Vibrations of the steam generator tubes in nuclear power plants induce stochastic impacts between the tubes and their supports. As a consequence, wear is generated. A test rig is designed and used to perform impacts between two metal crossed cylinders with various incidence angles and impact velocities. The normal and tangential components of the contact load are measured during the tests. Rate and duration of impacts, instantaneous ratio between normal and tangential loads for each impact are deduced. Influence of incidence angle and impact velocity on impact duration, ratio between tangential and normal loads during impact and wear volume is highlighted

Le Bot, Alain

Phalippou, Christian

Rigaud, Emmanuel

Souilliart, Thibaut

I-Revues

22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
 
 
 
Wear generated by sliding impacts 
 
 
T. SOUILLIARTa,b, E.RIGAUDa, A. LE BOTa, C.PHALIPPOUb 
 
 
a. Laboratoire de Tribologie et Dynamique des Systèmes, UMR CNRS 5513, 
Ecole Centrale de Lyon, Université de Lyon, 
36, avenue Guy de Collongue, 69134 Ecully, France 
 
b. Commissariat à l'Energie Atomique et aux Energies Alternatives CEA-Saclay, 
DEN, DM2S, SEMT, DYN, 91191 Gif-sur-Yvette, France 
 
 
Abstract  
 
Vibrations of the steam generator tubes in nuclear power plants induce stochastic impacts between the tubes 
and their supports. As a consequence, wear is generated. A test rig is designed and used to perform impacts 
between two metal crossed cylinders with various incidence angles and impact velocities. The normal and 
tangential components of the contact load are measured during the tests. Rate and duration of impacts, 
instantaneous ratio between normal and tangential loads for each impact are deduced. Influence of 
incidence angle and impact velocity on impact duration, ratio between tangential and normal loads during 
impact and wear volume is highlighted. 
 
Keywords: wear, impact, sliding impact, erosion, tribology 
 
1 Introduction 
 
Heat exchangers of Pressurized Water Reactor (PWR) are composed of thousands of tubes supported by 
baffles and Anti-Vibration Bars (AVB). Functional clearances are needed between tubes and bars because 
of thermal expansion and assembly purposes. In steam generators, tubes are excited by high flow rates. This 
excitation could lead to a dynamic response characterized by sliding impacts between tubes and AVB and 
generate wear [1]. For mechanical systems subjected to sliding impacts, several types of wear exist 
according to the motions and the bodies involved [2]. Sliding impacting is usually studied as an erosive and 
percussive process which leads to both surface and volume degradation. Surface degradation can be 
associated with adhesion [3]  (metal transfer due to sheared asperities junctions) and abrasion [4] (cutting 
of the rubbing surface by hard asperities). Volume degradation is often described as the formation and 
propagation of subsurface fatigue cracks in the material (delamination) [5,6]. Engel [7–9] develops a model 
to predict impact wear based on surfaces conformance in terms of wear formation and a strong dependence 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
with shear stress concerning wear evolution during time. Levy [10] proposes a model based on a 
proportionality with load and sliding distance during impact. Connors [11], Frick [12] and Hoffman [13] 
also propose impact wear models derived from Archard equation. The wear law proposed by Lewis includes 
both a term derived from Engel model and a dependency with sliding distance [14]. Erosion results from 
the impact of streams of solid particles on a surface and not from the impact of two macroscopic bodies. 
Nevertheless, asperities which constitute the contact have a size similar to erosive particles and kinetic 
energy of the solid impactor and an erosive particle have the same order of magnitude. Therefore, erosive 
models can be relevant to describe wear of macroscopic bodies [15,16].  An experimental work is performed 
in order to confirm this hypothesis and to highlight influence of test parameters on wear volume. The first 
section presents the test rig that have been designed and used to generate impacts with various incidence 
angles and velocities. Load and wear measurement protocols, wear conditions and testing parameters are 
explained. The second section goes through the obtained impact characteristics in terms of load evolution 
during impact and generated wear. Experimental results are shown in the third section. Influence of 
incidence angle and impact velocity on impact duration, ratio between tangential and normal loads during 
impact and wear volume is highlighted and discussed. 
 
2 Principle of experiment 
2.1 Test rig 
 
The test rig is shown in Figure 1. Two shakers are placed at ±45° to the vertical and excite a hard steel 
cylinder sample. Two identical springs with the same stiffness (k = 590 N/m) provide the connection 
between the shaker and the sample holder (m = 0.17 kg). Thus, the natural frequency f0 of the impactor is 
9.5 Hz. The incidence angle α to the horizontal is obtained by setting a specific ratio between the amplitudes 
of each of the two shakers sinusoidal inputs. Therefore, any test with an incidence angle between 10° and 
90° can be performed. During its motion, the impactor hits a mild steel cylinder sample that is expected to 
wear. Cylinders are crossed so that a point contact is obtained. 
 
 
 
Figure 1. Test rig 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
2.2 Test samples 
 
The impactor cylinder (Ø = 7 mm, L = 7 mm) has a Vickers hardness of 820 Hv whereas the target (Ø = 7 
mm, L = 7 mm) has a Vickers hardness of 145 Hv. Both have a Young modulus of 200 GPa. 
 
2.3 Load measurement protocol and signal processing 
 
The three components of the contact load are measured by a 3-axis piezoelectric load transducer placed 
behind the sample. Its stiffness is equal to 740 N/µm for the vertical component and 170 N/µm for the X 
and Y components. The mass supported by the load transducer is about 0.1 kg (sample and sample holder), 
so the measure of the contact load is accurate up to 7 kHz for the tangential components and 14 kHz for the 
normal component. Signals are acquired with a dynamic signal acquisition card and a high sampling rate of 
50 kHz in order to correctly measure the contact load during impact. A complete acquisition of the contact 
load during the full length of the test is impossible due to storage space limitations. Therefore, signals are 
acquired during 1500 evenly distributed acquisition windows of 1 second. Signals are processed in order to 
automatically find each impact and retrieve the impact rate, flight and contact durations, normal and 
tangential components of the contact load during impact. Ratio between maxima of tangential and normal 
loads µ is then calculated for each impact. 
 
2.4 Wear conditions and testing parameters 
 
All tests are performed with the following characteristics. The test duration is 17 h, the excitation frequency 
f is chosen about 30 Hz and the excitation levels of the shakers are adjusted in order to obtain a maximal 
normal load during impact of 12 N in average. The Hertz theory applied to an equivalent static contact 
predicts a maximal contact pressure about 1.5 GPa, a contact diameter of 120 µm and a depth of indentation 
𝛿𝛿𝑛𝑛 of 2.1 µm. As the actual contact area is smaller than the apparent one, pressure would be concentrated at 
the top of surface asperities and could generate local plastic deformation. Moderate contact loads are applied 
to focus more on erosive wear than on fatigue or delamination. The set of parameters is chosen to get a 
substantial amount of wear in a relative short time. 
 
2.5 Wear volume analysis 
 
At the end of a test, worn sample is removed from test rig and wear scars are analyzed with an optical 
interferometer (Figure 2). Negative, positive and natural volumes of wear are then retrieved. Uncertainty on 
volume is calculated based on uncertainties of the interferometer measurement and the surface adjustment. 
Minimal wear volume that can be measured is estimated at 10-3 mm3. 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
 
Figure 2. Interferogram of a wear scar 
3 Impacts characteristics 
3.1 Large time scale 
 
Figure 3 shows the time evolution of normal load during 1 s. Impacts are clearly distinguishable as quick 
variations of the contact load. A free flight period separate two successive main impacts which usually last 
about 50 ms. Some main impacts are followed by multiple lower amplitude impacts during a short period 
(about 30 ms). It can be understood as successive rebounds of the impactor that occur after the main impact. 
The dynamics of the system is highly nonlinear due to impacts. The resulting trajectory may therefore be 
periodic, aperiodic or even chaotic. In this case, the trajectory is clearly not periodic and therefore the 
magnitude of impacts is not constant. The impact rate also differs from the excitation frequency for the same 
reason. During a 17 hours duration test, the total number of impacts typically ranges from 1.8 to 3.7 million 
that is to say from 30 to 60 impacts per second. 
 
 
Figure 3. Large time scale evolution of 𝐹𝐹𝑛𝑛 
3.2 Short time scale 
 
Figure 4 shows the time evolution of normal load during a single impact. This curve has a bell shape like 
expected for a typical shock [15]. Contact duration is retrieved from the main peak of normal load and 
usually ranges from 0.4 to 0.8 ms. The maximal value of load during this particular impact is about 20 N. 
The free oscillation of the sample is observable after the impact and its frequency is about 2 kHz. The slight 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
perturbation of the bell shape near the maximal value is also due to the influence of this eigenmode. This 
free response is supposed to have a minimal influence on the value of the maximal load amplitude. 
 
 
Figure 4. Short scale time evolution of 𝐹𝐹𝑛𝑛 during impact 
 
 
3.3 Wear characteristics 
 
Observed wear scars are typically oval and their shapes give information about the mechanical processes 
that take place during impacts. Material is either removed as wear debris or displaced by plastic deformation. 
Thus, positive volumes correspond to displaced material and natural volumes correspond to removed 
material. In the following, wear volumes 𝑊𝑊𝑡𝑡𝑡𝑡𝑡𝑡 and 𝑊𝑊𝑖𝑖𝑖𝑖𝑖𝑖 are defined as natural volume and natural volume 
per impact, that is to say difference between positive and negative measured volumes. In this way, only 
removed material is taken into account. 
 
4 Experimental results and discussion 
4.1 Impact duration and 𝝁𝝁� 
 
The observed impact durations range from 0.4 to 0.9 ms and the corresponding load curve is systematically 
bell-shaped. Figure 5 shows average impact duration 𝑡𝑡𝚤𝚤𝑖𝑖𝑖𝑖������ versus ?̅?𝜇 defined as the average of instantaneous 
ratio between 𝐹𝐹𝑡𝑡 and 𝐹𝐹𝑛𝑛 during a complete test. 𝑡𝑡𝚤𝚤𝑖𝑖𝑖𝑖������  increases with ?̅?𝜇, from 0.4 ms for normal impacts to 
0.9 ms for impacts with a high tangential component. This increase of 𝑡𝑡𝚤𝚤𝑖𝑖𝑖𝑖������  may highlight an increase of 
the sliding distance 𝛿𝛿𝑡𝑡 during contact. 
 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
 
Figure 5. Impact duration versus ?̅?𝜇 
4.2 Instantaneous ratio 𝝁𝝁� and incidence angle 
 
Experiments with various incidence angles are performed. Whereas ?̅?𝜇 and 𝛼𝛼� are usually independent, ?̅?𝜇 is 
here observed to be inversely proportional to incidence angle in the explored range (Figure 6). The linear 
dependence between ?̅?𝜇 and 𝛼𝛼� is expressed in equation (1) and is consistent with previous observations [15] 
under similar experimental conditions. 
 
?̅?𝜇 =  −0.02𝛼𝛼� + 1.9         (15° ≤  𝛼𝛼�  ≤ 70°)                  (1) 
 
 
Figure 6. ?̅?𝜇 versus incidence angle 
4.3 Incidence angle and wear 
 
Wear volume is compared with 𝛼𝛼� to make the connection with erosive wear models (Figure 7). Indeed, most 
of these models relate wear with incidence angle [17–21]. Experimental results show that wear increases as 
the incidence angle is more and more grazing. These experimental values are compared to the erosive wear 
model of Brach [20,22] and Sundararajan [21] in which a normalized shear energy 𝑇𝑇∗ is introduced 
(equations (2) and (3)). In this model, wear volume is assumed to be proportional to this shear energy. 
 
 𝑇𝑇∗ = 1(1+𝜆𝜆) 𝜇𝜇�µ𝑐𝑐 �2 − 𝜇𝜇�µ𝑐𝑐� cos2 𝛼𝛼�                           (2) 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
 
 
 µ𝑐𝑐 = 1(1+𝜆𝜆)(1+𝑒𝑒) tan𝛼𝛼�               (3) 
 
𝑇𝑇∗ is defined as a dimensionless energy transferred to target during an impact. This definition takes two 
sources of energy dissipation into account: an energy associated with the impactor rebound (through 𝑒𝑒) and 
an energy associated with friction (through ?̅?𝜇 and 𝛼𝛼�). Considering asperities as spherical erosive particles 
treated as point masses, it is assumed that 𝜆𝜆 = 0. Furthermore, 𝑇𝑇∗ can be expressed only with ?̅?𝜇 considering 
the experimental law between ?̅?𝜇 and 𝛼𝛼� (equation 1). ?̅?𝜇 is obtained from load measurements during the test. 
The definition of the restitution coefficient 𝑒𝑒 is chosen as the ratio between rebound velocity and incident 
velocity. It is measured with a laser vibrometer on several impacts and we obtain in average 𝑒𝑒 =  0.85. 
Figure 7 shows a very fine agreement between measured wear volumes per impact and the normalized shear 
energy as predicted by Brach in the range [15° 70°]. No experimental investigation has been made for 
incidence angle under 15°. This result confirms that erosive models can be relevant to describe wear of 
macroscopic bodies [16]. 
 
 
Figure 7. Evolution of t* (-) and  
𝑊𝑊𝑖𝑖𝑖𝑖𝑖𝑖 (o) versus 𝛼𝛼� 
4.4 Instantaneous ratio 𝝁𝝁� and wear 
 
Wear is compared with ?̅?𝜇 (Figure 8). As ?̅?𝜇 and 𝛼𝛼� are found to be related with a nearly linear relation (equation 
(2)), it is consistent to find that wear increases with ?̅?𝜇. It is interesting to note that ?̅?𝜇 = 1 seems to be a 
transitional value between two wear modes. Observed wear for ?̅?𝜇 > 1 is much more important than for ?̅?𝜇 <1.  
 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
 
Figure 8. 𝑊𝑊𝑖𝑖𝑖𝑖𝑖𝑖 versus ?̅?𝜇 
Conclusion 
 
Impact wear between two steel crossed cylinders is studied. Experiments are performed and influence of ?̅?𝜇 
on impact duration is highlighted as well the linear dependence between ?̅?𝜇 and 𝛼𝛼�. The influence of ?̅?𝜇 on 
wear is highlighted and experimental results are compared to an erosive wear model. These results confirm 
the importance of shear stress on wear formation. Further work is in progress and aims at adapting the test 
rig in order to make impacts between real heat exchanger tubes and AVB instead of steel cylinders. In this 
way, experimental contact geometry and materials will be more consistent with the real ones. Displacement 
of the impactor will also be measured in order to obtain information about incidence and rebound velocities 
and angles and about sliding distance during impact. 
References 
  
[1] Phalippou, C., Herms, E., and Ruffet, F., 2013, “PWR steam generator tube and AVB wear under 
perpendicular impacting,” Proc. ASME 2013 Press. Vessel. Pip. Conf. 
[2] Ko, P., 1987, “Metallic wear—a review with special references to vibration-induced wear in power 
plant components,” Tribol. Int., 20(2), pp. 66–78. 
[3] Bowden, F. P., and Tabor, D., 1954, The Friction and Lubrication of Solids. 
[4] Rabinowicz, E., 1965, “Friction and Wear of Materials.” 
[5] Suh, P. N., 1973, “The delamination theory of wear,” Wear, 25(1), pp. 111–124. 
[6] Rice, S. L., Nowotny, H., and Wayne, S. F., 1981, “Characteristics of metallic subsurface zones in 
sliding and impact wear,” Wear, 74, pp. 131–142. 
[7] Engel, P. A., 1978, Impact Wear of Materials. 
[8] Engel, P. A., 1978, “Percussive impact wear: A study of repetitively impacting solid components in 
engineering,” Tribol. Int., 11(June), pp. 169–176. 
[9] Engel, P. A., Lyons, T. H., and Sirico, J. L., 1973, “Impact wear model for steel specimens,” Wear, 
23(2), pp. 185–201. 
[10] Levy, G., and Morri, J., 1985, “Impact fretting wear in CO2-based environments,” Wear, 106(1-3), 
pp. 97–138. 
[11] Connors, H., 1981, “Flow-induced vibration and wear of steam generator tubes,” Nucl. Technol. 
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22ème Congrès Français de Mécanique                                                     Lyon, 24 au 28 Août 2015 
[12] Frick, T. M., 1997, “An empirical wear projection technology with steam generator tube applications 
and relations to work-rate and wear simulations/tests,” ASME, 2, pp. 275–282. 
[13] Hofmann, P., Schettler, T., and Steininger, D. A., 1992, “PWR steam generator tube fretting and 
fatigue wear phenomena and correlations,” ASME Vib. Noise, 1, pp. 211–236. 
[14] Lewis, R., 2007, “A modelling technique for predicting compound impact wear,” Wear, 262(11-12), 
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[15] Rigaud, E., and Le Bot, A., 2013, “Influence of incidence angle on wear induced by sliding impacts,” 
Wear, 307(1-2), pp. 68–74. 
[16] Kaiser, A.-L., Bec, S., Vernot, J.-P., and Langlade, C., 2006, “Wear damage resulting from sliding 
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Phys. D. Appl. Phys., 39(15), pp. 3193–3199. 
[17] Finnie, I., 1960, “Erosion of surfaces by solid particles,” Wear, 3, pp. 87–103. 
[18] Bitter, J. G. a., 1963, “A study of erosion phenomena,” Wear, 6, pp. 169–190. 
[19] Tilly, G., 1973, “A two stage mechanism of ductile erosion,” Wear, 23(1), pp. 87–96. 
[20] Brach, R. M., 1988, “Impact dynamics with applications to solid particle erosion,” Int. J. Impact 
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[21] Sundararajan, G., 1991, “A comprehensive model for the solid particle erosion of ductile materials,” 
Wear, 149, pp. 111–127. 
[22] Brach, R. M., 1993, “Classical planar impact theory and the tip impact of a slender rod,” Int. J. 
Impact Eng., 13(1), pp. 21–33.  
 
 9  


Wear generated by sliding impacts

International audienceVibrations of the steam generator tubes in nuclear power plants induce stochastic impacts between the tubes and their supports. As a consequence, wear is generated. A test rig is designed and used to perform impacts between two metal crossed cylinders with various incident angles and impact velocities. The normal and tangential components of the contact load are measured during the tests. Rate and duration of impacts, instantaneous ratio between normal and tangential loads for each impact are deduced. Influence of incidence angle and impact velocity on impact duration, ratio between tangential and normal loads during impact and wear volume is highlighted

Souilliart, T.

Rigaud, E.

Le Bot, A.

Phalippou, C.

HAL Descartes

Colloque avec actes et comité de lecture. Internationale.International audienceVibrations of the steam generator tubes in nuclear power plants induce stochastic impacts between the tubes and their supports. As a consequence, wear is generated. A test rig is designed and used to perform impacts between two metal crossed cylinders with various incidence angles and impact velocities. The normal and tangential components of the contact load are measured during the tests. Rate and duration of impacts, instantaneous ratio between normal and tangential loads for each impact are deduced. Influence of incidence angle and impact velocity on impact duration, ratio between tangential and normal loads during impact and wear volume is highlighted

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Wear generated by sliding impacts

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