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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 B 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 . 66 L 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 DW Fa0 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 2π (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 1 + JS 2 l : Lead (cm) Ta : Normal operation torque (N · cm) Ta : Drive torque at constant speed ⎩N ⎭2 G2 ⎩ ⎭ 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: 0.05 K = —––— η1 : Normal efficiency (η1 = 0.9 – 0.95) Fa : Axial load (N) T2 : Maximum drive torque at time of tanβ 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) 2π 2 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 m (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 T1 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 ) 3 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