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Mechanical engineering design and analysis
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| name | mechanical-engineering |
| description | Mechanical engineering design and analysis |
| license | MIT |
| compatibility | opencode |
| metadata | {"audience":"engineers, designers, manufacturers","category":"engineering"} |
import numpy as np
# Basic stress calculations
def normal_stress(P, A):
"""σ = P/A"""
return P / A
def shear_stress(V, A):
"""τ = V/A"""
return V / A
def bending_stress(M, y, I):
"""σ = My/I"""
return M * y / I
def torsion_stress(T, r, J):
"""τ = Tr/J"""
return T * r / J
# Strain calculations
def axial_strain(delta_L, L):
"""ε = ΔL/L"""
return delta_L / L
def poisson_ratio(epsilon_lat, epsilon_ax):
"""ν = -ε_lat/ε_ax"""
return -epsilon_lat / epsilon_ax
# Hooke's Law
def youngs_modulus(sigma, epsilon):
"""E = σ/ε"""
return sigma / epsilon
# Material properties database
MATERIALS = {
"steel_1040": {
"E": 200, # GPa
"nu": 0.29,
"yield": 290, # MPa
"ultimate": 520,
"density": 7850 # kg/m³
},
"aluminum_6061": {
"E": 69,
"nu": 0.33,
"yield": 275,
"ultimate": 310,
"density": 2700
},
"titanium": {
"E": 110,
"nu": 0.34,
"yield": 880,
"ultimate": 950,
"density": 4500
}
}
def select_material(stress, safety_factor, requirements):
"""Material selection based on requirements"""
working_stress = stress * safety_factor
candidates = []
for name, props in MATERIALS.items():
if props["yield"] >= working_stress:
if props["density"] <= requirements.get("max_density", 10000):
candidates.append(name)
return candidates
# Shaft design
class ShaftDesign:
@staticmethod
def torsion_stress(T, d):
"""τ = 16T/(πd³)"""
return 16 * T / (np.pi * d**3)
@staticmethod
def combined_stress(M, T, d, E, nu):
"""Using distortion energy theory"""
bending = 32 * M / (np.pi * d**3)
torsion = 16 * T / (np.pi * d**3)
von_mises = np.sqrt(bending**2 + 3 * torsion**2)
return von_mises
@staticmethod
def deflection(M, L, E, I):
"""Simply supported beam with point load at center"""
return M * L**2 / (48 * E * I)
# Gear design
class GearDesign:
@staticmethod
def pitch_diameter(n, p):
"""D = nP or D = N/p"""
return n / p
@staticmethod
def gear_ratio(N_large, N_small):
"""GR = N_large/N_small"""
return N_large / N_small
@staticmethod
def tangential_velocity(d, n):
"""V = πdn/12 (ft/min)"""
return np.pi * d * n / 12
@staticmethod
def gear_tooth_strength(J, V, F, K):
"""Lewis equation modified"""
return F * Y / (P * K * J)
# Hydraulic system
class HydraulicSystem:
@staticmethod
def cylinder_force(pressure, bore_area):
"""F = pA"""
return pressure * bore_area
@staticmethod
def cylinder_speed(flow, area):
"""v = Q/A"""
return flow / area
@staticmethod
def pump_power(pressure, flow, efficiency):
"""HP = pQ/1714 × efficiency"""
return pressure * flow / 1714 / efficiency
# Heat transfer
class HeatTransfer:
@staticmethod
def conduction(Q, k, A, dT, L):
"""Conduction: Q = kA(dT/L)"""
return k * A * dT / L
@staticmethod
def convection(Q, h, A, dT):
"""Convection: Q = hA(dT)"""
return h * A * dT
@staticmethod
def radiation(Q, emissivity, A, T_hot, T_cold):
"""Radiation: Q = εσA(T_hot⁴ - T_cold⁴)"""
sigma = 5.67e-8
return emissivity * sigma * A * (T_hot**4 - T_cold**4)
@staticmethod
def overall_heat_transfer(U, A, LMTD):
"""Q = U × A × LMTD"""
return U * A * LMTD