path: root/blender/diferencial.py

# -*- coding: utf-8 -*-
"""DIFERENCIAL - why the two wheels can turn at different speeds.

Every part is generated in code and moves with the exact kinematics of the
mechanism:  w_left + w_right = 2 * w_carrier, and the spider gear spins about
its own axis at (w_right - w_left)/2 relative to the carrier. Pinion and ring
gear keep their ratio: 14 and 43 teeth, with cone half-angles adding up to 90
degrees."""
import math, os, sys
sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
import bpy
from mathutils import Vector
from base import *

NAME_KEY = "diferencial"
AXIS_X = 1.32          # where the wheels go
R_WHEEL = 0.52
OMEGA = 1.45          # rad/s of the carrier
RADIO_GIRO = 3.9
TRACK_W = 1.70
INCL = -0.72          # strongly diagonal: in 9:16 that is what uses the height

N_COR, N_PIN = 43, 14          # 3.07:1 ratio, like a road differential
G_COR, G_PIN = 72.0, 18.0      # the half-angles add up to 90: that is the meshing condition
N_LAT = 16
X_COR = -0.50                  # common apex of ring gear and pinion: far from the spider gears
D_I, D_O = 0.70, 1.00          # the toothed face, the same on both
P_PHASE = math.pi / 2       # so the tooth lands in the gap
P_ESP = -0.62             # opposite hand to the ring gear
P_NEXT = 1.0

# the assembly is 3.68 from end to end; tilted 41 degrees that is 2.77 wide
# and 2.41 high, which is what sets these numbers
FRAMING = [(0, 6.2), (2, 5.0), (3, 4.2), (4, 5.6), (5, 4.6),
            (6, 5.0), (7, 5.6), (8, 5.6), (9, 5.8), (10, 5.2)]
DIR_CAM = Vector((0.30, -0.93, 0.21)).normalized()


def alto_en(T, f):
    tabla, altos, v = dict(FRAMING), [], FRAMING[0][1]
    for i in range(len(T.beats)):
        v = tabla.get(i, v)
        altos.append(v)
    i = 0
    for k in range(len(T.beats)):
        if f >= T.span(k)[0]:
            i = k
    start, fin = T.span(i)
    p = min(1.0, (f - start) / max(1.0, (fin - start) * 0.55))
    return mix_m(altos[i - 1] if i else altos[0], altos[i], p)


def build_scene(T):
    sc = scene_setup()
    studio_world(0.65)                      # what the steel reflects
    cam = camera_obj((0, -6, 0), (0, 0, 0), lens=50)
    cam.data.sensor_fit = 'VERTICAL'
    cam.data.sensor_height = 36.0

    light_obj("key", 'AREA', (-3.4, -4.6, 4.4), 1400, "blanco", size_u=6.0, sight=(0, 0, 0))
    light_obj("fill", 'AREA', (4.2, -3.2, -1.6), 420, "#BFD4FF", size_u=5.0, sight=(0, 0, 0))
    light_obj("rim", 'AREA', (-0.8, 4.6, 2.8), 900, "blanco", size_u=4.0, sight=(0, 0, 0))

    M = {
        "acero": metal("acero", "#B7BEC9", rough=0.22),
        "acero2": metal("acero2", "#9BA3B0", rough=0.30),
        "fundido": metal("fundido", "#5E6774", rough=0.62, met=0.85),
        "eje_i": metal("eje_i", "#C2C8D2", rough=0.24),
        "eje_d": metal("eje_d", "#C2C8D2", rough=0.24),
        "goma": material("goma", "#1E222C", rough=0.52),
        "alu": metal("alu", "#CBD3DE", rough=0.15),
        "freno": metal("freno", "#79818E", rough=0.45, met=0.9),
    }

    # --- top view: the car turning --------------------------------------
    floor_obj = bpy.data.objects.new("suelo_g", None)
    bpy.context.collection.objects.link(floor_obj)
    arc_list, wheels_a = [], []
    for k, (rr, c) in enumerate(((RADIO_GIRO - TRACK_W / 2, "rosa"),
                                 (RADIO_GIRO + TRACK_W / 2, "verde"))):
        pts = []
        for i in range(120):
            th = -0.62 + 1.24 * i / 119.0
            pts.append((-RADIO_GIRO + rr * math.cos(th), rr * math.sin(th), 0.0))
        cu = curve_poly(f"arco{k}", [pts], thickness_px=0.045, radios=[[0.0] * 120],
                        mat=material(f"m_arco{k}", c, emit=2.4, rough=0.5))
        cu.parent = floor_obj
        arc_list.append((cu, pts))
        r = full_wheel(f"ra{k}", M, R=R_WHEEL, r=0.185, width_px=0.28)
        r.parent = floor_obj
        wheels_a.append(r)
    axis_a = cylinder("eje_a", 0.075, TRACK_W, M["acero2"])
    axis_a.parent = floor_obj
    patina = curve_poly("patina", [[(0, 0, 0)] * 60], thickness_px=0.11,
                        radios=[[0.0] * 60], mat=material("m_pat", "blanco", emit=3.4))
    patina.parent = floor_obj

    # --- the differential --------------------------------------------------
    diff = bpy.data.objects.new("dif", None)
    bpy.context.collection.objects.link(diff)
    diff.scale = (0, 0, 0)

    cage = bpy.data.objects.new("jaula", None)
    bpy.context.collection.objects.link(cage)
    cage.parent = diff
    # carrier housing: two annular flanges and two curved walls around the pin
    # axis. The +-Y sides stay open: that is where the gears show, which is how a
    # real differential housing looks
    # everything in the carrier stays inside r=0.52: the pinion never goes below
    # r=0.59, so the carrier can spin without running over it
    for sx in (0.58, -0.58):
        br = flat_ring(f"brida{sx}", 0.13, 0.52, 0.08, M["fundido"])
        br.rotation_euler = (0, math.pi / 2, 0)
        br.location = (sx, 0, 0)
        br.parent = cage
    for k, center_pt in enumerate((math.pi / 2, -math.pi / 2)):
        pared = ring_sector(f"pared{k}", 0.43, 0.52, 1.16,
                              center_pt - 0.62, center_pt + 0.62, M["fundido"])
        pared.rotation_euler = (0, math.pi / 2, 0)
        pared.parent = cage
    bolt = cylinder("perno", 0.062, 1.00, M["acero2"])
    bolt.parent = cage

    corona = bevel_gear("corona", (1, 0, 0), N=N_COR, gamma=G_COR,
                              d_i=D_I, d_o=D_O, alto=0.042, mat=M["acero"],
                              spiral=0.62, thickness=0.14, gap_m=0.58,
                              per_tooth=24)
    corona.location = (X_COR, 0, 0)
    corona.parent = cage
    screws("bulones", 10, 0.78, -0.11, largo=0.10, r_t=0.035,
              mat=M["acero2"], padre=cage)

    lat = {}
    for nm_key, axis_obj, sx in (("izq", (-1, 0, 0), -1), ("der", (1, 0, 0), 1)):
        g = bpy.data.objects.new(f"lat_{nm_key}", None)
        bpy.context.collection.objects.link(g)
        g.parent = diff
        eng = bevel_gear(f"eng_{nm_key}", axis_obj, N=N_LAT, gamma=45.0,
                               d_i=0.26, d_o=0.50, alto=0.042, mat=M["acero"],
                               spiral=0.30, thickness=0.12, gap_m=0.09)
        eng.parent = g
        # stepped half-shaft + flange
        for (largo, radio, x0) in ((0.48, 0.110, 0.50), (AXIS_X - 0.82, 0.080, 0.95)):
            se = cylinder(f"se_{nm_key}_{radio}", radio, largo, M[f"eje_{nm_key[0]}"])
            se.rotation_euler = (0, math.pi / 2, 0)
            se.location = (sx * x0, 0, 0)
            se.parent = g
        flange = flat_ring(f"bw_{nm_key}", 0.09, 0.22, 0.07, M["acero2"])
        flange.rotation_euler = (0, math.pi / 2, 0)
        flange.location = (sx * (AXIS_X - 0.20), 0, 0)
        flange.parent = g
        wheel_obj = full_wheel(f"rue_{nm_key}", M, R=R_WHEEL, r=0.185, width_px=0.28)
        wheel_obj.location = (sx * AXIS_X, 0, 0)
        wheel_obj.parent = g
        lat[nm_key] = g

    sat = []
    for k, axis_obj in enumerate(((0, 0, 1), (0, 0, -1))):
        g = bpy.data.objects.new(f"sat{k}", None)
        bpy.context.collection.objects.link(g)
        g.parent = cage
        eng = bevel_gear(f"eng_s{k}", axis_obj, N=N_LAT, gamma=45.0,
                               d_i=0.26, d_o=0.50, alto=0.042, mat=M["acero2"],
                               spiral=-0.30, thickness=0.12, gap_m=0.09, phase=math.pi)
        eng.parent = g
        if k == 0:
            p = sphere(f"testigo{k}", 0.050, material("m_test", "ambar", emit=3.0))
            p.location = (0.30, 0.0, 0.42)
            p.parent = g
        sat.append(g)

    input_shaft = bpy.data.objects.new("entrada", None)
    bpy.context.collection.objects.link(input_shaft)
    input_shaft.parent = diff
    # same face as the ring gear, opposite-hand spiral and a phase so the
    # tooth lands in the gap
    pinion = bevel_gear("pinon", (0, -1, 0), N=N_PIN, gamma=G_PIN,
                             d_i=D_I, d_o=D_O, alto=0.042, mat=M["acero"],
                             spiral=P_ESP, thickness=0.12, gap_m=0.07,
                             phase=P_PHASE, per_tooth=24)
    pinion.location = (X_COR, 0, 0)
    pinion.parent = input_shaft
    cardan_joint = cylinder("cardan", 0.095, 1.30, M["acero2"])
    cardan_joint.rotation_euler = (math.pi / 2, 0, 0)
    cardan_joint.location = (X_COR, -1.50, 0)
    cardan_joint.parent = input_shaft
    fork = flat_ring("horquilla", 0.10, 0.24, 0.10, M["acero2"])
    fork.location = (X_COR