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Permissible Rotational Speed 513-1E Permissible Rotational Speed [Critical Speed of the Screw Shaft] When the rotational speed reaches a high magnitude, the Ball Screw may resonate and eventually become unable to operate due to the screw shaft’s natural frequency. Therefore, it is necessary to select a model so that it is used below the resonance point (critical speed). Fig.13 on A15-34 shows the relationship between the screw shaft diameter and the critical speed. If determining the critical speed by calculation, it can be obtained from the equation (7) below. Note that in this equation, a safety factor of 0.8 is multiplied to the result. λ 2 3 60 • 1 E 10 • I d1 7 1 λ2 ………（7） N = ℓ 2 0.8 = ••2 10 2π • b γ • A ℓb N1 : Permissible rotational speed determined by the critical speed (min-1) ℓ b : Distance between two mounting surfaces (mm) E : Young’s modulus (2.06×105 N/mm 2) I : Minimum geometrical moment of inertia of the shaft (mm4) π 4 I = d1 d1: screw-shaft thread minor diameter (mm) 64 : Density (specifi c gravity) (7.85×10-6kg/mm3) A : Screw shaft cross-sectional area (mm 2) π 2 A = d1 4 1, 2 : Factor according to the mounting method Fixed - free 1=1.875 2=3.4 Supported - supported 1=3.142 2=9.7 Fixed - supported 1=3.927 2=15.1 Fixed - fi xed 1=4.73 2=21.9 A15-32 513-1E Point of Selection Permissible Rotational Speed [DN Value] The permissible rotational speed of the Ball Screw must be obtained from the critical speed of the screw shaft and the DN value. The permissible rotational speed determined by the DN value is obtained using the equations (8) to (17) below. Permissible rotational speed determined Guideline for Model No. by the DN value maximum rotational N2 speed Model SBK 210000 N2 = ………（8-1） 5000 (SBK3636, SBK4040, and SBK5050) D Large lead Model SBK 160000 (Other than the above model num- N2 = ………（8-2） 4230 D bers and the small size model SBK*) 160000 Models SBN-V (Medium), HBN-V N2 = ………（9-1） 5000 Caged Ball D Models SBN-V (Small), HBN, and Standard 130000 N2 = ………（9-2） 5000 SBKH lead D 120000 N2 = ………（9-3） 1810 Model HBN-K (Large) D Standard lead/ 160000 N2 = ………（10） 5000 Models SDA-V and SDAN-V Large lead D Models SDA-VZ and SDAN-VX 130000 N2 = ………（11-1） 4480 (shaft diameters 28 to 50) Standard lead/ D Models SDA-VZ and SDAN-VX Large lead 100000 N2 = ………（11-2） 5000 Precision (shaft diameters 12 to 25) D 120000 Model WHF N2 = ………（12-1） 5000 Super D lead 70000 Ball Screw Model WGF N2 = ………（12-2） 5000 Full- D Complement Models BLW, BLK, BLR, BNS, 70000 Ball Large lead N2 = ………（13） 5000 BNS-B, BNS-A, and NS D Models BIF-V (Medium), BNFN-V 130000 N2 = ………（14-1） 4950 (Medium), and BNF-V (Medium) D Models BIF-V (Small), BNFN-V Standard 100000 N2 = ………（14-2） 5000 (Small), and BNF-V (Small) lead D Models BIF, DIK, BNFN, DKN, BNF, 70000 N2 = ………（14-3） 5000 BNT, DK, MDK, MBF, BNK, and DIR D Full-Complement Ball Models EPB-V, EBB-V (2806 to 8020) Standard 130000 4480 N2 = ………（14-4） (DIN Standard Compliant) Models EPB-V, EBB-V (1605 to 2512) lead D 5000 70000 Models WTF and CNF Super lead N2 = ………（15） 4440 D 70000 Models BLK and BLR Large lead N2 = ………（16） 4440 Full- D Complement 100000 Rolled Ball Model BTK-V N2 = ………（17-1） 5000 Standard D lead 50000 Models JPF, BNT, and MTF N2 = ………（17-2） 5000 D ‒1 N2 : Permissible rotational speed determined by the DN value (min ) D : Ball center-to-center diameter (indicated in the specifi cation tables of the respective model number) When considering the rotational speed, the permissible rotational speed is regarded as the lower of the following maximum rotational speed guidelines: the critical speed of the screw shaft (N 1) or the permissible rotational speed determined by the DN value (N 2). If the service rotational speed exceeds the guidelines for maximum rotational speed, contact THK. A15-33 513-1E 10000 8000 6000 4000 2000 1000 φ 100 φ 80 800 φ 70 φ 63 φ 55φ 50 600 φ 45φ 40 φ 36 Distance between two mounting surfaces (mm) φ 32φ 30 φ 28φ 25 400 φ 20 φ 18φ 16φ 15 φ 14φ 12 φ 10 φ 8 φ 6 200 Fixed - free 4 6 8 102 2 4 6 8 103 2 Fixed - supported 2 4 6 8 103 2 4 6 8 104 Fixed - fixed 4 6 8 103 2 4 6 8 104 2 Mounting method Rotational speed (min-1) Fig.13 Permissible Rotational Speed Diagram A15-34.
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