1、1.Balance Purposes13.1 Introduction A rotating shaft or rotor will experience centrifugal forces if its center of mass does not lie exactly on the rotating centerline.The centrifugal force exerted on the frame by moving machine member will be time varying and impart vibratory motion to the frame.Thi
2、s vibration and accompanying noise can produce human discomfort,alter the desired machine performance or may cause failure of the rotor or the support.The purpose of balance is to reduce unbalance to an acceptable level and possibly to eliminate it entirely.(1)Balance of rigid rotors When a rotor is
3、 rotating about its own centerline of rotation at an angular velocity,the deformation of the rotor is small and can be negligible,and it is said to be the rigid rotor,otherwise,it is a flexible rotor.Fig 13-1 shows a rigid rotor at a constant angular velocity.Fig.13-1Centrifugal forces ofthe rotor(转
4、子的惯性力)2.Classification of Balance(2)Balance of flexible rotors When a rotor is rotating about its own centerline of rotation at an angular velocity,the deformation of the rotor can not be negligible,it is said to be a flexible rotor.(3)Balance of linkages The rotating links of a linkage,such as cran
5、k and rockers,can be individually balanced by the rotating balance methods.The coupler is in complex motion and has no fixed pivot,thus its mass center is always in motion,and the inertia force of the link has variable magnitude and sense.We can not attach a mass to the link for balancing it.The glo
6、bal mass center of the linkage normally will change position as the linkage moves.So balance of a linkage is more difficult than balance of rotors.If we can somehow force this global mass center to be stationary in the frame,we will have a state of balance for the overall linkage.1.Static Balance of
7、 Rigid Rotors13.2 Balance Design of Rigid Rotors The unbalanced forces of a rigid rotor are due to the acceleration of masses in the rotor.The requirement for static balance is that the sum of all forces in the rotating rotor must be zero.Fig13-2 shows a rigid rotor rotating with a constant angular
8、velocity of .A number of masses,such as three,are depicted by point masses at different radii in the same transverse plane.Fig.13-2Static balance of rigidrotor(刚性转子的静平衡)2.Dynamic Balance of Rigid Rotors The most general case of distribution of masses on a rigid rotor is that in which the masses lie
9、in various transverse planes as shown in Fig13-3.The rotor revolves with a uniform angular velocity,and m1,m2,m3 are the masses attached to the rotor in planes 1,2,3 respectively and at radii r1,r2,r3.Fig.13-3Dynamic balance of rigid rotors(转子的动平衡)1.Static Balance Test13.3 Balance Test of Rigid Roto
10、rsIf the distance b of a rotor is small,usually b/d 0.2,the inertia moment causing a bending of the shaft can be neglected.Static balance machines are used for rotors of small axial dimensions such as fans,gears,belt wheels and impellers,etc.Fig.13-4 shows a rigid rotor 1 with the shaft laid on the
11、horizontal parallel ways 2.By gravity G,the rotor will roll until the center of the rotor gravity lies on the lowest position.Fig.13-4Static balance test(静平衡实验)2.Dynamic Balance TestFig.13-5Dynamic balance machine in industry(工业动平衡机)1Base(底座)2Power box(动力箱)3Computer system(计算机系统)4Spindle(主轴)5Rotor(转
12、子)6Carriage(支承架)For dynamic balance of a rotor,two balance of counter masses are required to be used in any two correct planes.Dynamic balance is achieved by adding or removing masses in these two planes.This requires a dynamic balance machine.Fig.13-5 shows a common type of dynamic balance machine,
13、which is used in industry.3.Balance PrecisionAfter a rigid rotor has been balanced by using a balance machine,the centerline of mass of the rotor will be coincident with the centerline of rotation of the rotor theoretically,but in practice,they can not be coincident completely.An offset between the
14、centerline of mass and the centerline of rotation of the rotor always exists.To assure the balance precision,the actual unbalance must be less or equal to the allowable unbalance.There are two types of the allowable unbalance.They are allowable mass radius product and allowable offset.The relationsh
15、ip between the mr and the e is as follows:Fig.13-6Distribution of theallowed mass-radius product(许用质径积的分配)13.4 Balance of Planar Mechanisms We have known that all the inertia forces acting on the moving links in a mechanism can be replaced by a single total inertia force and a single total moment of
16、 inertia which act on the frame of the mechanism.If the resultant of all the inertia forces and the resultant of all the inertia couples acting on the frame are zero,there are no shaking forces and shaking couples.The mechanism runs smoothly.We will discover that in most mechanisms,by adding appropr
17、iate balance masses,the shaking forces and the shaking couples can be reduced.The reciprocating unbalance is caused by the inertia forces associated with translating mass.Its effects are very evident in machines such as piston engines and compressors.Balance of reciprocate machines is more difficult
18、 than balance of rotors.Fig.13-7Balance of linkages(机构的平衡)Fig 13-7a shows a slider rank mechanism.The counter mass m22 is mounted at the extension line of the connecting rod,so that the mass center of the rod and the slider is located at the pivot B.The counter mass m11 is mounted at the extension line of the crank,so that the mass center of the crank is located at the pivot A.The total mass center of the mechanism is stationary at the fixed pivot A,and the acceleration of pivot A is zero.Thus the mechanism has been balanced completely.
