Inner Ring Fracture Characteristics Under Rolling Contact by fdh56iuoui

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									    Inner Ring Fracture Characteristics
    under Rolling Contact
    Kiyoshi Hirakawa, Norifumi Ikeda, Shigeru Okita and Akihiro Kiuchi
    Basic Technology Research & Development Center

ABSTRACT
   Inner ring fracture sometimes occurs if a rolling bearing is mounted with relatively high hoop stress. NSK has
developed a life test method for inner ring fracture in order to study and develop appropriate materials and effective heat
treatment processes. This method enables accurate simulation of actual inner ring fracture by providing a minute half-
ellipse fatigue crack at a selected “origin point” on the inner ring raceway.
   Using this method, life test results on inner ring fracture caused by hoop stress showed that inner ring fracture life and
hoop stress correlate relatively well. Next, the effect of material and heat treatment on inner ring fracture life was
studied. It was confirmed that compressive residual stress is effective in extending inner ring fracture life. In particular,
it was shown that a fatigue crack in M50NiL at 280 MPa hoop stress propagates negligibly.
   Applying results obtained through this test method, NSK developed a special steel and heat treatment (“TL”
specification) that results in excellent dimensional stability and superior inner ring fracture life and rolling fatigue life,
even under conditions of high temperature and contaminated lubrication.


1. Introduction                                                       resistance, it is necessary to have suitable evaluation
                                                                      technology. Tensile, impact and fracture toughness testing
   The inner ring of a roller bearing mounted with                    are not effective for evaluating inner ring fracture
relatively high hoop stress sometimes fractures in the                resistance. Concerning this problem, Aberbach and co-
axial direction after a certain period of usage. Particularly         researchers used Compact Tension Specimens to analyze
in the aerospace industry, demand is high for increased               the influence of residual stress on the rate of crack
resistance to inner ring fracture as bearings in today’s jet          propagation, as well as consider compressive residual
engines are subjected to ever-higher centrifugal forces.              stress.1) Clark performed tests under hoop stress after
Fatigue cracking and ultimately in some cases, fracture,              using electrical discharge machining to introduce semi-
are believed to result from repeated rolling stress being             circular defects (0.36 × 0.71 mm) onto the inner ring
applied to an inner ring raceway that is under tensile                raceway surfaces of cylindrical roller bearings made of
stress caused by hoop and centrifugal stress. Fatigue                 M50 and M50NiL steel.2) Under hoop stress of 30 ~ 38 ksi
cracking is thought to originate at surface or subsurface             (206 ~ 261 MPa), the inner ring of the M50 bearing
stress concentrations caused by nonmetallic inclusions,               fractured as a result of the defect while that of the
flaking or rust. Fig. 1 shows an example of the inner ring            M50NiL bearing did not. Additionally, Pearson, based on
fracture of a spherical roller bearing with a tapered bore            both experiments and an analysis of the literature,
used in a paper-making machine.                                       discussed the stress limits of crack propagation in
   In order to develop effective materials and heat                   AISI52100 and M50NiL steel under hoop stress in the
treatment methods that improve inner ring fracture                    range of 170 ~ 400 MPa.3) However, he did not discuss the



                                           Origin point




                                                                                                                     100 µm
                                                               5 mm
    a. Fracture surface                                               b. Magnified area of fracture’s origin

Fig. 1 Example of inner ring fracture of a spherical roller bearing



15        Motion & Control No. 7 (December 1999)
                                          Electrode




                                                                                             Bending load
               Notch




                                                                                                               Notch

    a. Schematic of notch produced by electrical discharge machining              b. Cracking propagation by bending fatigue




                                        Notch




          Fatigue crack

                                                                                                     Fatigue crack (Pre-crack)




            c. Notch and fatigue crack from bending fatigue                             d. Removal of notch




                                                                      0.8~1.2mm
                                                              3~4mm




                                                      e. Shape of pre-crack

Fig. 2 Making a fatigue pre-crack


relationship between inner ring fracture life and hoop stress.           2. Procedure for Inner Ring Fracture
   As summarized above, no data was found in the                            Life Tests
literature to connect hoop stress or residual stress and
inner ring fracture life. Considering the need for such data               Inner ring fracture and flaking of rolling bearings
and understanding the necessity of creating a method that                originate from stress concentrations caused by dents, rust,
produces inner ring fracture without generating flaking,                 or nonmetallic inclusions. When the hoop stress of the
NSK developed an inner ring fracture life test that can                  inner ring is low and the stress concentration is at the
reproduce and confirm the morphology of inner ring                       subsurface site of a nonmetallic inclusion, a fatigue crack
fractures that occur during actual applications. Using this              will initiate from the nonmetallic inclusion, propagate
method, we conducted tests to determine the relationship                 around the bearing’s circumference almost parallel to the
between hoop stress, residual stress and inner ring                      raceway surface and flaking will occur. If hoop stress is
fracture life in roller bearings. In this report, we present             high, the fatigue crack will propagate perpendicularly to
our method for inner ring fracture life testing, discuss test            the raceway surface (i.e., down toward the shaft), expand
results on various types of steel (including NSK’s own TL-               axially and eventually lead to inner ring fracture.4)
specification steel), and analyze how hoop stress and                      It is necessary to be able to make artificial crack origin
residual stress affect inner ring fracture life.                         points of a consistent size and shape in order to evaluate



                                                                   Motion & Control No. 7 (December 1999)                        16
the effectiveness of heat treatments and materials against                        during the rotation test. The tests discussed here were
inner ring fracture. As defects made just by electric                             conducted with bearing loads of 19 600 N (P/C = 0.19) and
discharge processing can result in flaking originating from                       29 400 N (P/C = 0.28) at a rotational speed of 1 800 rpm.
the defect’s edge, NSK has developed a method to                                  Fracture life (N) in these tests is defined as the number of
introduce fatigue “pre-cracks” to avoid flaking. Fatigue                          revolutions until the inner ring is fractured or bearing
pre-cracks are half-ellipse-shaped and positioned                                 vibration becomes excessively high from the propagation of
perpendicularly to the raceway surface in the center of the                       the pre-crack into a fatigue crack over the width of the
inner ring raceway of cylindrical roller bearings (NU216).                        raceway surface. Hoop stress is calculated from the
There are three steps in the process of making a fatigue                          amount of expansion of the bore of the inner ring that is
pre-crack. First, a half-ellipse shaped notch is made on the                      mounted on the tapered shaft. Hoop stress is also
raceway surface by electrical discharge processing (Fig. 2-                       measured using a strain gauge. The calculated values
a). Then, by applying bending fatigue, cracking propagates                        correlate well with measured ones.
from the notch (Figs. 2-b and c). Finally, the notch is
removed by machining leaving only the fatigue pre-crack
(Figs. 2-d and e). The pre-cracks in these tests had a                            3. Results of Inner Ring Fracture
length of 3 ~ 4 mm and a depth of 0.8 ~ 1.2 mm. The width                            Life Tests
of the pre-cracks was so small that it could only be
detected by magnetic particle detection. Generally                                  Hoop stress was the primary variable in these tests
speaking, rolling contact stress causes fatigue cracking to                       because it is the most important factor influencing inner
propagate from the pre-crack. In some cases this                                  ring fracture life in most applications. Table 1 shows the
ultimately leads to fracture.                                                     hardness, heat treatment, and material of the inner rings
  In our inner ring fracture testing, an inner ring with a                        used in these tests. Fig. 4 presents the results of inner ring
fatigue pre-crack is mounted on the tapered shaft of the                          fracture life tests.
test rig (Fig. 3). Both hoop stress and load are applied
                                                                                  3.1 Results of AISI52100 bearing steel inner
                                                                                      ring fracture life tests
                                                                                    Fig. 5-a shows the pre-crack in an inner ring made of
                                                                                  standard 52100 bearing steel before testing. Fig. 5-b shows
                                                                                  the inner ring after fracture and Fig. 5-c shows the
                                      Test bearing                                fracture surface. There are three areas labeled in Fig. 5-c:
                                                                                  A is the area of the pre-crack, B is the area that
                                                                                  progressively fractured due to rolling contact fatigue, and
                                                                                  C is where the fracture rapidly progressed.
                                                                                    Because inner ring fracture often occurs in applications
                                   Pre-crack                                      with higher temperatures and hoop stress, high-
                                                                                  temperature-tempered 52100 inner rings and bainite-
                                                                                  treated 52100 inner rings were tested in addition to
                                                                                  standard heat-treated ones. The results are included in
                                                                                  Fig. 4. As shown in the figure, the bainite-treated 52100
Fig. 3 Cross-section of inner ring fracture test rig
                                                                                  inner rings exhibited much longer fracture life than either

Table 1 Materials, heat treatment and hardness
                                                                    Chemical composition
No.         Classification                     Material                                                      Heat treatment                  Hardness
                                                              C      Cr     Mo      V      Ni
      Bearing steel, standard
 1                                         AISI52100         1.0     1.5     —      —      —     840°C, oil quenching, 180°C tempering     HRC      62.5
      heat treatment

      High-temperature-                                                                          840°C, oil quenching,
 2                                         AISI52100         1.0     1.5     —      —      —                                               HRC      60
      tempered bearing steel                                                                     high-temperature tempering

      Bainite-treated
 3                                         AISI52100         1.0     1.5     —      —      —     850°C, 240°C salt quenching (4 hrs)       HRC      59
      bearing steel

      High-speed steel for high-
 4                                               M50         0.8     4.0    4.2    1.0     —     1100°C, oil quenching, 550°C tempering    HRC      62
      temperature bearings

      Carburized high-speed steel                                                                Carburizing, 1100°C, oil quenching,       Raceway surface
 5                                             M50 NiL       0.13    4.1    4.2    1.2     3.4                                             HRC      62
      for high-temperature bearings                                                              550°C tempering
                                                                                                                                           Core HRC 38
      High-temperature-
 6                                          SAE5120          0.2     1.0     —      —      —     Carburizing, high-temperature tempering   HRC      59.5
      tempered carburized steel

                                       Newly developed,                                          Carbo-nitriding,
 7    TL specification steel                                          Patent pending                                                       HRC      61
                                       case-hardened steel                                       high-temperature tempering




17        Motion & Control No. 7 (December 1999)
                                          500
                                                            Standard heat-treated bearing steel with pre-crack ( σ R = 0 ~ 20 MPa)
                                                            Standard heat-treated bearing steel without pre-crack
                                                            High-temperature-tempered bearing steel with pre-crack
                                          450               Bainite-treated bearing steel with pre-crack (σ R = -120 MPa)
                                                            Bainite-treated bearing steel without pre-crack
                                                            M50 with pre-crack ( σ R = -20 ~ -50 MPa)
                                          400               M50NiL with pre-crack ( σ R = -250 MPa)
                                                            TL specification with pre-crack (σ R = -250 MPa)
                                                            TL specification without pre-crack
                                                            Carburized steel with pre-crack (σ R = -200 MPa)
                                          350
           Fitting stress σ t , MPa




                                                Marks with an arrow pointing to the right indicate that
                                                no fatigue cracking was observed.

                                          300



                                          250



                                          200



                                          150
                                                                                 P/C = 0.28


                                          100


                                                      105                          106                        107                    108    109

                                                                                                  Fracture life N, rev.
Fig. 4 Results of inner ring fracture test (P/C = 0.19)




                                                                          1 mm
                                                                                                                                           5 mm
   a. Pre-crack (magnetic particle detection image)
                                                                                                    b. Inner ring after fracture


                                      B          A




                       C                                             5 mm

   c. Fracture surface (A-Pre-crack, B-Fatigue cracking, C-Section of rapid fracture)

Fig. 5 Pre-crack and inner ring fracture of 52100 inner ring (Standard heat treatment, Hoop stress σt = 210 MPa, N = 6 × 106 rev.)



                                                                                               Motion & Control No. 7 (December 1999)             18
the standard heat-treated or high-temperature-tempered                   inner ring fractured (Fig. 5-b), whereas the fatigue crack of
inner rings. This result is attributed to the higher                     the M50 inner ring stopped at the raceway width and then
compressive stress in the surface of the bainite-treated                 propagated like flaking (Fig. 6-b).
inner rings. Overall, the test results indicate a good                     The circumferential sections of the 52100 and M50 inner
correlation between hoop stress (σt) and inner ring                      rings in Figs. 7-a and b show how the fatigue cracks
fracture life (N) and show that inner ring fracture life                 developed. The fatigue crack of the 52100 inner ring is
decreases with increasing bearing load.                                  almost straight while that of the M50 inner ring branches
                                                                         out in different directions. The nature of the M50 fatigue
3.2 Results of M50 inner ring fracture life tests                        crack is believed to be due to M50’s high tempering
  M50 is a bearing steel for high-temperature                            temperature.
applications. It is used for bearings, such as those in gas
turbines and jet engines, that exceed operating                          3.3 Results of M50NiL inner ring fracture
temperatures of 200°C.                                                       life tests
  Testing of M50 inner ring fracture life was conducted on                  M50NiL is case-hardened M50 steel that was developed
two bearings at two levels of hoop stress: 200 MPa and 270               for the high rotating speeds of jet engine bearings.
MPa. In both bearings, fatigue cracks propagated almost                  Because M50NiL has lower carbon content and contains
over the entire raceway width and vibration increased                    Ni, its core has greater toughness and its case higher
after about N = 3 × 106 revolutions. As testing continued,               compressive residual stress than M50.
the inner ring under hoop stress of 270 MPa fractured at                    M50NiL exhibited longer inner ring fracture life than
N = 1.5 × 107 revolutions while that under hoop stress of                both 52100 and M50. Virtually no fatigue cracking was
200 MPa managed N = 2.2 × 107 revolutions without                        observed after N = 1.7 × 108 rotations under hoop stress of
fracturing before the test was discontinued due to                       280 MPa. When the hoop stress was raised to 390 MPa
excessive vibration. As Fig. 4 shows, the inner ring                     and after N = 5 × 107 rotations, a fatigue crack propagated
fracture life of M50 is almost equivalent to 52100.                      from the pre-crack across the raceway width but the inner
However, comparing Figs. 5-b and 6-b, the condition of the               ring did not fracture (Fig. 8). Similar to the fatigue crack
fatigue cracking on the raceway surface of the M50 inner                 in the M50 inner ring, the fatigue crack in the M50NiL
ring is different from that of the 52100 inner ring. The                 ring branches out in different directions (Fig. 7-c).
fatigue crack of the 52100 inner ring propagated in an                      It is believed that the higher compressive residual stress
almost straight line in the axial direction and then the                 (-250 ~ -300 MPa) of M50NiL is primarily responsible for



                                                                                                  Raceway width




                                                 1 mm

     a. Pre-crack (magnetic particle detection image)



                     B                 A
                                                                                                                           5 mm

                                                                         b. Fatigue crack propagation from pre-crack




                 C                              5 mm

    c. Raceway cross-section (A-Pre-crack, B-Fatigue cracking, C-Section fractured on purpose to facilitate observation)


Fig. 6 Pre-crack and fatigue crack propagation from pre-crack (M50, Hoop stress σt = 200 MPa, N = 2.2 × 107 rev.)



19        Motion & Control No. 7 (December 1999)
                                                      Fatigue
                                                      progression
                                                      area



                                                       Area
                                                       rapidly
                                                       fractured
                                             1 mm                                                                   1 mm

   a. 52100 (Standard heat treatment, σt = 210 MPa,                           a. Pre-crack (magnetic particle detection image)
      N = 6 × 106 rev.)




                                                      Fatigue
                                                      progression
                                                      area



                                                      Area fractured
                                                      on purpose to
                                                      facilitate
                                             1 mm     observation                                                  5 mm
                                                                              b. Fatigue crack propagation from pre-crack
   b. M50 (σt = 200 MPa, N = 2.2 × 107 rev.)



                                                                                             A              B
                                                      Fatigue
                                                      progression
                                                      area



                                                      Area fractured
                                                      on purpose to
                                                      facilitate                           C                       5 mm
                                             1 mm     observation
                                                                              c. Raceway cross-section (A-Pre-crack, B-Fatigue cracking,
   c. M50NiL (σt = 390 MPa, N = 5 × 107 rev.)
                                                                                 C-Section fractured on purpose to facilitate observation)


 Fig. 7 Fatigue crack propagation                                          Fig. 8 Pre-crack and fatigue crack propagation from pre-crack
        (Circumferential sections of inner rings)                                 (M50NiL, Hoop stress σt = 390 MPa, N = 5 × 107 rev.)


its long inner ring fracture life.                                          In rolling contact fatigue (flaking) life tests, TL bearings
                                                                          showed exceptionally long life under conditions of
3.4 Inner ring fracture life and rolling contact                          contaminated lubrication at high temperatures due to the
    fatigue life of TL bearings                                           high hardness of their raceways (see the Weibull plotting
  NSK’s new TL bearings are made of special case-                         of test results in Fig. 9).
hardened steel and undergo carbo-nitriding. (TL stands for
Tough and Long-life.) Their compressive residual stress is                  3.5 Results of inner ring fracture life tests
equivalent to conventional carburized steel bearings and                      without pre-cracks
they have higher raceway hardness than high-                                We have already discussed the influence of heat
temperature-tempered 52100 bearings or conventional                       treatment, material, and hoop stress on the fracture life of
carburized steel bearings. As shown in Fig. 4, the inner                  inner rings with pre-cracks. Next, considering inner ring
ring fracture life of TL bearings is on the same level as                 fracture in actual applications, we review tests done on
M50NiL and carburized steel.                                              inner rings without pre-cracks and present analyses of the



                                                                       Motion & Control No. 7 (December 1999)                                20
                                                     99.9

                                                      99

                                                      95
                                                      90
                Accumulated failure probability, %




                                                      50




                                                      10
                                                                                               High-temperature-tempered
                                                                                               bearing steel
                                                                                               Bainite-treated bearing steel
                                                       5
                                                                                               TL-specification steel
                                                                                               High-temperature-tempered
                                                                                               carburized steel

                                                                                           Thrust bearing life test
                                                                                           P max: 4 900 MPa
                                                                                           Test temperature: 130°C
                                                       1
                                                            1   5   10             50    100                   500             1 000
                                                                                                                               ( 105 )




                                                                                                                               +
                                                                         Stress cycles


Fig. 9 Rolling contact fatigue test under high temperature and contaminated oil


origin points of fractures and the effect of hoop stress on                4. Residual Stress and Fracture Life of
fracture life. Tests were conducted on standard heat-                         Inner Rings
treated 52100, bainite-treated 52100 and TL bearings. The
test results are shown in Fig. 4.                                            Fig. 11 shows measurement results on residual stress
  The standard heat-treated 52100 inner ring fractured at                  (σR). Residual stress measurements were made on
N = 1.2 × 108 revolutions under hoop stress of 280 MPa.                    untested inner rings that received the same heat
The fracture surface is shown in Fig. 10-a. The origin point               treatments as the tested inner rings.
of the fracture can be seen near the raceway surface. Fig.                   Fig. 11 shows that the residual stress at the surface of
10-b is a magnified image of the fracture origin point. Fig.               the inner rings ranges from -300 to -500 MPa. This level of
10-c is a further magnification of the origin point showing                stress is attributed to the grinding process. The residual
a nonmetallic inclusion site. Located about 40 µm below                    stress approximately 0.5 mm below the surface of both
the raceway surface, the concave section can be seen                       standard heat-treated and high-temperature-tempered
running almost parallel to the raceway surface. The                        52100 inner rings is approximately 0 ~ +20 MPa. At the
elements Mn, Ca, and S were detected in this concave area                  same approximate depth, the residual stress values for the
by EDS analysis (Fig. 10-d). It was concluded that the                     other inner rings in the tests are as follows: bainite-
inner ring fracture occurred due to the presence of CaS                    treated 52100, approximately -120 MPa; TL specification,
inclusions. Also, an Al2O3 and CaS inclusion site was                      approximately -240 MPa; and M50NiL, approximately
determined to be the fracture origin point in a test under                 -280 MPa.
hoop stress of 230 MPa, and a CaS inclusion was the                          Comparing the inner ring fracture life test results in
fracture origin point in a test under hoop stress of 400                   Fig. 4 to the residual stress values in Fig. 11, inner ring
MPa. As for the bainite-treated 52100 inner rings,                         fracture life becomes longer as compressive residual stress
fractures occurred at Al2O3 and CaS inclusions under hoop                  increases. In the tests, the standard heat-treated 52100
stress ranging from 380 to 410 MPa. In contrast, TL steel                  inner ring fractured at about N = 1 × 107 revolutions under
inner rings did not fracture under hoop stress as high as                  hoop stress of 400 MPa and at about N = 3 × 108
420 MPa. Fractures did finally occur at Al2O3 inclusion                    revolutions under hoop stress of 240 MPa. A bainite-
sites under hoop stress ranging from 470 to 490 MPa. To                    treated 52100 inner ring fractured under hoop stress of
summarize, inner ring fracture occurred at Al2O3 and CaS                   380 MPa at about N = 7 × 107 revolutions. In contrast,
inclusion sites in tests without pre-cracks.                               another bainite-treated 52100 inner ring under hoop
                                                                           stress of 350 MPa and the TL specification inner ring



21       Motion & Control No. 7 (December 1999)
                                         A




                                     B                                     0.5 mm
                                                                                                                                              100 µm
             a. Fracture surface (A-Origin point of fracture,
                                                                                                b. Magnified image of fracture origin point
                B-Fatigue cracking)




                                                                           10 µm

             c. Nonmetallic inclusion site at crack origin                                      d. EDS analysis of chemical composition of nonmetallic
                                                                                                   inclusions at crack origin


Fig. 10 Example of inner ring fracture test result without pre-crack (fatigue crack propagated from nonmetallic inclusions)
        (52100, Hoop stress σt = 280 MPa, N = 1.3 × 108 rev.)


under hoop stress of 430 MPa did not fracture even after N                                  cracks, the importance of compressive residual stress is
= 3 × 108 revolutions.                                                                      clear. There is a distinct tendency for inner rings with
  From the results on inner ring fracture without pre-                                      higher compressive residual stress to have longer fracture
                                                                                            life when fractures originated from nonmetallic inclusions.
                                                                                            We believe the correlation is strong enough to support the
                              +100                                                          conclusion that higher compressive residual stress
                                                                                            prolongs inner ring fracture life.

                                 0
   Residual stress σ R, MPa




                                                                                            5. Conclusion
                              -100

                                                                                            (1) Inner ring fracture life correlates well with
                              -200
                                                                                                compressive residual stress. Compressive residual
                                                                                                stress is effective in extending inner ring fracture life.
                              -300                                                              In particular, it was shown that a fatigue crack
                                               Bearing steel (Standard heat treatment)
                                               Bearing steel (Bainite-treated)                  propagates negligibly in an M50NiL inner ring with a
                              -400             M50                                              pre-crack under 280 MPa hoop stress. The residual
                                               M50NiL
                                               TL specification                                 stress of M50NiL is approximately -280 MPa.
                              -500
                                     0   0.5     1.0       1.5       2.0        2.5         (2) In the tests on inner rings without pre-cracks (results
                                               Depth below surface, mm                          in Fig. 4), the standard heat-treated 52100 inner ring
Fig. 11 Results of residual stress measurements                                                 (residual stress approximately 0 ~ +20 MPa) fractured



                                                                                         Motion & Control No. 7 (December 1999)                          22
   under hoop stress of 400 MPa after about N = 1 × 107              Kiyoshi Hirakawa
   revolutions, and the bainite-treated 52100 inner ring
   (residual stress approximately -120 MPa) fractured
   under approximately the same hoop stress after at
   about N = 7 × 107 revolutions. In contrast, the TL inner
   ring (residual stress approximately -240 MPa) did not
   fracture under hoop stress of 430 MPa after about N =
   3 × 108 revolutions.

(3) The origin points of the inner ring fractures in the tests       Norifumi Ikeda
    without pre-cracks were nonmetallic inclusions such as
    Al2O3 and CaS.

(4) TL-specification bearings with higher raceway surface
    hardness showed longer rolling contact fatigue life
    under high temperature and contaminated oil.


References:                                                          Shigeru Okita
1) B. L. Aberbach, et al, “Fatigue Crack Propagation in
   Carburized High Alloy Bearing Steels,” Metal. Trans., A 16A
   (1985) 1253-1265.
2) J. C. Clark, “Fracture Tough Bearing for High Stress
   Applications,” AIAA-85-1138 AIAA/SAE/ASME/ASEE 21st
   Joint Propulsion Conference July 8 -10 (1985).
3) P. K. Pearson, “Fracture and Fatigue of High Hardness
   Bearing Steels under Low Tensile Stresses,” SAE Technical
   Paper 901628, International Off-Highway and Exposition,
                                                                     Akihiro Kiuchi
   Milwaukee, September 10-13 (1990).
4) T. Czyzwski, “Influence of a Tension Stress Field Introduced in
   the Elastohydrodynamic Contact Zone on Rolling Contact
   Fatigue,” Wear, 34 (1975) 201-214.




23       Motion & Control No. 7 (December 1999)

								
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