324 TECHNICAL INFORMATION 10 1.5 2 3 4 5678910 1.5 2 3 4 5 6 7 2 3 4 5 6 8 2 3 8 6 5 4 3 2 1.5 10 1.5 2 3 4 5 6 8 3 102 104 102 2 3 4 5 6 8 8 6 5 4 3 2 1.5 10 1.5 2 3 3 10 8 1.5 Method of Screw Support Thread outer diameter(mm) Distance of Supports (mm) Fixed-Free Fixed-Fixed Fixed-Support Support -Support Allowable Rotational Speed (rpm) Ø10 Ø15 Ø20 Ø25 Ø32 102 5 6 8 8 6 5 4 3 2 1.5 10 1.5 2 3 4 5 6 8 3 104 1.5 2 102 3 4 5 6 8 8 6 5 4 3 2 1.5 10 1.5 2 3 4 5 6 8 3 104 1.5 "MMPXBCMF 3PUBUJPOBM 4QFFE Ball screw rotational speed is determined by required feed speed and the given screw lead, and needs to be less than the Allowable Maximum Rotational Speed. Ball screw rotational speed is evaluated based on the shaft's critical speed and ball recirculation speed limitation DmN value. $SJUJDBM 4QFFE Allowable rotational speed is defined as a speed 80% or less of the Critical Speed where the rotational speed coincides with a natural resonant frequency of the screw shaft. The Allowable Rotational Speed can be obtained by the following formula. Additionally, approximate Allowable Rotational Speeds can be obtained from Table 2. Allowable Maximum Rotational Speed Graph. 60 2 EI×103 d Nc=fa = g 107 (min−1) 2πℓ2 ℓ2 Where: ℓ: Distance of Supports (mm) fa: Safety Factor (0.8) E: Young's Modulus (2.06×105N/mm2) I: Min. Geometrical Moment of Inertia of Across Root Thread Area (mm4) π I= d4 64 d: Thread Root Diameter (mm) : Specific Gravity (7.8×10–6kg/mm3) A: Root Thread Section Area (mm2) π A= d2 4 g, : Coefficient Determined by Method of Screw Support t"MMPXBCMF 3PUBUJPOBM 4QFFE SQN Method of Screw Support g Support - Support 9.7 π Fixed - Support 15.1 3.927 Fixed - Fixed 21.9 4.73 Fixed- Free 3.4 1.875 "MMPXBCMF 3PUBUJPOBM 4QFFE $BMDVMBUJPO &YBNQMF Find the Allowable Maximum Rotational Speed for Fig.2 <How to use> · Thread shaft diameter ø15, Lead 5 · Mounting method Fixed - Support · Distance between Points of Buckling Load ℓ1 790mm <Calculations> g=15.1 since the mounting method is Fixed-Supported, the Allowable Rotational Speed (Nc) is, d 12.5 Nc= g 107(rpm) = 15.1 × × 107(rpm) = 3024(rpm) l2 7902 Therefore, the rotational speed will need to be 3024rpm or less. 5BCMF Distance of Supports (Critical speed : Fixed-Support) ℓ2 t'JHVSF "MMPXBCMF 3PUBUJPOBM 4QFFE (SBQI t"MMPXBCMF 3PUBUJPOBM 4QFFE NJO−1 "MMPXBCMF 3PUBUJPOBM 4QFFE $BMDVMBUJPO &YBNQMF <Requirements> · Thread outer diameter 20 · Distance of Supports 1500mm · Mounting method Fixed - Support <Calculations> (1) From Table 2., find an intersection of a vertical line from Supported Span Distance 1500mm and Screw Shaft O.D. Ø20 line. (2) The value 1076rpm on the Fixed-Supported scale (Y-Axis) that corresponds to the intersection of (1) above is the Allowable Maximum Speed. 4DSFX 4IBGU %JB $BMDVMBUJPO &YBNQMF <Requirements> · Distance of Supports 2000mm · Maximum Rotational Speed 1000rpm · the max. axial load Fixed - Fixed <Calculations> (1) From Table 2., find a intersection of a vertical line from Supported Span Distance 2000mm and a horizontal line from Fixed-Fixed max. speed scale (Y-Axis) at 1000rpm. (2) A line that reaches down to the intersection in (1) is the Ø25 ball screw that satisfies the required speed of 1000rpm. %N/ 7BMVF The DmN value represents a ball recirculation (orbit) speed limit within a ball nut. If this vale is exceeded, the recirculation components will be damaged. The DmN value can be calculated with the following formula. DmN≤70000 (Precision Ball Screws) DmN≤50000 (Rolled Ball Screws) Where: Dm: Thread outer diameter (mm)+A Value N: Maximum Rotational Speed (min−1) Ball Dia. A Value 1.5875 2.3812 3.175 4.7625 6.35 0.3 0.6 0.8 1.0 1.8
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