| """Map STEP arm stiffness to dynamic tool-tip tracking error.""" |
|
|
| import argparse |
| import hashlib |
| import json |
| import math |
| import subprocess |
| import sys |
| from pathlib import Path |
|
|
| ROOT = Path(__file__).resolve().parent |
|
|
|
|
| def measure(step: Path, setup: dict) -> dict: |
| import cadquery as cq |
| import gmsh |
| from OCP.BRepGProp import BRepGProp |
| from OCP.GProp import GProp_GProps |
|
|
| shape = cq.importers.importStep(str(step)).val() |
| if shape.ShapeType() != "Solid" or not shape.isValid() or len(shape.Solids()) != 1: |
| raise ValueError(f"Expected one valid solid: {step}") |
| props = GProp_GProps() |
| BRepGProp.VolumeProperties_s(shape.wrapped, props) |
| if props.Mass() <= 0: |
| raise ValueError("Beam volume must be positive") |
| pad0 = cq.Solid.makeBox(10, 20, 10, cq.Vector(0, -10, -5)) |
| pad1 = cq.Solid.makeBox(10, 20, 10, cq.Vector(110, -10, -5)) |
| slabs = [cq.Solid.makeBox(10, 20, 14, cq.Vector(x, -10, -7)) |
| for x in (0, 110)] |
| envelope = cq.Solid.makeBox(120, 20, 14, cq.Vector(0, -10, -7)) |
| pads = (pad0, pad1) |
| pad_overlap = sum(pad.intersect(shape).Volume() for pad in pads) |
| slab_overlap = sum(slab.intersect(shape).Volume() for slab in slabs) |
| result = { |
| "step_sha256": hashlib.sha256(step.read_bytes()).hexdigest(), |
| "volume_mm3": props.Mass(), |
| "mass_kg": props.Mass() * setup["material_density_kg_m3"] * 1e-9, |
| "end_pad_missing_mm3": max(0.0, sum(p.Volume() for p in pads) - pad_overlap), |
| "end_pad_excess_mm3": max(0.0, slab_overlap - pad_overlap), |
| "envelope_excess_mm3": max(0.0, shape.Volume() - |
| shape.intersect(envelope).Volume()), |
| "meshes": {}, |
| } |
| gmsh.initialize() |
| try: |
| gmsh.option.setNumber("General.Terminal", 0) |
| gmsh.model.add("robot_tool_arm") |
| gmsh.model.occ.importShapes(str(step)) |
| gmsh.model.occ.synchronize() |
| if len(gmsh.model.getEntities(3)) != 1: |
| raise ValueError("STEP import must produce one volume") |
| for size in setup["mesh_sizes_mm"]: |
| gmsh.model.mesh.clear() |
| gmsh.option.setNumber("Mesh.CharacteristicLengthMin", size) |
| gmsh.option.setNumber("Mesh.CharacteristicLengthMax", size) |
| gmsh.option.setNumber("Mesh.Algorithm3D", 1) |
| gmsh.model.mesh.generate(3) |
| tags, coordinates, _ = gmsh.model.mesh.getNodes() |
| nodes = {str(int(tag)): [coordinates[3 * i + axis] / 1000 |
| for axis in range(3)] |
| for i, tag in enumerate(tags)} |
| types, _, element_nodes = gmsh.model.mesh.getElements(3) |
| tets = [] |
| for kind, connectivity in zip(types, element_nodes): |
| if kind != 4: |
| raise ValueError(f"Expected first-order tetrahedra, got {kind}") |
| tets.extend([[int(value) for value in connectivity[i:i + 4]] |
| for i in range(0, len(connectivity), 4)]) |
| if not nodes or not tets: |
| raise ValueError("Gmsh produced an empty mesh") |
| result["meshes"][str(size)] = {"nodes": nodes, "tets": tets} |
| finally: |
| gmsh.finalize() |
| return result |
|
|
|
|
| def dynamics(meshes: dict, arm_mass_kg: float, setup: dict) -> dict: |
| import pychrono as ch |
| import pychrono.fea as fea |
|
|
| results = {} |
| for size, data in meshes.items(): |
| system = ch.ChSystemSMC() |
| system.SetGravitationalAcceleration(ch.ChVector3d(0, 0, 0)) |
| system.SetSolver(ch.ChSolverSparseLU()) |
| mesh = fea.ChMesh() |
| material = fea.ChContinuumElastic() |
| material.SetYoungModulus(setup["young_modulus_Pa"]) |
| material.SetPoissonRatio(setup["poisson_ratio"]) |
| material.SetDensity(setup["material_density_kg_m3"]) |
| tip_ids = [key for key, point in data["nodes"].items() |
| if abs(point[0] - 0.12) < 1e-8] |
| fixed_ids = [key for key, point in data["nodes"].items() |
| if abs(point[0]) < 1e-8] |
| if len(tip_ids) < 4 or len(fixed_ids) < 4: |
| raise ValueError("Mesh is missing a clamp or load face") |
| nodes = {} |
| for key, point in data["nodes"].items(): |
| node = fea.ChNodeFEAxyz(ch.ChVector3d(*point)) |
| if key in fixed_ids: |
| node.SetFixed(True) |
| if key in tip_ids: |
| node.SetForce(ch.ChVector3d( |
| 0, setup["lateral_test_force_N"] / len(tip_ids), 0)) |
| mesh.AddNode(node) |
| nodes[int(key)] = node |
| for a, b, c, d in data["tets"]: |
| element = fea.ChElementTetraCorot_4() |
| element.SetNodes(nodes[a], nodes[b], nodes[c], nodes[d]) |
| element.SetMaterial(material) |
| mesh.AddElement(element) |
| system.Add(mesh) |
| system.DoStaticLinear() |
| deflections = [nodes[int(key)].GetPos().y - data["nodes"][key][1] |
| for key in tip_ids] |
| mean_deflection = sum(deflections) / len(deflections) |
| if not math.isfinite(mean_deflection) or mean_deflection <= 0: |
| raise ValueError("Invalid lateral tool-arm deflection") |
| stiffness = setup["lateral_test_force_N"] / mean_deflection |
| effective_mass = (setup["tool_mass_kg"] + |
| setup["modal_arm_mass_fraction"] * arm_mass_kg) |
| damping = (2 * setup["damping_ratio"] * |
| math.sqrt(stiffness * effective_mass)) |
| tracking = {} |
| for frequency in setup["acceleration_frequencies_Hz"]: |
| tracking_system = ch.ChSystemSMC() |
| tracking_system.SetGravitationalAcceleration(ch.ChVector3d(0, 0, 0)) |
| tracking_system.SetSolver(ch.ChSolverSparseLU()) |
| fixed = ch.ChBody() |
| fixed.SetFixed(True) |
| tracking_system.Add(fixed) |
| tool = ch.ChBody() |
| tool.SetMass(effective_mass) |
| tool.SetInertiaXX(ch.ChVector3d(0.01, 0.01, 0.01)) |
| tracking_system.Add(tool) |
| guide = ch.ChLinkMateGeneric() |
| guide.SetConstrainedCoords(True, False, True, True, True, True) |
| guide.Initialize(tool, fixed, ch.ChFramed(ch.ChVector3d(0, 0, 0))) |
| tracking_system.Add(guide) |
| force = ch.ChForce() |
| tool.AddForce(force) |
| force.SetMode(ch.ChForce.FORCE) |
| force.SetDir(ch.ChVector3d(0, 1, 0)) |
| dt = setup["time_step_s"] |
| steps = round(setup["duration_s"] / dt) |
| if dt <= 0 or abs(steps * dt - setup["duration_s"]) > 1e-12: |
| raise ValueError("Invalid tracking time grid") |
| peak_error = 0.0 |
| for index in range(steps): |
| time = index * dt |
| base_acceleration = (setup["base_acceleration_amplitude_m_s2"] * |
| math.sin(2 * math.pi * frequency * time)) |
| displacement = tool.GetPos().y |
| velocity = tool.GetPosDt().y |
| force.SetMforce(-effective_mass * base_acceleration - |
| stiffness * displacement - damping * velocity) |
| tracking_system.DoStepDynamics(dt) |
| peak_error = max(peak_error, abs(tool.GetPos().y)) |
| tracking[str(frequency)] = peak_error |
| results[size] = { |
| "mean_lateral_tip_deflection_m": mean_deflection, |
| "lateral_stiffness_N_m": stiffness, |
| "effective_tool_mass_kg": effective_mass, |
| "tracking_error_m": tracking, |
| "node_count": len(nodes), |
| "tetrahedron_count": len(data["tets"]), |
| "clamped_node_count": len(fixed_ids), |
| "loaded_node_count": len(tip_ids), |
| } |
| return results |
|
|
|
|
| def invoke(python: str, phase: str, payload: dict) -> dict: |
| run = subprocess.run([python, str(Path(__file__).resolve()), "--phase", phase], |
| input=json.dumps(payload), text=True, capture_output=True) |
| if run.returncode: |
| raise RuntimeError(f"{phase} failed:\n{run.stderr[-1600:]}") |
| return json.loads(run.stdout) |
|
|
|
|
| def main() -> None: |
| parser = argparse.ArgumentParser() |
| parser.add_argument("--cad-python", default=sys.executable) |
| parser.add_argument("--physics-python", default=sys.executable) |
| parser.add_argument("--phase", choices=("measure", "dynamics")) |
| args = parser.parse_args() |
| if args.phase: |
| payload = json.load(sys.stdin) |
| result = (measure(Path(payload["step"]), payload["setup"]) |
| if args.phase == "measure" |
| else dynamics(payload["meshes"], payload["arm_mass_kg"], |
| payload["setup"])) |
| print(json.dumps(result)) |
| return |
| setup = json.loads((ROOT / "setup.json").read_text()) |
| results = {} |
| for name in ("before", "after"): |
| properties = invoke(args.cad_python, "measure", { |
| "step": str(ROOT / f"{name}.step"), "setup": setup, |
| }) |
| meshes = properties.pop("meshes") |
| results[name] = { |
| "step_properties": properties, |
| "simulation_result": invoke(args.physics_python, "dynamics", { |
| "meshes": meshes, "arm_mass_kg": properties["mass_kg"], |
| "setup": setup, |
| }), |
| } |
| before = results["before"] |
| after = results["after"] |
| bp, ap = before["step_properties"], after["step_properties"] |
| bs, gs = before["simulation_result"], after["simulation_result"] |
| sizes = [str(size) for size in setup["mesh_sizes_mm"]] |
| cases = [(size, str(frequency)) for size in sizes |
| for frequency in setup["acceleration_frequencies_Hz"]] |
| baseline = [bs[size]["tracking_error_m"][frequency] |
| for size, frequency in cases] |
| candidate = [gs[size]["tracking_error_m"][frequency] |
| for size, frequency in cases] |
| reductions = [1 - a / b for a, b in zip(candidate, baseline)] |
| checks = { |
| "tracking_error_reduced_all_cases": min(reductions) >= |
| setup["required_relative_tracking_error_reduction"], |
| "candidate_tracking_error_limit": max(candidate) <= |
| setup["maximum_candidate_tracking_error_m"], |
| "mesh_tracking_response_stable": all( |
| abs(results["simulation_result"][sizes[1]]["tracking_error_m"][str(frequency)] / |
| results["simulation_result"][sizes[0]]["tracking_error_m"][str(frequency)] - 1) <= |
| setup["maximum_relative_mesh_tracking_error_change"] |
| for results in (before, after) |
| for frequency in setup["acceleration_frequencies_Hz"]), |
| "mass_fixed": abs(ap["mass_kg"] / bp["mass_kg"] - 1) <= |
| setup["maximum_relative_mass_change"], |
| "end_pads_fixed": ap["end_pad_missing_mm3"] <= |
| setup["maximum_end_pad_missing_mm3"] and |
| ap["end_pad_excess_mm3"] <= setup["maximum_end_pad_excess_mm3"], |
| "envelope_fixed": ap["envelope_excess_mm3"] <= |
| setup["maximum_envelope_excess_mm3"], |
| } |
| after["comparison_to_before"] = { |
| "relative_tracking_error_reductions": reductions, |
| "checks": checks, "passed": all(checks.values()), |
| } |
| for name, result in results.items(): |
| (ROOT / f"{name}.results.json").write_text(json.dumps(result, indent=2) + "\n") |
| print(f"Tool-tip tracking error: {baseline} -> {candidate} m") |
| print(f"Task passed: {all(checks.values())}") |
| if not all(checks.values()): |
| raise SystemExit(1) |
|
|
|
|
| if __name__ == "__main__": |
| main() |
|
|
