菜单
Look up any mechanical engineering formula with full derivation, term table, units, and worked numerical example. Covers all ME domains from Shigley, Hibbeler, Roark, AISC, ASME.
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Abrasive wear — Archard wear law, two-body vs. three-body abrasion, hardness ratio, abrasion-resistant steels, ceramics, rubber liners, slurry wear, ASTM G65/G105/G75 testing.
Anti-lock braking system (ABS) — wheel slip control, slip ratio, hydraulic modulator, ECU logic, brake force distribution, stability, SAE J2246, vehicle dynamics.
Absorption refrigeration — LiBr-water and NH3-water cycles, COP, generator/absorber/condenser/evaporator heat duties, waste heat driven cooling, double-effect cycles, ASHRAE standards.
基于 SOC 职业分类
正在显示 SKILL.md
| name | formula-lookup |
| description | Look up any mechanical engineering formula with full derivation, term table, units, and worked numerical example. Covers all ME domains from Shigley, Hibbeler, Roark, AISC, ASME. |
| metadata | {"priority":7,"promptSignals":{"phrases":["formula for","equation for","what is the formula","how do you calculate","formula lookup","find the formula"],"minScore":3}} |
For any formula request:
State: what it calculates, which domain (SOM, dynamics, fluids, heat transfer, etc.)
Full equation in proper mathematical notation.
| Symbol | Name | Meaning | Imperial units | SI units |
|---|---|---|---|---|
| σ | Normal stress | Stress at fiber distance c from NA | psi, ksi | Pa, MPa |
| ... | ... | ... | ... | ... |
When does this formula apply? When does it break down? (e.g., "Valid for elastic behavior, σ < Sy")
Starting from first principles, show the logical path to the formula. For students: derivation builds physical intuition.
What other formulas connect to this one? (e.g., "Flexure formula → shear formula VQ/Ib → transverse shear stress")
Plug in real numbers: show substitution, check units, interpret result.
σ = Mc/I (bending stress) σ = P/A (axial stress) τ = VQ/Ib (transverse shear stress) τ = Tc/J (torsional shear) σ_von = √(σ_x² - σ_xσ_y + σ_y² + 3τ_xy²) (von Mises) δ = PL/AE (axial deformation) δ = PL³/3EI (cantilever tip) δ = 5wL⁴/384EI (SS midspan, UDL)
F = ma (Newton 2nd) T = Iα (rotational Newton) ω_n = √(k/m) (natural frequency) X/X_st = 1/|1-r²| (DMF, undamped) E_k = ½mv², E_p = ½kx² (energy)
Q = A×V (continuity) P₁/γ + V₁²/2g + z₁ = P₂/γ + V₂²/2g + z₂ + h_L (Bernoulli) h_f = f(L/D)(V²/2g) (Darcy-Weisbach) Re = ρVD/μ (Reynolds) τ_w = μ(du/dy) (Newton's viscosity)
q = kA ΔT/L (conduction) q = hA ΔT (convection) q = εσA T⁴ (radiation) Nu = hL/k (Nusselt) Bi = hL/k (Biot) Fo = αt/L² (Fourier)
n = Sy/σ or n = Se/σ_a (factor of safety) F_i = 0.75 A_t S_p (bolt preload) T = K d F_i (bolt torque) W_t = 63025 H/n (gear tangential force, lbf, in, rpm, hp) L₁₀ = (C/P)³ × 10⁶/60n (bearing life, hours)
PV = mRT (ideal gas) q - w = Δh (steady flow energy) η_Carnot = 1 - T_L/T_H (max efficiency) η_Rankine = w_net/q_in (steam cycle) COP = q_L/w_c (refrigeration)
If you cannot recall the exact formula:
Every formula answer must include unit verification: [N][m]/[m⁴] = [N/m²] = [Pa] ✓ [kg][m/s²][m] = [N·m] = [J] ✓ Never present a dimensionally inconsistent result.