TECHNICAL PAPER

Clarification of Tribological Behavior on Tooth Surface ofResin Worm Gear for Electric Power Steering
T. KUNISHIMA K. MIYAKE T. KUROKAWA

H. ARAIWe have clarified the tribological behavior on tooth surface by devising a simplified sliding test which simulatesa resin worm gear. It was confirmed that the main factor of tooth surface deformation was creep deformation, andincrease of molecular mass of the polyamide contributed to long-term durability. In addition, surface roughness
and temperature dependence of the friction coefficient were gathered through variation of film thickness ratiousing EHL theories and applied to rotating torque reduction by controlling tooth surface roughness.
Key Words: polyamide, worm gear, simplified test, abrasion, creep deformation, EHL, torque reduction

1. Introduction
Demands for weight reduction (energy conservation,
reduced CO 2 emissions) in automotive parts are1), 2)
as a result of energy-related problems suchrisingas global warming. In addition, requirements for highlevel quietness associated with electronization andhybridization of automobiles have caused an upsurge inthe proportion of resin usage in automotive components
with sliding mechanisms. Amidst these situations, resin
gears have in recent years become widely utilized in
3)
automotive parts due to the high level of quietness, self4)
lubricity, and reduction in mass they achieve withinsuch parts. The usage of resin worm gears (hereafter“worm gears”) is especially high for the reduction gear
used in electric power steering (EPS), which is illustrated
in Fig. 1. EPS is an important safety part which assists
steering force by supporting the load on the front axleof the automobile, and is also a tribological element
for which high reliability is expected. Furthermore, thedownsizing of automotive parts in recent years, coupledwith the high demand for application of EPS on large
vehicles due to its effects on improved fuel efficiency, hasemphasized the necessity of high-output support in worm
gears.
The necessary characteristics of worm gears include
suppression of rattling caused by decrease in tooth
thickness, known as backlash, in addition to assurance of
durability life and reduction of steering torque. Figure 2
illustrates the contact form of the resin worm gear, which
during usage is easily affected by sliding in addition torolling, and upon which heat generation and cooling arerepeated due to the process of sliding. This combination

JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

Metal worm shaft

Resin worm gear

Fig. 1 Basic structure of JTEKT EPS and internal structure of
reduction gear
Heat generated
at meshing area

Worm gear
meshing area
Worm shaft
Coolingduringrolling

Worm shaft

Worm gear

Worm gear

Intermittent rolling + sliding contact

Fig. 2 Contact form of resin worm gear

creates a complex mechanism of tribological behavior on
the tooth surface. Wear and creep deformation are factors
which influence decrease in tooth thickness, however it
is difficult to isolate wear and creep deformation fromthe tooth surface for evaluation after gear operation.
Furthermore, high output exacerbates the decrease in
tooth thickness by increasing load on the tooth surface,which in turn reduces durability life. Consequently, it isessential to ensure wear resistance and creep resistancewithin material development and the design of the worm27

−Clarification of Tribological Behavior on Tooth Surface of Resin Worm Gear for Electric Power Steering−

2. 1 Establishment of reproducible basic testing
method for sliding mode of worm gear
Issues that have occurred up until now within thedevelopment of worm gears have been reproduced within
the basic test in the complex sliding mode of the worm
gear. The worm gear is employed under conditions ofhigh surface pressure and high sliding speed which
exceed the PV limit of general resin materials, and it is
known that the temperature of the sliding contact face
is low. This is because the lubrication conditions of thesliding contact surface due to grease and the suppressionof heat generation in the intermittent contact cause theheat generated on the sliding contact surface to dissipate,
thereby suppressing temperature rise. Such a uniquesliding mode was difficult to reproduce in conventional
basic tests such as the Suzuki frictional wear test, andrequired a durability test using the actual worm gear
during actual development. Nevertheless, the durability
test necessitated a large amount of time which in turnlengthened development time, and in addition, themechanism of tribological behavior was difficult to
identify.
To resolve this issue, we developed a basic testing
method simulating the sliding mode of the actual worm
gear. An outline of this test is shown in Fig. 3. By
substituting the disk of an ordinary disk-on-ring test witha metal roller, we were able to reproduce the contact form
with high surface pressure seen on the tooth surface of theworm gear. In addition, by changing the diameter of themetal roller, we were able to simulate different contact
forms originating from the elastic modulus and presenceor absence of reinforced fibers in the gear material, as
shown in Fig. 4. Also, by designing a wedge-shaped
contact area and grease reservoir on the fixture, we

28

Load

5)-7)

2. Basic testing method

reproduced stable flow of grease on the friction surface
as well as intermittent contact. This, combined with theintroduction of an intermittent process and adjustment of
its interval, suppressed temperature rise and improved theconformity of the simulated results to the tooth surface
temperature of the actual worm gear. The developed
method is also able to accurately identify the ratios ofwear and creep deformation from the changes in weightand height of the resin ring before and after the test.
The above enable the simulation of the contact formof the actual worm gear tooth within the developed basic
testing method. As seen in Fig. 5, it has also become
possible to estimate the decrease in tooth thickness of
the worm gear from changes in height during the basic5)-7)
test .

Application of vertical load
+ rotation on the resin ringResin
Rotation

Resin ringAffixture ofStressseveral metal Metal roller
concentrationrollers(affixed)

Change in height= Wear + creep deformation

Fig. 3 Outline of basic test

Low-elasticity resin:
Tooth surface contact

Metal worm shaft
Metal
worm

R10

Resin worm
gear

R1.75
Resin worm gear

High-elasticity resin: Contact at tooth tip

Fig. 4 Contact form of worm gear

Comparison of decrease in
tooth thickness on actual gear

gear, as these properties affect the decrease in tooth
thickness. It is also necessary to lower rotation torquein the worm gear in order to improve steering feeling.
However, as there are multiple agents of sliding resistanceon the tooth surface which affect rotation torque, it is
impossible to give a simple estimation of which of theseagents is the primary cause. It is therefore important to
conduct integrated analysis on the factors affecting sliding
resistance on the tooth surface, and apply the results inthe design of the worm gear and the conditions of the gear
teeth.
This paper describes, as a measure for the above
mentioned issues, the development of a basic testing
method simulating the worm gear to clarify thetribological behavior acting upon the gear tooth surface,
and the application of the test results to the developmentof worm gears with long-term durability and low torque.

80°C

2
1.6

PA66

1.2
PA6

0.8

POM

0.4
0
0.01

0.015

0.02

Change in height during basic test, mm

Fig. 5 Change in height during basic test and comparison of
decrease in tooth thickness on actual gear

JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

−Clarification of Tribological Behavior on Tooth Surface of Resin Worm Gear for Electric Power Steering−

2. 2 Test conditions
For the test specimen, we used Polyamide 66 (hereafter“polyamide”), which has excellent self-lubricity. The
conditions of the test are shown in Table 1. The basic
test was conducted using the method described in 2.1.
After verifying the correlation between decrease in tooth
thickness and gear life by comparing the basic test witha durability test, we evaluated wear resistance and creep
resistance which both affect tooth surface deformationand durability life, and the friction coefficient which
influences steering torque.
Table 1 Basic test conditions

Evaluated items
Roller R
RollerspecimenRollermaterial

Resin ring
Conforms Shapedimensions
to JIS
K7218A

Wear resistance/ Friction
creep resistance coeﬃcientevaluation
evaluation
1.75mm10mm

S45C
Induction heat
treatment

S45C

O.D. ：25.6mm
I.D.
：20mm
Height ：12mm

Sliding speed

1.016 m/s

0.166 m/s

Load surfacepressure

90〜160 MPa

23 MPa

240 min.
(with intervals)

3 min.

Testing
Testtime
conditions
Atmospherictemperature
Lubrication
conditions

25℃ to 120℃
Grease lubrication(Barium complex)

3. Technology for lengthening long-term
durability of worm gears
Figure 6 shows the observed tooth images from SEM
back-scattered electron images of the non-reinforced
polyamide worm gear and the glass fiber (GF) reinforced
polyamide worm gear after durability tests on the actual
gears. No remarkable wear was found on the nonreinforced polyamide, although there were slight sliding
marks caused by contact with the worm shaft. In contrast,a large amount of flaking of the resin due to wear andcohesion of GF which had broken off was observed on
the GF reinforced polyamide. From the observations of
tooth surface post durability testing, however it is unclear
how much wear and creep deformation had contributed
to these flaws, and impossible to pinpoint measures formaterial development.

JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

The results of the developed basic test are shownin Fig. 7. Using this test, it was possible to isolate theamounts of wear and creep deformation by measuring thechanges in weight and height before and after the test.
The results showed that the non-reinforced material had
a smaller overall decrease in tooth thickness. In addition,
it was found that, while creep deformation was the main
factor in decrease in tooth thickness of the non-reinforced
material, wear was the main factor in decrease in tooth
thickness of the GF reinforced material. In regard to thesefindings, a cross section of the tooth surface of an actual
damaged worm gear is shown in Fig. 8, which clearlyshows that creep deformation has progressed, and that acrack has occurred near the bottom of the tooth, damaging
the gear. We believe that the creep deformation of theresin is caused by the plastic flow of the molecular chain
due to sliding, and that a high molecular weight increases
creep-rupture elongation due to the strength of themolecular bond, thereby suppressing crack progression.
Figure 9 shows the results of an evaluation on the effectof resin viscosity (molecular mass) on the failure life of
the polyamide. These results identify a strong correlation
between the molecular mass and durability life of theworm gear, confirming that the polyamide with high9)molecular mass contributes to longer gear life .
Furthermore, as shown in Fig. 10, by tracking the timebased change in the sliding contact face after the basic
test, it is now possible to estimate the wear mechanism
6)of the GF reinforced polyamide . When the GF on thesurface of the tooth make contact with the metal worm at
a high surface pressure, the GF breaks off from the resin,
adheres to the surface of the gear, and acts as an abrasive.
The GF then causes flaking of the resin due to wear,
after which stress concentrates in the holes from which
the GF has broken off and causes cracks to occur, which
eventually leads to flaking over a large area.
In consideration of the above, we have developed anon-reinforced high molecular mass polyamide material
with long-term durability and low level of decrease in
tooth thickness. We then applied the developed polyamide
as the material used for resin worm gears, which are now
currently being mass-produced.
Non-reinforced polyamide

500 µmDirection of observation

Flaking ofresin

GF reinforced polyamide①

Cohesion of
broken off GF②①②

Fig. 6 Observed results of tooth surface after durability testof actual worm gear29

−Clarification of Tribological Behavior on Tooth Surface of Resin Worm Gear for Electric Power Steering−

Creep deformation amount

0.25

4. Torque-lowering technologies for the8), 9)
worm gear

Change in height, mm

Wear amount
0.2

4. 1 Friction coefficient

0.15
0.1
Selected

0.05
0

Non-reinforced polyamide

GF reinforced polyamide

Fig. 7 Results of measurement of change in height due tobasic test

Cracksby creep
deformation

Fig. 8 Observed results of tooth surface after durability testof high molecular mass polyamide

8

0.12

6

0.10

Friction coefficient, µDurability life ratio

10

There exist many factors (atmospheric temperature,
tooth surface roughness, resin elastic modulus, grease
base oil viscosity, oil film thickness, etc.) which act
upon the steering torque of a steering system. If thesefactors can be categorized and steering torque (=friction
coefficient) estimated, then these factors and steering
torque can be included in machining conditions to reduce
torque from the aspect of the material. The research
described in this paper identifies the active mechanismof steering torque through the basic testing method wehave developed, thus establishing a method of estimating
steering torque.
Figures 11 and 12 respectively show the non-reinforcedhigh molecular mass polyamide material that we havedeveloped, and the relationship of the sliding contact
surface temperature and sliding surface roughness of theabovementioned GF reinforced polyamide material to thefriction coefficient. Both materials showed that increased
surface roughness and higher sliding contact surface8), 9)
temperature lead to increased friction coefficient .
These factors were verified by film thickness ratio (acomparison of minimum oil film thickness of grease tosynthetic surface roughness of sliding contact surface),
which is an indicator of grease lubrication conditions.

4
2
0

0

20
40
Resin viscosity ratio

Ra=0.8 µm
Ra=0.44 µm

Non-reinforced material

0.08 Ra=0.37 µm
0.06
Ra=0.10 µm

0.04
0.02
0.00

Ra=0.04 µm
0

20

40

60

80

Fig. 9 Relationship between viscosity (molecular mass) of
non-reinforced polyamide and durability life

Fig. 11 Relationship of temperature and surface roughness of
non-reinforced high molecular mass polyamide
material to friction coefficientWhite areas: GF

GF reinforced material

Metal worm

Resin

Breaking off +adhesion = abrasive
Deformation

Contact at
high surface
Glass fiber pressure

Flaking progresses

Metal worm
Cracksform fromholes

Stress concentration

Fig. 10 Wear mechanism of GF filler

30

Resin breaks off

Friction coefficient, µ

0.12

GF breaks off ⇒ forms abrasive
Causes abnormal wear

100

Temperature, °C

Ra=1.23 µm

0.10
0.08

Ra=0.93 µm

0.06

Ra=0.45 µm

Ra=0.20 µm

0.04
0.02
0.00

Ra=0.13 µm
0

20

40

60

80

100

Temperature, °C

Fig. 12 Relationship of temperature and surface roughness of
GF-reinforced polyamide material to friction coefficient

JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

−Clarification of Tribological Behavior on Tooth Surface of Resin Worm Gear for Electric Power Steering−

10)

The following lubrication theory was used in orderto calculate film thickness. The map of the lubrication
region on line contact (Hooke’s chart) is shown in
Fig. 13. From the calculated results of Johnson’selasticity parameter gE and viscosity parameter gV, shown
in Formula ⑵, in the sliding conditions of the developed
non-reinforced high molecular mass polyamide, it isevident that the lubrication conditions of this study arewithin the IE lubrication region (equivalent viscosity region of elasticity). In other words, it is not necessary
to consider the rise in pressure seen in hard EHL (PEregion) as the surface pressure is low (approximately 20
MPa), however it is necessary to take into account elastic
deformation during sliding since the resin used has highviscoelasticity. The minimum oil film thickness hmin of thegiven region was calculated by the Dowson-Higginson
indication by Herrebrugh, as shown in Formula ⑶.
Figure 14 shows the results of the minimum oil film
thickness calculated from the tensile modulus of elasticityof the resin and base oil viscosity of the grease at eachtemperature. When compared with the effect of reduced
elastic modulus of the resin associated with a rise intemperature, decreased base oil viscosity shows a higher
amount of contribution, and therefore it was found thatminimum oil film thickness is reduced as temperaturerises.
h min⑴
K＝
r 12 + r 22
K: Film thickness ratio
h min : Minimum oil film thickness⇒Calculated from theoretical formula
r 1 : Surface roughness Ra of T/P resinr 2 : Surface roughness Ra (=0.0945 µm)of metal roller

gE =

w2
g0 uERE1, m1R1
R2 E2, m2

1/2

gv =

Effective radius R:
1
1
1
=
+
R
R1 R2

R1 = Roller radius
R2 = ∞ (Flat contact)
E: Elastic modulus
m: Poisson's ratio

h min ＝ 3.10

g0 u
ER

a2 w 3g0 uR 2

Metal worm
Resin tooth surface

r2

h min
r1

1/2

⑵

Effective elasticity coefficient E:
1−m12
1−m22
2
+
=
E1
E2
E

E: Effective elasticity coefficient
g0: Base oil viscosity
w: Load per unit lengtha: Pressure-viscosity coefficient
R: Effective radius
u: Friction speed

0.6

w
ER

−0.2

R

⑶

JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

Viscosity parameter, gV

10 000High-pressure
viscosity

PE
1 000
PR

gE=6.90gV=3.81

100
10

IE

IR

1

Effective
viscosity

0.1
Elastic body
Rigid body
0.1
1
10
100
1 000
Elasticity parameter, gE

Fig. 13 Map of lubrication region (Hooke’s chart)
Minimum oil film thickness hmin, µm

4. 2 Calculation of oil film thickness

0.20

Non-reinforced polyamide
GF reinforced polyamide

0.16
0.12
0.08
0.04
0.00

0

30

60

90

120

Atmospheric temperature, °C

Fig. 14 Calculated minimum film thickness

4. 3 Study on friction control using film thickness
ratio
Film thickness ratio was obtained by substituting theminimum oil film thickness calculated in 4.2 within
Formula ⑴, and the relationship of this ratio to thefriction coefficient was examined. The film thickness
ratio-friction coefficient relationship within the developed
non-reinforced high molecular mass polyamide is shownin Fig. 15. The film thickness ratio-friction coefficient
relationship within the GF reinforced polyamide, which
was used as a comparative material, is shown in Fig. 16.
It was found that in both cases, the friction coefficient
did not depend on sliding contact surface temperature
nor surface roughness, but did depend on film thickness
ratio, and decreased as film thickness ratio increased.
As illustrated in Fig. 17, the friction coefficients of bothmaterials are equivalent at no lubrication when the film
thickness ratio is in the smaller range, and it is thoughtthat this is a result of boundary lubrication, where theratio of direct solid contact between two objects islarge. On the other hand, it is also estimated that friction
coefficient decreases due to the slightly mixed lubrication
conditions, since the film thickness ratio increases alongwith the decrease in the ratio of direct solid contact. Fromthese results, the dependence of the friction coefficienton surface roughness and temperature is clearly visible
through the change in film thickness ratio.

31−Clarification of Tribological Behavior on Tooth Surface of Resin Worm Gear for Electric Power Steering−

Ra=0.04

0.12
Friction coefficient, µRa=0.100.10

Ra=0.37
Ra=0.440.08

Ra=0.80

0.06
0.04
0.02
0.00
0.0

0.5

1.0

1.5

2.0

Film thickness ratio

Fig. 15 Relationship between film thickness ratio and friction
coefficient (Non-reinforced high molecular mass
polyamide material)

Friction coefficient, µ0.12

Ra=0.13
Ra=0.200.10

Ra=0.45
Ra=0.930.08

Ra=1.23

0.06
0.04
0.02
0.00
0.0

0.2

0.4

0.6

0.8

1.0

4. 4 Application in actual EPS worm gear
The knowledge obtained from 4.3 is described below inan example of the practical application of the developed
resin in torque reduction of actual worm gears. Figure 18
shows the relationship between the friction coefficient,obtained from a basic test using four materials withdifferent friction coefficients, and the rotation torque ratioof an actual worm gear. A strong correlation can be seen
between the friction coefficient of the resin material androtation torque. From this relationship, we can estimate
the tooth surface roughness that will enable us to obtainthe target rotation torque under prescribed temperature
conditions. For a high surface roughness, it is possible forrotation torque to increase at high temperatures (80°C:
temperature inside the vehicle), however it is also possible
to suppress torque by maintaining the film thickness ratio.
As Fig. 18 shows, a friction coefficient at or less than
0.07 and a film thickness ratio at or above approximately
0.6 (calculated from the relationship shown in Fig. 17)
are both necessary in order to obtain the target torquevalue. To obtain such a film thickness ratio, Formulas ⑴and ⑵ show that it is necessary to set the tooth surface
roughness as Ra=0.2 or less by performing an inverse
operation substituting each physical property value at 80°C within the formulas. We applied the surface roughness
obtained in the gear formation conditions of hobbing
and gear break-in, which enabled torque reduction in theworm gear of the reduction gear used in EPS.

Film thickness ratio

Fig. 16 Relationship between film thickness ratio and friction
coefficient (GF-reinforced polyamide material)

Non-reinforced high molecular mass polyamide
GF reinforced polyamide

Friction coefficient, µ

0.12
0.10

Region ①µ at no lubrication (boundary lubrication)

0.08
0.06
0.04
0.02

0.00
0.0

Target
value
0.07
0

0.02

0.04

0.06

0.08

0.1

Friction coefficient (basic test), µ

Region ③
Region ③
0.5

1.0

1.5

2.0

Film thickness ratio
Region ①

Region ②−③

Metal worm

Metal worm

Resin tooth surface

Resin tooth surface

Large solid
contact ratio

Large ratio of area
separated by oil film

Fig. 17 Relationship between film thickness ratio and friction
coefficient

32

1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

Fig. 18 Relationship between friction coefficient and gear
torque ratio

Region ②
Region ②

Gear torque ratio

Comparison of non-reinforced material
and GF reinforced material

Large surface roughness/high temperature (80°C)

5. Conclusion
We have established a basic testing method simulatinga resin worm gear, identified the sliding mode of the tooth
surface, and applied the gathered results to achieve a resin
worm gear with long-term durability and low torque forusage in electric power steering.
1) We have developed a basic testing method that enables
the isolation of wear and creep deformation, which
are the causes of tooth surface deformation. We have

JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

−Clarification of Tribological Behavior on Tooth Surface of Resin Worm Gear for Electric Power Steering−

applied this testing method to the development of a
new resin material. In addition, by clarifying creep
deformation as the main factor in polyamide tooth
surface deformation, we have improved the durability
life of the resin worm gear by utilizing a highmolecular mass polyamide.
2) The basic test has clarified that the lubrication
conditions of the resin worm gear are within the IE
lubrication region. We have also confirmed that within
this lubrication region, the dependence of the friction
coefficient on surface roughness and temperaturedepends in turn on the change in film thickness
ratio, and that it is possible to estimate surface
roughness that will achieve the target rotation torque.
These technologies, which lower rotation torque bycontrolling the roughness of the resin tooth surface,have been applied to the resin worm gear for electric
power steering.

10) M. Muraki, Tribology Science of wear and lubrication
technology, Nikkan kogyo shinbunsha, 2007, 217

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JTEKT ENGINEERING JOURNAL English Edition No. 1013E (2016)

T. KUNISHIMA*

K. MIYAKE*

T. KUROKAWA*

H. ARAI**

Material R&D Dept., Research & Development
Headquarters

33