Page 1598 - MISUMI SINGAPORE Economy Series

[Technical Data]
Selection of Ball Screws 3

6. Life Span
Ball screw's life is defined as: Total number of rotations, time, or distance where either the ball rolling surfaces or the balls begin to exhibit
repetitive stress caused flaking. Ball screw's life can be calculated based on Basic Dynamic Load Rating with the following formula.
6-1. Life Hours (Lh)
10 6 C 3 Life Calculation Example
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
4400
Impactless Run fw = 1.0 ～ 1.2 Lh＝ 10 6 ( 250×1.2 ) 3 ＝24824(hr)
Normal Run fw = 1.2 ～ 1.5 60×2118
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 defined as: An axial load which a group of same ball screws are
6
subjected and 90% of the specimen will reach 1 million rotations (10 ) without experiencing any
flaking 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 satisfies the set life span hours is
expressed by the following formula.
( 60LhNm ) 1 3
C＝ 10 6 Pmfw(N)

6-2. Axial Load
Axial loads that apply on the screw shafts will vary depending on applicable motion profile 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 coefficient (0.02 or Linear Guides)
W: Load Mass N
g: Gravitational Acceleration 9.8m/s 2
: Acceleration (*) m/s2
(*) Acceleration (α)＝(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 profiles.
Average Axial Load and Average Rotational Speed for Motion Motion Rotational Hours
profiles in Table 1. can be calculated with the formula 2. Profile Axial Load Speed Ratio
A 343N 1500min 29.4％
[Table 1. Motion Profile] (t1＋t2＋t3＝100％ ) B 10N 3000min 41.2％
Motion Axial Rotational Hours Ratio C 324N 1500min 29.4％
Profile Load Speed
A P1N N1min -1 t1％ <Calculations>
B P2N N2min -1 t2％ ① 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
N1t1＋N2t2＋N3t3 ② Average Rotational Speed
Nm＝ (min －1 )
1500M0.294＋3000M0.412＋1500M0.294
t1＋t2＋t3 ( )
0.294＋0.412＋0.294
For machine tool applications, max. load (P1) is applicable for the “Heaviest Nm ＝ ＝ 2118(min －1 )
cutting”. Regular Load (P2) is for the general cutting conditions, and Minimum Therefore, the Average Rotational Speed Nm will be 2118rpm.
1593 Load (P3) is for the non-cutting rapid feeds during positioning moves. 1594