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الكلية كلية الهندسة
القسم الهندسة الميكانيكية
المرحلة 3
أستاذ المادة نوال حسين عبد الامير الرهيمي
05/07/2018 14:18:29
Balancing of Several Masses Rotating in Different Planes
Let us consider four masses m1, m2, m3 and m4 revolving in planes 1, 2, 3 and 4
respectively as shown in Fig. 5(a). The relative angular positions of these masses
are shown in Fig. 5(b). The magnitude of the balancing masses mA and mB in planes A and B may be obtained as discussed below:
1. Take one of the planes, say A as the reference plane (R.P.).
2. Tabulate the data as shown in Table: 2.
3. The couples about the reference plane must balance, i.e. the resultant couple
must be zero.
?_(i=1)^n??m_(i ) r_(i ) l_(i ) cos?_i ?+m_(B ) r_(B ) l_(B ) cos?_B=0
?_(i=1)^n??m_(i ) r_(i ) l_(i ) sin?_i ?+m_(B ) r_(B ) l_(B ) sin?_B=0
4. The forces in the reference plane must balance, i.e. the resultant force must be zero.
?_(i=1)^n??m_(i ) r_(i ) cos?_i ?+m_(B ) r_(B ) cos?_B=0
?_(i=1)^n??m_(i ) r_(i ) sin?_i ?+m_(B ) r_(B ) sin?_B=0
Where n: number of masses
are shown in Fig. 5(b). The magnitude of the balancing masses mA and mB in planes A and B may be obtained as discussed below:
1. Take one of the planes, say A as the reference plane (R.P.).
2. Tabulate the data as shown in Table: 2.
3. The couples about the reference plane must balance, i.e. the resultant couple
must be zero.
?_(i=1)^n??m_(i ) r_(i ) l_(i ) cos?_i ?+m_(B ) r_(B ) l_(B ) cos?_B=0
?_(i=1)^n??m_(i ) r_(i ) l_(i ) sin?_i ?+m_(B ) r_(B ) l_(B ) sin?_B=0
4. The forces in the reference plane must balance, i.e. the resultant force must be zero.
?_(i=1)^n??m_(i ) r_(i ) cos?_i ?+m_(B ) r_(B ) cos?_B=0
?_(i=1)^n??m_(i ) r_(i ) sin?_i ?+m_(B ) r_(B ) sin?_B=0
Where n: number of masses
Graphical Representation
1. Draw moment polygon (assuming that the moment direction is toward the centrifugal force) as shown in Fig .5(c).
2. Draw force polygon as shown in Fig .5(d).
Example: 1
Four masses m1, m2, m3 and m4 are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45°, 75° and 135°.
Find the position and magnitude of the balance mass required, if its radius of
rotation is 0.2 m.
Solution:
Let m = Balancing mass, and
? = The angle which the balancing mass makes with m1.
Analytical method
?H = ?_(i=1)^n??m_(i ) r_(i ) cos?_i ?
?H = 40 cos0 + 45 cos45 + 60 cos120 + 78 cos255 = 21.63 kg.m
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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