328 TECHNICAL INFORMATION 12. Example of Selection of Ball Screws (in case of X-axis) Condition of Use t8PSL 5BCMF .BTT t.BYJNVN 4USPLFT t5ISFBEJOH 4QFFE t"DDFMFSBUJPO $POTUBOU t1PTJUJPOJOH 1SFDJTJPO t3FQFBU "DDVSBDZ t-JGF 4QBO tLinear Motion Guide Friction Coefficient t%SJWJOH .PUPS t%VUZ $ZDMF .PEFM %JBHSBN W=40(kg) Smax.=720 (mm) Vmax.=1000 (mm/s) t=0.15(s) ±0.1/720(mm) ±0.01(mm) Lh=30000Hours μ=0.02 Nmax.=3000 (min−1) 0.15 0.09 0.15 0.51 0.15 0.57 0.15 0.53 0.9 0.9×3=2.7 1.4 720mm 1000mm/s V mm/s s 4.1 (1Cycle) 240mm(Stroke) Workpiece Table Couplings Drive motor Distance between Load Acting Points (Buckling Load:Fixed-Fixed) ℓ1 Distance of Supports (Critical Speed:Fixed-Support) ℓ2 1. Setting Lead (L) Set lead based on maximum motor revolutions and threading speed. Use the following formula. Vmax×60 1000×60 L = = 20(mm) Nmax 3000 Required lead is 20mm or higher. 2. Nut selection (1) Calculating Axial Load The axial load calculation formula on Clause 6-2, P.325 is used to calculate the axial loads for each segment of a motion profile. · At Constant Speed Axial Load (Pb) =μWg=0.02×40×9.8≈8 (N) · In Acceleration Acceleration( ) = (Vmax/t)×10-3 = (1000/0.15)×10-3=6.67 (m/s2) Axial Load (Pa) =W +μWg=40×6.67+0.02×40×9.3≈274 (N) · In Deceleration Axial Load (Pc) W -μWg=40×6.67-0.02×40×9.8≈260 (N) (2) Actual moving time during each segment in a motion profile Below derived from Duty Cycle Model Diagram. (3) Summary of Axial Loads, Rotational Speeds, and Operation Time for Each Motion Profile (7) Tentative Ball Screw Selection A ball screw to satisfy the requirements of Lead 20 and Basic Dynamic Load Rating of 2970N, BSS1520 is tentatively selected. (6) Calculation of the required basic dynamic load rating (1) Calculating Continuous Operational Life (Lho) A Continuous Operational Life which is derived by subtracting Resting time from Desired Life while a motion profile of 4.01s with a moving time of 2.04s can be calculated as follows. 2.04 Lho=Desired Life (Lh)× =14927 (Hours) 4.1 (2) Calculating Required Basic Dynamic Load Rating The formula on Clause 6-1., P.325 is used to calculate the basic dynamic load rating required to retain the net operational life of ball screw. 60LhoNm 60×14927×2118 C= ×Pm×fw= ×200×1.2=2970 (N) 106 106 (5) Calculating the mean turns N1t1+N2t2+N3t3 Mean Turns (Nm)= =2118(min−1) t1+t2+t3 (4) Calculating the Average Axial Load with a formula in P.325, 6-3. P13N1t1+P23N2t2+P33N3t3 Mean Axial Load(Pm)= =200(N) N1t1+N2t2+N3t3 Operating Pattern In Acceleration At Constant Speed In Deceleration Total Operating Time Operating Time 0.60 0.84 0.60 2.04 Operating Pattern In Acceleration At Constant Speed In Deceleration Axial Load 274N 8N 260N Rotational Speed 1500min−1 3000min−1 1500min−1 Operating Time Ratio 29.4% 41.2% 29.4% 3. Accuracy Evaluation (1) Evaluating Accuracy Grades and Axial Clearances By referencing the “Ball Screw Lead Accuracy” table on Section 2., P.321, it is found that the Accuracy Grade C5 with ±ep0.040 / 800~1000m of actual mean travel error satisfies the positioning accuracy: ±0.1/720mm and therefore, that BSS1520 is fully applicable. Additionally, the Precision Screws axial clearance table on P.322 shows that axial clearance of BSS1520 is 0.005 or less. The required positioning repeatability is ±0.01mm, and it can be confirmed that BSS1520 satisfies the requirement. 4. Screw Shaft Selection (1) Determining the Overall Length Screw Shaft O.A.L. (L)= Max. Stroke+Nut Length+Margin+Shaft End Terminations (both sides). Therefore, Max Stroke: 720mm Nut Length: 62mm Margin: Lead×1.5=60mm Shaft End Termination Dims.: 72 Screw Shaft O.A.L. (L)=720+62+60+72=914 (mm) * The Margin is provided as a countermeasure against overruns, and the amount is typically set as 1.5~2 times as much as the screw lead. Lead 20×1.5×2(Both Ends)=60(mm) (2) Evaluating the Allowable Axial Load Load Applicable Span Distance l1 is 820mm, and the Axial Load can be obtained by the formula on P.323, "4. Allowable Axial Load" as indicated below. d4 12.54 P=m 104=10× ×104=3660 (N) ℓ2 8202 The above formula produces an Axial Load value of 343N which is well within the Allowable Max. Axial Load 3660N, and suitability is confirmed. (3) Evaluating the Allowable Max. Rotational Speed Shaft supported span is 790mm, and the Critical Speed Nc value is calculated as follows by using the formula on "5-1. Critical Speed" in P.324: d 12.5 Nc=g 107=15.1× ×107=3024 (min−1) ℓ2 7902 The max. speed requirement of 3000rpm is within the Critical Speed of 3024min-1, and the suitability is confirmed. Additionally, the DmN value can be calculated by using the formula in P.324, "5-2. DmN Value" as: DmN=(Shaft O.D.+A value)×Max Rotational Speed=15.8×3000=47400≤70000 and the suitability is confirmed. 5. Selection Result From the above, it is determined that a suitable ball screw model is BSS1520-914.
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