转贴： 直流无刷/碳刷马达各项计算公式

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原帖： http://www.rcfans.com/bbs/forum.php?mod=viewthread&tid=105381&extra=page=1

直流无刷/碳刷马达各项计算公式

你知道你的直流马达输出多少马力吗?
為什麼马达会过热?是否扭力不足?
以下计算可以让你更了解你的马达.
只要你有转速表,电压表,电流表,就可以知道你的马达是否在最佳状态下工作.

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)
每分鐘转速: 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 = 每分鐘转速
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 為例,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,量得转速為12200rpm,电流為26A,装置8x5桨转速為10900rpm,电流為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為例,kt = 1458 rpm , Rm = 0.324 Ohm
假设以12V驱动空转,量得转速為17500rpm,电流為0.95A,装置负载转速為15080rpm,电流為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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