Ball screws

i Calculation without errors.

ii Informace o projektu
Project information
? Input section
1.0 Preliminary design. Units selection
1.1 Calculation units
1.2 Calculation of screw revolutions, feed and pitch
1.3 Lead Ph 20.000 [mm]
1.4 Travel speed v 800.00 [mm/s]
1.5 Ball screw rotational speed ns 2400.00 [/min]
1.6 Transmission ratio i=(z2/z1) 0.6250 [~]
1.7 Engine speed ne 1500.00 [/min]
1.8 Preliminary calculation of dynamic load capacity and screw diameter
1.9 Equivalent axial load Fm 1000.0 [N]
1.10 Equivalent rotational speed nm 2400.0 [/min]
1.11 Load factor fw 1.20 [~]
1.12 Desired service life Lh-req 20000 [h]
1.13 Required dynamic load rating (ISO) Ca-req 17073.1 [N]
1.14 Required dynamic load rating (ANSI) Pi-req 15765.6 [N]
1.15 Preliminary design of the ball screw diameter d1-req 20(5) - 50(1) [mm]
1.16 Check values
1.17 Ball Screw mounting (ends)
1.18 Unsupported length of ball screw shaft Ls [mm] 1200.00 < 1280
1.19 Ball screw nominal diameter d1 [mm] 32.0000 > 20 1.32 Table of diameters and leads
1.20 Dn - characteristic speed (d1*ns) Dn 76800 < 110000
1.21 Buckling - permissible axial load on screw Fmax 42400.1 [N]
1.22 Maximum allowable speed nmax 2972.9 [/min]
1.23 Screw and nut friction coefficient f 0.01 [~]
1.24 Efficiency (rotational force / axial force) η 0.9484 [~]
1.25 Torsional moment Mk 3.3564 [Nm]
1.26 Engine power Pw 0.844 [kW]
1.27 Tolerance class (ISO 3408) IT 0 IT 1 IT 3 IT 5 IT 7 IT 10 --- ---
1.28 Tolerance on specified travel ±ep 9 13 24 47 208 840 --- --- [µm]
1.29 Tolerance on travel variation uu 6 9 16 30 52 210 --- --- [µm]
1.30 Tolerances on travel variation u300p 3.5 6 12 23 52 210 --- --- [µm]
1.31 Tolerances on travel variation u2pp 3 4 6 8 --- --- --- --- [µm]
2.0 Material parameters
2.1 Ball srew shaft material
2.2 Modulus of elasticity Es 210000 [MPa]
2.3 Yield strength in tension Rp0.2 350.0 [MPa]
2.4 Poison's Ratio ms 0.300 [~]
2.5 Density ros 7850.0 [kg/m³]
2.6 Linear expansion coefficient α 11.50 [10^-6/°C]
2.7 Ball material
 2.8 Modulus of elasticity Eb 210000 [MPa]
2.9 Poison's Ratio mb 0.300 [~]
2.10 Nut material
2.11 Modulus of elasticity En 210000 [MPa]
2.12 Poison's Ratio mn 0.300 [~]
3.0 Definition of mechanism, load and screw parameters
3.1 Transfer of values from preliminary design [1]
3.2 Definition of accuracy, design, load, life ...
3.3 Tolerance class
3.4 Required reliability
3.5 1. Ball Screw mounting (ends)
3.6 2. Ball Screw mounting (stiffness)
3.7 3. Nut type
3.8 Equivalent axial load, direction 1 Fma1 1374.10 [N]
3.9 Equivalent axial load, direction 2 Fma2 888.30 [N]
3.10 Maximum axial load Fmax 1624.21 [N]
3.11 Equivalent rotational speed, direction 1 nm1 1273.47 [/min]
3.12 Equivalent rotational speed, direction 2 nm2 1273.47 [/min]
3.13 Maximal rotational speed nmax 2400.00 [/min]
3.14 Ball nut preload Fpr [N] 1700.00 [N]
3.15 Load factor fw 1.20 [~]
3.16 Desired service life Lh-req 20000 [h]
3.17 Required dynamic load rating (ISO) Ca-req 20227.5 [N]
3.18 Required dynamic load rating (ANSI) Pi-req 18678.4 [N]
3.19 Selection, definition of ball screw and nut parameters
3.20 Unsupported length of ball screw shaft Ls 1200.00 [mm]
3.21 Unsupported length of ball screw shaft Ls2 600.00 [mm]
3.22 Number of loaded turns (nut) i 3.00 [~]
3.23 Number of unloaded balls in the recirculation system zu 0
3.24 Reduction factor of dynamic load rating Ca exp
3.25 Table of ball screws
3.26 Dimensions of ball screw (d1 x Ph) [mm,N]
3.27 Nominal diameter d1 32.000 [mm]
3.28 Diameter of the inside hole db0 0.000 [mm]
3.29 Ball diameter Dw 5.556 [mm]
3.30 Lead Ph 20.0000 [mm]
3.31 Pitch circle diameter Dpw 33.3890 [mm]
3.32 Lead angle f 10.7949 [°]
3.33 Nominal contact angle α 45.00 [deg]
3.34 Conformity ratio (rn/Dw) frn 0.550 [~]
3.35 Conformity ratio (rs/Dw) frs 0.550 [~]
3.36 Dynamic axial load rating (ISO) Ca 22041.0 [N]
3.37 Static axial load rating C0a 52810.0 [N]
3.38 Ball screw shaft root diameter d2 27.833 [mm]
3.39 Ball nut body diameter D1 56.0 [mm]
400
 400
3.40 Ball nut root diameter D2 38.945 [mm]
3.41 Ball nut internal diameter D3 34.778 [mm] 300

3.42 Preload created by double nut 200

3.43 Ball nut aproximate length Ln 184 [mm] 100

3.44 Aproximate useful travel Lu 1016 [mm] 0
3.45 Listing of important results -200 0 200 400 600 800 1000 1200 1400
-100
3.46 Dn - characteristic speed (d1*ns) Dn 76800 < 110000 [~] -200
3.47 Resulting life with reliability factor Lrhr 25876 > 20000 [h]
-300
3.48 Total Rigidity with the preloaded nut unit R,pr 95 [N/µm]
-400
3.49 Elastic deformation for maximum force and maximum screw length Δmax 17 [µm]
3.50 Tolerances on specified travel (Lu = 1016 [mm]) ±ep 24 [µm]
3.51 Deflection (dead weight load) ymax 0.08481 < 0.36 [mm]
3.52 Safety factor (tension, compression, torsion) SFc 100.72 > 2.00 [~]
3.53 Safety factor (buckling) SFb 52.21 > 3.50 [~]
3.54 Static safety factor SFs 32.51 > 1.4 [~]
3.55 Critical speed ncr 3680 [/min]
3.56 Rate of Permissible operating speed to Critical speed r (nmax/ncr) 0.652 < 0.80 [~]
3.57 Efficiency η 0.951 [~]
? Results section
4.0 Nominal life, modified life (ISO 3408-5)
4.1 Required reliability
4.2 Reliability factor far 1.00 [~]
4.3 Unidirectional external axial load
4.4 Life in revolution L 2388334360 [rev]
4.5 Life in hours Lh 31257.56607 [h]
4.6 Life in path Lm 47766687.2 [m]
4.7 Life in hours with reliability factor Lhr 31257.56607 [h]
4.8 Life in path with reliability factor Lmr 47766687.2 [m]
4.9 Bidirectional external axial load and ball screw with preloaded ball nuts
4.10 Life in revolution L1 2388334360 [rev]
4.11 Life in hours Lh1 31257.56607 [h]
4.12 Life in revolution L2 8840384597 [rev]
4.13 Life in hours Lh2 115699.4223 [h]
4.14 Resulting life in revolution Lr 1977144917 [rev]
4.15 Resulting life in hours Lrh 25876.0829 [h]
4.16 Resulting life in path Lrm 39542898.34 [m]
4.17 Resulting life with reliability factor Lrhr 25876.0829 [h]
4.18 Resulting life in path with reliability factor Lrmr 39542898.34 [m]
5.0 Static axial rigidity. Ball screw, ball nut unit... (ISO 3408-4)
5.1 Static axial rigidity
5.2 Ball Screw mounting (ends)
5.3 Ball Screw mounting (stiffness)
5.4 Unsupported length of ball screw shaft Ls 1200.000 [mm]
5.5 Unsupported length of ball screw shaft Ls2 600.000 [mm]
5.6 Diameter of load application on the ball screw shaft dc 29.460 [mm]
 5.7 Diameter of load application on the ball nut Dc 37.318 [mm]
5.8 Rigidity of ball screw shaft (Rs)
5.9 Rigidity (Rigid mounting at one end) Rs1 119.3 [N/µm]
5.10 Rigidity (Rigid mounting at both ends) Rs2 477.2 [N/µm]
5.11 Rigidity of ball screw shaft for Ls2=Ls/2 Rs2,min 477.2 [N/µm]
5.12 Rigidity of nut body and screw shaft under resulting radial components of load (Rn/s)
5.13 Rigidity of the nut body and screw shaft Rn/s 22005.9 [N/µm]
5.14 Rigidity of nut body and screw shaft under preload Rn/s,pr 44011.8 [N/µm]
5.15 Rigidity of the ball/baltrack area (Rb/t) 5.31 Auxiliary calculations (ISO 3408-4)
5.16 Rigidity of the ball/balltrack area Rb/t 435.8 [N/µm] Ʃros Ʃron cosTaus cosTaun sinTaus sinTaun
5.17 Rigidity of the ball/balltrack area under preload Rb/t,pr 882.2 [N/µm] 0.4407 0.354799 0.851488 0.815531 0.524374 0.578713
5.18 Rigidity of ball nut unit (Rnu) Ys Yn cEs cEn z1 z2
5.19 Rigidity of ball nut unit with backlash Rnu 427.4 [N/µm] 0.952987 0.998521 0.464314 0.464314 19 0
5.20 Rigidity of preloaded ball nut unit Rnu,pr 864.9 [N/µm] FN ck k
5.21 Rigidity of ball nut unit with the correction factor (Rnu*far) 34.71 1.432106 44.533197
5.22 Correction factor for the selected tolerance class far 0.55
5.23 Rigidity of the ball nut unit with the correction factor Rnu,ar 235.0 [N/µm]
5.24 Rigidity of the preloaded ball nut unit with the correction factor Rnu,pr,ar 475.7 [N/µm]
5.25 Total Rigidity of Linear Motion system
5.26 Rigidity of screw bearings RS 10000000.0 [N/µm]
5.27 Rigidity of nut mounting RB 10000000.0 [N/µm]
5.28 Total Rigidity with the nut unit with backlash R 79.1 [N/µm]
5.29 Total Rigidity with the preloaded nut unit R,pr 95.4 [N/µm]
5.30 Elastic deformation for maximum force and maximum screw length Δmax 17 [µm]
6.0 Tolerances, accuracy (ISO 3408-3, ANSI B5.48)
6.1 Tolerance class
6.2 Useful travel Lu 1016.00 ~1016 [mm] (Lu = 1016.00 mm)
6.3 Tolerance on specified travel (±ep) and travel variation (±uup)
Lu [mm] IT0 IT1 IT3 IT5
> <= ±ep [µm] υup [µm] ±ep [µm] υup [µm] ±ep [µm] υup [µm] ±ep [µm] υup [µm]
0 315 4 3.5 6 5 12 8 23 18
315 400 5 3.5 7 5 13 10 25 20
400 500 6 4 8 5 15 10 27 20
500 630 6 4 9 6 16 12 32 23
630 800 7 5 10 7 18 13 36 25
800 1000 8 6 11 8 21 15 40 27
1000 1250 9 6 13 9 24 16 47 30
1250 1600 11 7 15 10 29 18 55 35
1600 2000 - - 18 11 35 21 65 40
2000 2500 - - 22 13 41 24 78 46
2500 3150 - - 26 15 50 29 96 54
3150 4000 - - 32 18 62 35 115 65
4000 5000 - - - - 76 41 140 77
5000 6300 - - - - 90 50 170 93
6300 8000 - - - - 110 60 213 115
8000 10000 - - - - - - 265 140
 10000 12500 - - - - - - 320 170
ISO +JIS +NSK
6.4 Travel deviation and variation
6.5 Tolerance class IT0 IT1 IT3 IT5 IT7 (x) IT10 (x)
6.6 Tolerances on specified travel ±ep [µm] 9 13 24 47 --- ---
6.7 Tolerances on specified travel (x) ±ep [µm] 11.9 20.3 40.6 77.9 176.1 711.2
6.8 Tolerances on travel variation υup [µm] 6 9 16 30 --- ---
6.9 Tolerances on travel variation υ300p [µm] 3.5 6 12 23 52 210
6.10 Tolerances on travel variation υ2πp [µm] 3 4 6 8 --- ---
(x) Only for transport ball screws
X - Travel
6.11 Limiting deviation ΔTpp for the dynamic drag torque Tp0 Y - Preload drag torque
6.12 Dynamic drag torque with preload Tp0 0.6196 [Nm]
4000
6.13 Permissible deviation ±ΔTpp 30 [%]
6.14 Permissible deviation ±ΔTpp 0.1859 [Nm] 3000

2000

1000
6.15 Measurement of preloaded nut axial rigidity: Rnu Graph data
0
6.16 Axial load F1 [N] 850 [N] x-value y-value
-10 -5 0 5 10
6.17 Axial load F2 [N] 3400 [N] -7.147771
-1000 -3400
6.18 Elastic deformation ΔL1 [µm] 3.57 [µm] -1.786943
-2000 -850
6.19 Elastic deformation ΔL2 [µm] 14.30 [µm] 0 0
-3000
6.20 Rigidity in the range +- F1 Rnu1 475.7 [N/µm] 1.786943 850
-4000
6.21 Rigidity in the range +F1 to +F2 and -F1 to - F2 Rnu2 475.7 [N/µm] 7.147771 3400

6.22 Tolerance class and Deviations (ANSI B5.48)

6.23 Tolerance class Class1 Class2 Class3 Class4 Class5 Class6 Class7 Class8
6.24 Maximum permissible lead error (Inch) 0.000472 0.000472 --- 0.001181 0.001181 --- --- --- [inch]
6.25 Maximum permissible lead error (Micrometer) 11 11 --- 28.6 28.6 --- --- --- [µm]
6.26 Maximum rate error (inch / 12inch) --- 0.0002 0.0002 --- 0.0005 0.0005 0.001 0.006 [inch]
6.27 Maximum rate error (µm / 300 mm) --- 5 5 --- 13 13 25 150 [µm]
6.28 Wobble error peak to peak (Inch) 0.0002 0.0002 0.0002 0.0004 0.0004 0.0004 0.0004 0.0015 [inch]
6.29 Wobble error peak to peak (Micrometer) 5 5 5 10 10 10 10 38 [µm]
7.0 Calculation of warming, expansion and compensating force
7.1 Ball screw length Ls 1200.00 [mm]
7.2 Ball screw shaft root diameter d2 27.833 [mm]
7.3 Diameter of the inside hole db0 0.000 [mm]
7.4 Linear expansion coefficient α 11.50 [10^-6/°C]
7.5 Temperature increase Δt 10.0 [°C]
7.6 The thermal elongation of the screw ΔLs 0.138000 [mm]
7.7 Requested screw preload ΔLp 0.138000 [mm]
7.8 The pretensioning force FT 14693.6 [N]
8.0 Check for buckling, tension, compresion, torsion, critical speed, efficiency.....
8.1 Ball screw input parameters
8.2 Ball Screw mounting (ends) Fixed - Supported
8.3 Additional load force (preload, temp. dilatation...) Fadd 0.000 [N]
 8.4 Unsupported length of ball screw shaft Ls 1200.000 [mm]
8.5 Ball screw shaft root diameter d2 27.8330 [mm]
8.6 Ball screw shaft root area A 608.43 [mm^2]
8.7 Quadratic moment of inertia Ix 29458.46 [mm^4]
8.8 Ball screw weight m 5.731 [kg]
8.9 Deflection (dead weight load) ymax 0.08481 < 0.36 [mm]
8.10 Check - tension, compression, torsion
8.11 Sum of loading forces Fmax+Fadd 1624.21 [N]
8.12 Torsional moment (max.) Mk 5.4380 [N/m]
8.13 Tensile stress / Compressive stress Ϭ 2.67 < 350 [MPa]
8.14 Torsional stress τ 1.28 < 210 [MPa]
8.15 Equivalent stress Ϭred 3.48 < 350 [MPa]
8.16 Safety factor (tension, compression, torsion) SFc 100.71793 > 2.00 [~]
8.17 Check - buckling
8.18 Buckling factor Coeffb 2.00 [~]
8.19 Load force Fmax+Fadd 1624.21 [N]
8.20 Limiting slenderness ratio (short / intermediate / long) SRcs/SRc 17.3 108.8 [~]
8.21 Slenderness ratio SR 138.0
8.22 Permissible buckling load Fb 84800.13 [N]
8.23 Safety factor (buckling) SFb 52.21016 > 3.50 [~]
8.24 Check - Critical speed
8.25 Critical speed factor Coeffncr 3.93 [~]
8.26 Permissible operating speed ncrp 2400.0 [/min]
8.27 Critical speed ncr 3680.5 [/min]
8.28 Rate of Permissible operating speed to Critical speed r (ncrp/ncr) 0.65209 < 0.80
8.29 Static safety factor
8.30 Maximum axial load Fmax 1624.21 [N]
8.31 Basic static axial load rating C0a C0a 52810.00 [N]
8.32 Static safety factor SFs 32.51 > 1.4 [~]
8.37 Oil lubrication - efficiency calculation
8.38 Recommended min. oil quantity ov 2.7 [mm³/min]
8.39 Operating temperature T 30.0 [°C]
8.40 Oil type
8.41 Recommended oil viscosity grade (ISO) grade VG46
8.42 Kinematic viscosity of the lubricant at operating temperature 79.8 [cSt]
8.43 Efficiency calculation
8.44 Friction coefficient f 0.00952 0.00952
8.45 Efficiency (normal operation) η 0.9507 [~]
8.46 Efficiency (reverse operation) ηr 0.9484 [~]
? Additions section
9.0 Formulas for calculation: acceleration, forces, moments, revolutions, friction…
1. Cylinder - Moment of inertia; Mass: I = 0.5 * Ro * 3.14 * r⁴ * H; m = 3.14 * Ro * r² * H 8. Screw speed: n = 60 * v / Ph n = 1000 * v / Ph
[I-Moment of inertia; r-Radius; H-High; Ro-Density; m-Weight] [n-Screw speed; v-Velocity; Ph-Lead]
I [kg*m²] r [m] H [m] Ro[kg/m³] m [kg] n [/min] v [mm/s] Ph [mm] n [/min] v [m/min] Ph [mm]
0.003196 0.06 0.02 7850 1.775628 600 10 1 10000 10 1
 2. Acceleration: a = (v2 - v1) / (t2 - t1) 9. Lead: Ph = 60 * v / n Ph = 1000 * v / n
[a-Acceleration; v1-Initial velocity; v2-Final velocity; t1-Start time; t2-End time] [n-Screw speed; v-Velocity; Ph-Lead]
a [m/s²] v1 [m/s] v2 [m/s] t1 [s] t2 [s] Ph [mm] v [mm/s] n [/min] Ph [mm] v [m/min] n [/min]
1.0000 0 1 0 1 1 10 600 100 1 10
3. Acceleration: a = 0.5 * (v2² - v1²) / s 10. Shear friction - force: F = Q * f; FI = atan(f)
[a-Acceleration; v1-Initial velocity; v2-Final velocity; s-Displacement] [F-Force; Q-Normal force; f-Friction coefficient; FI-Angle of friction cone]
a [m/s²] v1 [m/s] v2 [m/s] s [m] F [N] Q [N] f [~] FI [°]
0.5000 0 1 1 100 1000 0.1 5.710593
4. Angular acceleration: a = 0.1047198 * n / t 11. Friction in V-groove - force: F = Q * (f1*cos(B2) + f2*cos(B1))/sin(B1+B2)
[a-Angular acceleration; n-Speed; t-Time] [F-Force; Q-Normal force; f1-Friction coefficient; f2-Friction coefficient; B1-Angle; B2-Angle]
a [rad/s²] n [rpm] t [s] F [N] Q [N] f1 [~] f2 [~] B1 [°] B2 [°]
10.4720 100 1 141.42 1000 0.1 0.1 45 45
5. Force: F = m * a
[F-Force; m-Weight; a-Acceleration]
F [N] m [kg] a [m/s²]
10 1 10
6. Force: F = 0.5 * m * (v2² - v1²) / s
[F-Force; m-Weight; v1-Initial velocity; v2-Final velocity; s-Displacement]
F [N] v1 [m/s] v2 [m/s] m [kg] s [m]
150.0000 10 20 1 1
7. Torque: Mk = 0.10472 * (n2 - n1) * I / t
[Mk-Torque; n1-Initial speed; n2-Final speed; I-Moment of inertia; t-Time]
Mk [Nm] n1 [/min] n2 [/min] I [kg*m²] t [s]
10.47198 10 20 10 1
10.0 Design of the load spectrum table
10.1 Definition of the mechanism
10.2 Lead Ph 20.000 [mm]
10.3 Nominal diameter d1 32.000 [mm]
10.4 Pitch circle diameter Dpw 33.389 [mm]
10.5 Screw shaft full length L 1520.00 [mm]
10.6 Vertical rotation of the mechanism β 0.00
10.7 Mass of moving object (table, workpiece …) m 100.00 [kg]
10.8 Moment of inertia converted from the linear motion to rotation movement
Iw 0.001013212 [kg*m²]
10.9 Inertia moment of Screw Is 0.001228324 [kg*m²]
10.10 Inertia moment of gears on screw side Ia(2) 0.0006 [kg*m²]
10.11 Inertia moment of gears on motor side Ia(1) 0.003 [kg*m²] 3000 1500
10.12 Transmission ratio i=(z2/z1) 0.6250 [~]
10.13 Inertia moment for acceleration torque Iacc 0.010274333 [kg*m²] 2000 1000
10.14 Ball nut preload Fpr 1700.00 [N]
10.15 Preload dynamic drag torque Tpr 0.619627519 [Nm] 1000 500
10.16 Sliding surface friction coefficient (table, workpiece …) f 0.05 [~]
10.17 Frictional force created by the movement of the table, workpiece...
Ffrict 49.050 [N]
0 0
10.18 Force from own weight (table, workpiece...) Fmg 0.000 [N] 0 1 2 3 4 5 6
10.19 Efficiency η 0.97 0.97
-1000 -500
10.20 Torque from the friction (table, workpiece) Tfrict 0.2575 [Nm]
10.21 Torque from the dead weight Tmg 0.0000 [Nm]
-2000 -1000
10.22 Bearing frictional torque Tbr [Nm] 0.0925 0.0925
10.23 Move values to equivalent load table [11.0]
-3000 -1500
10.24 Definition table
nestart neend dt tend nsend α a vstart vend ds s F Facc Fsum Tacc Tsum Power
i [/min] [/min] [s] [s] [/min] [rad/s²] [m/s²] [m/s] [m/s] [mm] [mm] [N] [N] [N] [N/m] [N/m] [kW]
1 0 750 0.1 0.1 1200 785.3982 4 0 0.4 20.00 20.00 400.0 449.1 8.069 9.502 0.373
2 750 750 2.5 2.6 1200 0 0 0.4 0.4 1000.00 1020.00 1000.0 0.0 1049.1 0.000 6.683 0.525
3 750 0 0.1 2.7 0 -785.3982 -4 0.4 0 20.00 1040.00 -400.0 -351.0 -8.069 -6.637 -0.261
4 0 0 0.5 3.2 0 0 0 0 0 0.00 1040.00 0.0 0.0 0.000 0.000 0.000
5 0 -1500 0.2 3.4 -2400 -785.3982 -4 0 -0.8 -80.00 960.00 -400.0 -449.1 -8.069 -9.502 0.746
6 -1500 -1500 1.1 4.5 -2400 0 0 -0.8 -0.8 -880.00 80.00 0.0 -49.1 0.000 -1.432 0.225
7 -1500 0 0.2 4.7 0 785.3982 4 -0.8 0 -80.00 0.00 400.0 351.0 8.069 6.637 -0.521
8 0 0 0.2 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
9 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
10 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
11 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
12 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
13 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
14 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
15 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
16 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
17 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
18 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
19 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
20 0 4.9 0 0 0 0 0 0.00 0.00 0.0 0.0 0.000 0.000 0.000
11.0 Equivalent rotational speed and equivalent axial load (ISO3408-5)
11.1 Transfer of values to paragraph [3.0]
11.2 Number of different load conditions
11.3 Nut type
11.4 Ball nut preload Fpr [N] 1700.00 ~ 750
11.5 Limiting axial load Flim [N] 4808.33
11.6 Operational preload factor fop [~] 0.60

11.7 Table of loads

i F1,2j [N] Fa1j [N] Fa2j [N] nj [/min] q [%] tj [s] Description
1 449.1 1267.2 818.1 600.0 2.0 0.10
2 1049.1 1624.2 575.2 1200.0 51.0 2.50
3 -351.0 860.7 1211.7 600.0 2.0 0.10
4 0.0 1020.0 1020.0 0.0 10.2 0.50
5 -449.1 818.1 1267.2 1200.0 4.1 0.20 1500

6 -49.1 997.1 1046.1 2400.0 22.4 1.10

1000
7 351.0 1211.7 860.7 1200.0 4.1 0.20
8 0.0 1020.0 1020.0 0.0 4.1 0.20 500

9 0 0
0
 0
10 0 0 0 20 40 60 80 100 120
11 0 0 -500
12 0 0
-1000
13 0 0
14 0 0 11.8 Equivalent and maximum speed and load
15 0 0 11.9 Equivalent rotational speed nm1 1273.47 [/min]
16 0 0 11.10 Equivalent rotational speed nm2 1273.47 [/min]
17 0 0 11.11 Maximal rotational speed nmax 2400.0 [/min]
18 0 0 11.12 Equivalent axial load Fma1 1374.1 [N]
19 0 0 11.13 Equivalent actual axial load Fma2 888.3 [N]
20 0 0 11.14 Maximal axial load Fmax 1624.2 [N]
12.0 Calculation of basic and modified static and dynamic load rating (ISO3408-5, ANSI B5.48)
12.1 Transfer of values to paragraph [3.0]
12.2 Input parameters
12.3 Number of loaded turns (nut) i 3.00 [~]
12.4 Number of unloaded balls in the recirculation system zu 0 [~]
12.5 Nominal diameter d1 32.000 [mm]
12.6 Ball diameter Dw 5.5560 [mm]
12.7 Lead Ph 20.000 [mm]
12.8 Pitch circle diameter Dpw 33.389 [mm]
12.9 Lead angle f 10.7949 [deg]
12.10 Nominal contact angle α 45 [deg]
12.11 Conformity ratio (rn/Dw) frn 0.550
12.12 Conformity ratio (rs/Dw) frs 0.550
12.13 Number of effectively loaded balls per turn of thread z1 19 [~]
12.14 Basic static axial load rating C0a
12.15 Characteristic of basic static axial load rating k0 43.21054944 [~]
12.16 Reciprocal curvature radii ro11,ro21 0.359971202 [1/mm]
12.17 Reciprocal curvature radii ro12 -0.327246548 [1/mm]
12.18 Reciprocal curvature radii ro22 0.048004021 [1/mm]
12.19 Basic static axial load rating C0a C0a 52810.5 [N]
12.20 Basic dynamic axial load rating Ca
12.21 Dynamic load rating for the ball screw per single loaded turn Ci 8568.5 [N]
12.22 Exponent for Cs calculation exp 0.86
12.23 Dynamic load rating for the ball screw shaft per single loaded turn Cs 9177.4 [N]
12.24 Dynamic load rating for the ball nut per single loaded turn Cn 13793.3 [N]
12.25 Geometric factor fc 81.12787358 [~]
12.26 Geometric factor f1 7.642977396 [~]
12.27 Geometric factor f2 0.426108899 [~]
12.28 Geometric factor f3 0.665353986 [~]
12.29 Geometric factor gama 0.117664059 [~]
12.30 Ratio Cs/Cn Cs/Cn 0.665353986 [~]
12.31 Basic dynamic axial load rating Ca Ca 22040.9 [N]
12.32 Modified static and dynamic axial load rating C0am, Cam
12.33 Surface hardness AH 654.00 [HV10]
12.34 Hardeness factor for static axial load rating fh0 1.00 [~]
12.35 Correction factor for tolerance grades fac 1.00 [~]
12.36 Modified static axial load rating C0am 52810.5 [N]
12.37 Hardeness factor for dynamic axial load rating fh 1.00 [~]
12.38 Material processing factor fm 1.00 [~]
12.39 Modified dynamic axial load rating Cam 22040.9 [N]
12.40 Basic Load Rating (ANSI B5.48-1977)
12.41 Basic Load Rating (1 000 000 Inches Rated Life) Pi 4935.3 [lbf]
12.42 Basic Static Thrust Capacity (Imperial) Ti 27272.9 [lbf]
12.43 Rated life for X inches LIix 1000000 [in]
12.44 Load Rating at Other Than One Million Inches of Travel Pix 4935.3 [lbf]
12.45 Basic Load Rating (25400 Meters Rated Life) Pm 21956.6 [N]
12.46 Basic Static Thrust Capacity (Metric) Tm 121320.3 [N]
12.47 Rated life for Y meters LImy 25400 [m]
12.48 Load Rating at Other Than 25400 Meters of Travel Pmy 21956.6 [N]
12.49 Recalculation Pi on to Ca Ca' 23773.7 [N]
12.50 Generating ISO and ANSI ball screw tables
12.51 Generating C0am and Cam to ISO table 100% OK
12.52 Generating Pix and Ti to ANSI table 100% OK
13.0 Graphical output, CAD systems
13.1 2D drawing output to:
13.2 2D drawing scale
13.3 Number of threads (screw) on the drawing nts 60 60 [~]
13.4 Number of threads (nut) on the drawing ntn 3 3 [~]
13.5 Ball nut length Ln 184 184 [mm]
13.6 Moving the nut from the left (the number of threads) k 27 27 [~]