CIRP Annals - Manufacturing Technology 59 (2010) 429–432

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CIRP Annals - Manufacturing Technology

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Correlation between feed velocity and preloading in ball screw drives

A. Verl (2)a,b,*, S. Frey a
a
Institute for Control Engineering of Machine Tools and Manufacturing Units (ISW) – University of Stuttgart, Germany
b
Frauenhofer Institute for Manufacturing Engineering and Automation (IPA) – Stuttgart, Germany

A R T I C L E I N F O A B S T R A C T

Keywords: The efficiency and reliability of ball screw feed drives is a mayor issue concerning the productivity of
Machine tool
modern machine tools. The preloading of a ball screw thereby determines the dynamical operational
Wear
behavior as well as the attainable life span. The research results presented in this paper now clearly show
Ball screw
that the value of pretension changes depending on the velocity of the feed motion. This correlation has a
major impact on the actual equivalent load on a ball screw during operation and therefore has to be
considered when estimating the operating life of a feed drive.
ß 2010 CIRP.

1. Introduction preloading ball screws, the purpose of this additional load in all
cases is to eliminate backlash and ensure the rigidity of the
Ball screws are the machine component most frequently used component during operation. An increase of the preloading will
for transforming rotational into linear motion of a feed drive. raise the stiffness of the ball screw and therefore improve the
Optimized geometrical design, the choice of material, special dynamical operational behavior of the feed drive [4]. At the same
surface hardening methods and improved manufacturing accuracy time, however, the pretension results in an elevated stress on the
have led to ball screws with high efficiency and durability. ball screw.
Nevertheless feed drives belong to the assemblies of a machine tool According to DIN ISO 3408-5 [5] the nominal life expectancy of
causing the most downtimes and a failure of the ball screw usually a ball screw based on material fatigue can be estimated by the
leads to a total breakdown of the axis [1]. The attainable life of this dynamical load rating of the component Ca and the effective
component is therefore an important issue concerning the equivalent load Fma.
availability and productivity of modern machine tools.  3
Due to the kinematics and the necessity of the ball refeeding, Ca
L¼ 106 (1)
ball screws are subject to much greater wear than common ball F ma
bearings [2]. The various frictional components namely rolling,
The effective load Fma is determined by the overall applied
bore and sliding friction, lead to different wear mechanisms such
external forces Fm and the influence of the preloading Fpr
as material fatigue, abrasion or adhesion [2,3]. The calculation of
respectively.
the nominal life expectancy is based on wear due to material
fatigue and therefore predominantly considers the effective load  
F m 3=2
on the ball screw. Operating conditions such as acceleration, F ma ¼ F pr 1 þ (2)
3 F pr
lubrication or rotational speed also have an influence on the
durability of a ball screw, however are usually not taken into Depending on the application the value of pretension can have a
account when calculating the nominal life. major influence on the overall applied load during operation. The
The experimental results presented in this paper now show the equivalent mean load Fm can be calculated using the load spectrum
existence of a quantifiable correlation between feed velocity and in Eq. (3), where Fi stands for the acting forces during the individual
load on a ball screw. stages and pi for the corresponding travel/revolution ratio [6].
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3
2. Preloading and nominal life of a ball screw F m ¼ jF 1 j3 p1 þ jF 2 j3 p2 þ . . . þ jF n j3 pn (3)

The preloading of a ball screw is a fundamental characteristic In most cases it is reasonable to divide a machine task into
for the operational behavior of a feed drive. Preloading thereby can operating states with different load intensities such as roughing,
be described as the tension induced on the ball screw when no finishing or rapid motion.
external loads are applied. While there are several ways of The stress exerted on the ball screw due to the preloading is
expressed by the drag torque. The emerging friction of the ball
screw under no load is proportional to the level of preloading. The
* Corresponding author at: Institute for Control Engineering of Machine Tools and friction losses thereby have a negative effect on the thermal
Manufacturing Units (ISW) – University of Stuttgart, Germany. behavior as well as on the wear of the component [7]. Hence, the

0007-8506/$ – see front matter ß 2010 CIRP.

doi:10.1016/j.cirp.2010.03.136
430 A. Verl, S. Frey / CIRP Annals - Manufacturing Technology 59 (2010) 429–432

Fig. 2. Correlation between preloading, rotational speed of the shaft and drag torque
of the ball screw (without sealings).

4. Experimental results
Fig. 1. Test bench.

Numerous experiments concerning the operational behavior of

ball screws have been carried out. The results presented in this
path of drag torque is often used as an attribute of the quality and paper focus on the continuous operational behavior at constant
the efficiency of a ball screw [8]. speed and with no external load applied. For a better under-
standing in the following we will distinguish between effective
3. Experimental setup pretension Fpr and static value of pretension Fpr0, where the static
value of pretension stands for the pretension measured at the
At the ISW of the University of Stuttgart there exists a versatile resting state of the feed axis.
test bench for the research on the operational behavior of ball
screw drives. The setup can be described as a characteristic feed 4.1. Correlation between preloading, feed velocity and drag torque
axis for machine tools using a high precision ball screw with
preloaded double nut. Fig. 1 schematically shows the experimental A direct identification of the preloading is generally associated
setup with its two different configurations. with high complexity and expenses and therefore is not used in
Configuration 1 is used for measuring the drag torque of the ball practice. Usually the preloading level of a ball screw resulting from
screw. Therefore, the double nut is shored up against the linear assembly is determined by measuring the drag torque at 100 rpm
guides by a strain-gauge beam arrangement. The symmetric [9].
structural design thereby allows a measurement of the drag torque With the presented test bench a large number of drag torque
in both directions and over the entire travel range of the feed axis. measurements at different feed velocities and various static values
The flexible mounting of the nut avoids any possible effects on the of pretension have been conducted. Fig. 2 shows the mean value of
operational behavior due to mounting tolerances in the alignment the drag torque over the travel distance at different operating
of linear guides and ball screw. points.
In configuration 2 the ball screw nut is directly mounted on the As already described in previous works [10,11], there is a linear
tool carriage instead of on the bending beam. In this case the test correlation between preloading, feed velocity and friction pro-
bench complies with a typical feed axis as used in machine tools. duced by a ball screw. Similarly to the influence of the pretension,
Depending on the test case extra mass can be added on the tool an increase of rotational speed will lead to an elevation of the drag
carriage. torque. On this account losses accumulate, temperature rises and
The double nut used in this setup consists of two separate nuts the wear of the component increases. As respects the calculation of
preloaded in an ‘O’ configuration, whereas an adjustable device the nominal life presented in section two, the feed velocity remains
allows the change of the preloading level in the course of the disregarded. Only in a few cases manufacturers provide correction
measurements. Furthermore a highly rigid sensor system has been factors for different feed velocities and load cases.
developed and installed between the two halves of the nut [4]. The As already mentioned, the presented test bench provides the
sensor system allows the measurement of the stress within the possibility to measure the preloading or rather the stress ratio
nut, which is according to the pretension when no external loads within the double nut during operation. By the simultaneous
are applied. Due to the specific arrangement of the sensor system, detection of drag torque and pretension at different feed velocities
the inner forces can be detected when measuring the drag torque a new phenomenon could be observed: Analogous to the
as well as when operating with the tool carriage. characteristics of the drag torque, the effective force within the
Table 1 gives an overview on the specifications of the test nut is proportional to the feed velocity. Fig. 3 shows the measured
bench. effective values of pretension within the double nut, corresponding
to the drag torque measurements of Fig. 2.
Table 1 The plotted data points represent the mean value of the force
Specifications of the test bench. within the double nut at feed motion with constant velocity and a
Description Value
fixed static value of pretension. Clearly, it can be seen that with
rising rotational speed the effective force within the nut and
Nominal diameter ball screw d0 40 mm
therefore the load on the ball screw increases. Consequently, there
Ball screw lead Ph 20 mm
Dynamical load value Cn 39700 N exists an interaction between the gradient of the friction produced
Nominal ball diameter Dw 6 mm by a ball screw at increasing velocity and the effective load.
Number of ball track turns 3 The experimental results show that the interpretation of the
Travel range 600 mm preloading as a constant value is not adequate during operation. In
Mass of tool carriage 200 kg
fact, there is a fixed correlation between preloading and drag
 A. Verl, S. Frey / CIRP Annals - Manufacturing Technology 59 (2010) 429–432 431

Table 2
Gradient of pretension and drag torque.

Static value of DFpr (N/krpm) DTpr (Nm/krpm) DFpr/DTpr (N/Nm)

pretension (N)

1000 420 0.39 1075

1500 570 0.44 1299
2000 460 0.42 1351
2500 580 0.46 1266
3000 530 0.47 1123
3500 540 0.53 1020
4000 610 0.49 1250
5000 600 0.51 1176

Thus the knowledge of the drag torque at different feed

velocities allows a conclusion about the prevailing pretension
during operation.
Fig. 3. Correlation between the static value of pretension, rotational speed and
effective pretension. One explanation for the dependency between rotational speed
of the shaft and the measurable increase of stress within the nut is
the displacement of the rolling balls as described in [11]. Due to the
torque throughout the whole range of the rotational speed. Hence friction conditions in the contact points A and B, the balls are
the increase of the rotational speed not only has a negative effect exerted by a radial force component other than the tangential
on the abrasive wear and the thermal behavior of a ball screw, but component in the direction of the lead geometry. Therefore with
also on the load and therefore on the material fatigue. increasing velocity the balls are forced against the flank of the nut,
until the restoring forces avoid a further displacement. Fig. 5 shows
4.2. Characteristic and cause for the increase of pretension a schematic sectional view of a preloaded ball screw nut and the
displacement of the rolling balls within the tangent plane at
In order to allow a quantifiable statement about the character- increasing rotational speed.
istics of the increasing forces, the mean value of pretension and The displacement of the balls induces an additional elastic
drag torque at different static values of pretension have been deformation in the contact points A0 and B0 , which finally leads to
evaluated and compared to one another. Fig. 4 shows, for example, an increasing stress within the nut. The necessary strain energy
the measured values at a static value of pretension of 2000 N. The therefore is provided by the applied torque of the servo drive. The
individual data points were approximated by linear regression and recirculation of the balls has a minor impact on the effective
the gradient of drag torque DTpr and effective pretension DFpr at pretension, as has been shown in [12].
increasing rotational speed were calculated. The individual values
are listed in Table 2. 4.3. Effect on the load during operation with tool carriage
The increase in pretension and drag torque for increasing
rotational speed is approximately constant throughout the entire To demonstrate that this effect also is apparent in ball screw feed
adjustment range of the preloading. For the given ball screw an drives as used in production machines, measurements with
increase of the rotational speed of 1000 rpm will lead to a gain of configuration 2 of the test bench were carried out. Here the effective
pretension of roughly 500 N. The ratio of the two gradients as pretension was measured at different motion profiles resulting from
specified in Eq. (4) determines the correlation between increasing real operating conditions. An example of a positioning movement of
drag torque and the resulting tension within the considered ball the tool carriage at rapid motion is shown in Fig. 6.
screw nut. Apart from the distinctive variation of the forces within the nut
during acceleration and deceleration, a conspicuous gain of the
DF pr pretension can be seen at constant feed velocity. The correlation
 1200 N=Nm (4) between rotational speed of the shaft and effective pretension
DT pr
within the nut can be expressed by Eq. (5) with the gradient DFpr
determined in Section 4.2.

F pr ðnÞ ¼ F pr0 þ DF pr n (5)

A gain of the pretension level thereby can be detected at either

direction of travel. The slight difference in pretension between
forward and backward movement is due to the friction of the linear
guides working against the feed direction. Nevertheless, in both
cases an extensive elevation of the load on the ball screw at
constant feed velocity can be seen.

Fig. 4. Effective pretension and drag torque at different speeds for a static value of
pretension of 2000 N. Fig. 5. Ball displacement within a double nut at increasing speed.
432 A. Verl, S. Frey / CIRP Annals - Manufacturing Technology 59 (2010) 429–432

Fig. 6. Positioning movement at rapid motion with 36 m/min.

The same phenomenon has been detected for different motion can be transferred onto different ball screws. Additionally, ball
profiles and loading conditions. While the change of pretension at screw systems with 4-point-contact should be examined in order
lower speeds is rather small, it can have a major impact on the to allow a generally accepted statement.
overall load when moving at high feed velocity. In this manner
depending on the respective operating condition, the change of
pretension should be considered when estimating the effective
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