Page 992 - MiSUMi FA Mechanical Components Economy Series

[Technical Data]
Selection of Ball Screws 3

6. Life Span
Ball screw's life is defi ned as: Total number of rotations, time, or distance where either the ball rolling surfaces or the balls begin to exhibit
repetitive stress caused fl aking. Ball screw's life can be calculated based on Basic Dynamic Load Rating with the following formula.
6-1. Life Hours (Lh)
Life Calculation Example
10 6 C 3
Lh ) (hrs) <Requirements>
60Nm ( Pmfw · Ball Screw Model BSS1520(Ø15 Lead 5(Thread Pitch 20))
Where: · Mean Axial Load Pm 250N
Lh: Life Span Hours (hrs) · Mean Rotational Speed Nm 2118(min 1 )
C: Basic Dynamic Load Rating (N) · Work Factor fw 1.2
Pm: Mean Axial Load (N) <Calculations>
Nm: Mean Rotational Speed (rpm) Since Basic Dynamic Load Rating C for BSS1520 is 4400N,
fw: Work Factor
Impactless Run fw = 1.0 ։ 1.2 Lh 10 6 4400 ) 3 24824(hr)
Normal Run fw = 1.2 ։ 1.5 60–2118 ( 250–1.2
Run with Impact fw = 1.5 ։ 2.0 Therefore, Life will be 24824 hours.

•Basic Dynamic Load Rating : C
Basic Dynamic Load Rating (C) is defi ned as: An axial load which a group of same ball screws are
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subjected and 90% of the specimen will reach 1 million rotations (10 ) without experiencing any
fl aking of the rolling surfaces. See product catalog pages for the Basic Dynamic Load Ratings.
* Setting life span hours longer than what is actually necessary not
only requires a larger ball screw, but also increases the price.
In general, the following standards are used for life span hours:
Machine Tools: 20,000hrs Automatic Control Equipment: 15,000hrs
Industrial Machinery: 10,000hrs Measuring Instruments: 15,000hrs
* The basic dynamic load rating that satisfi es the set life span hours is
expressed by the following formula.
( 60LhNm ) 1 3 Pmfw(N)
C 10 6

6-2. Axial Load
Axial loads that apply on the screw shafts will vary depending on applicable motion profi le such
as acceleration, constant velocity, and deceleration phases. Following formula can be used.
-Axial Load Formula-
Constant Velocity· · ·Axial Load (Pb)=μWg
Acceleration· · · · · · ·Axial Load (Pa)=W +μWg
Deceleration· · · · · · Axial Load (Pc)=W -μWg
* Omit the "O" for vertical applications.
O: Linear bearing friction coeffi cient (0.02 or Linear Guides)
W: Load Mass N
g: Gravitational Acceleration 9.8m/s 2
: Acceleration (*) m/s2
(*) Acceleration (ē)(Vmax/t)–10 3
Vmax: Rapid Feed Rate mm/s
t: Acceleration/Deceleration Time s
6-3. Formulas for Average Axial Load and Average Rotational Speed Average Axial Load and Average Rotational Seed Calculation Example
Average Axial Load and Average Rotational Speed are calculated <Requirements>
based on proportions of motion profi les.
Average Axial Load and Average Rotational Speed for Motion Motion Axial Load Rotational Hours
profi les in Table 1. can be calculated with the formula 2. Profi le Speed Ratio
A 343N 1500min 29.4
[Table 1. Motion Profi le] (t1t2t3100 )
B 10N 3000min 41.2
Motion Axial Rotational Hours Ratio C 324N 1500min 29.4
Profi le Load Speed
A P1N N1min -1 t1 <Calculations>
B P2N N2min -1 t2 ΍ Average Axial Load
C P3N N3min -1 t3 343 3 M1500M0.29410 3 M3000M0.412324 3 1
M1500M0.294 3
Pm   250(N)
[Formula 2. Average Axial Load Calculation] ( )
1500M0.2943000M0.4121500M0.294
3
3
( )
3
P1 N1t1P2 N2t2P3 N3t3 3 1
Pm (N) Therefore, the Average Axial Load Pm will be 250N.
N1t1N2t2N3t3
Ύ Average Rotational Speed
N1t1N2t2N3t3
Nm (min 1 )
1500M0.2943000M0.4121500M0.294
t1t2t3 ( )
Nm   2118(min 1 )
For machine tool applications, max. load (P1) is applicable for the “Heaviest 0.2940.4120.294
cutting”. Regular Load (P2) is for the general cutting conditions, and Minimum Therefore, the Average Rotational Speed Nm will be 2118rpm.
Load (P3) is for the non-cutting rapid feeds during positioning moves.
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