Ex. 10-1 There are four imbalances in a disk-like rotor Ex.10-1 There are four imbalances in a disk-like rotor. The masses, rotating radii and angular orientations are: m1=8kg, m2=10kg, m3=8kg and m4=7kg, r1=10mm, r2=10mm, r3=15mm and r4=20mm. The rotor is to be balanced by removing a mass mC at a rotating radius of 25mm. Find the magnitude mC and its location angle C.
Ex. 10-1 There are four imbalances in a disk-like rotor Ex.10-1 There are four imbalances in a disk-like rotor. The masses, rotating radii and angular orientations are: m1=8kg, m2=10kg, m3=8kg and m4=7kg, r1=10mm, r2=10mm, r3=15mm and r4=20mm. The rotor is to be balanced by removing a mass mC at a rotating radius of 25mm. Find the magnitude mC and its location angle C.
c=-45135
by removing a mass mC！！
Ex.10-2 Among the following rotors, rotors are statically balanced only, rotors are dynamically balanced.
Ex.10-2 Among the following rotors, rotors a, d are statically balanced only, rotors b, c are dynamically balanced.
Ex. 10-3 On a circular rotating disk, there are two circular holes Ex.10-3 On a circular rotating disk, there are two circular holes. d1=40mm, d2=50mm. The rotating radii of the hole centers is r1=100mm and r2=140mm, respectively. The location of the two holes are shown below. The disk is to be balanced by drilling third hole. The rotating radius of the third hole center is to be r3=150mm. Find the diameter d3 and its location angle 3.
d1=40mm, d2=50mm. r1=100mm and r2=140mm. The rotating radius of the third hole center is to be r3=150mm.
d1=40mm, d2=50mm. r1=100mm and r2=140mm. The rotating radius of the third hole center is to be r3=150mm.
d1=40mm, d2=50mm. r1=100mm and r2=140mm. The rotating radius of the third hole center is to be r3=150mm.
d1=40mm, d2=50mm. r1=100mm and r2=140mm. The rotating radius of the third hole center is to be r3=150mm.
d1=40mm, d2=50mm. r1=100mm and r2=140mm. The rotating radius of the third hole center is to be r3=150mm.
d1=40mm, d2=50mm. r1=100mm and r2=140mm. The rotating radius of the third hole center is to be r3=150mm.
r3=150mm,
Ex. 10-4 m1r1=3kgmm, m2r2=2kgmm, m3r3=5kgmm, and m4r4=4kgmm Ex.10-4 m1r1=3kgmm, m2r2=2kgmm, m3r3=5kgmm, and m4r4=4kgmm. Suppose the system is to be balanced fully by two balancing mass-radius products, Pb1 and Pb3, on the planes I and III, respectively. Determine the amounts and angular locations of the two balancing mass-radius products.
Ex.10-5: m1=10kg, m2=15kg, m3=20kg and m4=10kg, r1=40mm, r2=30mm, r3=20mm and r4=30mm and 1=120, 2=240, 3=300 and 4=30. L12 =L23 =L34. The system is to be balanced dynamically by adding a mass mA on the balancing plane A at a rotating radius rA of 50mm and removing a mass mB on the balancing plane B at a rotating radius rB of 60mm.
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10-4 The disk-like rotor in Fig 10-4 The disk-like rotor in Fig.10-2 has unbalanced masses m1=10kg, m2=21.4kg and m3=36kg at rotating radii r1=100mm, r2=112mm and r3=110mm, and angular orientations 1=30, 2=130 and 3=270. Determine the magnitude mC and the location angle C of the counterweight if it is to be placed at a rotating radius rC of 115mm.
Solution: 247.44, 不是要你求钻孔的位置！
C = ------(10-6) 注意：式（10－6）上下都有负号！
建议用AutoCAD求解！直观。方向容易判断
10-5 Shown in Fig.10-10 is a disk-like rotor on which there are four imbalances. The masses, rotating radii, and angular orientations are: m1=5kg, m2=10kg, m3=8kg and m4=7kg, r1=10mm, r2=10mm, r3=15mm and r4=20mm. The rotor is to be balanced by removing a mass mC at a rotating radius of 25mm. Find the magnitude mC and its location angle C.
Solution:
C = ------(10-6) 注意：式（10－6）上下都有负号！
10-7 An unbalanced mass m is mounted outboard of balancing planes A and B, as shown in Fig.10-11. m=2kg, r=10mm. The rotor is to be balanced dynamically by adding two counterweights mA and mB on the balancing planes A and B, respectively, at a rotating radius of 50mm. L1=100mm, L2=200mm. Determine the amounts (mA and mB) and angular locations of the two counterweights.
MArA=30， MA=30/50=0.6kg MBrB=10, MB=10/50=0.2kg
10-8 Three unbalanced masses m1, m2 and m3 exist on three transverse planes 1, 2 and 3, respectively, as shown in Fig.10-12. Their mass-radius products are: m1r1=2kgmm, m2r2=6kgmm, m3r3=3kgmm, respectively. The locations are as shown. Suppose the system is to be balanced fully by two balancing mass-radius products, Pb1 and Pb3, on the planes 1 and 3, respectively. Determine the amounts and angular locations of the two balancing mass-radius products.
Mass-radius product m2r2 can be replaced dynamically by (m2r2)1 and (m2r2)3 on planes 1 and 3. (m2r2)1=2, (m2r2)3=4
Pb3=1kgmm