326 TECHNICAL INFORMATION 4DSFX 4IBGU .PVOUJOH "SSBOHFNFOUT Representative ball screw mounting arrangements are shown below. 3JHJEJUZ To improve positioning accuracy and control response of a machine, considerations must be given to the rigidity of feed screw elements. Rigidity (K) of feed screw system can be expressed with the following formula. 5FNQFSBUVSF BOE -JGF When ball screws are continuously used at 100°C or higher, or used momentarily at very high temperatures, Basic Dynamic/Static Load Ratings will be reduced according to the temperature rise due to changes in material compositions. However, there will be no effects up to 100°C. Basic Dynamic Load Rating C" and Basic Static Load Rating Co" at 100°C or higher with the temperature factors ft and ft' can be expressed with the following formula. C”=ftC (N) C0”=ft'C0 (N) & For high temperature applications, the current grease should be replaced with the heat resistant type and the current components should be checked for the heat resistant temperature. tScrew Shaft Compressive/Tensile Rigidity : Kℓ The expansion and contraction are expressed in the following formula. The expansion and contraction will directly appear as ball screw backlash. P K= (N/μm) Where: P: Axial Loads Applied on Feed Screw System (daN) : Elastic Deformation of Feed Screw System (μm) Additionally, the following relationship exists between the feed screw system rigidity and other various construction element rigidity. P Kℓ= (N/μm) ℓ Where: P: Axial Load (N) ℓ: Screw Shaft Expansion/Contraction (μm) (1) Fixed-Free Arrangement (2) Fixed-Fixed Arrangement 4Pℓ ℓ= ×103 (μm) Eπd2 4Pℓℓ , ℓ= ×103 (μm) Eπd2L Where: P: Axial Load (N) E: Young's Modulus (2.06x105N/mm2) d: Screw Shaft Root Diameter (mm) ℓ: Load Applicable Span Distance (mm) Where: P: Axial Load(N) E: Young's Modulus (2.06x105N/mm2) d: Screw Shaft Root Diameter (mm) ℓ, ℓ’: Load Applicable Span Distance (mm) L: Mounting Span Distance (mm) The formula produces the max. value when ℓ= ℓ’= Therefore, the max. shaft expansion and contraction will be 1/4 of Fixed-Free arrangement. Where: Kℓ: Screw Shaft Compressive, Tensile Rigidity Kn: Nut Rigidity Kb: Support Bearing Rigidity Kh: Nut and Bearing Mount Rigidity 1 1 1 1 1 = + + + K Kℓ Kn Kb Kh ( ) PL ℓ= ×103 Eπd2 L 2 L ℓ ℓ’ Fixed Fixed ℓ Fixed Free .PVOUJOH .FUIPET "QQMJDBUJPO &YBNQMF · Typical method · Medium~ High Speeds · Medium~High Accuracy For Support Units, Standard Type BRW / BUR is selected. · Medium Speeds · High Accuracy · For Support Units, Standard Type BRW is selected. · Low Speeds · For Short Screw Shafts · Medium Accuracy · For Support Units, Economy Type BRWE is selected Fixed Fixed Fixed Supported Supported Span Distance (Critical Speed: Fixed – Supported ) Load Applicable Span Distance (Buckling Load: Fixed – Fixed) Fixed Fixed Supported Span Distance (Critical Speed: Fixed – Fixed) Load Applicable Span Distance (Buckling Load: Fixed – Fixed) Fixed Fixed Free Supported Span Distance (Critical Speed: Fixed – Free) Load Applicable Span Distance (Buckling Load: Fixed – Fixed) Temperature °C 100 or less 125 150 175 200 225 250 350 ft 1.0 0.95 0.90 0.85 0.75 0.65 0.60 0.50 ft' 1.0 0.93 0.85 0.78 0.65 0.52 0.46 0.35
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