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第五章　机械的效率和自锁

第五章　机械的效率和自锁. Chapter 5 Efficiency and Self-lock in Mechanism. §5-1 The efficiency of mechanism 机械的效率. Main concept ：. Input work ( 输入功 ) ： The work that is produced by the drive force. （ W d ） Output work ( 输出功 ) ：

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第五章　机械的效率和自锁

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  1. 第五章　机械的效率和自锁 Chapter 5 Efficiency and Self-lock in Mechanism

  2. §5-1The efficiency of mechanism 机械的效率 • Main concept： Input work(输入功)： The work that is produced by the drive force.（Wd） Output work(输出功)： The work that is produced by conquering the effective resistance force.（Wr） Lost work(损耗功)： The work that is produced by the conqueringnoneffectiveresistance force.（Wf）

  3. 机械稳定运转时: • Main concept： The efficiency of the mechanism（机械效率）： The degree of utilization of the input work.（η） The ideal mechanism（理想机械）： The mechanism without friction. The ideal drive force（理想驱动力）： The magnitudes of the drive force, not taking friction into account. A group of mechanisms（机组）： It consists of many mechanisms which assemble in certain ways.

  4. The method of denoting the efficiency of mechanism：（表示方法） 1. Using the form of work（功） h = Wr / Wd = 1- Wf / Wd (Wf↗→ h↘) (h = 1——理想机器——永动机) 2.Using the form of power（功率） h = (Wr /t) /(Wd /t) = Nr / Nd = 1- Nf / Nd t ——一个运动循环时间 h = Wr / Wd

  5. vQ F Q vF 3. Using the form of ideal drive force力(矩)表示 设：F——实际驱动力；Q——实际生产阻力；VF、VQ作用点沿力方向线速度。 h = Nr / Nd = QVQ /FVF 设想机器中无有害阻力——理想机器。设F0为对应(克服)同一生产阻力Q时的理想阻力。对于理想机器，有 h0= QVQ /F0VF = 1 即：QVQ = F0VF ∴ h = F0 / F 同理有：h0= Q0VQ /FVF = 1 Q0VQ = FVF ∴ h = Q / Q 0 驱动力的效率表示 生产阻力的效率表示 F0-------ideal drive force F------real drive force Q0-------ideal drive force Q------real drive force

  6. h 实际生产阻力矩 理想驱动力 实际生产阻力 理想驱动力矩 = = h = = 理想生产阻力矩 实际驱动力矩 理想生产阻力 实际驱动力 Similarly, h can also be represented by torque(力矩）： h = MF0/ MF = MQ/ MQ0 生产阻力矩的效率表示 驱动力矩的效率表示 Conclusion:

  7. Working machine Gear bearing Belt transmission motor Application: example：cylinder gear 圆柱齿轮 6~7级 0.98~0.99 8级 0.97 Belt transmission(V-belt) 带传动(v带) 0.96 Rolling-contact bearing 滑动轴承： 0.94(润滑不良) ；0.97(润滑正常) ；0.99(滚体润滑)

  8. The way of the structure in mechanism group(机组) … Nr1 Nr2 Nr3 NrK-1 NrK h1 h2 h3 hK Nd Nd2 Nd3NdK …… Nr2 Nr3 NrK-1 NrK Nr1 = …… Nd1 Nd2 Nd3 NdK-1 NdK NrK h = Nd 1. serial structure串联 h1=Nr1/Nd1、h2=Nr2/Nd2、hK=NrK/NdK =h1h2……hK Conclusion: The efficiency of one mechanism will greatly affect the whole efficiency of the mechanism group.

  9. … Nr1 Nr2 Nr3 NrK-1 NrK h1 h2 h3 hK Nd Nd2 Nd3NdK 1. serial structure串联 h =h1h2……hK 结论：(1) 串联机器(组)的总效率等于组成该机器(组)各机械部分效率的连乘积； (2) h <himin≤hi——总效率小于组成该机器任一机械部分的效率，当某一部分效率太低时，将直接影响到机器总效率； (3) K↗→h↙——用尽可能短的传递路线。

  10. (Nd1h1 + Nd2h2 + …+ NdKhK) Nd ∴h = = (Nd1 + Nd2 + …+ NdK) Nd1 Nd2 Nd3 NdK h1 h2 h3 hK Nr Nr1 Nr2 Nr3 NrK Nd Nr 2. parallel structure并联 Input power： Nd = Nd1 + Nd2 + …+ NdK Output power： Nr = Nr1 + Nr2 + …+ NrK ∵hi= Nri/Ndi and Nr = Nd1h1 + Nd2h2 + …+ NdKhK Conclusion: We should enhance the efficiency of the mechanism which has greater power to improve the efficiency of the whole mechanism group. 在并联机组中，要提高并联机组的效率，应着重提高传递功率大的传动路线的效率。

  11. §5-2 The phenomenon of the self-lock机械的自锁现象 1. The definition of self-lock ：(定义) According to the structure of some mechanisms, a movement will arise along the direction of the drive force when a enough big force applies to the mechanism. But because of the existence of the friction, the mechanism will keep resting whatever the force’s increasing. This phenomenon is called as self-lock. 有些机械，由于其结构的形式以及摩擦影响，导致当沿某一方向施加无论多大的驱动力(矩)时，都无法使它运动的现象，这种现象就叫作机械的自锁。

  12. 2. The meaning of researching the self-lock(意义)： On one hand we should avoid the self-lock to make the expected movement appear. On the other hand some mechanism can not work without self-lock.

  13. P P′ P″ N R R21 j N j P 1 Px F 2 a P Py R21 N P j a Py 1 F Px 2 F 3.The discriminant of the self-lock(自锁条件): tga = Px / Py，tgj = F / N= f ∵ Py = N ∴ Px = (tga/tgj)* F Discussion： (1) a > j 摩擦圆锥 主动力P的作用线在摩擦角j 之外。Px > F，即滑块加速。 (2) a = j P与R共线。Px = F a.原本运动——滑块等速运动； b. 原不动——静止不动；具有运动趋势。

  14. P P a R21 N P a j a Py 1 F Px 2 (3) a < j P作用线在j之内，Px <F。 a.原本运动——减速至静止； b. 原不动——滑块保持静止——不论P力有多大。 • 归纳：由此可见，在a≤j时，tga/tgj≤1。这说明： • 随着P↗→Px↗、Py↗→F↗，而(F-Px)↗，故原静止不动的滑块不会发生运动。 • 无法使受力对象产生运动的现象称为机械的自锁。 • Conclusion: The discriminant of the self-lock is a≤j. • a---transmission angle(传动角）; • j---friction angle（摩擦角） • 平面自锁条件——a≤j；

  15. 4.The discriminant of the self-lock in form of power 机械自锁的效率表示 The reason of self-lock is that the input work done by drive force will never be greater than friction work caused by drive force: Wd ≤ Wf. h = Wr / Wd = 1- Wf / Wd = Nr / Nd = 1- Nf / Nd Conclusion： self-lock: h≤ 0 (机械自锁的效率表示条件) 设计机械时，可以利用上式来判断其是否自锁及出现自锁的条件。当然，因机械自锁时已根本不能作功，故此时，h已没有一般效率的意义，它只表明机械自锁的程度。当h＝0时，机械处于临界自锁状态；若h＜0，则其绝对值越大，表明自锁越可靠。

  16. n θ θ N R21 a v j 1 1 P 2 F 2 a N′ N′ Q n Q 5.self-lock of vee-slot 楔形面自锁条件 与平面摩擦相对应，对于楔形面摩擦可以直接用fv代替f，相应地可以用jv代替j。 结论：自锁条件——a≤jv 6. self-lock of slot斜面自锁条件 1) Sliding up along the slope in constant velocity (等速上升): Balance: P = Q tg (a + j) and：P0 = Q tg a (ideal drive force) efficiency: h= P0 /P = Q tg a / Q tg (a +j) Let, h ≤ 0，so: (a + j) ≥ 90° Self-lock discrimination ： a≥ 90°- j

  17. n R21 α N j F v P 1 n 2 α Q 2) Sliding down along the slope in constant velocity(等速下降): P = Q tg (a-j) (resistance force) and P0 = Q tg a(ideal resistance force) Efficiency: h = P / P0 = Q tg (a-j)/ Q tg a Let,h ≤ 0，so：(a-j) ≤ 0 Self-lock discrimination：a ≤j

  18. Q′ ″ h Q′ Q″ Md Q r ω12 0 r R21 1 2 7. self-lock in shaft neck（轴颈自锁条件） ∵Md=Qh, Mf= R21r =Qr, h = Md / Q ∴ 1. 当h > r 时，构件加速回转。 2. 当h = r时， a.构件原运动，仍等速运动； b.构件原静止，仍保持静止。 3. 当h < r时， a.构件原运动，将减速至静止； b.构件原静止，仍保持静止。 结论：自锁条件为： h ≤ r，即表现为驱动合力与摩擦圆相割或相切。

  19. Q 1 2 m a n j j R23 R42 3 P n a R32 m v 4 R43 j Example: a slot-presser is shown in Fig. Calculate the self-lock discriminant when horizontal force P is released. Solution： The balance equation of link 2 and link 3： Q + R42 +R32 = 0 P + R43 + R23 = 0

  20. Q 1 P 2 (a– j) m (90°+ j) a n j R43 j R23 R23 R42 3 P j n a Q R32 R32 m (α– 2j) v 4 R43 R42 j (90°- j) ∴Q = R32 *sin(a-2j) /cosj P = R23 *cos(a-2j) /cosj That is Q = P *ctg(a-2j) And Q0 = P *ctga (ideal drive force) ∴h=Q0 / Q =tg(a-2j)/tga Result: a≤2j Q + R42 +R32 = 0 P + R43 + R23 = 0 自锁条件

  21. 本章结束

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