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无刷马达/有碳刷马达效能计算
扭力常数: Kt=Kb x 1.345 Kt=1345 / kv 消耗电流: I = [V-(Kb x kRPM)] / Rm I = [V-(RPM / kv)] / Rm 输出扭力: J = (Kt x I) - (Kt x Inl) 每分钟转速: kRPM = (V - RmI) / Kb kRPM = (V - RmI) x kv / 1000 输出功率: Po = (J x RPM) / 1345 消耗功率: Pi = V x I 马达效率: Eff = (Po / Pi) x 100 最高效率电流: Ie max = Sqrt [(V x Inl) / Rm] 符号定义: Eff = 效率 I = 消耗电流值 Iemax=发挥最高效率之电流量 Inl = 无负载量测电流值 J = 扭力 (oz-in) Kb = 电压常数 (Volt / 1000 RPM) Kt = 扭力常数 (oz-In / A) Pi = 消耗功率 (Watts) Po = 机械输出功率 (Watts) Rm = 马达内阻 RPM = 每分钟转速 V = 电压 kv = 电压常数 (RPM / V) 1 oz-In = 72 g-cm = 7.07 mN.m 1 HP = 735.5 W 无刷马达范例: 以MEGA 16/25/3 为例,kt = 1700 rpm , Rm = 0.017 Ohm 计算前需做以下量测 假设以7.2V驱动空转,量得转速为12200rpm,电流为26A,装置8x5桨转速为10900rpm,电流为20A kt = 1345 / kv = 0.7912 oz-In/A I = [V-(RPM / kv)] / Rm = [7.2-(10900 / 1700)] / 0.017 = 46.36 A J = (Kt x I) - (Kt x Inl) = (0.7912 x 46.36) - (0.7912 x 26) = 16.109 oz-In kRPM = (V - RmI) x kv / 1000 = (7.2 - 0.017 x 46.36) x 1700 / 1000 = 10.900 kRPM = 10900 RPM Po = (J x RPM) / 1345 = (16.109 x 10900) / 1345 = 130.55 W Pi = V x I = 7.2 x 20 = 144 W Eff = (Po / Pi) x 100 = ( 130.55 / 144 ) x 100 = 90.66 % Ie max = Sqrt [(V x Inl) / Rm] = Sqrt [(7.2 x 26) / 0.017] = 104.9 A 碳刷马达范例: 以RS-540SH/SF为例,kt = 1458 rpm , Rm = 0.324 Ohm 假设以12V驱动空转,量得转速为17500rpm,电流为0.95A,装置负载转速为15080rpm,电流为5.93A kt = 1345 / kv = 0.9225 oz-In/A I = [V-(RPM / kv)] / Rm = [12-(15080 / 1458)] / 0.324 = 5.1144 A J = (Kt x I) - (Kt x Inl) = (0.9225 x 5.1144) - (0.9225 x 0.95) = 3.84 oz-In kRPM = (V - RmI) x kv / 1000 = (12 - 0.324 x 5.1144) x 1458 / 1000 = 15.080 kRPM = 15080 RPM Po = (J x RPM) / 1345 = (3.84 x 15080) / 1345 = 43.05 W Pi = V x I = 12 x 5.93 = 71.16 W Eff = (Po / Pi) x 100 = ( 43.05 / 71.16 ) x 100 = 60.5 % Ie max = Sqrt [(V x Inl) / Rm] = Sqrt [(12 x 0.95) / 0.324] = 5.93 A |
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