Example of Calculating the Nominal Life
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1 Condition (Horizontal Installation) Assumed model number : KR 5520A LM Guide unit (C = 800N, C 0 = 6900N) Ball Screw unit (C a = 620N, C 0a = 9290N) Bearing unit(fixed Side) (C a = 7600N, P 0a = 990N) Mass : m = 0kg Speed : v = 500mm/s Acceleration : =2.4m/s 2 Stroke : l s = 200mm Gravitational acceleration : g = 9.807m/s 2 Velocity diagram : see Fig. mm/s v m m 9 Thrust center s mm s mm Fig. Velocity Diagram Consideration Studying the LM Guide Unit Load Applied to the Inner Block Assuming that a single inner block is used, convert applied moments M A and M B into applied load by multiplying them by the moment equivalent factor (K A = K B = ). Assuming that a single shaft is used, convert applied moment M C into applied load by multiplying it by the moment equivalent factor (K C = ).
2 During uniform motion: P = mg + K C mg 40 = 627 N During acceleration: P a = P + K A m 9 = 826 N P at = K B m 40 = 249 N During deceleration: P d = P K A m 9 = 572 N P dt = K B m 40 = 249 N Since the groove under a load is different from the assumed groove, give 0 (zero) to P at and P d. Combined Radial And Thrust Load During uniform motion: P E = P = 627 N During acceleration: P ae = P a + P at = 826 N During deceleration: P de = P d + P dt = 249 N C0 C0 fs = = =.9 Pmax PaE Average load Pm = l S fw Pm (PE 095+ PaE 52.5+PdE 52.5) = 790 N C L = ( ) 50 = km f W : Load factor (.2)
3 Studying the Ball Screw Unit Axial load During forward uniform motion: Fa = mg + f = N : Friction coefficient(0.005) f : Rolling resistance of one KR inner block + seal resistance(0.0 N) During forward acceleration: Fa 2 = Fa + m = 8 N During forward deceleration: Fa = Fa m = 6 N During uniform backward motion Fa 4 = Fa = N During backward acceleration: Fa 5 = Fa 4 m = 8 N During backward deceleration: Fa 6 = Fa 4 + m = 6 N Since the groove under a load is different from the assumed groove, give 0 (zero) to Fa, Fa 4 and Fa 5. C0a fs = = =.9 Famax Buckling Load P = C0a Fa2 n π 2 E I 2 l a 0.5 = 000 N P : Buckling load (N) l a : Distance between two mounting surfaces (00 mm) E : Young s modulus ( N/mm 2 ) n : Factor for mounting method (fixed-fixed: 4.0, see A ) 0.5 : Safety factor I : Minimum geometrical moment of inertia of the shaft (mm 4 ) π I = d 4 64 d : Screw-shaft thread minor diameter (7.5 mm)
4 Permissible tensile Compressive Load P2 = δ π 4 d 2 = 500 N P 2 : Permissible tensile compressive load (N) : Permissible tensile compressive stress (47 N/mm 2 ) d : Screw-shaft thread minor diameter (7.5mm) Dangerous Speed 60 λ 2 N = E 0 I 0.8 = 560 min 2 2π l b γ A N : Dangerous speed (min ) l b : Distance between two mounting surfaces (00mm) : Density ( kg/mm ) : Factor according to the mounting method (fi xed-supported.927, see A ) 0.8 : Safety factor DN Value DN=25( 50000) D : Ball center-to-center diameter (20.75mm) N : Maximum working rotation speed (500min ) Average axial load Fam = 2 l S L = Ca ( fw ) Fam (Fa Fa Fa6 52.5) = 26.2 N l = km f W : Load factor (.2) l : Ball Screw lead (20mm)
5 Bearing Unit (Fixed Side) Axial Load (Same as the Ball Screw Unit) Fa = N Fa 2 = 8 N Fa = 0 N Fa 4 = 0 N Fa 5 = 0 N Fa 6 = 6 N P0a P0a fs = = = 48.0 Famax Fa2 Average axial load Fam = 2 l S L = Ca ( fw Fam ) (Fa Fa Fa6 52.5) = 26.2 N 0 6 =.4 0 rev f W : Load factor (.2) Convert the above nominal life into the service life in travel distance of the Ball Screw. L S = L l 0 6 = km Result The table below shows the result of the examination. KR5520A LM guide unit Ball screw unit Bearing unit (Fixed side) Static safety factor Buckling load(n) 000 Permissible tensile compressive load(n) 500 Dangerous speed(min - ) 560 DN Value 25 Nominal life(km) Maximum working rotation speed(min ) 500 Note) From the static safety coefficient and other values above, it is judged that the assumed model can be used. Note2) Of the rated lives of the three components, the shortest value (of LM Guide unit) is considered the nominal life of the assumed model KR 5520A.
6 Condition (Vertical Installation) Assumed model number : KR 5520A LM Guide Unit (C = 800 N, C 0 = 6900N) Ball Screw Unit (C a = 620 N, C 0a = 9290 N) Bearing Unit(Fixed Side) (C a = 7600 N, P 0a = 990 N) Mass : m = 0 kg Speed : v = 500mm/s Acceleration : =2.4 m/s 2 Stroke : l s = 200 mm Gravitational acceleration : g = m/s 2 Velocity diagram see Fig.2 40 m Thrust center m mm/s v s mm s mm Fig.2 Velocity Diagram
7 Consideration Studying the LM Guide Unit Load Applied to the Inner Block Assuming that a single inner block is used, convert applied moments M A and M B into applied load by multiplying them by the moment equivalent factor (K A = K B = ). During uniform motion: P = K A mg 9 = 4900 N P T = K B mg 40 = 06 N During acceleration: P a = P + K A m 9 = 600 N P at =P T + K B m 40 = 264 N During deceleration: P d = P K A m 9 = 70 N P dt = P d K B m 40 = 767 N Combined Radial And Thrust Load During uniform motion: P E = P + P T = 596 N During acceleration: P ae = P a + P at = 764 N During deceleration: P de = P d + P dt = 4468 N C0 C0 fs = = = 8.4 Pmax PaE Average load Pm = l S fw Pm (PE 095+ PaE 52.5+PdE 52.5) = 5947 N C L = ( ) 50 = km f W : Load factor (.2)
8 Studying the Ball Screw Unit Axial Load During upward uniform motion: Fa = mg + f = 04 N f : Sliding resistance per block (0.0 N) During upward acceleration: Fa 2 = Fa + m = 76 N During upward deceleration: Fa = Fa m = 22 N During downward uniform motion: Fa 4 = mg f = 284 N During downward acceleration: Fa 5 = Fa 4 m = 22 N During downward deceleration: Fa 6 = Fa 4 + m = 56 N C0a fs = = = 24.7 Fmax C0a Fa2 Buckling Load Same as Horizontal Installation Permissible Tensile Compressive Load Same as Horizontal Installation Dangerous Speed Same as Horizontal Installation DN Value Same as Horizontal Installation Average axial load Fm = 2 l S (Fa Fa Fa Fa Fa Fa6 52.5) = 296 N L = Ca ( fw ) Fm l = km f W : Load factor (.2) l : Ball Screw lead (20mm)
9 Bearing Unit (Fixed Side) Axial Load (Same as the Ball Screw Unit) Fa = 04 N Fa 2 = 76 N Fa = 22 N Fa 4 = 284 N Fa 5 = 22 N Fa 6 = 56 N P0a P0a fs = = = 0.6 Fmax Fa2 Average axial load Fm = 2 l S (Fa Fa Fa Fa Fa Fa6 52.5) = 296 N L = Ca ( fw Fm ) 0 6 = rev f W : Load factor (.2) Convert the above nominal life into the service life in travel distance of the Ball Screw. L S = L l 0 6 = km Result The table below shows the result of the examination. KR5520A LM guide unit Ball screw unit Bearing unit (Fixed side) Static safety factor Buckling load(n) 000 Permissible tensile compressive load(n) 500 Dangerous speed(min - ) 560 DN Value 25 Nominal life(km) Maximum working rotation speed(min - ) 500 Note) From the static safety coeffi cient and other values above, it is judged that the assumed model can be used. Note2) Of the rated lives of the three components, the shortest value (of LM Guide unit) is considered the nominal life of the assumed model KR 5520A.
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