メニュー
Worm gear design — lead angle, velocity ratio, efficiency, self-locking, AGMA stress, thermal rating, bronze gear materials, center distance.
デフォルトでは、最初にソースを確認する Prompt が選択されています。直接コマンドに切り替えるか、ローカルコピーをダウンロードすることもできます。
インストールを決める前に、SKILL.md と SkillsMP に表示されている付属ファイルをお読みください。
Codex または Claude でインストール この Prompt をコピーして Codex、Claude、または他のアシスタントに貼り付けると、Skill ページを確認してインストールできます。
直接コマンドでは確認用 Prompt が省略されます。実行前にソースを確認してください。
npx skills add https://github.com/MP-AI-20/mechanical-engineering-skills --skill worm-gearsコマンドは1行のまま表示されます。コピー前に横へスクロールして全体を確認してください。
ローカルで確認しますか？SkillsMP が現在取得できるファイルをダウンロードできます。
SOC 職業分類に基づく
SKILL.md を表示中
| name | worm-gears |
| description | Worm gear design — lead angle, velocity ratio, efficiency, self-locking, AGMA stress, thermal rating, bronze gear materials, center distance. |
| metadata | {"priority":7,"promptSignals":{"phrases":["worm gear","worm wheel","lead angle","self-locking","worm drive"],"minScore":3}} |
m_x = axial module of worm = m_n (normal module at worm pitch cylinder) d_w = worm pitch diameter [mm] z_w = number of worm starts (1, 2, 4 typical) z_g = number of gear teeth
Velocity ratio: i = z_g / z_w (typically 5:1 to 80:1 in single stage) Lead: L = z_w × m_x × π [axial distance per revolution of gear = helical pitch × starts] Lead angle (worm): tan(λ) = L / (π d_w) = z_w × m_x / d_w λ = 3-30° (higher λ = higher efficiency; lower λ = self-locking tendency)
Center distance: a = (d_w + d_g) / 2 d_g = m_x × z_g (gear pitch diameter)
AGMA center distance recommendation: d_w ≈ (0.875 to 1.75) × a^0.875 [mm, a in mm] — for best efficiency
Worm geometry ratio: z_w² + (a/m_x - z_w/2)² → usually 1-4 starts
η = tan(λ) / tan(λ + φ') φ' = arctan(μ / cos(φ_n)) [virtual friction angle] μ = coefficient of friction (depends on sliding velocity V_s)
Friction coefficient vs. sliding speed: V_s = V_w / cos(λ) [m/s]; V_w = π d_w n_w / 60000 [m/s] V_s < 0.05 m/s: μ = 0.15; 0.5 m/s: μ = 0.05; 5 m/s: μ = 0.025; >10 m/s: μ = 0.015
Typical efficiency: Single-start (z_w=1): η = 40-60% (low λ, low efficiency) Four-start (z_w=4): η = 70-90% (high λ)
Self-locking condition: λ < φ' → no back-driving possible For steel worm / bronze gear: self-locking when λ < ~5-6° (μ ≈ 0.1)
W_t,g = 2T_g / d_g [tangential force on gear = output torque] W_a,g = W_t,g × tan(λ + φ') / tan(λ) [NOT simple — includes friction]
Exact force analysis: W_N = W_t,g / (cos(φ_n) × cos(λ)) [resultant tooth force] W_t,w = W_N × (cos(φ_n) sin(λ) + μ cos(λ)) [tangential on worm = input] W_r,w = W_N sin(φ_n) [radial on worm] W_a,w = W_t,g [axial on worm = tangential on gear]
Gear tooth bending: F_t = C_s × d_g^0.8 × F_e × m_n [allowable tangential force] C_s = strength factor for material (bronze: 60-70; hardened steel: 80-90) F_e = effective face width = min(F_actual, 0.67 d_w)
Contact durability: Limited by gear material (bronze wears against hardened steel worm) Bronze: max Hertz stress ~690 MPa (tin bronze), ~825 MPa (aluminum bronze)
Power lost as heat: P_loss = P_input × (1 - η) Heat dissipation (natural convection): P_allowed = k_s × A_housing × (T_oil - T_ambient) [W] k_s ≈ 15 W/m²K (natural), 30 W/m²K (forced) T_oil,max = 120°C (synthetic), 90°C (mineral); T_ambient = 40°C
If P_loss > P_allowed: add cooling fan, oil bath cooling, or external cooler
Worm: hardened alloy steel (case-hardened Rc 58-62) OR through-hardened (Bhn 250-300) Gear: phosphor tin bronze (C90700) for high loads; aluminum bronze (C95400) for corrosion; centrifugal cast for best grain structure
Provide: λ [°], i (velocity ratio), η [%], self-locking check, W_t,w and W_t,g [N], T_output [N·m], thermal rating P_thermal [kW] vs. P_input, center distance a [mm], d_w and d_g [mm].