Chapter 10 : Balance of Machinery

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1 Chapter 10 : Balance of Machinery
(第10章 机械的平衡)

2 10.1 Purposes and content of machinery balance
(机械平衡的目的和内容) Purposes 大多数机械都是由回转构件和作往复运动的构件所组成，除了中心惯性主轴与回转轴线重合，且作等速回转的构件外，其它所有的构件都要产生惯性力。 如果转速增加至6000rpm,则 F=400N。 由此可知，不平衡所产生的惯性力对机 械的运转有很大的影响。

3 1.Balance of rotors/转子的平衡 (1) 刚性转子(Rigid rotors)的平衡
平衡的目的 研究惯性力的分布及其变化规律，并采取相应的措施对其进行平衡，将惯性力引起的附加动压力加以消除或减小，减轻振动，改善机械工作性能和提高使用寿命。 Contents 1.Balance of rotors/转子的平衡 (1) 刚性转子(Rigid rotors)的平衡 刚性转子:转子的工作转速＜ (0.6～0.7)nc1 nc1---第一阶共振(临界)转速

4 空间力系图 平面力系图 (2)挠性转子(flexible rotors)的平衡 挠性转子:转子的工作转速＞(0.6～0.7)nc1 y 这种转子在高速转动中会发生弯 曲变形,这样的问题较复杂,可以参看 有关专著。

5 2 3’ 3 1 2’ 4 2.Balance of mechanisms/机构的平衡 机构的平衡:主要是讨论对于移动和作
平面复合运动的构件惯性力的平衡问题。 (1)完全平衡 /complete balance C A B D 2 4 3 1 1 2 3 4 2’ 3’ A B D C 1 2 3 4

6 (2)部分平衡/partial balance
K B C A D 1 2 3 4 A B C A B C 1 2 3 4

7 10.2 Balance calculation of rigid rotors
(刚性转子的平衡) Static balance of rigid rotors/刚性转子的静平衡 Rotors whose axial dimensions b are smaller compared to their diameters D (b/D长径比<0.2) are called disk-like rotors. The mass of such rotors are assumed practically to lie in a common transverse plane. b D gears, pulleys/带轮, cams, flywheels, fans, grinding wheels/砂轮, impellers/叶轮

8 mi —mass-radius product/质径积 “Wi”
EXAMPLE: The disk-like rotor in Figure has unbalanced masses m1, m2 and m3 at rotating radii r1, r2 and r3. Determine the magnitude mb and the location angle of the counterweight rb. If the rotor is balancing Solution： centrifugal force → r1 r2 r3 → rb mi —mass-radius product/质径积 “Wi” → ri As shown in Figure, direction adding mb ，or the opposite Direction reduce mb , the latter is in practice. → r2 →rb

9 Condition for the static balance of disk-like rotor/静平衡条件：
The vector sum of all inertia forces or the vector sum of all mass-radius products must be zero. Note: Restricted by actual structure, when b/D＜0.2，adding or reducing mass is not permitted in balance plane, two plane should be considered to make the rotor balance by installing counterweight .

10 Fb′+ Fb″= Fb Fb′l′= Fb″l″ If rb′= rb″=rb EXAMPLE:
single cylinder crankshaft /单缸曲轴 l rb rb″ rb′ l′ l″ T′ T″ Choose two balance planes T′and T〞 Balance conditions: Fb′+ Fb″= Fb Fb′l′= Fb″l″ mb mb′ mb″ Fb Fb′ Fb″ l = l′+ l″ If rb′= rb″=rb

11 10.2.2 Dynamic balance of rigid rotors/
刚性转子的动平衡 Any rotating rotor which is relatively long in the axial direction (b) compared to the radial direction (D) requires dynamic balance, including inertia forces balance and moment balance.

12 EXAMPLE: Three unbalanced masses m1, m2, m3 exist on three transverse planes 1, 2 and 3, and the corresponding radius are r1, r2 , r3 respectively, as shown in Figure. Determine the counterweights in the two balance planes mb1 and mb2? L l3 l2 l1 I → r3 → r2 → r1

13 L 3 1 l3 2 l2 l1 I similarly： r1 r2 r3 For unbalanced plane 3
→ r1 r2 r3 For unbalanced plane 3 For unbalanced plane 1 For unbalanced plane 2 Solution: 3 1 2 similarly：

14 I → For balance plane I: To represent by mass-radius product

15 II → Similarly, for balance plane II:

16 Condition for the dynamic balance ：
The sum of the inertia forces must be zero plus the sum of the moments must also be zero.

17 10.3 Balance test and precision of rigid rotors
(刚性转子的平衡试验和平衡精度) Static balance test/静平衡试验 导轨式静平衡架 圆盘式静平衡架 静平衡架

18 10.3.2 Dynamic balance test/动平衡试验
该动平衡机由机械部分、振动信 号预处理电路和微机三部分组成。

19 10.3.3 Balance precision/平衡精度
许用不平衡量(allowable unbalance)有两种表示方法 1.质径积法:[mr]----相对量(allowable mass-radius product) 2.偏心距法:[e]----绝对量 (allowable offset) 两种表达式的关系

20 目前我国用平衡精度来表示转 子的不平衡量。平衡精度用“A” 表示。

21 转子的平衡等级分别为G4000、G1600、G630、G250、G100、 G40、 G16、G6. 3、G2. 5、G1. 0、G0
转子的平衡等级分别为G4000、G1600、G630、G250、G100、 G40、 G16、G6.3、G2.5、G1.0、G0.4，共11个精度等级。G表示精度等级，其后的数字代表平衡精度A的数值。例如 ，G40表示A=40mm/s。 G16、G6.3为最常用的两种转子平衡精度等级。

22 (1)对于静不平衡转子 许用不平衡 量由A查表算出。 (2)对于动不平衡转子 根据A求出 [e]并根据式[mr]=[e]m求出[mr]后,应 将其分配到两个平衡面，得两平衡基面 的[mr]Ⅰ和[mr]Ⅱ，再平衡转子。

23 EXAMPLE: Shown in fig. is a common mechanical rotor
EXAMPLE: Shown in fig. is a common mechanical rotor. The balance precision is A = 6.3mm/s,mass m=70kg, working rotational speed n=3000r/min, a=40cm and b=60cm. Try to determine the allowable unbalance in two balance plane I and II. I solution： II

24 Unbalanced mass-radius products in two balance planes are：