r""" Motorized pitch arc sector (-6 .. +20 deg) for the 6-component balance + roll spindle. Pitch is a rotation about the lateral (y) axis through the BMC, so the model stays on the tunnel centreline. MOVING (pitches): roll housing assembly (housing, caps, adapter, NMRV030 + NEMA 23, encoder), spindle, sting, balance, puck, pod, 4 cam-follower rollers on the housing studs, drive bracket, pinion, pitch gearmotor. FIXED (on the yaw carriage): 2 cheek plates with arc tracks, rack plate with an internal curved rack, base plate, 2 bottom spacers + top tie. - 4x 3/4 in cam followers (3/8-24 stud) at x = 17.3 / 19.4 in on both housing side faces run in arc tracks of radius 17.3 / 19.4 in cut through the 1/2 in cheeks (y = +-1.50 .. +-2.00). - +y cheek stays inside r = 20.5 in: the roll NEMA 23 sticks out in +y beyond r = 20.65 in. - Pitch drive on the -y side: module 1.25 internal curved rack, pitch radius 22.0 in, on a fixed rack plate (y = -2.60 .. -3.10); 20-tooth pinion on a bearing block bolted to the roll gearbox's -y face; 40:1 worm gearmotor (NEMA 17) outboard. Gravity always loads the mesh the same way (no backlash crossing). - Base plate 0.75 in = interface to the yaw carriage (to be designed); its underside is 1.5 in above the duct floor. Coordinates: inches, x aft of the BMC, y spanwise, z up; STEP exported in mm. Run (from this folder): ..\..\.venv\Scripts\python build_pitch_sector_cad.py """ import math import sys from pathlib import Path import cadquery as cq HERE = Path(__file__).resolve().parent for d in ("aluminum_balance", "six_component_balance", "roll_spindle"): sys.path.insert(0, str(HERE.parent / d)) from build_balance_cad import box # noqa: E402 import build_6c_balance_cad as K # noqa: E402 import build_roll_spindle_cad as R # noqa: E402 IN = 25.4 ALPHA_MIN, ALPHA_MAX = -6.0, 20.0 TS_L, TS_W, TS_H, X_TS_BMC = 30.0, 26.25, 11.25, 17.0 Z_FLOOR = -22.7 / 2 # downstream duct floor (assumed - confirm on the tunnel) CARRIAGE_GAP = 1.5 # yaw carriage + rails between floor and sector base BASE_T = 0.75 Z_BASE_BOT = Z_FLOOR + CARRIAGE_GAP Z_BASE_TOP = Z_BASE_BOT + BASE_T # cheeks stand on this # followers / tracks R_TRK = R.FOLLOWERS # (17.3, 19.4) - follower stud x on the sting axis = track radii ROLLER_D, ROLLER_W = 0.75, 0.50 SLOT_W = ROLLER_D + 0.002 CH_T = 0.50 Y_CH_IN = R.HOUS_HALF + 0.05 # 1.50 Y_CH_OUT = Y_CH_IN + CH_T # 2.00 CH_R_IN, CH_R_OUT = 15.8, 20.5 # cheek band CH_TH_LO, CH_TH_HI = -32.0, 16.0 # polar-angle range of the band (deg, + = above the axis) # rack / drive MODULE = 1.25 / 25.4 # in R_RACK = 22.0 # rack pitch radius (internal teeth, facing the BMC) PIN_Z = 20 # pinion teeth R_PIN = PIN_Z * MODULE / 2 # 0.492 in pitch radius R_PIN_C = R_RACK - R_PIN # pinion centre radius 21.51 RK_Y0, RK_Y1 = -3.10, -2.60 # rack plate RK_R_OUT = 23.3 RK_TH_LO, RK_TH_HI = -27.0, 12.0 PIN_Y0, PIN_Y1 = -3.02, -2.68 # pinion face width 0.34 in def polar(r, th): t = math.radians(th) return (r * math.cos(t), r * math.sin(t)) def xz_prism(pts, y0, y1): return cq.Workplane("XZ").polyline(pts).close().extrude(y1 - y0).translate((0, y1, 0)) def band(r0, r1, t0, t1, y0, y1, n=80): pts = [polar(r1, t0 + (t1 - t0) * i / n) for i in range(n + 1)] + \ [polar(r0, t1 - (t1 - t0) * i / n) for i in range(n + 1)] return xz_prism(pts, y0, y1) def arc_slot(r, w, t0, t1, y0, y1): s = band(r - w / 2, r + w / 2, t0, t1, y0, y1) for t in (t0, t1): cx, cz = polar(r, t) s = s.union(cq.Workplane("XZ").center(cx, cz).circle(w / 2).extrude(y1 - y0).translate((0, y1, 0))) return s def above_base(shape): return shape.intersect(box(-50, 60, -10, 10, Z_BASE_TOP, 30)) # ================================================================== fixed parts def follower_theta_range(extra=1.5): """Polar angles a follower on the sting axis visits (+ roller radius margin).""" return -ALPHA_MAX - extra, -ALPHA_MIN + extra def make_cheek(side): y0, y1 = (Y_CH_IN, Y_CH_OUT) if side > 0 else (-Y_CH_OUT, -Y_CH_IN) c = band(CH_R_IN, CH_R_OUT, CH_TH_LO, CH_TH_HI, y0, y1) # foot forward of the band down to the base (keeps clear of the sting, which is between the cheeks) pi = polar(CH_R_IN, CH_TH_LO) c = c.union(xz_prism([(13.6, Z_BASE_TOP - 0.01), (pi[0] + 0.4, pi[1] + 0.2), (pi[0] + 2.0, pi[1] - 0.5), (pi[0] + 2.0, Z_BASE_TOP - 0.01)], y0, y1)) c = above_base(c) t0, t1 = follower_theta_range() for r in R_TRK: c = c.cut(arc_slot(r, SLOT_W, t0, t1, y0 - 0.1, y1 + 0.1)) # top tie and spacer bolt holes (1/4 clearance) + base bolts (1/4-20 tapped into the bottom edge) for (x, z) in TIE_HOLES + SPACER_HOLES: c = c.cut(cq.Workplane("XZ").center(x, z).circle(0.1405).extrude(1).translate((0, y1 + 0.3, 0))) for x in BASE_BOLTS_X: c = c.cut(cq.Workplane("XY").center(x, (y0 + y1) / 2).circle(0.1005).extrude(0.75).translate((0, 0, Z_BASE_TOP))) return c TOP_TIE = (polar(17.6, 14.0), polar(19.6, 14.0)) # tie block between the cheeks, above the swept region TIE_HOLES = [polar(17.9, 14.2), polar(19.3, 14.2)] SPACER_POS = [(14.6, Z_BASE_TOP + 0.5), (17.0, Z_BASE_TOP + 0.45)] SPACER_HOLES = SPACER_POS BASE_BOLTS_X = [14.2, 15.6, 17.4] def make_top_tie(): (xa, za), (xb, zb) = TOP_TIE pts = [polar(17.4, 13.0), polar(19.8, 13.0), polar(19.8, 15.5), polar(17.4, 15.5)] t = xz_prism(pts, -Y_CH_IN, Y_CH_IN) for (x, z) in TIE_HOLES: t = t.cut(cq.Workplane("XZ").center(x, z).circle(0.1005).extrude(4).translate((0, 2, 0))) return t def make_spacer(x, z, h): s = box(x - 0.5, x + 0.5, -Y_CH_IN, Y_CH_IN, Z_BASE_TOP, Z_BASE_TOP + h) return s.cut(cq.Workplane("XZ").center(x, z).circle(0.1005).extrude(4).translate((0, 2, 0))) def make_rack_plate(teeth=True): rp = band(R_RACK + 1.25 * MODULE, RK_R_OUT, RK_TH_LO, RK_TH_HI, RK_Y0, RK_Y1) # root circle inside if teeth: # cosmetic internal teeth (module 1.25), tips at r = R_RACK - module pitch_ang = math.degrees(math.pi * MODULE / R_RACK) n = int((RK_TH_HI - RK_TH_LO - 2) / pitch_ang) th = RK_TH_LO + 1 for _ in range(n): a, b = th + pitch_ang * 0.12, th + pitch_ang * 0.88 pts = [polar(R_RACK + 1.25 * MODULE + 0.002, a), polar(R_RACK - MODULE, th + pitch_ang * 0.32), polar(R_RACK - MODULE, th + pitch_ang * 0.68), polar(R_RACK + 1.25 * MODULE + 0.002, b)] rp = rp.union(xz_prism(pts, RK_Y0, RK_Y1)) th += pitch_ang # leg to the base (outer side) and two 1/4-20 holes in its foot po = polar(RK_R_OUT, RK_TH_LO) pi = polar(R_RACK + 0.3, RK_TH_LO) rp = rp.union(xz_prism([(pi[0], pi[1]), (po[0], po[1]), (po[0] + 0.6, Z_BASE_TOP - 0.01), (pi[0] - 0.3, Z_BASE_TOP - 0.01)], RK_Y0, RK_Y1)) rp = above_base(rp) for x in (pi[0] + 0.1, po[0] + 0.3): rp = rp.cut(cq.Workplane("XY").center(x, (RK_Y0 + RK_Y1) / 2).circle(0.1005).extrude(0.75) .translate((0, 0, Z_BASE_TOP))) return rp BASE_NOTCH_X = 18.4 # aft of this, only a -y strip remains: the roll gearbox and NEMA 23 BASE_STRIP_Y = -2.3 # swing down through the notch at high pitch def make_base(): x0, x1 = 13.4, 22.6 b = box(x0, BASE_NOTCH_X, RK_Y0 - 0.3, Y_CH_OUT + 0.3, Z_BASE_BOT, Z_BASE_TOP) b = b.union(box(BASE_NOTCH_X - 0.01, x1, RK_Y0 - 0.3, BASE_STRIP_Y, Z_BASE_BOT, Z_BASE_TOP)) for x in BASE_BOLTS_X: # cheek bolts (clearance, c'bored from below) for y in ((Y_CH_IN + Y_CH_OUT) / 2, -(Y_CH_IN + Y_CH_OUT) / 2): b = b.cut(cq.Workplane("XY").center(x, y).circle(0.1405).extrude(2, both=True)) po, pi = polar(RK_R_OUT, RK_TH_LO), polar(R_RACK + 0.3, RK_TH_LO) for x in (pi[0] + 0.1, po[0] + 0.3): b = b.cut(cq.Workplane("XY").center(x, (RK_Y0 + RK_Y1) / 2).circle(0.1405).extrude(2, both=True)) for (x, y) in ((x0 + 0.5, RK_Y0), (x0 + 0.5, Y_CH_OUT), (BASE_NOTCH_X - 0.5, Y_CH_OUT), (x1 - 0.5, RK_Y0)): b = b.cut(cq.Workplane("XY").center(x, y).circle(0.203).extrude(2, both=True)) # 4x 3/8 to the carriage return b def make_test_section(): x0, x1, t = -X_TS_BMC, TS_L - X_TS_BMC, 0.5 ts = box(x0, x1, -TS_W / 2 - t, TS_W / 2 + t, -TS_H / 2 - t, TS_H / 2 + t) ts = ts.cut(box(x0 - 1, x1 + 1, -TS_W / 2, TS_W / 2, -TS_H / 2, TS_H / 2)) return ts.union(box(x1, x1 + 14, -18, 18, Z_FLOOR - t, Z_FLOOR)) # ================================================================== moving parts added by this design def make_followers(): out = [] for xf in R_TRK: for s in (1, -1): yr0 = s * (R.HOUS_HALF + 0.05) roller = (cq.Workplane("XZ").center(xf, 0).circle(ROLLER_D / 2).extrude(ROLLER_W) .translate((0, (yr0 + ROLLER_W) if s > 0 else yr0, 0))) stud = (cq.Workplane("XZ").center(xf, 0).circle(0.1875).extrude(0.05 + 0.001) .translate((0, (R.HOUS_HALF + 0.05) if s > 0 else -R.HOUS_HALF, 0))) out.append(roller.union(stud)) return out G_X0, G_X1 = R.GBX G_YM = -R.GBX_HALF # gearbox -y face def make_drive_bracket(): """Plate on the roll gearbox -y face + bearing block carrying the pinion shaft (axis along y) at r = 21.51.""" xc = R_PIN_C # pinion centre at alpha = 0: (21.51, 0) p = box(G_X0 + 0.15, G_X1 - 0.15, G_YM - 0.25, G_YM, -1.15, 1.15) # plate on the gearbox face blk = box(xc - 0.65, xc + 0.65, -2.55, G_YM - 0.25, -0.65, 0.65) # bearing block (outboard of cheek) b = p.union(blk) b = b.cut(cq.Workplane("XZ").center(xc, 0).circle(0.4331).extrude(1.05).translate((0, G_YM - 0.25, 0))) # 22 H7: 2x 608 b = b.cut(cq.Workplane("XZ").center(xc, 0).circle(0.20).extrude(3).translate((0, 0, 0))) # shaft clearance thru plate for x in (G_X0 + 0.45, G_X1 - 0.45): # 4x M6 to the gearbox (CONFIRM vendor) for z in (-0.90, 0.90): # clear of the bearing block b = b.cut(cq.Workplane("XZ").center(x, z).circle(0.128).extrude(1).translate((0, G_YM + 0.2, 0))) return b def make_pinion(): return (cq.Workplane("XZ").center(R_PIN_C, 0).circle(R_PIN - 1.25 * MODULE * 0.1).extrude(PIN_Y1 - PIN_Y0) .translate((0, PIN_Y1, 0)) .union(cq.Workplane("XZ").center(R_PIN_C, 0).circle(0.157).extrude(1.2).translate((0, -2.55 + 0.6, 0)))) def make_pitch_gearmotor(): """Envelope: small 40:1 worm gearbox (output along -y into the pinion) + NEMA 17 pointing aft.""" xc = R_PIN_C g = box(xc - 0.75, xc + 0.75, -4.55, -3.20, -0.75, 0.75) m = box(xc + 0.75, xc + 2.35, -4.38, -3.36, -0.83, 0.83) return g.union(m) def roll_assembly_parts(): parts = {"spindle": R.make_spindle(), "sting": K.make_sting(), "balance": K.make_balance(), "puck": K.make_puck(), "pod": K.make_pod()} parts.update({k: v for k, v in R.fixed().items()}) return parts def moving(alpha): parts = roll_assembly_parts() for i, f in enumerate(make_followers()): parts[f"follower{i}"] = f parts["drive_bracket"] = make_drive_bracket() parts["pinion"] = make_pinion() parts["pitch_gearmotor"] = make_pitch_gearmotor() return {k: v.rotate((0, 0, 0), (0, 1, 0), alpha) for k, v in parts.items()} def fixed(): f = {"cheek_plus_y": make_cheek(+1), "cheek_minus_y": make_cheek(-1), "rack_plate": make_rack_plate(), "base_plate": make_base(), "top_tie": make_top_tie()} for i, (x, z) in enumerate(SPACER_POS): f[f"spacer{i}"] = make_spacer(x, z, 0.9 if i == 0 else 0.8) return f def vol(a, b): return a.val().intersect(b.val()).Volume() # ================================================================== run if __name__ == "__main__": fx = fixed() ts = make_test_section() print(f"sector: cheeks r {CH_R_IN}-{CH_R_OUT} in, tracks r {R_TRK}, rack pitch r {R_RACK} (module 1.25, " f"{PIN_Z}-tooth pinion r {R_PIN:.3f}), base plate z {Z_BASE_BOT:.2f}..{Z_BASE_TOP:.2f}") print("INTERFERENCE SWEEP (in^3; rack x pinion is the gear mesh and is excluded)") worst_all = 0.0 for a in (ALPHA_MIN, -3, 0, 5, 10, 15, ALPHA_MAX): mv = moving(a) worst, hits = 0.0, [] for km, vm in mv.items(): for kf, vf in list(fx.items()) + [("test_section", ts)]: if km == "pinion" and kf == "rack_plate": continue v = vol(vm, vf) if v > 1e-6: hits.append(f"{km} x {kf} = {v:.4f}") worst = max(worst, v) worst_all = max(worst_all, worst) print(f" alpha {a:+5.1f}: max {worst:.5f}" + ("".join("\n " + h for h in hits) if hits else "")) # mesh check: pinion pitch circle tangent to the rack pitch circle at every alpha for a in (ALPHA_MIN, ALPHA_MAX): c = cq.Vector(R_PIN_C, 0, 0) cr = c.toTuple() ca = (cr[0] * math.cos(math.radians(a)), -cr[0] * math.sin(math.radians(a))) print(f" alpha {a:+.0f}: pinion centre radius {math.hypot(*ca):.3f} in, polar angle " f"{math.degrees(math.atan2(ca[1], ca[0])):+.1f} deg (rack teeth span {RK_TH_LO + 1:+.0f}..{RK_TH_HI - 1:+.0f})") # loads m_grav = 2.5 * 11.0 + 11.0 * 20.5 # sting + roll assembly (~11 lb incl. NEMA 23, gearbox, housing) about the BMC m_tot = m_grav + 15.0 f_t = m_tot / R_RACK print(f"\nLOADS: gravity moment about the BMC ~{m_grav:.0f} in-lbf + aero m 15 -> rack force {f_t:.1f} lbf, " f"pinion torque {f_t * R_PIN:.1f} in-lbf, NEMA 17 + 40:1 worm (35 % eff.) needs " f"{f_t * R_PIN / (40 * 0.35) * 0.113 * 1000:.0f} mN-m") N = 25.0 d = R_TRK[1] - R_TRK[0] print(f" followers at N = {N} lbf: {N * R_TRK[1] / d:.0f} / {N * R_TRK[0] / d:.0f} lbf (shared by 2 rollers each; " "3/4 in cam follower static rating ~1,000+ lbf)") print(f" pitch resolution: 1/16 step, 40:1 -> {360 / 3200 / 40 * R_PIN / R_RACK:.5f} deg per microstep") # export parts + assemblies exports = {**fx, "drive_bracket_6061": cq.Workplane().add(make_drive_bracket().val()), "pinion_m1.25_20T": make_pinion(), "pitch_gearmotor_envelope": make_pitch_gearmotor(), "cam_follower_3-4in_envelope": make_followers()[0]} for n, wp in exports.items(): cq.exporters.export(cq.Workplane().add(wp.val().scale(IN)), str(HERE / f"{n}.step")) print("exported:", ", ".join(exports)) for a in (ALPHA_MIN, 0, ALPHA_MAX): asm = cq.Assembly(name=f"pitch_sector_alpha{a:+.0f}") for k, v in moving(a).items(): asm.add(cq.Workplane().add(v.val().scale(IN)), name=f"m_{k}", color=cq.Color(0.6, 0.6, 0.66)) for k, v in fx.items(): asm.add(cq.Workplane().add(v.val().scale(IN)), name=f"f_{k}", color=cq.Color(0.85, 0.62, 0.22)) asm.export(str(HERE / f"assembly_pitch_sector_alpha{a:+.0f}.step")) print(f"assemblies at alpha {ALPHA_MIN:+.0f}, 0, {ALPHA_MAX:+.0f} written; worst interference {worst_all:.5f} in^3")