"""Параметрическая геометрия ТВВ-320. Встроенный Python FEMM 5. Самостоятельная реализация геометрических построений. Размеры читаются из machine.json; программы и модели sim не импортируются. Координаты — миллиметры. """ import math def hypot(x,y): # MicroPython FEMM 5 does not provide math.hypot. return math.sqrt(x*x+y*y) def rotate_point(point, angle): c, s = math.cos(angle), math.sin(angle) return (c * point[0] - s * point[1], s * point[0] + c * point[1]) def polar_point(radius, angle): return (radius * math.cos(angle), radius * math.sin(angle)) def fillet_corner(before, corner, after, radius): """Касательные и центр окружности, вписанной в угол двух прямых.""" a = (before[0] - corner[0], before[1] - corner[1]) b = (after[0] - corner[0], after[1] - corner[1]) la, lb = hypot(*a), hypot(*b) a, b = (a[0]/la, a[1]/la), (b[0]/lb, b[1]/lb) half = math.acos(max(-1.0, min(1.0, a[0]*b[0] + a[1]*b[1]))) / 2 distance = radius / math.tan(half) if distance >= min(la, lb): raise ValueError('Скругление не помещается между соседними вершинами') start = (corner[0]+a[0]*distance, corner[1]+a[1]*distance) end = (corner[0]+b[0]*distance, corner[1]+b[1]*distance) direction = (a[0]+b[0], a[1]+b[1]) norm = hypot(*direction) center = (corner[0]+direction[0]/norm*radius/math.sin(half), corner[1]+direction[1]/norm*radius/math.sin(half)) angle = math.atan2(end[1]-center[1], end[0]-center[0]) - math.atan2(start[1]-center[1], start[0]-center[0]) angle = (angle + math.pi) % (2*math.pi) - math.pi return start, end, center, angle * 180 / math.pi def stator_profile(machine): g, s = machine['geometry'], machine['stator'] radius = g['rotor_body_diameter_mm']/2 + g['air_gap_mm'] a, b = s['slot_width_mm']/2, s['slot_wedge_width_mm']/2 top = math.sqrt(radius*radius-a*a) bottom = radius + s['slot_height_mm'] shelf = bottom - s['slot_straight_height_mm'] neck = shelf - s['slot_wedge_height_mm'] slope = neck + (b-a)/math.tan(math.radians(s['slot_wedge_angle_deg'])) if not top < neck < slope < shelf < bottom: raise ValueError('Неверный порядок уровней паза статора') points = [(-a,top),(-a,neck),(-b,slope),(-b,shelf),(-a,shelf),(-a,bottom), (a,bottom),(a,shelf),(b,shelf),(b,slope),(a,neck),(a,top)] return [(points[i],points[i+1],0.0) for i in range(len(points)-1)] def rotor_profile(machine): g, r = machine['geometry'], machine['rotor'] radius = g['rotor_body_diameter_mm']/2 a, b = r['slot_width_mm']/2, r['slot_wedge_width_mm']/2 top = math.sqrt(radius*radius-a*a) ledge = radius-r['slot_l2_mm'] shelf = ledge-r['slot_l3_mm'] corner = (-a,radius-r['slot_l1_mm']) start,end,center,angle = fillet_corner((-a,top),corner,(-b,ledge),r['slot_fillet_radius_mm']) bottom = radius-r['slot_height_mm'] rb = r['slot_bottom_radius_mm'] if abs(rb-a)>1e-9: raise ValueError('В этом профиле полукруглое дно: R = b/2') left = [((-a,top),start,0.0),(start,end,angle),(end,(-b,ledge),0.0), ((-b,ledge),(-b,shelf),0.0),((-b,shelf),(-a,shelf),0.0), ((-a,shelf),(-a,bottom+rb),0.0)] edges = left + [((-a,bottom+rb),(a,bottom+rb),180.0)] for p,q,arc in reversed(left): edges.append(((-q[0],q[1]),(-p[0],p[1]),arc)) return edges def make_geometry(machine, winding, theta_deg=0.0, eccentricity_mm=0.0, rotor_discrete=True): """Создать геометрические объекты в памяти; здесь нет вызовов решателя.""" theta = math.radians(theta_deg) g, s, r = machine['geometry'],machine['stator'],machine['rotor'] edges, labels = [], [] def edge(a,b,angle=0.0,group=0,boundary=''): if hypot(a[0]-b[0],a[1]-b[1])<1e-8: raise ValueError('Вырожденное ребро') edges.append({'a':a,'b':b,'angle':angle,'group':group,'boundary':boundary}) def circle(radius,group,cx=0.0,boundary=''): edge((cx+radius,0),(cx-radius,0),180,group,boundary) edge((cx-radius,0),(cx+radius,0),180,group,boundary) def transform(p,phi,offset=0.0): x,y=rotate_point(p,phi-math.pi/2) return (x+offset,y) def label(p,material,group,circuit='',turns=0,role=''): labels.append({'x':p[0],'y':p[1],'material':material,'group':group, 'circuit':circuit,'turns':turns,'role':role}) def rectangle(x,y,width,height,phi,offset,group,material,circuit,turns,role): pts=[(x-width/2,y),(x+width/2,y),(x+width/2,y+height),(x-width/2,y+height)] pts=[transform(p,phi,offset) for p in pts] for i in range(4):edge(pts[i],pts[(i+1)%4],0,group) label(transform((x,y+height/2),phi,offset),material,group,circuit,turns,role) def slotted_circle(profile,angles,radius,group,offset=0.0): angles=sorted(a%(2*math.pi) for a in angles) alpha=math.asin(abs(profile[0][0][0])/radius) for i,phi in enumerate(angles): for a,b,arc in profile:edge(transform(a,phi,offset),transform(b,phi,offset),arc,group) nxt=angles[(i+1)%len(angles)] sweep=(nxt-phi)%(2*math.pi)-2*alpha if sweep<=0:raise ValueError('Пазы пересекаются на поверхности') edge(transform(profile[0][0],phi,offset),transform(profile[-1][1],nxt,offset), math.degrees(sweep),group) rr=g['rotor_body_diameter_mm']/2 rs=rr+g['air_gap_mm'] stator_angles=[math.radians(machine['conventions']['stator_slot1_deg'])+2*math.pi*k/s['slots'] for k in range(s['slots'])] slotted_circle(stator_profile(machine),stator_angles,rs,20) circle(g['stator_back_diameter_mm']/2,20) rotor_angles=[] for pole in range(2): for k in range(r['working_slots']//2): rotor_angles.append(theta+math.pi/2+pole*math.pi+(k-(r['working_slots']/2-1)/2)*2*math.pi/r['slot_divisions']) slotted_circle(rotor_profile(machine),rotor_angles,rr,10,eccentricity_mm) circle(g['rotor_inner_diameter_mm']/2,10,eccentricity_mm) circle(g['outer_air_radius_factor']*g['stator_back_diameter_mm']/2,90,0,'Внешняя граница A=0') label((eccentricity_mm,0),'Воздух',10,role='центральное отверстие') label((eccentricity_mm+rr*.5,0),'Сталь ротора',10,role='бочка ротора') label(polar_point((rs+g['stator_back_diameter_mm']/2)/2,math.radians(3)),'Сталь статора',20,role='ярмо статора') label((rr+g['air_gap_mm']/2,0),'Воздух',0,role='зазор и открытые пазы') label((g['stator_back_diameter_mm']*.75,0),'Воздух',90,role='внешний воздух') # Пара катушки: нижняя сторона s и верхняя сторона s+y с противоположным знаком. by_slot={int(row['slot']):row for row in winding} for k,phi in enumerate(stator_angles): for layer in ('lower','upper'): row=by_slot[k+1] origin=k if layer=='lower' else (k-s['coil_span_slots'])%s['slots'] source=by_slot[origin+1] phase=source['lower_phase'] sign=int(source['lower_sign'])*(1 if layer=='lower' else -1) if phase!=row[layer+'_phase'] or sign!=int(row[layer+'_sign']): raise ValueError('Обмоточная таблица не согласована с шагом катушки') branch=1 if int(source['lower_sign'])>0 else 2 off=s['lower_winding_offset_mm'] if layer=='lower' else s['upper_winding_offset_mm'] rectangle(0,rs+s['slot_height_mm']-off-s['conductor_height_mm'], s['conductor_width_mm'],s['conductor_height_mm'],phi,0,100+2*'ABC'.index(phase)+branch, 'Область обмотки',phase+str(branch)+' — ветвь статора',sign, 'паз %d, %s'%(k+1,layer)) for k,phi in enumerate(rotor_angles): bottom=rr-r['slot_height_mm']+r['winding_bottom_offset_mm'] sign=1 if k