of coordinate of key point of coil, and the key point number of the initial arc section of involute is
N1, the number of involute section key point is N2, and involute terminates the key point number of arc section for N3, N1=5, N2=20, N3=5,
Then have：
1) cycle calculations obtain the coordinate of the initial each key point in arc section inside of involute respectively, wherein：
The N1 polar diameter of key point is RB ', and polar angle is THTB '-THTA ', the rectangular co-ordinate X of remaining k-th key point
Value, K=1,2 ... ..., (N1-1)：
XTEMP=XO1 '+TECR1cos (TEMPTHTA+TEMPTHTABK/N1),
The rectangular co-ordinate Y value of k-th key point：
YTEMP=YO1 '+TECR1sin (TEMPTHTA+TEMPTHTABK/N1)；
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA ' of k-th key point, wherein：
2) cycle calculations obtain the coordinate of each key point of involute intersegmental part respectively, wherein：
The N2 polar diameter of key point is RC ', and polar angle is THTC '-THTA ', the rectangular co-ordinate X of remaining k-th key point
Value, K=1,2 ... ..., (N2-1)：
XTEMP=TECRJcos (ANGB+TEMPBCK/N2)+
TECRJ (ANGB+TEMPBCK/N2) π/180sin (ANGB+TEMPBCK/N2) '
The rectangular co-ordinate Y value of k-th key point：
YTEMP=TECRJsin (ANGB+TEMPBCK/N2)-
TECRJ (ANGB+TEMPBCK/N2) π/180cos (ANGB+TEMPBCK/ IV 2) '
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA ' of k-th key point, wherein：
TEMPBC=ANGC-ANGB：
3) cycle calculations obtain the coordinate that involute terminates each key point in arc section inside respectively, wherein：
The N3 polar diameter of key point is RD ', and polar angle is THTD '-THTA ', the rectangular co-ordinate X of remaining k-th key point
Value, K=1,2 ... ..., (N3-1)：
XTEMP=XO2 '+TECR2cos (TEMPTHTC-TEMPTHTCDK/N3)；
The rectangular co-ordinate Y value of k-th key point：
YTEMP=YO2 '+TECR2sin (TEMPTHTC-TEMPTHTCDK/N3)；
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA ' of k-th key point, wherein：
If negative value, then it is modified to
TEMPTHTCD=TEMPTHTC-TEMPTHTD；
If negative value, then it is modified to
Step 3.4, the polar coordinates of each key point of coil are converted into cartesian coordinate using cycle calculations, wherein, k-th
KPCS (Isosorbide-5-Nitrae+K)=TECITEMPRsin (TEMPTHT) of key point,
KPCS (2,4+K)=TEMPRcos (TEMPTHT),
KPCS (3,4+K)=ICS (1, K) cos (CONTP)+OZ, wherein：
TEMPR=ICS (1, K) sin (CONTP), ICS (1, K) are the polar diameter of k-th key point；TEMPTHT=ICS (2,
K)/sin (CONTP), ICS (2, K) are the polar angle of k-th key point；
Step 3.5, set up key point：According to each crucial point coordinates that draws is solved in step 3.4, each key point is set up；
Step 3.6, the SPL for setting up coil：The key point set up in Connection Step 3.5, that is, generate the batten of coil
Curve；
Step 4, set up coil FEM model.
Claims (1)
1. a kind of parametric modeling method suitable for Generator Stator Winding Ends coil, it is characterised in that step is：
Step 1, input coil geometric parameter, at least including coil section overall width ECBW, coil section total height ECBH, coil
Section copper cash partial width ECBCW, coil section copper cash Partial Height ECBCH, coil section hollow copper wire hole width ECBCHW,
Coil section hollow copper string holes height ECBCHH, coil to core center linear distance TECRH, coil base radius TECRJ, coil
Straight line terminates place to the excessive chamfer radius TECR0 of the conical surface, coil involute beginning chamfer radius TECR1, coil involute
Chamfer radius TECR2, coil go out groove straight line portion length TECHZ, coil involute and start preceding length of straigh line TECBH1, coil
The involute that involute terminates across angle TECBYY, P point of rear length of straigh line TECBH2, coil conical degree of conical surface CONTP, coil launches
The involute angle of spread DEFAY of difference DEFAX, the C point of angle and polar angle, wherein, P points were the coil of O points in polar coordinates
Under involute launch after the intersection point for gradually opening the tangent line and the involute that terminate arc section, O points be coil under polar coordinates gradually
The basic circle center of circle burst at the seams after launching, C points are the terminal of the involute section after involute of the coil under polar coordinates launches；
Step 2, the cross sectional shape for defining coil；
Step 3, the modeling of stator winding end coil launcher, including：
Step 3.1 solves coil key point coordinates：
The geometrical curve of coil is formed by connecting by multiple key points, and the coordinate of each key point is stored in aray variable KPCS (i, j)
In, wherein i is coordinate components, i=1, and 2,3 represent the X-axis of key point, Y-axis and Z axis coordinate respectively, and j is key point numbering, fixed
Adopted aray variable KPCS (m, n), wherein m be coordinate components, m=1,2 respectively represent key point polar polar diameter R and polar angle
φ, n are numbered for key point, and the formula for calculating crucial point coordinates at each section of coil is as follows：
Coil beginning straightway key point coordinates：
Starting point coordinate：KPCS (1,1)=0,
KPCS (2,1)=TECRH,
KPCS (3,1)=0；
Terminal point coordinate：KPCS (1,2)=0,
KPCS (2,2)=TECRH,
KPCS (3,2)=TECHZ；
The crucial point coordinates of coil cone angle transition circle section：
Starting point coordinate：KPCS (1,3)=0,
KPCS (2,3)=TECRH+TECR0-TECR0cos (CONTP),
KPCS (3,3)=TECHZ+TECR0sin (CONTP)；
Terminal point coordinate：KPCS (Isosorbide-5-Nitrae)=0,
KPCS (2,4)=TECRH+TECR0-TECR0cos (CONTP)+TECBH1sin (CONTP),
KPCS (3,4)=TECHZ+TECR0sin (CONTP)+TECBH1cos (CONTP)；
The coordinate of the initial circular arc waypoint of involute：
1) A point coordinates, A points are the starting point of the initial arc section of involute：
A point polar diametersA point polar angles THTA=45；
A points rectangular co-ordinate X values XA=RAcos (THTA), A point rectangular co-ordinate Y value YA=RAsin (THTA), vertex of a cone Z coordinate
OZ=KPCS (3,4)-RAcos (CONTP)；
2) coordinate of fillet center of circle O1 is sought according to A point coordinates, O1 is the center of circle of the initial arc section of involute：
O1 points rectangular co-ordinate X values XO1=XA+TECR1cos (THTA+90), O1 point rectangular co-ordinate Y value YO1=YA+TECR1
sin(THTA+90)；
O1 point polar diametersO1 point polar angles
3) E point coordinates, E points are the point of contact of O1 points and basic circle tangent line：
E points rectangular co-ordinate X values XE=TECRJcos (THTE), E point rectangular co-ordinate Y value YE=TECRJsin (THTE), its
In, THTE=THTO1+THTEOO1,
4) B point coordinates, B points are the starting point of involute section：
B points rectangular co-ordinate X values XB=XO1+TECR1cos (THTO1E), B point rectangular co-ordinate Y value
YB=YO1+TECR1sin (THTO1E), wherein,
B point polar diametersB point polar angles
The involute angle of spread of B points：
5) angle of spread of the coil in sector：
TECBEA=TECBYYsin (CONTP)；
After step 3.2, zero point of launching polar coordinates zero point and involute overlap, each point coordinates is solved again：
1) A point coordinates：
A points rectangular co-ordinate X values XA'=RAcos (THTA'), A point rectangular co-ordinate Y value
YA'=RAsin (THTA'), wherein, THTA'=THTA+ANGB-THTB；
2) O1 point coordinates：
O1 points rectangular co-ordinate X values XO1'=XA'+TECR1cos (THTA'+90), O1 point rectangular co-ordinate Y value
YO1'=YA'+TECR1sin (THTA'+90)；
O1 point polar angles
3) E point coordinates：
E points rectangular co-ordinate X values XE'=TECRJcos (THTE'),
E points rectangular co-ordinate Y value YE'=TECRJsin (THTE'), wherein,
THTE'=THTO1'+THTEOO1；
4) B point coordinates：
B points rectangular co-ordinate X values XB'=XO1'+TECR1cos (THTO1E'),
B points rectangular co-ordinate Y value YB'=YO1'+TECR1sin (THTO1E'),
Wherein,
B point polar anglesB point polar diameters
5) P point coordinates：
P point polar angle ANGP=DEFAX+THTP, wherein, THTP=TECBEA+THTA'；
6) C point coordinates：
C point rectangular co-ordinate X values
XC'=TECRJcos (ANGC)+TECRJANGC π/180sin (ANGC),
C point rectangular co-ordinate Y values
YC'=TECRJsin (ANGC)-TECRJANGC π/180cos (ANGC),
Wherein, ANGC=DEFAY；
C point polar diametersC point polar angles
7) O2 point coordinates, O2 points terminate the center of circle of arc section for involute：
O2 point rectangular co-ordinate X values：
XO2'=TECRJcos (ANGC)+[TECRJANGC π/180SIN (ANGC)] sin (ANGC)；
O2 point rectangular co-ordinate Y values：
YO2'=TECRJsin (ANGC)-[TECRJANGC π/180COS (ANGC)] cos (ANGC)；
8) D point coordinates, D points terminate the terminal of arc section for involute：
D points rectangular co-ordinate X values XD'=XO2'+TECR2cos (THTP+90),
D points rectangular co-ordinate Y value YD'=XD'tan (THTP),
D point polar diameters
Step 3.3, continuation solve each section of coordinate of key point of coil, and the key point number of the initial arc section of involute is N1, gradually
The number of open segment key point is N2, and the key point number that involute terminates arc section is N3, then have：
1) cycle calculations obtain the coordinate of the initial each key point in arc section inside of involute respectively, wherein：
The N1 polar diameter of key point is RB', and polar angle is THTB'-THTA', the rectangular co-ordinate X values of remaining k-th key point, K
=1,2 ... ..., (N1-1)：
XTEMP=XO1'+TECR1cos (TEMPTHTA+TEMPTHTABK/N1),
The rectangular co-ordinate Y value of k-th key point：
YTEMP=YO1'+TECR1sin (TEMPTHTA+TEMPTHTABK/N1)；
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA' of k-th key point, wherein：
2) cycle calculations obtain the coordinate of each key point of involute intersegmental part respectively, wherein：
The N2 polar diameter of key point is RC', and polar angle is THTC'-THTA', the rectangular co-ordinate X values of remaining k-th key point, K
=1,2 ... ..., (N2-1)：
XTEMP=TECRJcos (ANGB+TEMPBCK/N2)+
TECRJ·(ANGB+TEMPBC·K/N2)·π/180·sin(ANGB+TEMPBC·K/N2)
The rectangular co-ordinate Y value of k-th key point：
YTEMP=TECRJsin (ANGB+TEMPBCK/N2)-
TECRJ·(ANGB+TEMPBC·K/N2)·π/180·cos(ANGB+TEMPBC·K/N2)
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA' of k-th key point, wherein：
TEMPBC=ANGC-ANGB；
3) cycle calculations obtain the coordinate that involute terminates each key point in arc section inside respectively, wherein：
The N3 polar diameter of key point is RD', and polar angle is THTD'-THTA', the rectangular co-ordinate X values of remaining k-th key point, K
=1,2 ... ..., (N3-1)：
XTEMP=XO2'+TECR2cos (TEMPTHTC-TEMPTHTCDK/N3)；
The rectangular co-ordinate Y value of k-th key point：
YTEMP=YO2'+TECR2sin (TEMPTHTC-TEMPTHTCDK/N3)；
The polar diameter of k-th key point
Polar angle atan (YTEMP, XTEMP)-THTA' of k-th key point, wherein：
If negative value, then it is modified to
TEMPTHTCD=TEMPTHTC-TEMPTHTD；
If negative value, then it is modified to
Step 3.4, the polar coordinates of each key point of coil are converted into cartesian coordinate using cycle calculations, wherein, k-th is crucial
KPCS (Isosorbide-5-Nitrae+K)=TECRJTEMPRsin (TEMPTHT) of point,
KPCS(2,4+K)=TEMPR·cos(TEMPTHT),
KPCS (3,4+K)=ICS (1, K) cos (CONTP)+OZ, wherein：
TEMPR=ICS (1, K) sin (CONTP), ICS (1, K) are the polar diameter of k-th key point；TEMPTHT=ICS (2,
K)/sin (CONTP), ICS (2, K) are the polar angle of k-th key point；
Step 3.5, set up key point：According to each crucial point coordinates that draws is solved in step 3.4, each key point is set up；
Step 3.6, the SPL for setting up coil：The key point set up in Connection Step 3.5, that is, the batten for generating coil is bent
Line；
Step 4, set up coil FEM model.
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