Question

In a three-point balancing test without phase the values for the original vibrations are V0=10 mm, and the values of the amplitude of vibration for the three points in the test with a trial mass, mt, of 50 g are:
V1=14 mm at 0 degrees
V2=20 mm at 120 degrees
V3=7 mm at 240 degrees
Apply the mathematical method,

Answer 1

Refer the diagram below:

In the above diagram

V =Vibrational amplitude at the measuring point due to original unbalance of rotor.

V_t =Vibrational amplitude at the measuring point due to a trial mass mounted at any angle on the balancing plane. V_0⁰= Vibrational amplitude at the measuring point due to the original unbalance plus a trial mass mounted at ( 0⁰ ) angle on the balancing plane.

V_120⁰= Vibrational amplitude at the measuring point due to the original unbalance plus a trial mass mounted at ( 120⁰) angle on the balancing plane.

V_240⁰= Vibrational amplitude at the measuring point due to the original unbalance plus a trial mass mounted at ( 240 ⁰) angle on the balancing plane.

= Phase angle due to original unbalance of rotor.

M =Magnitude of balancing mass.

M_trial= trial mass= 50 g

Applying cosine law of triangle to angle O12

Or

-------(1)

Applying cosine law to triangle O13

Or

------(2)

Applying cosine law to triangle O14

Or

----(3)

Adding eqns (1) (2) and (3)

Or

Substracting (2) from (3)

Or

The balancing mass is given by

With

Balancing mass is