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B Friction Torque and Drive Torque


									                                                                                                                                 B-2-7 Friction Torque and Drive Torque
The criterion of the preload to ball screw                                   (5) Axial rigidity of the ball nut and bearing      Operations that use ball screw drives require a                                                            "brakeaway torque." This torque is 2 to 2.5 times
Nut rigidity increases by a larger preload                                       mounting section: KH                            motor torque which is equivalent to the total of                                                           larger than preloaded dynamic (friction) torque
volume. But excessive preload shortens life, and                             The effect of rigidity of mounting section on       two:                                                                                                       which is described below. Starting friction
generates heat. Set the maximum preload about                                positioning accuracy is big, we recommend           • Friction torque, i.e. the friction of the ball screw                                                     torque quickly diminishes once the ball screw
at 0.1 Ca (0.05 for P Preload). Table 6.1 shows the                          incorporating high rigidity of the mounting          itself                                                                                                    begins to move.
criteria for preload for different application.                              sections of ball nut and support bearings into      • Drive torque which is required for operation
                                                                             the design at the early stage of designing the                                                                                                                   (2) D y n a m i c p r e l o a d e d d r a g t o r q u e
               Table 6.1 Criteria of preload                                 machine.                                            B-2-7.1 Friction Torque                                                                                          (preloaded dynamic friction torque)
                                                     Preload (relative to    (a) Torsional rigidity of the feed screw system     (1) Starting friction torque (Break away                                                                   When the ball screw is moving, two types of
       Ball screw application
                                                   dynamic load rating Ca)   Major torsion factors in the rotating system that       torque)                                                                                                torque generate: 1. Dynamic friction torque
 Robots,material handling systems, etc. Axial play or under 0.01 Ca          bring about error in positioning accuracy are       A large torque is necessary to start ball screw.                                                           by preload; 2. Friction torque associated with
Semiconductor manufacturing systems, etc.                                    given three points below.                           This is called "starting friction torque" or                                                               ball recirculation. JIS B1192 sets standard of
                                                    0.01 Ca – 0.04 Ca
  That require highly accurate positioning                                      • Torsional deformation of the screw shaft                                                                                                                  dynamic preloaded torque, which is the total
Medium- high-speed machine tools for cutting        0.03 Ca – 0.07 Ca           • Torsional deformation of the joint section                                                                                                                of these two torque types. They are defined in
                                                                                • Torsional deformation of the motor                                                                                                                        Fig. 7.1.
  Low to medium-speed systems that                                                                                                                                    Nut
                                                     0.07 Ca – 0.1 Ca                                                                                                                                                                       The preload dynamic friction torque is
    require especially high rigidity                                         The value of the effect of torsional strain to                                           Screw shaft
                                                                             positioning accuracy is smaller than axial                                                                                                                     calculated by following formula. When screw
(4) Axial rigidity of support bearing: KB                                    deformation. However, check the effect when                                                                                                                    shaft is rotated as Fig. 7.2 in following measure
Rigidity of the combined thrust angular contact                              designing equipment that requires high                                                                                                                         condition, measuring the nut stop power F and
ball bearings which is widely used as a support                              positioning accuracy.                                                                                                                                          the distance from action line and right angle
bearing of the ball screw for high-precision                                                                                                                                                                                                direction to the measured screw shaft multiple
equipment can be obtained by the following                                   (b) Suppress thermal error                                                                                                                                     by it's power value F .

formula.                                                                     It is necessary to minimize the thermal error for
                                                                                                                                                                                                                                                      Tp = F • L                                                                                                         (2-26)
       3Fa0                                                                  ever increasing demand for positioning accuracy                  F
  KB H      (N/µm)                                                  (2-24)
       δ a0                                                                  give three points below.                                                                                                                                           • Measuring rotational speed 100 min–1
In this formula:                                                                • Suppress heat                                                                                                                                                 • Viscosity of lubrication is prescribed in JIS K
                                                                                • Forced cooling                                                                                                                                                    2001 ISO VG 68
  KB : Rigidity of the combined thrust angular
                                                                                • Avoid effect of temperature rise                                                                                                                              • Without measurement Seal
         contact ball bearings (N/µm)                                                                                                                Load cell
                                                                             Refer to "Measures against thermal expansion"
  Fao : Preload of the bearings (N)
                                                                             on Page B44.
  δ ao : Axial elastic deformation by preload (µm)                                                                                      Fig. 7.2 Preload dynamic torque
                                                                                                                                                 measuring method
                               ⎧         ⎫
                                     2       1/3
                     0.44          Q
          δ a0 H                                   (µm)             (2-25)
                     sin α     ⎩         ⎭

                                                                                                                                                                                                                                                                                                                           Basic torque variation
                                                                                                                                                                                                         Actual torque variation
          Q=            • sin α                                                                                                                          Starting torque   Actual torque                                           (+&Tp a)                Actual torque      (+&Tp0)
                    Z                                                                                                                                                                                                              (–&Tp a)                                  (–&Tp0)

  α : Contact angle
  DW : Ball diameter (mm)

                                                                                                                                                                                                                                                                                       Mean value of actual torque (Tpa)

                                                                                                                                                                                                                                                                                                                                                    Basic torque (Tp0)
  Z : Number of balls                                                                                                                                                                                                                                      Starting torque

Refer to Page B457 for data regarding thrust                                                                                                                                     Direction of rotation                             Direction of rotation

angular contact ball bearings which support
                                                                                                                                                            Effective nut travel distance                                                    Effective nut travel distance
high-precision ball screws (TAC Series).
                                                                                                                                 Fig. 7.1 Definitions of dynamic preloaded drag torque

B65                                                                                                                                                                                                                                                                                                                                                                        B66
                                                                                 B-2-7.2 Drive Torque
(3) Calculation of basic torque                                                  (1) Operating torque of the ball screw                                        (2) Drive torque of the motor
Basic torque of preloaded ball screw Tp0 can be                                  1 Normal drive                                                                1 Drive torque at constant speed                                           2 Drive torque at acceleration
obtained by the following formula.                                               The torque when converting rotational motion                                  Torque which is necessary to drive a ball screw                            Accelerating the ball screw resisting axial
                                                                                 to linear motion (normal operation) is obtained                               at constant speed resisting to external loads can                          load requires maximum torque. Drive torque
         Fa0 • l
Tp0 = K ——–— H0.014Fa0 dm • l                         (N · cm)                   by the following formula.                                                     be obtained by the following formula.                                      necessary for this occasion can be obtained by
                                                              (2-27)                                                                                                                                                                      the following formula.
                                                                                                    Fa • l                                                                                 N1
                                                                                            Ta =              (N · cm)                             (2-28)         T1 = (Ta + Tpmax + Tu) × N                                     (2-30)                     ⋅
 In this formula:                                                                                  2π • η1                                                                                   2                                                T2 = T1 + J • ω                                         (2-31)
                                                                                                                                                                                                                                                            ⎧N ⎫                     + m ⎧ 2π ⎫
                                                                                                                                                               In this formula:
                                                                                                                                                                                                                                                                        [J                  l
                                                                                                                                                                                                                                                                                                  ] (kg · m )
                                                                                                                                                                                                                                                                    2                         2
    Fa0 : Preload (N)                                                            In this formula:                                                                                                                                            J = JM + JG1
                                                                                                                                                                                                                                                                              + JS                           2

    l   : Lead (cm)                                                                          Ta : Normal operation torque (N · cm)                                      Ta : Drive torque at constant speed                                                 ⎩N ⎭2
                                                                                                                                                                                                                                                                                         ⎩ ⎭
    K : Torque coefficient of ball screw                                                     Fa : Axial load (N)                                                                      Fa • l                                                                                                          (2-32)
                                                                                                                                                                                Ta = 2π • η                                      (2-28)
                                                                                             l     : Lead (cm)
                                                                                                                                                                                             1                                            In this formula:
          K = —––—                                                                           η1 : Normal efficiency (η1 = 0.9 – 0.95)                                   Fa : Axial load (N)                                                 T2 : Maximum drive torque at time of
                                                                                 2 Back-drive operation                                                                 The value of Fa in Fig. 7.3 is:                                         acceleration (N · m)
    β : Lead angle (deg.)                                                                                                                                                                                                                   ⋅
                                                                                 The torque when converting linear motion                                               Fa = F + µ • m • g                                                  ω : Motor's angular acceleration (rad/s2)
    dm : Ball pitch circle diameter (cm)
                                                                                 to rotational motion (back-drive operation) is                                         F : Such as cutting force to axial direction (N)                    J : Moment of inertia applied to the motor
Allowable values of torque variation rate relative                                                                                                                                                                                                          2
                                                                                 obtained by the following formula.                                                     µ : Friction coefficient of the guide way                                (kg · m )
to basic torque are regulated as shown in Table
                                                                                                                                                                        m : Volume of the traveling section (table                          JM : Moment of inertia of the motor (kg · m2)
7.1.                                                                                               Fa • l • η2
                                                                                            Tb =               (N · cm)                            (2-29)                       mass plus work mass kg)                                     JG1 : Moment of inertia of Gear 1 (kg · m2)
                                                                                                                                                                        g : Gravitational acceleration (9.80665 m/s )                       JG2 : Moment of inertia of Gear 2 (kg · m2)
                                                                                 In this formula:                                                                                                                                                                                                                B
                                                                                                                                                                        Tpmax : Upper limit of the dynamic friction                         JS : Moment of inertia of the screw shaft
                                                                                             Tb : Reverse operation torque (N · cm)                                                                                                                                                                              68
                                                                                                                                                                                      torque of ball screw (N · cm)                              (kg · m2)
                                                                                             η2 : Reverse efficiency (η2 = 0.9 - 0.95)
                                                                                                                                                                        Tu : Friction torque of the support bearing                       When selecting a motor, it is necessary to
                                                                                 3 Dynamic drag torque of the preloaded ball screw
                                                                                                                                                                                (N · cm)                                                  examine the maximum torque of the motor
                                                                                 Operation torque of preloaded ball screw can be
                                                                                                                                                                        N1 : Number of teeth in Gear 1                                    relative to maximum drive torque T2 at time of
                                                                                 obtained by Formula 2-27.
                                                                                                                                                                        N2 : Number of teeth in Gear 2                                    acceleration of ball screw.
                                                                                                                                                               Generally, though it depends on the type of                                Calculation of the moment of inertia of a
                                                                                                                                                               motor, T1 shall be kept under 30% of the motor                             cylindrical object (ball screw, gear, etc.), please
                                                                                                                                                               rating torque.                                                             refer to below.
              Table 7.1 Range of allowable values of torque variation rates (Source: JIS B 1192)
                                                            Effective length of the screw thread (mm)                                                                                                                                      Formula for the moment of inertia of a
                                                                                                                                                               Support bearing (Tu)                   F          Travel
 Basic torque                                              4000 or under                                               Over 4000 and 10000 or under                Gear 2 (N2)
                                                                                                                                                                                                                                           cylindrical object
   (N · cm)                                    (1)
                        Slenderness ratio : 40 or less                                (1)
                                                                     Slenderness ratio : More than 40 and 60 or less                   —                                                                                                           π•γ
                                                                                                                                                                                                                                              J=       D 4•L (kg · cm2)                             (2-33)
                                 Accuracy grade                                    Accuracy grade                              Accuracy grade                                                                                                      32
 Over      Incl.       C0          C1         C2, 3         C5          C0           C1            C2, 3      C5          C1         C2, 3          C5                                           Ta
                                                                                                                                                                                                              Support bearing (Tu)         In this formula:
   20       40      ±30%         ±35%        ±40%         ±50%        ±40%         ±40%            ±50%      ±60%          —           —            —                                   Gear 1 (N1)           Ball nut (Tpmax)
                                                                                                                                                                                                                                              γ : Material density (kg/cm )

   40       60      ±25%         ±30%        ±35%         ±40%        ±35%         ±35%            ±40%      ±45%          —           —            —                          Motor
                                                                                                                                                                                                                                              D : Diameter of the cylindrical object (cm)
   60      100      ±20%         ±25%        ±30%         ±35%        ±30%         ±30%            ±35%      ±40%          —        ±40%         ±45%
                                                                                                                                                                    Fig. 7.3 Driving mechanism of ball screw                                  L : Length of the cylindrical object (cm)
  100      250      ±15%         ±20%        ±25%         ±30%        ±25%         ±25%            ±30%      ±35%          —        ±35%         ±40%
  250      630      ±10%         ±15%        ±20%         ±25%        ±20%         ±20%            ±25%      ±30%          —        ±30%         ±35%
  630     1000         —         ±15%        ±15%         ±20%           —           —             ±20%      ±25%          —        ±25%         ±30%
Remarks 1. Slenderness ratio: The value obtained by dividing the length of the screw thread section of screw shaft (mm) by diameter of the screw shaft (mm).
        2. NSK independently sets torque standards which are under 20 N • cm.

B67                                                                                                                                                                                                                                                                                                     B68

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