Linear Motion. Optimized.

Engineering Guidelines for Ball and Lead Screws

Critical Speed Limits Chart for Lead Screws and Rolled Ball Screws
Every screw shaft has a rotational speed limit. That is the point at which the rotational speed sets up excessive
vibration. This critical point is modified by the type of end bearing support used.
To use this chart, determine the required rpm and the maximum length between bearing supports. Next, select one
of the four types of end support shown below. The critical speed limit can be found by locating the point at which
rpm (horizontal lines) intersects with the unsupported screw length (vertical lines) as modified by the type of supports
selected below. We recommend operating at no more than 80% of the critical speed limit to allow for misalignment
and/or lack of screw straightness. If speed falls into dotted line, consult factory.
Warning: Curves for the screw diameters shown are based on the smallest root (minor) diameter of the standard screws within the
nominal size range and truncated at the maximum ball nut rotational speed. DO NOT EXCEED this rpm regardless of screw length.

3,000

2,000

1,500

1,000
900
800
ROTATIONAL SPEED (RPM)

700
600

500
1/
4
400

5/
16
300
4
3/
8 7/
16
3
1/
2
200
5/
8
2 1/2
3/
4
2
1
1 1/4 1 1/2

100
MAXIMUM LENGTH (INCHES) BETWEEN BEARINGS
Fixed-Free
Inches 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 120 126
A mm 152 304 457 609 762 914 1056 1219 1371 1524 1676 1828 1981 2133 2286 2438 2590 2743 3048 3200

Simple-Simple
Inches 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
B mm 254 508 762 1016 1270 1524 1778 2032 2286 2540 2794 3048 3302 3556 3810 4064 4318 4572 4826 5080

Fixed-Simple
Inches 12 24 36 48 61 73 85 97 109 121 133 145 158 170 182 194 206 218 230 242
C mm 304 609 914 1219 1549 1854 2159 2463 2768 3073 3378 3683 4013 4318 4622 4927 5232 5537 5842 6146

Fixed-Fixed
Inches 15 30 45 60 75 90 105 119 134 149 164 179 194 209 224 239 254 269 284 298
D mm 381 762 1143 1524 1905 2286 2667 3022 3403 3784 4165 4546 4927 5308 5689 6070 6451 6832 7213 7569

84 www.thomsonbsa.com
 Lead and Ball Screws

Load Life Relationship

Column Loading Capacities
For Ball Screws
Ball screws are rated for 1,000,000 inches of travel at the rated dynamic load. This is the load at which 90% of a group of
identical ball screws will run without flaking for their lifetime. However, they will travel farther than this at lower limits.
These load-life relationships are analogous to the B10 rating common in the ball bearing industry. The relationship of
load to life is an inverse cube relation. For example, reducing the load by 1/2 increases life eight times. Doubling the
load decreases life by 1/8. Every attempt should be made to design for loads that do not exceed the dynamic load rating
of the nut.† Never exceed twice the rated dynamic load rating of the nut while in motion.

To use the load/life equation, look up the rated dynamic load for the assembly you are interested in. Use a diagram load
that covers your typical worst case loading and compute the predicted theoretical design life as follows:

Fr
L = ( D • f )3 x 1 x 106
w

L = life in inches
D= Design Load
Fr = Dynamic Load Rating
fW = 1.2–1.5 Nominal Operation
1.5–3.0 Operation with impact or vibration

† BSA assumes no liability for assemblies used at above the dynamic load rating of the nut.

www.thomsonbsa.com 85
 Linear Motion. Optimized.

Engineering Guidelines for Lead Screws

Column Loading Capacities Chart for Lead Screws and Ball Screws
Use the chart below to determine the Maximum Compression Load for Screw Shaft. Usually, screw operated in
tension can handle loads up to the rated capacity of the nut, providing the screw length is within standard lengths.
End supports have an effect on the load capacity of screws. The four standard variations are shown below with
corresponding rating adjustments. Find the point of intersecting lines of load (horizontal) and length (vertical) to
determine the minimum safe diameter of screw. If loads fall into dotted lines, consult factory.
Warning: DO NOT EXCEED ball nut capacity. Curves for the screw diameters shown are based on the smallest root
(minor) diameter of the standard screws within the nominal size range.

477,000

254,000
138,000

100,000
90,000
80,000
70,000
60,000
50,000
40,000
4
30,000

20,000
15,000
3
COMPRESSION LOAD (LBS)

10,000
9,000 21/2
8,000
7,000
6,000
5,000
4,000
2

3,000

2,000
1,500

1,000 11/2
900
800
700
600
500
11/4
400

300

1
200

5/8 3/
4
100
1/4 5/16 3/8 7/16 1/2 MAXIMUM LENGTH (INCHES) BETWEEN BEARINGS
Fixed-Free
Inches 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
A mm 127 254 381 508 635 762 889 1016 1143 1270 1397 1524 1651 1778 1905 2032 2159 2286 2413

Simple-Simple
Inches 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190
B mm 254 508 762 1016 1270 1524 1778 2032 2286 2540 2794 3048 3302 3556 3810 4064 4318 4572 4826

Fixed-Simple
Inches 14 28 42 57 71 85 99 113 127 141 156 170 184 198 212 226 240 255 270
C mm 356 711 1067 1448 1803 2159 2515 2870 3226 3581 3962 4318 4674 5029 5385 5740 6096 6477 6858

Fixed-Fixed
Inches 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380
D mm 508 1016 1524 2032 2540 3048 3556 4064 4572 5080 5588 6096 6604 7112 7620 8128 8636 9144 9652

LOAD LOAD

Compression (Column) Load Tension (Pulling) Load

86 www.thomsonbsa.com
 Lead and Ball Screws

Glossary

General Definitions DIAMETER - PITCH Ball Contact

The nominal diameter of a theoretical
Pitch Dia.
Major
cylinder passing through the centers 45° Contact Angle
Minor
(Root) Dia. Screw Dia. of the balls when they are in contact
with the ball bearing screw and ball Groove
Radius
nut tracks. Applied
Ball Nut
Ball Nut Load

Gothic Form
Lead EFFECTIVE BALL TURNS (Ogival)

The number of ball groove revolu-

tions within the ball nut body; a ball Ball Screw

nut with seven effective ball turns will

have a higher load carrying capability
than one with five, all other charac- GOTHIC (OR OGIVAL) GROOVE
Axial Lash teristics being equal. A ball track cross-section shaped like
(Backlash)
Screw
Shaft
a Gothic arch.
LEAD
The axial distance a screw travels CONFORMITY RATIO
AXIAL LASH/BACKLASH during one revolution. Ratio of the ball track radius to the
The axial free motion between the
ball diameter.
ball nut and screw; a measure of sys- LEAD TOLERANCE
tem stiffness. The maximum variation from nomi- CONTACT ANGLE
nal, measured in inches per foot, Nominal angle between a plane per-
BEARING BALL CIRCUIT cumulative. pendicular to the screw and a line
The closed path of recirculating
drawn between the theoretical points
balls within the ball nut assembly. A LOAD CARRYING BALLS of tangency between a ball and the
multiple circuit nut with two or more The balls in contact with the ball ball tracks and projected on a plane
individual circuits has a greater load grooves of both the nut and the passing through the screw axis and
carrying capability than a single screw for load carrying purposes. the center of the ball. The angle at
circuit ball nut assembly of the same
which the ball contacts the groove.
diameter. RIGHT HAND THREAD
The direction of the threads on the
CYCLE screw shaft causing the ball nut to
The complete forward and reverse travel away from the end viewed
motion of the screw (or nut) when when rotated in a counter clockwise
moving the load. One cycle is equiva- direction.
lent to two load carrying strokes (one
forward and one backward). SCREW STARTS
The integral number of independent
DIAMETER—MAJOR threads on the screw shaft; typically
The outside diameter of the ball one, two or four.
bearing screw shaft. In dealing with
ball bearing screws, this is the basic
measurement.

DIAMETER—MINOR (ROOT)
Diameter of the screw measured at
the bottom of the ball track.

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 Linear Motion. Optimized.

Glossary

Loading SIDE LOAD (RADIAL) c) A pair of spaced bearings for added

A load from the side that will reduce rigidity (rigid support).
Side Load (Radial)
the rated life and must be considered
Side Load (Radial)
Thrust Load
in the selection of the ball bearing
Side Load (Radial)
(Concentric) screw.
Thrust Load
(Concentric) Four combinations of bearing sup-
Thrust Load
Off Center Load ports are used throughout this cata-
(Concentric)
(Eccentric)
Off Center Load
Load/Life log for selection purposes. They are:
(Eccentric)
Off Center Load RIGID (least support) FREE
(Eccentric) A rolling contact device such as a
RIGID (least support) FREE
ball bearing screw is said to have
DYNAMIC LOAD RATING
reached the end of its usable life at RIGID (least support) FREE
Dynamic load rating is the maximum
the first sign of fatigue on the rolling
load which a ball bearing screw as- Type C
surfaces. Fatigue results from the
sembly can maintain for a prescribed Type C
repeated flexing of metal as the balls
length of travel. Type C
pass overBallany given point under load.
Bearing Screw Assembly Life vs. Travel
SIMPLE RIGID SIMPLE
SIMPLE RIGID SIMPLE
Assemblies

STATIC LOAD 100 Ball Bearing Screw Assembly Life vs. Travel
90
Rated Life (B10)

SIMPLE RIGID SIMPLE

Assemblies

80
Static load is the maximum non- 100
Rated Life (B10)
Not Fatigued

90 Ball Bearing Screw Assembly Life vs. Travel

Average Life
60
80
operating load capacity above which
Assemblies

100
Ball Screw
Not Fatigued

90
40
60
Rated Life (B10) Average Life Type A Type A
brinelling of the ball track occurs. 80
% ofScrew

Type A Type A
Not Fatigued

20
40 Average Life
60
Screw
Ball

200
40 0 Type A
RIGID RIGID Type A
SIMPLE
2 4 6 8 10
THRUST LOAD
% of

0
RIGID RIGID SIMPLE
% of Ball

20 Million Inches of Travel

0 2 4 6 8 10
Thrust load is loading parallel to and 0 Million Inches of Travel
RIGID RIGID SIMPLE
concentric with the centerline of the 0 2 4 6
Million Inches of Travel
8 10

screw shaft which acts continuously LOAD/LIFE RATING Type C Type A

in one direction. Thrust loading is the The usable life of a ball bearing Type C Type A
proper method of attaching the load screw assembly measured in inches Type C Type A
RIGID RIGID RIGID
to the ball bearing screw assembly. of travel under a specific load. The RIGID RIGID RIGID
length of travel that 90 percent of
RIGID RIGID RIGID
PRELOAD a group of ball bearing screws will
The use of one group of bearing balls complete, or exceed, before the first Type C Type C
set in opposition to another to remove evidence of fatigue develops. (B10) Type C Type C
axial lash or backlash and increase Type C Type C
ball bearing screw stiffness. All axial MOUNTING-ENDS ANNEALED ENDS
freedom is eliminated in preloading. A manufacturing process which
END BEARING SUPPORT (END removes brittleness while softening
TENSION LOAD FIXITY) screw stock to allow for machining of
Tension load is a load which would The three basic bearing configura- end journals.
tend to stretch the ball screw shaft. tions that are commonly used to sup-
port the ends of a ball screw are:
COMPRESSION LOAD
Compression load is a load which a) A single journal or ball type bearing
would tend to compress or buckle the (simple support).
ball screw shaft.

OFF CENTER LOAD (ECCENTRIC)

b) A pair of back-to-back, angular
A load tending to cock the ball nut
contact bearings to control end
on the screw, reducing the rated
play (simple support).
life. This must be considered in the
selection of the ball bearing screw
assembly.

88 www.thomsonbsa.com
 Lead and Ball Screws

Glossary

Backdriving BACKDRIVING TORQUE

Ball bearing screws can be backdriv- The backdriving torque (Tb) is the
en. A load on the nut will drive the torque created by an applied load.
screw because of the inherent high Tb = .143 (P) (L) = in-lbs
efficiency (90%).
PRELOAD TORQUE
Load Load TPL = PPL x L x .2
2π
or
TPL = .032 x PPL x L

Effect TPL = Torque (lb-inches)

(Screw Turns)
PPL = Preload setting (pounds)
L = Lead

If backdriving is required in a particu- ANGULAR VELOCITY

lar application, the lead of the screw
should be at least one third the screw RPM = Velocity (inches/min.)
Lead (inches/rev.)
diameter. Ideally the lead should be
equal to the screw diameter.
HORSEPOWER
DRIVING TORQUE HP = RPM x Torque (in-lbs)
63,000
P
Td
ROTATIONAL TORQUE
P
To accelerate the screw
Load Moves
WR2 (RPM)
The amount of effort, measured in Tr = = lb-in
3700 (t)
pound-inches, required to turn the
ball screw and move the load. Tr =Torque (lb-in)
WR2 = Inertia (lb-in)
Td = P x L = .177 P x L (lb-inches) t = Time to accelerate (sec.)
2πe
Td = Direct Torque (lb-inches) ACCELERATION TORQUE
P = Load Under load
L = Screw Lead (inches/turn)
e = Ball Bearing Screw Efficiency (p/g) (A) (L)
Ta = = lb-in
(90%) 2πe

A = Acceleration (in/sec2)
g = 386 in/sec2
p =Load (lb)
L = Screw lead (in/turn)

Thermal expansion of screw

= 6.25 x 10-6 in/in/°F

www.thomsonbsa.com 89
 Linear Motion. Optimized.

Design Considerations
Most Frequently Asked Questions About Ball Screws

Question How do you restrict the a) Life expectancy is the total inches Question How are torque require-
flange from turning off the nut in of travel that an assembly will provide ments for preload nuts calculated?
reversing load applications? under a stated load. (Life is sensitive
to load.) Use the Load Life Relation- Answer Driving torque increases
ship on page 85 to calculate the only slightly with preload since a
expected life of a particular assembly preload unit continues to be highly
in inches. efficient.

b) To determine the inches of re- Springs Flange

Answer The flange may be held to quired life: multiply inches of stroke x Rear Nut Front Nut
the nut by three alternative methods: two (only on vertical applications) x Springs Flange
cycles per hour x hours of operation Rear Nut Front Nut
a) The most positive method of hold- per day x number of working days per
ing the flange to the nut is to order year x years of expected service.
factory “drill and pin” prior to bearing
loading. The flange and nut are c) Compare the expected life to the
drilled to accept a roll pin from the required life. Expected life can be
flange face. First, determine the driving torque for
increased by choosing a ball screw
a single nut working at a given load.
with a larger load rating.
b) The flange may be drilled and Second, determine the torque
tapped from the O.D. into the nut required for the preload load setting.
Question Is lubrication necessary?
threads. A carbide spade drill may Add the driving torque and preload
be used to drill into the hardened nut torque together to determine total
Answer Proper and frequent lubrica-
threads. Avoid getting metal chips torque requirement.
tion must be provided for satisfactory
into the nut. service and life. A 90% reduction
Question What is meant by lead
in ball bearing screw life should Lead
c) Commercially available adhesives error?
be allowed where dry operation is
such as Loctite may be used. Take unavoidable. Lubricants reduce Lead 360°
care to avoid getting adhesive on the abrasive wear and dissipate heat
ball track. (Light loads only). caused by metal-to-metal contact 360°
between bearing surfaces. See page
Question How do you calculate ap- 78 for BSA lubricants.
plication life requirement in inches? Answer Lead error is the average
deviation from the nominal lead that
Answer Each ball bearing screw occurs in one foot of nut displace-
application will have an expected life ment. Most screws are offered in
given Ball
theBearing
stroke length, duty cycle, standard and precision grades. (See
Screw Assembly Life vs. Travel
years
100 of required service and load.
pages 41 – 59 for more details.)
% of Ball Screw Assemblies

Rated Life (B10)

90
80
Ball Bearing Screw Assembly Life vs. Travel
Not Fatigued

Average Life
60
% of Ball Screw Assemblies

100
Rated Life (B10)
4090
80
Not Fatigued

20 Average Life
60
0
40
0 2 4 6 8 10
20 Million Inches of Travel

0
0 2 4 6 8 10
Million Inches of Travel

90 www.thomsonbsa.com
 Lead and Ball Screws

Design Considerations

Question How are ball bearing Question What is the standard Question Can backlash be mini-
screws synchronized? straightness on machined screws mized?
with standard ends or screws ma-
Answer Screw synchronizing chined to customer prints? Answer Yes, backlash can be mini-
is achieved by selecting screws mized or eliminated completely by
with similar lead error and driven Answer The threaded portion is .005 using a preloaded ball bearing screw.
by a positive single source drive. T.l.R. per foot and not to exceed .010 See pages 44, 48, and 52.
“Matched sets required” should be T.l.R. total length of screw.
specified when ordering screws Question What is a load locking
that should be timed to run together Question What is meant by spring and how does it work?
without binding because of lead mis- tangential design nuts?
match. (Special factory order). Answer The load locking spring is a
coil that is turned into the inactive
Question What can be done to ex- portion of the nut and conforms to
ceed calculated critical speed? the ball track. The spring does noth-
ing in normal operation and does not
touch the screw. In the event the ball
bearings are lost from the nut, the
load locking spring will not allow the
Figure 1 Figure 2 load carrying nut to free-fall down
L the screw.
Figure 1 Figure 2
L
Answer The tangential circuit (Fig.
Answer The chart for critical 1) consists of a pickup finger (or
speed is on page 84. Critical speed yoke deflector) geometry which
is a function of unsupported screw allows the circuit balls to enter and
length, mean diameter of screw and leave the load carrying portion of the
bearing supports. Rigid/rigid screw ball screw circuit in a straight line
mounting is the optimum support path—along the tangent to the pitch
for high speeds. Consider a faster diameter.
lead to reduce the RPM required. If
higher speed is still necessary, go to The standard ball nut design (Fig. 2)
a larger diameter screw. places the return tube holes closer
together resulting in a circuit which
Question What is the difference requires a change in direction of the
between pitch and lead? ball travel as the return tubes are
Pitch entered and exited.

Pitch Question What is the backlash

of single nuts?

Answer The backlash range in a

Lead
single nut is as follows:
Two Start Screw
Lead Model Max. Backlash
Two Start Screw R-0308 to R-0705 .007”
R-0702 to R-1105 .009”
Answer Pitch is the measurable dis-
R-1501 to R-1502 .013”
tance between screw grooves. Lead
R-2202 to R-2502 .015”
is the linear travel the nut makes per
R-3066 .018”
screw revolution. The pitch and lead
are equal with single start screws.
The pitch is 1/2 the lead in two start
screws, etc.

www.thomsonbsa.com 91
 Linear Motion. Optimized.

Design Considerations

Question Where is the lube hole in Question How should ball bearing Question What is the normal operat-
the large size nuts and what is the screws be protected from dirt and ing temperature range for ball bear-
thread size? contaminates? ing screws?

Answer The brush wipers help pro- Answer The normal operating
hibit contaminates from entering the temperature range is –65°F to 300°F
nut as it translates along the screw. (–55°C to 149°C) with suitable lubrica-
For heavily contaminated environ- tion. Temperatures in excess of this
ments, metal shields, bellow type may make the screw brittle, warped
Answer A 1/8-27 NPT pipe thread enclosures or extensions are recom- or annealed.
tapped hole is standard on most nuts mended to be used with wipers.
from R-1502 through R-3066.

Question How do you size a ball Question What causes premature

bearing screw? failure?
Side Load (Radial)
Answer Select the screw that will
satisfy the most critical requirement Side Load (Radial)
Thrust Load
of the application, such as high RPM, (Concentric)
heavy load, duty cycle, column load- Thrust Load
(Concentric)
ing or zero backlash. Design for the Off Center Load
(Eccentric)
worst case. See page 42.
Off Center Load
(Eccentric)
Question How is a hardened screw
annealed?
Answer Premature failure may be
Answer The ball bearing screws caused by any of the following:
are case hardened to Rockwell C56
minimum. The screw ends are coil a) Misalignment of ball nut to screw
annealed after they are cut to length which results in side loading or ec-
to reduce the case hardness to a
machinable state. Screws may be centric loading will reduce life. This
annealed in the field by heating the may cause the bearing balls to split
ends to a cherry red with a torch, or get flats on them. The bearings
then putting the ends in sand to cool. may even break out of the tubes.

b) Metal Chips or Dirt in the ball

nut will not allow the bearings free
circulation. The bearing balls may
get flats on them because of skidding
and spalling.

c) Lack of Lubrication Proper

lubrication will help dissipate heat
and reduce metal-to-metal wear of
components.

d) High speed operation Shaft

speeds resulting in screw surface
speeds above 8,000 IPM will reduce
rated life.

92 www.thomsonbsa.com