Friction Experiment of Linear Motion Roller Guide...

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3, pp. 545-551 MARCH 2014 / 545

© KSPE and Springer 2014

Friction Experiment of Linear Motion Roller Guide THK

SRG25

De-Jun Cheng1, Wan-Suk Yang1, Je-Hong Park1, Tae-Jo Park1, Su-Jin Kim1,#, Gyung-Ho Kim2, and Chun-Hong Park2

1 Department of Mechanical Engineering, Gyeongsang National University, Jinju, Korea2 Korea Institute of Machinery & Materials, Daejeon, Korea

# Corresponding Author / E-mail: [email protected], TEL: +825-5772-1636, FAX: +825-5772-1577

KEYWORDS: LM roller guide, External load, Dynamic friction, Stribeck effect, Coulomb friction, Viscous friction

Friction is a characteristic that can be found in machine elements in common engineering use, and it has great effect on the machining

performance of a machine tool. Linear motion (LM) guides supported by rolling elements are used for accurate positioning of

precision machine. For accurate positioning, the frictional behavior of the LM guide must be understood. In this investigation, a new

experiment is conducted to measure friction, and the behavior of LM roller guide friction is measured under various external loads,

preloads, velocities, and lubricants. The results obtained from experiment are compared with reference data, and the experimental

friction equation of LM roller guide THK SRG25 is achieved from experiment, which can be used to calculate LM roller guide friction

and control positioning accuracy.

Manuscript received: September 6, 2013 / Revised: December 10, 2013 / Accepted: January 12, 2014

1. Introduction

Linear motion (LM) guides have been widely used for precise

positioning devices to transport machine parts through a linear path in

machining centers and X-Y tables etc. As machine parts becoming

smaller and finer, the required order of precision has been increased.1

LM guides using roller bearing have many advantages such as high

stiffness, smooth motion. Linear motion guides also have a low friction

coefficient compared with sliding contact bearings. Usually, the static

friction is small and almost the same as dynamic friction. However,

high static friction with lower kinematic viscosity results in stick slip,

wherein the coefficient is separated and the difference between them

increases with increasing preload.2 Therefore, the study of LM guide

friction plays a crucial role in the machining center.

Andersson et al.3 deals with different friction models for sliding

contacts running under different conditions, friction models which have

been studied are: Coulomb friction model, Viscous friction model,

Stribeck effect model, Combined Coulomb and Viscous friction model.

The friction was observed by several authors4-9 that the variation of

friction depends on interfacial conditions such as sliding speed, the

normal load, temperature, stick slip and vibration.

When using an LM system, it is necessary to provide effective

lubrication, where the main function of lubricant is the reduction of

both friction and wear of the rolling elements. There has been a great

deal of research conducted in relation to the influence of lubrication on

journal bearing friction. However, only few studies have been proposed

to learn the influence of lubrication on the LM guide friction.

NOMENCLATURE

F = Friction force (N)

f0 = Base friction force (N)

k1 = Factor dependent on the type of bearing

k2 = Factor dependent on the type of bearing (1/µm)

P = External load (N)

1.5 for Normal

pc = Preload class (µm) 2.5 for C1 preload

3.5 for C0 preload

VSt = Sliding speed coefficient in the Stribeck force (m/s)

V = Sliding speed (m/s)

ν = Kinematic viscosity (mm2/s)

µSt = Stribeck effect force coefficient (kNmm/s)

µv = Viscous friction coefficient (Ns2/mm4)

DOI: 10.1007/s12541-014-0369-y

546 / MARCH 2014 INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3

The purpose of this research is to characterize the friction force of

LM Roller guide. A series of experiments are carried out to measure

friction, which consider the effects of external load, preload, velocity

and lubricant on LM roller guide friction. To characterize these

components, a new experimental method in which external load can be

applied easier is suggested to measure friction. Finally the experimental

equation achieved from experimental results can be used to calculate

LM Roller guide (THK SRG25) friction and the relationship among

friction characteristic, external load, preload, velocity and lubrication

can be analyzed using this empirical equation.

2. Experiment Method and Equipment

LM Roller Guide (THK SRG25) that consists of rail and block is

transported by 4 rows of rollers and each row has 58 rollers. Each row

of rollers is arranged at a contact angle of 45 so that the LM block

receives an equal load rating in all four directions (radial, reverse radial

and lateral direction), and the use of a roller cage can eliminate friction

between rollers, increase grease retention and minimize heat generation.

The preload codes of it are Normal (1.5 µm), C1 (2.5 µm) and C0 (3.5

µm), respectively. Fig. 1 shows schematic of the LM roller guide and

Table 1 shows the specification of the experimented LM roller guide.

In the previous research, the traditional method which fixes two

rails and places table on four blocks and the feed driven system

controlled by linear motor is used to measure friction. Besides, the

external load is applied to the LM guide by putting heavy work piece

on the working table, as shown in reference.4

In this investigation, a new experimental method is conducted to

measure friction. The double rails and four blocks are fixed by using

vice and compression load cell is put on the center of the face of the

block, moreover, the LM rail is connected to tension load cell which is

moved by NC machine. Furthermore, the steady-state LM guide velocity

is also controlled by NC machine. In this measurement system, the

external load is given by rotating vice handle which is measured by

compression load cell and the friction force affected by external load is

measured directly by tension load cell. A data acquisition system is

used to measure the force continuously when the system is working and

these data are sent directly to the computer. Fig. 2 shows the graph of

LM roller guide experiment method.

Comparing with previous methods, this one does not have global

error, slope error or rail paralleled error. In order to reduce the effect of

the moment on friction, double blocks are added on the other side of

the rail. Besides, the large external load can be applied easier than

traditional methods. Even though large external load is given, the inertia

force does not increase because the mass of inertia force is rail not

external weight, moreover, the inertia force is small because the mass

of rail is small.

Fig. 3 shows the friction of single block without external load test

method. In Fig. 2 test method, subtracting the double block friction

force without external load from measured friction force, the results are

the friction of LM guide. In this experiment, symmetrical method is

used, then measured friction force is twice the friction force of each

rail, therefore, the calculated friction of LM roller guide should be

divided by 2.

In this study, the LM rail moved along the horizontal direction in a

single direction motion and the single stroke is 200 mm. The friction

behavior of LM roller guide is measured under various external loads,

velocities, preloads and lubricants. Table 2 indicates the experimental

Fig. 1 Schematic of the LM roller guide THK SRG25

Table 1 Specifications of the LM roller guide THK SRG 25

Preload class

Normal

C1 (Light preload)

C0 (Medium preload)

Basic dynamic load rating 27.9 kN

Diameter of roller

Normal (2.47 mm)

C1 (2.48 mm)

C0 (2.49 mm)

Length of roller

Normal (3.76mm)

C1 (3.78 mm)

C0 (3.79 mm)

Number of rollers 58×4

Fig. 2 LM roller guide experiment method

INTERNATIONAL JOURNAL OF PRECISION ENGINEERING AND MANUFACTURING Vol. 15, No. 3 MARCH 2014 / 547

conditions and equipments.

3. Experimental Results

3.1 Relationship among external load, preload and friction

In order to study the effects of the load and preload on the friction

force, the friction force is measured for various loads. The external load

is changed from 1.5 kN to 10 kN, which is 5.3~35.8% of the basic

dynamic load rating. In this experiment, the velocity is 0.11 m/s,

kinematic viscosity is 99 mm2/s and three different preloads are used.

Fig. 4 shows how the friction force varied with respect to the external

load and preload. Selected experimental points are used to demonstrate

the effect; the results for combinations of different preloads are

indicated. It is noticed that the friction force increases as external load

increases, and friction force also increases as preload increases. The

slope of friction curve from Normal, C1 to C0 is decreasing, because the

deflection of LM bearing guide with a preload under a given load is

smaller, and the rigidity is much greater than that without a preload.10

Since an LM system makes rolling motion via its rolling elements

such as rollers between the raceways, its frictional coefficient is much

smaller than a sliding guide. The THK Company suggests the different

friction coefficients for different LM Roller Guides, and from THK

company catalog, the average coefficient of LM roller guide SRG

friction range is from 0.001 to 0.002.10

Friction coefficient, in general, has been determined as a function

normal force and friction force. Using this method, the average

coefficient of LM roller guide friction is calculated from Normal, C1

and C0. In Fig. 5, the results concerning the friction coefficient are

compared with friction coefficient reference diagram from THK

catalog. The reference diagram is drawn by calculating the average of

different types of the LM systems, preloads, velocities, temperatures

and so on.

As shown in Fig. 5, the friction coefficient has values between

0.001 and 0.0177. When the applied load ratio is smaller than 0.18, the

friction coefficient is decreasing large as the applied load ratio

increases. However, when the applied load ratio is larger than 0.18, the

friction coefficient decreases between 0.001 and 0.002. The value of

friction coefficient calculated from experiment results is the same as

the value of THK Company catalog.

Fig. 3 The graph of single block test method

Table 2 Experiment conditions and equipments

Travel distance 200 mm

External load From 1.5 to 10 kN

Velocity From 0.0017 to 0.13 m/s

AFE-CA Grease Kinematic

viscosity at 40oC99 mm2/s

AFA grease Kinematic

viscosity at 40oC25 mm2/s

Compression load cell CAS-Korea C1E-2TS 2000 kg

Tension load cell CAS-Korea CSBA-10LS 10 kg

Data logger Radian INC. SDL-350R

NC machine HYUNDAI-KIA machine KV 25

Fig. 4 Relationship among external load, preload and friction force

Fig. 5 Comparison of the calculated and friction coefficient reference

diagram from THK catalog


3.2 Relationship between velocity and friction

In order to investigate the effect of the velocity on the friction force,

the friction is measured at various constant velocities and different

preloads. In this experiment the single block test method is used which

has its velocities from 0.0017 m/s to 0.13 m/s and the kinematic viscosity

is 99 mm2/s.

In Fig. 6, a comparison of the results from different velocities and

preloads are illustrated. The results for this graph indicate that the

friction force takes a maximum value at very low velocity in three kinds

of preload. When the velocity is smaller than 0.005 m/s, the friction

force decreases exponentially with the increasing of velocity, which is

due to mixed lubrication.

The mixed lubrication can be defined as a friction contribution at

low velocities, which is decreasing exponentially, as shown in Fig. 7.

The Stribeck curve presents the relationship among friction coefficient,

kinematic viscosity, velocity and normal load. Regions I, II and III in

the Stribeck curve correspond to boundary lubrication, mixed lubrication

and hydrodynamic lubrication respectively. The mixed lubrication regime

refers to a combination of boundary lubrication with hydrodynamic

lubrication. Generally, the minimum friction coefficient appears in the

mixed lubrication regime (region II).11,12

In this regime, the two surfaces are partly separated, partly in contact.

As the speed increases, the metal-to-metal contact surface is reduced,

then, the friction force decreases. When the preload increases, the fluid

film thickness is further reduced and metal-to-metal contact become

stronger, and then friction force increases. Besides, the slope of friction

curve also becomes larger as the preload increases.

For velocities above 0.005 m/s, the friction force linearly increases

with increasing velocity due to hydrodynamic lubrication. In the

hydrodynamic lubrication friction regime where the viscous friction is

dominant, the dynamic viscosity of the fluid, the velocity and contact

area of the moving object determine the friction force to be overcome,

and the viscous friction force is assumed to be proportional to the

velocity.11 In addition, for three different preloads, the friction forces

increase as preload increases because the fluid film thickness becomes

thinner as the preload increases.

3.3 Relationship between lubricant and friction

In order to investigate the effect of lubricant on the friction force,

the friction force is measured under C1 preload without external load,

and the dynamic friction characteristics are studied under two viscosities

of grease (99 mm2/s and 25 mm2/s).

In Fig. 8, a comparison of the results from different greases is

illustrated. It can be seen from this graph that the friction force with high

kinematic viscosity is smaller than friction force with low kinematic

Fig. 6 Relationship between velocity and friction forceFig. 8 Relationship between lubricant and friction force

Fig. 7 Stribeck curve and regimes of lubrication (η: Kinematic

viscosity, P: Normal load and V: Velocity)


viscosity when the velocity is smaller than 0.005 m/s. The drop-off in

friction is called the mixed lubrication, for low value of kinematic

viscosity fluid, fluid film thickness is reduced, then the friction force

with low viscosity makes metal-to-metal contact stronger, therefore, the

friction force with low kinematic viscosity is higher than friction force

with high kinematic viscosity. This phenomenon is also shown at mixed

lubrication curve in Fig. 7.

For velocities above 0.005 m/s, the friction force with low kinematic

viscosity is smaller than friction force with high kinematic viscosity

because of viscous friction. In viscous friction regime, a lower viscosity

decreases the fluid film thickness which will also decrease the friction

force, then for small value of kinematic viscosity, friction force is

small.

3.4 Relationship between velocity and friction vibration

The friction force is measured under Normal preload at various

velocities (0.0017, 0.003, 0.025 and 0.042 m/s) along horizontal motion

direction and the external load is zero.

Fig. 9 shows the friction force variations with time. It can be seen

that the magnitude of friction vibration decreases with the increase of

velocity, which is due to stick-slip behavior. The stick-slip phenomenon

is the spontaneous jerky motion that can occur while two objects are

sliding each other. However, the steady sliding motion is achieved,

without stick-slip behavior, as the velocity increases.14,15

In this experiment, the value of friction force is calculated from the

mean value of the kinematic friction curve.

4. Discussion

4.1 Experimental equation

In this experiment, the effects of velocity, external load, lubricant

and preload on the friction force are taken into account. The empirical

equation is composed of Coulomb friction, Stribeck effect and Viscous

friction which is to estimate the friction of LM roller guide, and the

factors include the external load, preload, velocity and lubricant.

Coulomb and Viscous friction are modeled as shown in Eqs. (1) and

(2).

(1)

(2)

The Stribeck effect force is considered using an exponential model

similar to the model proposed by Jeong:13

(3)

A Stribeck curve11 presenting the relationship among velocity,

kinematic viscosity and normal load can be obtained by summing up

the Coulomb friction, Viscous friction and Stribeck effect force.

Therefore, the frictional equation of LM roller guide THK SRG25

can be expressed as Eq. (4):

(4)

The values of k1, k2, µν, VSt, µSt and f0 cannot be known before an

experiment is carried out. Therefore, their values are determined by

experiment results. The values of k1, k2 are achieved from Fig. 4, and

the values of µν, VSt, µSt and f0 are achieved from Figs. 6 and 8. The

fCoulomb

k1

k2pc

–( )P 103–×=

fViscous

µνpcνV f

0+=

fStribeck

µSt

pc

ν----e

V

VSt

-------–

=

F k1

k2pc

–( )P 103–× p

cµννV

µSt

ν------e

V

VSt

-------–

+⎝ ⎠⎜ ⎟⎛ ⎞

f0

+ +=

Fig. 9 Friction vibration for different constant velocities

Fig. 10 Friction force simulations


experimental friction equation of LM roller guide THK SRG25 can be

changed as Eq. (5):

(5)

For three kinds of preload Normal, C1 and C0, the friction force F

in response to the external load, velocity and lubricant can be calculated

by Eq. (5), respectively. Fig. 10 shows the simulation results for different

velocities and external loads. In this case, kinematic viscosity is 99

mm2/s and Normal, C1 and C0 are calculated. As shown in Fig. 10, the

friction graph calculated from experimental friction equation is similar

trend to the graph of experiment results. If kinematic viscosity, external

load and velocity are changed, the value of friction force will be

changed.

4.2 Validation of the experimental equation

To validate the developed experimental equation in this paper, the

predictions from experimental equation are compared with experimental

data. The friction forces are measured at various velocities (0.008,

0.025, 0.042 and 0.075 m/s) along horizontal motion direction, external

loads (2, 4, 6 and 8 kN) and three different preloads (Normal, C1 and C0).

Fig. 11 plots the comparison between the friction force from

experimental Eq. (5) and those from experimental data. The maximum

difference between experiment values and prediction values are about

18.3%, 17.8% and 14% with respect to Normal, C1 and C0 preload,

respectively. Although the predicted values of friction force are

different from experimental friction force, the agreement is reasonable.

And the same trend that friction force increases with increasing

external load and velocity is observed.

5. Conclusion

In this paper, a new experiment method is conducted to measure

LM guide friction force. And the friction behavior of LM roller guide

THK SRG25 in response to the external load, velocity, preload and

lubrication is examined experimentally. The experimental result proves

that the friction force increases as the external load increases and the

value of friction coefficient decrease with the increase of external load.

When the velocity is smaller than 0.005 m/s, the friction force with high

kinematic viscosity is smaller than friction force with low kinematic

viscosity. However, for velocities above 0.005 m/s, the friction force

with high kinematic viscosity is higher than friction force with low

kinematic viscosity. Furthermore, when a preload is applied to increase

rigidity, the friction force also increases. Therefore, the friction force

increases as the preload increases.

The experimental friction equation of LM roller guide is achieved

for the calculation of friction force. For verification, the friction forces

predicted from the equation are compared with those from the additional

experiment data. It is found from comparison that there is a good

agreement between friction forces predicted from derived equation and

those from the experiment.

Therefore, the experimental friction equation can express the behavior

of LM roller guide THK SRG25, and the relationship among friction

characteristic, external load, preload, velocity and lubrication can be

analyzed using this empirical equation.

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F 0.315 0.03pc

–( )P 103–× p

c0.244νV

30

ν------e

V

0.01----------–

+⎝ ⎠⎜ ⎟⎛ ⎞

3+ +=

Fig. 11 Predicted and experimental friction forces for different

preloads


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