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INTRODUCTION


             Balancing Elements


                  Balancing Definitions                             Balancing Coolent Chucks
                 Introduction                                                                                            TOOLING SYSTEMS
                 Balancing is the process of equalizing the mass                                m
                 distribution of a body so it rotates on its bearing
                 without unbalanced centrifugal forces.
                 Balancing causes reduced vibration, lower
                 spindle strain and improved machining qualities,                         r
                 which allows for higher cutting parameters.
                 The measuring equipment available today enables
                 unbalance to be reduced to low limits. However, it would
                 be uneconomical to exaggerate the quality requirements.   Example 1
                 It has therefore become necessary to determine to what   U=2 g x mm can be treated as an unbalance mass
                 extent the unbalance should be reduced and where   of m=2 g in radial distance of r=1 mm or as a mass
                 the optimum economic and technical compromise     of m=0.1 g in radial distance of r=20 mm, etc.
                 on balance quality requirements would be struck.
                                                                   Example 2
                 Definition                                        The residual unbalance is independent of the speed.
                                                                   This value reflects the unbalanced mass and its
                 G - Balance quality (mm/s)                        distance from the true center of mass. The residual
                 e  - Specific unbalance (gxmm/Kg)                 unbalance value is measured on balancing machines.
                 Ω - Speed (rad/s)
                                                                                   U
                 N  - Speed (rpm)                                  U = m ∙ r = >m =   =    4    = 0.2g
                 M - Mass of the body (kg)                                         r      20
                  m - Mass of the unbalance (g)                    G value reflects the balancing quality of a
                  r  - Radius of the unbalance (mm)                toolholder according to its rotational speed (N)
                  U  - Residual unbalance (gxmm)
                       U
                  e =   M    = > U = M ∙ e                         G = Ω ∙ e =   π ∙ N     ∙   U     =   U ∙ N ∙ π

                                                                                             M ∙ 30
                                                                                      M

                                                                                 30
                  Ω =   2πN    =   πN                              e =   G ∙ 30
                           60

                                                                           π ∙ N
                                 30
                 Operation                                         Example 3
                 Residual unbalance equals the tool’s mass (M)     G value reflects the balancing quality of a toolholder
                 times its eccentricity (e). Eccentricity measures the   according to its rotational speed (N).
                 extent to which the tool’s weight is off-center.
                                                                                    π
                                                                       π
                                                                               U
                 It is defined as the distance from the tool’s center of the   G =   ∙ N ∙   =   ∙ 15, 000 ∙     8        ≈ 6.3 (mm/s)

                                                                       30

                                                                               M

                                                                                                    000
                                                                                              2,
                                                                                   30
                 rotation to its true center of mass.
                 If eccentricity is measured in microns and tool
                                                                                8
                 mass is measured in kilograms, this unit yields   e =   U   = e =   = 4 (g ∙ mm/kg)
                 residual unbalance in gram-millimeters.               M        2
                 Any two sets of mass and eccentricity that yield the   The G value will change to G=2.5 mm/s when using the
                 same unbalance value will have the same effect on   same toolholder at a rotational speed
                 the tools, so long as the residual unbalance is in the   N=6, 000 rpm and to G=1.0 mm/s at
                 same plane perpendicular to the rotation axis.    N=2, 500 rpm.
                                                                   Balance quality grades for various
                 U = r ∙ m                                         groups of representative rotors:
                                                                 •  General machine tool parts - G6.3
                 The residual unbalance is independent of the speed.   •  General toolholders and machine drivers - G2.5
                 This value reflects the unbalance mass and its distance   •  Grinding machine drivers - G1.0
                 from the true center of mass. The residual unbalance   •  Spindles of precision grinders - G0.4
                 value is measured on balancing machines.

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