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Experimental investigation on identifying friction state in lubricated tribosystem based on friction-induced vibration signals
Mechanical Systems and Signal Processing 138 (2020) 106590
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Experimental investigation on identifying friction state in lubricated tribosystem based on friction-induced vibration signals Pengfei Xing, Guobin Li ⇑, Hongtao Gao, Guoyou Wang Marine Engineering College, Dalian Maritime University, Dalian 116026, China
a r t i c l e
i n f o
Article history: Received 21 May 2019 Received in revised form 29 November 2019 Accepted 18 December 2019
Keywords: Friction-induced vibration Lubricated tribosystem Friction state Identifying Experimental investigation
a b s t r a c t The aim of the present paper is to indicate how to identify friction state by the frictioninduced vibration in a lubricated tribosystem. The friction-induced vibration signals with two different amplitude-frequency characteristics were respectively extracted from the measured vibration signals and their relationships with friction state were discussed. The results show that the friction-induced vibration is closely related to the friction state and can be used to identify the friction state. Therefore, the proposed approach can be a reliable tool for identifying friction state. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction In a mechanical system, friction is an inevitable phenomenon, which not only leads to the energy consumption and material loss, but also affects the working performance and service life of machines [1–3]. Therefore, to extend fault-free operation time and to reduce material and energy losses as well, it is essential to know the friction state of machines. It is well known that the friction state can be characterized by some tribological characteristic parameters, such as friction torque [4], friction coefficient [5–7], and oil film thickness [8] etc.. However, in real-life machine systems, it is difficult to obtain these parameters on site due to limitations of measurement methods [9], though they are an available way to investigate the friction state. Hence friction-induced vibration (FIV) is introduced, as it is one of the most important tribological characteristic parameters [10], and it can be acquired easily in real-time. For these reasons, it is proposed by some studies that FIV could be used to distinguish the friction state [11–23]. However, most of them only focus on the vibrations caused by nonlubricated friction between the surfaces of friction pair, and it is still not clear how the FIV will change in the lubricated friction. Indeed, FIV can become more complicated when lubricated interfaces are involved [24,25]. Therefore, in order to identify the friction state in the lubricated friction, it is necessary to investigate the relationship between FIV and friction state. At present, according to the contact pressure level between the friction pairs, the FIV can be classified into two major categories, i.e. the ‘‘strong contact-induced vibration response” (the vibrational response triggered under strong contact) and the ‘‘weak contact-induced vibration response” (the vibrational response triggered under weak contact) [26]. Some studies [1,22,26,27] have shown that the ‘‘strong contact-induced vibration response” is often characterized by periodic signal of high peak value with a discontinuous narrowband frequency spectrum, lumped on the system natural frequencies ⇑ Corresponding author at: Marine Engineering College, Dalian Maritime University, No.1 Linghai Road, Dalian City, Liaoning Prov. 116026, China. E-mail addresses: [email protected] (P. Xing), [email protected] (G. Li), [email protected] (H. Gao), [email protected] (G. Wang). https://doi.org/10.1016/j.ymssp.2019.106590 0888-3270/Ó 2019 Elsevier Ltd. All rights reserved.
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(fundamental frequencies) and their harmonics (or sub-harmonics); while the ‘‘weak contact-induced vibration response” is often characterized by aperiodic signal of low peak value with a continuous broadband frequency spectrum, related to the eigenfrequencies of the roughness asperities. In fact, the differences in vibration response triggered by the friction pair largely arise from the variation of contact forces at the interface where the sliding surfaces meet [26]. Moreover, the contact forces between the friction pair ultimately depends on the specific mechanical system, the applied boundary conditions and contact interface features [1]. Therefore, considering different driving mechanisms of FIV, it is proposed to use these two types of vibrational response to identify the friction state of the system with a lubricated interface. More specifically, the ‘‘strong contact-induced vibration response” and the ‘‘weak contact-induced vibration response” are extracted from the FIV respectively, and their relationships with the friction state are investigated by the help of minimum oil film thickness and friction coefficient. The main contribution of this study is to reveal the relationships between two types of vibrational response and friction state in the case of lubricated friction, according to which a new method is proposed for identifying friction state. In order to verify the validity of the proposed method, in this paper, the experiments were conducted on the sliding bearing test bench by rotating sliding friction pairs under different friction state. The vibration signals of the bearing housing were collected during the experiments. According to the methodology in our previous researches [28,29], the harmonic wavelet packet transform (HWPT) was employed to extract the FIV signals with different amplitude-frequency characteristics from measured vibration signals, and then their relationships with minimum oil film thickness and friction coefficient were discussed. Finally, according to their relationships, a new method was proposed for identifying friction state. 2. Experimental details 2.1. Experimental equipment As is shown in Fig. 1, the experiments were conducted on a sliding bearing test bench consisting of a test system. In Fig. 1, a motor with the rotating speed ranging from 0 to 350 r/min was applied to drive the shaft through the V-belt. The shaft was installed in the box and immersed in the lubricating oil, and supported by two rolling bearings. A half shaft bearing was located above the shaft. The two dial indicators with the sensitivity of 0.001 mm and the range of 1 mm were equipped on the upper left corner and the upper right corner of the half shaft bearing respectively to measure the offset of the shaft. The friction force measurement device was laid on the test rig and it was used to measure friction force. The loading screw was designed to apply load on the half shaft bearing and the load was detected by a load sensor with the sensitivity of 0.5 N and the range of 980 N. A triaxle acceleration sensor with the sensitivity with 100 mV/g and the range of 50 g was fixed on the bearing housing to measure vibration signals. 2.2. Friction pairs material The shaft is made of 40 Cr hardened steel with 49HRC hardness, 65 mm diameter, and Ra = 0.8 lm surface roughness. The half shaft bearing is made of ZCnSn5Pb5Zn5 (ZQSn6-6-3) cast copper alloy with 65 mm inner diameter, 167 mm effective width, and Ra = 1.6 lm surface roughness. The CD40 lubricating oil with the density of 0.8957 g/cm3 and the viscosity of 139.6 cS at 40 and 12.5 cS at 100 was used as the lubricant in experiments. 2.3. Experiment set-up In order to obtain different friction state of sliding bearing system, the variable rotating speed experiments were performed under a certain constant load. The rotating speed was gradually increased from 15 r/min to 240 r/min with the step length of 15 r/min under a load of 700 N, and the running time at each rotating speed was 10 min.
Fig. 1. Schematic diagram of sliding bearing test bench.
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2.4. Acquisition of data (1) Tribological characteristic parameters During the experiments, the offset of shaft and the friction force were respectively measured under different rotating speeds, as is showed in Figs. 2 and 3. Based on the measured data, the minimum oil film thickness hmin [30] and friction coefficient f [31] can be obtained as follows:
hmin ¼ C e
ð1Þ
f ¼ F=W
ð2Þ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i2 h i2 pCffiffi d1 pCffiffi d2 In Eq. (1), C = 0.075 mm is the radius clearance; e is the eccentricity of the shaft, e ¼ þ ; d1 is the 2 2 offset of shaft in the upper left corner direction and d2 is the offset of shaft in the upper right corner direction. In Eq. (2), F is the friction force; W is normal load, W ¼ W 0 þ W 1 ; W 0 = 31.4 N is the weight of bearing housing and sensors ; W 1 = 700 N is the applied load. (2) Vibration signals A data acquisition system was applied to collect the vibration signals from the acceleration sensor with 10,240 sampling points and a sampling interval of 0.195 ms. During the experiments, a set of time series of vibration signal was collected every 20 s. At each rotating speed, 30 groups of vibration signals were obtained. 2.5. Determination of friction state According to the method reported in the literature [32], the friction state under different rotating speeds were determined by the film thickness ratio L, i.e. the boundary friction (L < 1), the mixed friction (1 < L < 3) and the fluid friction (L > 3). The film thickness ratio L can be calculated as follows:
d L ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R1 þ R22
ð3Þ
In Eq. (4), d is the minimum oil film thickness; R1 is the surface roughness of bearing; R2 is the surface roughness of shaft. During the experiments, the range of film thickness ratio under different rotating speeds was listed in Table 1. It is clearly seen from Table 1 that the system was in boundary friction state in the range of 15 r/min to 60 r/min; in mixed friction state in the range of 75 r/min to 150 r/min; in fluid friction state in the range of 165 r/min to 240 r/min.
Fig. 2. The measured offset of shaft under different rotating speeds.
Fig. 3. The measured friction force under different rotating speeds.
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P. Xing et al. / Mechanical Systems and Signal Processing 138 (2020) 106590 Table 1 Range of film thickness ratio under different rotating speeds. Rotating speed (r/min)
Film thickness ratio L
Friction state
15–60 75–150 165–240
0.311–0.863 1.811–2.953 3.936–4.825
Boundary friction (L < 1) Mixed friction (1 < L < 3) Fluid friction (L > 3)
3. Workflow and implementation method The proposed workflow showed in Fig. 4 involves three approaches: spectrum analysis of vibration signals, extraction of vibration signals, and root mean square (RMS) calculation of vibration signals. 3.1. Spectrum analysis of vibration signals In order to investigate the amplitude-frequency characteristics of the measured vibration signals, the spectrum analysis was performed. Fig. 5 is the time-domain waveform and spectrum of measured vibration signal (taking the signal at 45 r/min as an example). It can be seen from Fig. 5a and b that the measured vibration signal is an aliasing signal containing periodic and aperiodic components. Furthermore, it can be observed from Fig. 5b that the periodic components concentrate on the spectral lines with high amplitude values, such as the main frequency of 114 Hz and the frequency-doubling of 228 Hz; the aperiodic components distribute on the continuous spectra between the various spectral lines with low amplitude values, such as the continuous spectrums between 0 Hz and 100 Hz, 201 Hz and 300 Hz, etc..
Fig. 4. The proposed workflow.
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Fig. 5. The time-domain waveform and spectrum of measured vibration signal.
3.2. Extraction of vibration signals Although the measured vibration signals with different time-frequency components are mainly excited by frictions, the background noise originating from other excitations such as current excitation is inevitable. To eliminate the effects of background noise, based on previous researches [28,29], the HWPT was used to extract the FIV signals from the measured vibration signals. In this report, a 10-layer HWPT was selected to decompose the measured vibration signals into 1024 frequency bands, and the bandwidth of each frequency band is 2.5 Hz. According to driving mechanisms of FIV [1,22,26,27], the signals in different frequency bands are selected to reconstruct the FIV response with different time-frequency characteristics, and the details are as follows: 3.2.1. The ‘‘strong contact-induced vibration response” The ‘‘strong contact-induced vibration response” is often characterized by periodic signal of high peak value with a discontinuous narrowband frequency spectrum, lumped on the system natural frequencies (fundamental frequencies) and their harmonics (or sub-harmonics), thus the main frequency and frequency doubling components in the measured vibration signals were directly selected to reconstruct the ‘‘strong contact-induced vibration response”. 3.2.2. The ‘‘weak contact-induced vibration response” The ‘‘weak contact-induced vibration response” is often characterized by aperiodic signal of low peak value with a continuous broadband frequency spectrum, thus the aperiodic components in a certain frequency range were selected to reconstruct the ‘‘weak contact-induced vibration response”. In this paper, every 40 adjacent frequency bands with 2.5 Hz bandwidth were treated as one continuous broadband frequency spectrum with 100 Hz bandwidth, and 25 sets of signals in different bands (i.e. 0–100 Hz, 101–200 Hz until 2401–2500 Hz) were reconstructed. During the reconstruction of each set of signals, a mean amplitude of signal was used as a threshold to distinguish periodic and aperiodic components, i.e. the components with the amplitude greater than the threshold were considered as periodic components and they were removed from the reconstructed signal. Furtherly, to determine the frequency band in which the ‘‘weak contact-induced vibration response” exists, the root mean square (RMS) of each set of reconstructed signals was calculated under different rotating speeds. Based on previous researches [29], the reconstructed signal whose RMS value changes in accordance with the friction coefficient was chosen as the ‘‘weak contact-induced vibration response”. Therefore, in this paper, the aperiodic components in the frequency band of 0–100 Hz were selected to reconstruct the ‘‘weak contact-induced vibration response”. 3.2.3. Result analysis According to the method proposed above, the ‘‘strong contact-induced vibration response” and the ‘‘weak contactinduced vibration response” were respectively extracted from the measured signals under three types of friction states, as showed in Fig. 6. It is clearly observed from the time-domain waveform and spectrum in Fig. 6I–6III that the extracted ‘‘strong contact-induced vibration response” is the periodic signal with large amplitude value, and it has a discontinuous narrowband frequency spectrum; the extracted ‘‘weak contact-induced vibration response” is the aperiodic signal with small amplitude value, and it has a continuous broadband frequency spectrum. Moreover, it can be seen that the amplitudes of extracted signals are significantly different under three friction states, i.e. large amplitude values at boundary friction state (Fig. 6I (b),(c),(e) and (f)), intermediate amplitude values at mixed friction state (Fig. 6II (b),(c),(e) and (f)), and small amplitude values at fluid friction state (Fig. 6III (b),(c),(e) and (f)). Therefore, the amplitude of extracted vibration signals is different under different friction states, which implies that the extracted signals can be used to distinguish the friction state.
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Fig. 6. Time-domain waveform and spectrum of signals extracted under three friction states.
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3.3. Root mean square calculation of vibration signals The RMS of vibration signals can be calculated as follows:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMS ¼ t Ai 2 N i¼1
ð4Þ
In Eq. (3), N is the number of sampling points of the signal; Ai is the amplitude of vibration signal at different times. 4. Results and discussion 4.1. Relationship between FIV and friction state Based on the RMS of extracted ‘‘strong contact-induced vibration response” and extracted ‘‘weak contact-induced vibration response”, the relationship between the FIV and the friction state was discussed by the help of minimum oil film thickness and friction coefficient. 4.1.1. Relationship between extracted ‘‘strong contact-induced vibration response” and friction state The correlation between the extracted ‘‘strong contact-induced vibration response” and friction state was discussed by the minimum oil film thickness. Fig. 7 is the change of minimum oil film thickness with the different rotating speeds under different friction state. It can be observed that the minimum oil film thickness has three stages: the slowly ascending stage of small value, the sharply ascending stage of intermediate value, and the smoothing stage of large value, which implies that the contact between the shaft and bearing has three conditions: the strong contact condition, the weak contact condition, and the indirect contact condition (i.e. the contact transmitted through the oil film). Under three conditions, the RMS change of extracted ‘‘strong contact-induced vibration response” also show three stages: the ascending stage of large value, the descending stage of intermediate value, and the smoothing stage of small value, as shown in Fig. 8, which implies that the extracted ‘‘strong contact-induced vibration response” is closely related to the contact condition.
Fig. 7. Changes of minimum oil film thickness with rotating speed.
Fig. 8. RMS change of extracted ‘‘strong contact-induced vibration response” with rotating speed.
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(1) Strong contact condition When the rotating speed is from 15 r/min to 60 r/min, the minimum oil film thickness is very small, as shown in Fig. 7, and the calculated film thickness ratio is<1 (as shown in Table 1), which indicates that the system was in boundary friction state. In the boundary friction state, it is widely accepted that the oil film was not thick enough to separate the shaft from the bearing, and the applied load was carried by the contact asperities between the shaft and the bearing rather than by the oil film. Due to the applied load being completely carried by the contact asperities, the shaft and the bearing was in a strong contact condition. Under a strong contact condition, the ‘‘strong contact-induced vibration response” triggered by the contact has large amplitude characteristics, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” is large in the boundary friction state, as shown in Fig. 8. Moreover, the minimum oil film thickness rises slowly with increasing rotating speed, as shown in Fig. 7, which indicates that the lubricating oil slowly entered the contact area. This entry of lubricating oil could prevent the contact of asperity, which leaded to a decrease in the number of contact asperity. Due to the decrease in the number, each contact asperity gradually carried the larger load under a constant applied load, which caused the contact between the shaft and the bearing to enhance slowly. As a result, the ‘‘strong contact-induced vibration response” triggered by the contact also enhanced slowly, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” displays an ascending trend with increasing rotating speed, as shown in Fig. 8. (2) Weak contact condition When the rotating speed continues to increase from 60 r/min to 150 r/min, the minimum oil film thickness is larger than that in the boundary friction state, as shown in Fig. 7, and the calculated film thickness ratio is between 1 and 3 (as shown in Table 1), which indicates the system went into the mixed friction state. In the mixed friction state, it is widely accepted that the applied load was shared between the asperities and the oil film, which means that the bearing load of asperities was reduced. Therefore, despite the still existing asperities contact between the shaft and the bearing, this contact was weak due to a reduction in the bearing load of asperities, i.e. the shaft and the bearing was under a weak contact condition. Compared with the strong contact, the weak contact could trigger small amplitude ‘‘strong contact-induced vibration response”, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” in the mixed friction state is smaller than that in the boundary friction state, as shown in Fig. 8. Moreover, the minimum oil film thickness increases sharply with the increasing rotating speed, as shown in Fig. 7, which indicates that the applied load got transferred significantly to the oil film. Due to the transfer of the applied load to oil film, the contact asperities could share less applied load, which caused the contact between the shaft and the bearing to weaken significantly. As a result, the ‘‘strong contact-induced vibration response” triggered by the contact also weakened significantly, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” displays an obviously descending trend with increasing rotating speed, as shown in Fig. 8. (3) Indirect contact condition When the rotating speed exceeds 150 r/min, the minimum oil film thickness gradually reaches the maximum stable value with the increasing rotating speed, as shown in Fig. 7, and the calculated film thickness ratio is more than 3 (As shown in Table 1), which indicates that the system was in the fluid friction state. In the fluid friction state, it is widely accepted that the applied load was carried by the oil film rather than by the asperities, which means that the contact between the asperities disappeared, and the shaft and the bearing was in an indirect contact condition, i.e. the contact between the shaft and the bearing is transmitted through the oil film. In this research, it is found that under an indirect contact condition, the ‘‘strong contact-induced vibration response” could still be triggered, but its amplitude was very small, and correspondingly, the minimum RMS of extracted ‘‘strong contact-induced vibration response” appears in the fluid friction state, as shown in Fig. 8. Moreover, when the minimum oil film thickness gradually increases and then tends to be stable, the RMS of extracted ‘‘strong contact-induced vibration response” gradually decreases and then tends to be stable, which indicates that the triggered ‘‘strong contact-induced vibration response” was attribute to the role of oil film, but its driving mechanism needs to be further researched. As discussed above, the extracted ‘‘strong contact-induced vibration response” is closely related to the contact between two surfaces, and it can reflect the contact condition. This conclusion is consistent with the driving mechanism of FIV, i.e. the ‘‘strong contact-induced vibration response” is triggered by the contact between the surfaces of friction pair [1,22,26,27]. In this research, it is found that under the indirect contact condition, the ‘‘strong contact-induced vibration response” could also be triggered, but its driving mechanism needs to be further researched. 4.1.2. Relationship between extracted ‘‘weak contact-induced vibration response” and friction state The correlation between the extracted ‘‘weak contact-induced vibration response” and friction state was discussed by friction coefficient. Fig. 9 is the change of friction coefficient with different the rotating speed under different friction state. It can be clearly seen that the friction coefficient has three stages: sharply dropping stage of large value, slowly dropping stage of intermediate value, and smoothly fluctuating stage of small value, which implies that the friction between the journal and bearing has three conditions: the strong friction condition, the weak friction condition, and the liquid friction condition. The RMS of extracted ‘‘weak contact-induced vibration response” shows the same changing trend as the friction coefficient, as shown in Fig. 10, which implies that the extracted ‘‘weak contact-induced vibration response” is closely related to the friction condition.
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Fig. 9. Changes of friction coefficient with rotating speed.
Fig. 10. RMS changes of extracted ‘‘weak contact-induced vibration response” with rotating speed.
(1) Strong friction condition It can be observed from Fig. 9 that the friction coefficient is large under the boundary friction state, which demonstrates that the friction between the shaft and the bearing was severe, and they were in a strong friction condition. Under a strong friction condition, the ‘‘weak contact-induced vibration response” trigged by the friction was intense and its amplitude was large. Correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” is large in the boundary friction state, as shown in Fig. 10. Moreover, the friction coefficient decreases sharply with the increasing rotating speed, as shown in Fig. 9, which indicates that the friction between the shaft and the bearing weakened significantly. As a result, the trigged ‘‘weak contact-induced vibration response” also weakened significantly, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” presents a sharply dropping trend with the increasing rotating speed, as shown in Fig. 10. (2) Weak friction condition Under the mixed friction state, the friction coefficient is smaller than that under the boundary friction state, as shown in Fig. 9, which means that the friction between the shaft and the bearing changed from severe to slight, and they went into a weak friction condition. Compared with the strong friction, the weak friction could trigger small amplitude ‘‘weak contactinduced vibration response”, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” in the mixed friction state is smaller than that in the boundary friction state, as shown in Fig. 10. Moreover, the friction coefficient slowly decreases with the increasing rotating speed, as shown in Fig. 9, which indicates that the friction between the shaft and the bearing weakened slowly. As a result, the triggered ‘‘weak contact-induced vibration response” showed the same change, i.e. it also weakened slowly, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” presents a slowly dropping trend, as shown in Fig. 10. (3) Fluid friction condition Under the fluid friction state, the friction coefficient reaches a minimum value of 0.018, as shown in Fig. 9, which indicates that the weakest friction occurred in the fluid friction state. Therefore, in the fluid friction state, the triggered ‘‘weak contactinduced vibration response” was the weakest, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” also reaches a minimum value of 0.002, as shown in Fig. 10. Moreover, the friction coefficient no longer changes obviously during the increase of rotating speed and it shows a smooth fluctuation, as shown in Fig. 9, which demonstrates that a stable fluid friction was formed between the shaft and the bearing. Thus, the triggered ‘‘weak contact-induced vibration response” also no longer changed obviously, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” shows the same varying trend, i.e. it displays a smoothly fluctuating trend, as shown in Fig. 10.
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Fig. 11. Distributed area of intersection point between the two RMS under different friction states.
As is discussed above, the extracted ‘‘weak contact-induced vibration response” is closely related to the friction between the two surfaces, and it can reflect the friction condition. This conclusion is consistent with the driving mechanism of FIV, i.e. the ‘‘weak contact-induced vibration response” is triggered by the interactions between the surfaces of friction pair [1,26]. In this research, it is found that under the liquid friction, the ‘‘weak contact-induced vibration response” can also be excited, but its driving mechanism needs to be further researched. 4.2. Identification of friction state To identify the friction state by the extracted FIV signals, a plane rectangular coordinate system with the RMS of extracted ‘‘strong contact-induced vibration response” as horizontal axis (X-axis) and the RMS of extracted ‘‘weak contact-induced vibration response” as vertical axis (Y-axis) was established; and the distributed area of intersection point between the two RMS values under different friction states was given in Fig. 11. It can be seen that each friction state has an independent distribution area of intersection point, which indicates that the friction state could be identified by the position of intersection point in the coordinate system. Taking the point A in Fig. 11 as an example, it can be noted that the X coordinate value of point A may appear in three areas, i.e. boundary friction state, mixed friction state, and liquid friction state; while the Y coordinate value of point A may appear in two areas, i.e. boundary friction state and mixed friction state. However, the position of point A is uniquely determined and can only exist in the mixed friction state. Therefore, the identification of friction state can only be achieved by measuring ‘‘strong contact-induced vibration response” and ‘‘weak contact-induced vibration response” simultaneously, rather than only using the FIV signal with an individual amplitude-frequency characteristic. 5. Conclusion In a friction process in which the lubricating oil is involved, the FIV with two different amplitude-frequency characteristics can be simultaneously excited. By investigating the relationship between the FIV and friction state in a given lubrication tribological system, the following conclusions can be summed up from the present studies: (1) The FIV is closely related to the friction state. The extracted ‘‘strong contact-induced vibration response” in FIV signal can reflect the contact condition between the surfaces of friction pair; the extracted ‘‘weak contact-induced vibration response” in FIV signal can reflect the friction condition between the surfaces of friction pair. (2) The identification of friction state can be achieved by measuring extracted ‘‘strong contact-induced vibration response” and ‘‘weak contact-induced vibration response” simultaneously. In this research, it is found that the FIV with two different amplitude-frequency characteristics can be simultaneously excited under different friction state, but their driving mechanism needs to be further researched. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This present project is supported by the National Natural Science Foundation of China (Grant No. 51879020 and 51679022).
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Massi, Validation of a new frictional law for simulating friction-induced vibrations of rough surfaces, Tribol. Int. 121 (2018) 468–480. [23] D.G. Wei, J.W. Song, Y.H. Nan, W.W. Zhu, Analysis of the stick-slip vibration of a new brake pad with double-layer structure in automobile brake system, Mech. Syst. Sig. Process. 118 (2019) 305–316. [24] R.G. Bayer, Mechanical Wear Fundamentals and Testing, revised and expanded, CRC Press, 2004. [25] J-J. Sinou, J. Cayer-Barrioz, H. Berro, Friction-induced vibration of a lubricated mechanical system, Tribol. Int. 61 (2013) 156–168, https://doi.org/ 10.1016/j.triboint.2012.12.018. [26] A. Akay, Acoustics of friction, J. Acoust. Soc. Am. 111 (4) (2002) 1525. [27] H.B. Abdelounis, A. Le Bot, J. Perret-Liaudet, H. Zahouani, An experimental study on roughness noise of dry rough flat surfaces, Wear 268 (1–2) (2010) 335–345. [28] G.B. Li, Y.H. Lin, H.Z. Wang, H.J. Wei, G.Y. Wang, Harmonic wavelet packet analysis of friction-induced vibration, Tribol. 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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/ymssp
Experimental investigation on identifying friction state in lubricated tribosystem based on friction-induced vibration signals Pengfei Xing, Guobin Li ⇑, Hongtao Gao, Guoyou Wang Marine Engineering College, Dalian Maritime University, Dalian 116026, China
a r t i c l e
i n f o
Article history: Received 21 May 2019 Received in revised form 29 November 2019 Accepted 18 December 2019
Keywords: Friction-induced vibration Lubricated tribosystem Friction state Identifying Experimental investigation
a b s t r a c t The aim of the present paper is to indicate how to identify friction state by the frictioninduced vibration in a lubricated tribosystem. The friction-induced vibration signals with two different amplitude-frequency characteristics were respectively extracted from the measured vibration signals and their relationships with friction state were discussed. The results show that the friction-induced vibration is closely related to the friction state and can be used to identify the friction state. Therefore, the proposed approach can be a reliable tool for identifying friction state. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction In a mechanical system, friction is an inevitable phenomenon, which not only leads to the energy consumption and material loss, but also affects the working performance and service life of machines [1–3]. Therefore, to extend fault-free operation time and to reduce material and energy losses as well, it is essential to know the friction state of machines. It is well known that the friction state can be characterized by some tribological characteristic parameters, such as friction torque [4], friction coefficient [5–7], and oil film thickness [8] etc.. However, in real-life machine systems, it is difficult to obtain these parameters on site due to limitations of measurement methods [9], though they are an available way to investigate the friction state. Hence friction-induced vibration (FIV) is introduced, as it is one of the most important tribological characteristic parameters [10], and it can be acquired easily in real-time. For these reasons, it is proposed by some studies that FIV could be used to distinguish the friction state [11–23]. However, most of them only focus on the vibrations caused by nonlubricated friction between the surfaces of friction pair, and it is still not clear how the FIV will change in the lubricated friction. Indeed, FIV can become more complicated when lubricated interfaces are involved [24,25]. Therefore, in order to identify the friction state in the lubricated friction, it is necessary to investigate the relationship between FIV and friction state. At present, according to the contact pressure level between the friction pairs, the FIV can be classified into two major categories, i.e. the ‘‘strong contact-induced vibration response” (the vibrational response triggered under strong contact) and the ‘‘weak contact-induced vibration response” (the vibrational response triggered under weak contact) [26]. Some studies [1,22,26,27] have shown that the ‘‘strong contact-induced vibration response” is often characterized by periodic signal of high peak value with a discontinuous narrowband frequency spectrum, lumped on the system natural frequencies ⇑ Corresponding author at: Marine Engineering College, Dalian Maritime University, No.1 Linghai Road, Dalian City, Liaoning Prov. 116026, China. E-mail addresses: [email protected] (P. Xing), [email protected] (G. Li), [email protected] (H. Gao), [email protected] (G. Wang). https://doi.org/10.1016/j.ymssp.2019.106590 0888-3270/Ó 2019 Elsevier Ltd. All rights reserved.
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(fundamental frequencies) and their harmonics (or sub-harmonics); while the ‘‘weak contact-induced vibration response” is often characterized by aperiodic signal of low peak value with a continuous broadband frequency spectrum, related to the eigenfrequencies of the roughness asperities. In fact, the differences in vibration response triggered by the friction pair largely arise from the variation of contact forces at the interface where the sliding surfaces meet [26]. Moreover, the contact forces between the friction pair ultimately depends on the specific mechanical system, the applied boundary conditions and contact interface features [1]. Therefore, considering different driving mechanisms of FIV, it is proposed to use these two types of vibrational response to identify the friction state of the system with a lubricated interface. More specifically, the ‘‘strong contact-induced vibration response” and the ‘‘weak contact-induced vibration response” are extracted from the FIV respectively, and their relationships with the friction state are investigated by the help of minimum oil film thickness and friction coefficient. The main contribution of this study is to reveal the relationships between two types of vibrational response and friction state in the case of lubricated friction, according to which a new method is proposed for identifying friction state. In order to verify the validity of the proposed method, in this paper, the experiments were conducted on the sliding bearing test bench by rotating sliding friction pairs under different friction state. The vibration signals of the bearing housing were collected during the experiments. According to the methodology in our previous researches [28,29], the harmonic wavelet packet transform (HWPT) was employed to extract the FIV signals with different amplitude-frequency characteristics from measured vibration signals, and then their relationships with minimum oil film thickness and friction coefficient were discussed. Finally, according to their relationships, a new method was proposed for identifying friction state. 2. Experimental details 2.1. Experimental equipment As is shown in Fig. 1, the experiments were conducted on a sliding bearing test bench consisting of a test system. In Fig. 1, a motor with the rotating speed ranging from 0 to 350 r/min was applied to drive the shaft through the V-belt. The shaft was installed in the box and immersed in the lubricating oil, and supported by two rolling bearings. A half shaft bearing was located above the shaft. The two dial indicators with the sensitivity of 0.001 mm and the range of 1 mm were equipped on the upper left corner and the upper right corner of the half shaft bearing respectively to measure the offset of the shaft. The friction force measurement device was laid on the test rig and it was used to measure friction force. The loading screw was designed to apply load on the half shaft bearing and the load was detected by a load sensor with the sensitivity of 0.5 N and the range of 980 N. A triaxle acceleration sensor with the sensitivity with 100 mV/g and the range of 50 g was fixed on the bearing housing to measure vibration signals. 2.2. Friction pairs material The shaft is made of 40 Cr hardened steel with 49HRC hardness, 65 mm diameter, and Ra = 0.8 lm surface roughness. The half shaft bearing is made of ZCnSn5Pb5Zn5 (ZQSn6-6-3) cast copper alloy with 65 mm inner diameter, 167 mm effective width, and Ra = 1.6 lm surface roughness. The CD40 lubricating oil with the density of 0.8957 g/cm3 and the viscosity of 139.6 cS at 40 and 12.5 cS at 100 was used as the lubricant in experiments. 2.3. Experiment set-up In order to obtain different friction state of sliding bearing system, the variable rotating speed experiments were performed under a certain constant load. The rotating speed was gradually increased from 15 r/min to 240 r/min with the step length of 15 r/min under a load of 700 N, and the running time at each rotating speed was 10 min.
Fig. 1. Schematic diagram of sliding bearing test bench.
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2.4. Acquisition of data (1) Tribological characteristic parameters During the experiments, the offset of shaft and the friction force were respectively measured under different rotating speeds, as is showed in Figs. 2 and 3. Based on the measured data, the minimum oil film thickness hmin [30] and friction coefficient f [31] can be obtained as follows:
hmin ¼ C e
ð1Þ
f ¼ F=W
ð2Þ
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h i2 h i2 pCffiffi d1 pCffiffi d2 In Eq. (1), C = 0.075 mm is the radius clearance; e is the eccentricity of the shaft, e ¼ þ ; d1 is the 2 2 offset of shaft in the upper left corner direction and d2 is the offset of shaft in the upper right corner direction. In Eq. (2), F is the friction force; W is normal load, W ¼ W 0 þ W 1 ; W 0 = 31.4 N is the weight of bearing housing and sensors ; W 1 = 700 N is the applied load. (2) Vibration signals A data acquisition system was applied to collect the vibration signals from the acceleration sensor with 10,240 sampling points and a sampling interval of 0.195 ms. During the experiments, a set of time series of vibration signal was collected every 20 s. At each rotating speed, 30 groups of vibration signals were obtained. 2.5. Determination of friction state According to the method reported in the literature [32], the friction state under different rotating speeds were determined by the film thickness ratio L, i.e. the boundary friction (L < 1), the mixed friction (1 < L < 3) and the fluid friction (L > 3). The film thickness ratio L can be calculated as follows:
d L ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R1 þ R22
ð3Þ
In Eq. (4), d is the minimum oil film thickness; R1 is the surface roughness of bearing; R2 is the surface roughness of shaft. During the experiments, the range of film thickness ratio under different rotating speeds was listed in Table 1. It is clearly seen from Table 1 that the system was in boundary friction state in the range of 15 r/min to 60 r/min; in mixed friction state in the range of 75 r/min to 150 r/min; in fluid friction state in the range of 165 r/min to 240 r/min.
Fig. 2. The measured offset of shaft under different rotating speeds.
Fig. 3. The measured friction force under different rotating speeds.
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P. Xing et al. / Mechanical Systems and Signal Processing 138 (2020) 106590 Table 1 Range of film thickness ratio under different rotating speeds. Rotating speed (r/min)
Film thickness ratio L
Friction state
15–60 75–150 165–240
0.311–0.863 1.811–2.953 3.936–4.825
Boundary friction (L < 1) Mixed friction (1 < L < 3) Fluid friction (L > 3)
3. Workflow and implementation method The proposed workflow showed in Fig. 4 involves three approaches: spectrum analysis of vibration signals, extraction of vibration signals, and root mean square (RMS) calculation of vibration signals. 3.1. Spectrum analysis of vibration signals In order to investigate the amplitude-frequency characteristics of the measured vibration signals, the spectrum analysis was performed. Fig. 5 is the time-domain waveform and spectrum of measured vibration signal (taking the signal at 45 r/min as an example). It can be seen from Fig. 5a and b that the measured vibration signal is an aliasing signal containing periodic and aperiodic components. Furthermore, it can be observed from Fig. 5b that the periodic components concentrate on the spectral lines with high amplitude values, such as the main frequency of 114 Hz and the frequency-doubling of 228 Hz; the aperiodic components distribute on the continuous spectra between the various spectral lines with low amplitude values, such as the continuous spectrums between 0 Hz and 100 Hz, 201 Hz and 300 Hz, etc..
Fig. 4. The proposed workflow.
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Fig. 5. The time-domain waveform and spectrum of measured vibration signal.
3.2. Extraction of vibration signals Although the measured vibration signals with different time-frequency components are mainly excited by frictions, the background noise originating from other excitations such as current excitation is inevitable. To eliminate the effects of background noise, based on previous researches [28,29], the HWPT was used to extract the FIV signals from the measured vibration signals. In this report, a 10-layer HWPT was selected to decompose the measured vibration signals into 1024 frequency bands, and the bandwidth of each frequency band is 2.5 Hz. According to driving mechanisms of FIV [1,22,26,27], the signals in different frequency bands are selected to reconstruct the FIV response with different time-frequency characteristics, and the details are as follows: 3.2.1. The ‘‘strong contact-induced vibration response” The ‘‘strong contact-induced vibration response” is often characterized by periodic signal of high peak value with a discontinuous narrowband frequency spectrum, lumped on the system natural frequencies (fundamental frequencies) and their harmonics (or sub-harmonics), thus the main frequency and frequency doubling components in the measured vibration signals were directly selected to reconstruct the ‘‘strong contact-induced vibration response”. 3.2.2. The ‘‘weak contact-induced vibration response” The ‘‘weak contact-induced vibration response” is often characterized by aperiodic signal of low peak value with a continuous broadband frequency spectrum, thus the aperiodic components in a certain frequency range were selected to reconstruct the ‘‘weak contact-induced vibration response”. In this paper, every 40 adjacent frequency bands with 2.5 Hz bandwidth were treated as one continuous broadband frequency spectrum with 100 Hz bandwidth, and 25 sets of signals in different bands (i.e. 0–100 Hz, 101–200 Hz until 2401–2500 Hz) were reconstructed. During the reconstruction of each set of signals, a mean amplitude of signal was used as a threshold to distinguish periodic and aperiodic components, i.e. the components with the amplitude greater than the threshold were considered as periodic components and they were removed from the reconstructed signal. Furtherly, to determine the frequency band in which the ‘‘weak contact-induced vibration response” exists, the root mean square (RMS) of each set of reconstructed signals was calculated under different rotating speeds. Based on previous researches [29], the reconstructed signal whose RMS value changes in accordance with the friction coefficient was chosen as the ‘‘weak contact-induced vibration response”. Therefore, in this paper, the aperiodic components in the frequency band of 0–100 Hz were selected to reconstruct the ‘‘weak contact-induced vibration response”. 3.2.3. Result analysis According to the method proposed above, the ‘‘strong contact-induced vibration response” and the ‘‘weak contactinduced vibration response” were respectively extracted from the measured signals under three types of friction states, as showed in Fig. 6. It is clearly observed from the time-domain waveform and spectrum in Fig. 6I–6III that the extracted ‘‘strong contact-induced vibration response” is the periodic signal with large amplitude value, and it has a discontinuous narrowband frequency spectrum; the extracted ‘‘weak contact-induced vibration response” is the aperiodic signal with small amplitude value, and it has a continuous broadband frequency spectrum. Moreover, it can be seen that the amplitudes of extracted signals are significantly different under three friction states, i.e. large amplitude values at boundary friction state (Fig. 6I (b),(c),(e) and (f)), intermediate amplitude values at mixed friction state (Fig. 6II (b),(c),(e) and (f)), and small amplitude values at fluid friction state (Fig. 6III (b),(c),(e) and (f)). Therefore, the amplitude of extracted vibration signals is different under different friction states, which implies that the extracted signals can be used to distinguish the friction state.
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Fig. 6. Time-domain waveform and spectrum of signals extracted under three friction states.
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3.3. Root mean square calculation of vibration signals The RMS of vibration signals can be calculated as follows:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X RMS ¼ t Ai 2 N i¼1
ð4Þ
In Eq. (3), N is the number of sampling points of the signal; Ai is the amplitude of vibration signal at different times. 4. Results and discussion 4.1. Relationship between FIV and friction state Based on the RMS of extracted ‘‘strong contact-induced vibration response” and extracted ‘‘weak contact-induced vibration response”, the relationship between the FIV and the friction state was discussed by the help of minimum oil film thickness and friction coefficient. 4.1.1. Relationship between extracted ‘‘strong contact-induced vibration response” and friction state The correlation between the extracted ‘‘strong contact-induced vibration response” and friction state was discussed by the minimum oil film thickness. Fig. 7 is the change of minimum oil film thickness with the different rotating speeds under different friction state. It can be observed that the minimum oil film thickness has three stages: the slowly ascending stage of small value, the sharply ascending stage of intermediate value, and the smoothing stage of large value, which implies that the contact between the shaft and bearing has three conditions: the strong contact condition, the weak contact condition, and the indirect contact condition (i.e. the contact transmitted through the oil film). Under three conditions, the RMS change of extracted ‘‘strong contact-induced vibration response” also show three stages: the ascending stage of large value, the descending stage of intermediate value, and the smoothing stage of small value, as shown in Fig. 8, which implies that the extracted ‘‘strong contact-induced vibration response” is closely related to the contact condition.
Fig. 7. Changes of minimum oil film thickness with rotating speed.
Fig. 8. RMS change of extracted ‘‘strong contact-induced vibration response” with rotating speed.
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(1) Strong contact condition When the rotating speed is from 15 r/min to 60 r/min, the minimum oil film thickness is very small, as shown in Fig. 7, and the calculated film thickness ratio is<1 (as shown in Table 1), which indicates that the system was in boundary friction state. In the boundary friction state, it is widely accepted that the oil film was not thick enough to separate the shaft from the bearing, and the applied load was carried by the contact asperities between the shaft and the bearing rather than by the oil film. Due to the applied load being completely carried by the contact asperities, the shaft and the bearing was in a strong contact condition. Under a strong contact condition, the ‘‘strong contact-induced vibration response” triggered by the contact has large amplitude characteristics, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” is large in the boundary friction state, as shown in Fig. 8. Moreover, the minimum oil film thickness rises slowly with increasing rotating speed, as shown in Fig. 7, which indicates that the lubricating oil slowly entered the contact area. This entry of lubricating oil could prevent the contact of asperity, which leaded to a decrease in the number of contact asperity. Due to the decrease in the number, each contact asperity gradually carried the larger load under a constant applied load, which caused the contact between the shaft and the bearing to enhance slowly. As a result, the ‘‘strong contact-induced vibration response” triggered by the contact also enhanced slowly, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” displays an ascending trend with increasing rotating speed, as shown in Fig. 8. (2) Weak contact condition When the rotating speed continues to increase from 60 r/min to 150 r/min, the minimum oil film thickness is larger than that in the boundary friction state, as shown in Fig. 7, and the calculated film thickness ratio is between 1 and 3 (as shown in Table 1), which indicates the system went into the mixed friction state. In the mixed friction state, it is widely accepted that the applied load was shared between the asperities and the oil film, which means that the bearing load of asperities was reduced. Therefore, despite the still existing asperities contact between the shaft and the bearing, this contact was weak due to a reduction in the bearing load of asperities, i.e. the shaft and the bearing was under a weak contact condition. Compared with the strong contact, the weak contact could trigger small amplitude ‘‘strong contact-induced vibration response”, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” in the mixed friction state is smaller than that in the boundary friction state, as shown in Fig. 8. Moreover, the minimum oil film thickness increases sharply with the increasing rotating speed, as shown in Fig. 7, which indicates that the applied load got transferred significantly to the oil film. Due to the transfer of the applied load to oil film, the contact asperities could share less applied load, which caused the contact between the shaft and the bearing to weaken significantly. As a result, the ‘‘strong contact-induced vibration response” triggered by the contact also weakened significantly, and correspondingly, the RMS of extracted ‘‘strong contact-induced vibration response” displays an obviously descending trend with increasing rotating speed, as shown in Fig. 8. (3) Indirect contact condition When the rotating speed exceeds 150 r/min, the minimum oil film thickness gradually reaches the maximum stable value with the increasing rotating speed, as shown in Fig. 7, and the calculated film thickness ratio is more than 3 (As shown in Table 1), which indicates that the system was in the fluid friction state. In the fluid friction state, it is widely accepted that the applied load was carried by the oil film rather than by the asperities, which means that the contact between the asperities disappeared, and the shaft and the bearing was in an indirect contact condition, i.e. the contact between the shaft and the bearing is transmitted through the oil film. In this research, it is found that under an indirect contact condition, the ‘‘strong contact-induced vibration response” could still be triggered, but its amplitude was very small, and correspondingly, the minimum RMS of extracted ‘‘strong contact-induced vibration response” appears in the fluid friction state, as shown in Fig. 8. Moreover, when the minimum oil film thickness gradually increases and then tends to be stable, the RMS of extracted ‘‘strong contact-induced vibration response” gradually decreases and then tends to be stable, which indicates that the triggered ‘‘strong contact-induced vibration response” was attribute to the role of oil film, but its driving mechanism needs to be further researched. As discussed above, the extracted ‘‘strong contact-induced vibration response” is closely related to the contact between two surfaces, and it can reflect the contact condition. This conclusion is consistent with the driving mechanism of FIV, i.e. the ‘‘strong contact-induced vibration response” is triggered by the contact between the surfaces of friction pair [1,22,26,27]. In this research, it is found that under the indirect contact condition, the ‘‘strong contact-induced vibration response” could also be triggered, but its driving mechanism needs to be further researched. 4.1.2. Relationship between extracted ‘‘weak contact-induced vibration response” and friction state The correlation between the extracted ‘‘weak contact-induced vibration response” and friction state was discussed by friction coefficient. Fig. 9 is the change of friction coefficient with different the rotating speed under different friction state. It can be clearly seen that the friction coefficient has three stages: sharply dropping stage of large value, slowly dropping stage of intermediate value, and smoothly fluctuating stage of small value, which implies that the friction between the journal and bearing has three conditions: the strong friction condition, the weak friction condition, and the liquid friction condition. The RMS of extracted ‘‘weak contact-induced vibration response” shows the same changing trend as the friction coefficient, as shown in Fig. 10, which implies that the extracted ‘‘weak contact-induced vibration response” is closely related to the friction condition.
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Fig. 9. Changes of friction coefficient with rotating speed.
Fig. 10. RMS changes of extracted ‘‘weak contact-induced vibration response” with rotating speed.
(1) Strong friction condition It can be observed from Fig. 9 that the friction coefficient is large under the boundary friction state, which demonstrates that the friction between the shaft and the bearing was severe, and they were in a strong friction condition. Under a strong friction condition, the ‘‘weak contact-induced vibration response” trigged by the friction was intense and its amplitude was large. Correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” is large in the boundary friction state, as shown in Fig. 10. Moreover, the friction coefficient decreases sharply with the increasing rotating speed, as shown in Fig. 9, which indicates that the friction between the shaft and the bearing weakened significantly. As a result, the trigged ‘‘weak contact-induced vibration response” also weakened significantly, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” presents a sharply dropping trend with the increasing rotating speed, as shown in Fig. 10. (2) Weak friction condition Under the mixed friction state, the friction coefficient is smaller than that under the boundary friction state, as shown in Fig. 9, which means that the friction between the shaft and the bearing changed from severe to slight, and they went into a weak friction condition. Compared with the strong friction, the weak friction could trigger small amplitude ‘‘weak contactinduced vibration response”, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” in the mixed friction state is smaller than that in the boundary friction state, as shown in Fig. 10. Moreover, the friction coefficient slowly decreases with the increasing rotating speed, as shown in Fig. 9, which indicates that the friction between the shaft and the bearing weakened slowly. As a result, the triggered ‘‘weak contact-induced vibration response” showed the same change, i.e. it also weakened slowly, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” presents a slowly dropping trend, as shown in Fig. 10. (3) Fluid friction condition Under the fluid friction state, the friction coefficient reaches a minimum value of 0.018, as shown in Fig. 9, which indicates that the weakest friction occurred in the fluid friction state. Therefore, in the fluid friction state, the triggered ‘‘weak contactinduced vibration response” was the weakest, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” also reaches a minimum value of 0.002, as shown in Fig. 10. Moreover, the friction coefficient no longer changes obviously during the increase of rotating speed and it shows a smooth fluctuation, as shown in Fig. 9, which demonstrates that a stable fluid friction was formed between the shaft and the bearing. Thus, the triggered ‘‘weak contact-induced vibration response” also no longer changed obviously, and correspondingly, the RMS of extracted ‘‘weak contact-induced vibration response” shows the same varying trend, i.e. it displays a smoothly fluctuating trend, as shown in Fig. 10.
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Fig. 11. Distributed area of intersection point between the two RMS under different friction states.
As is discussed above, the extracted ‘‘weak contact-induced vibration response” is closely related to the friction between the two surfaces, and it can reflect the friction condition. This conclusion is consistent with the driving mechanism of FIV, i.e. the ‘‘weak contact-induced vibration response” is triggered by the interactions between the surfaces of friction pair [1,26]. In this research, it is found that under the liquid friction, the ‘‘weak contact-induced vibration response” can also be excited, but its driving mechanism needs to be further researched. 4.2. Identification of friction state To identify the friction state by the extracted FIV signals, a plane rectangular coordinate system with the RMS of extracted ‘‘strong contact-induced vibration response” as horizontal axis (X-axis) and the RMS of extracted ‘‘weak contact-induced vibration response” as vertical axis (Y-axis) was established; and the distributed area of intersection point between the two RMS values under different friction states was given in Fig. 11. It can be seen that each friction state has an independent distribution area of intersection point, which indicates that the friction state could be identified by the position of intersection point in the coordinate system. Taking the point A in Fig. 11 as an example, it can be noted that the X coordinate value of point A may appear in three areas, i.e. boundary friction state, mixed friction state, and liquid friction state; while the Y coordinate value of point A may appear in two areas, i.e. boundary friction state and mixed friction state. However, the position of point A is uniquely determined and can only exist in the mixed friction state. Therefore, the identification of friction state can only be achieved by measuring ‘‘strong contact-induced vibration response” and ‘‘weak contact-induced vibration response” simultaneously, rather than only using the FIV signal with an individual amplitude-frequency characteristic. 5. Conclusion In a friction process in which the lubricating oil is involved, the FIV with two different amplitude-frequency characteristics can be simultaneously excited. By investigating the relationship between the FIV and friction state in a given lubrication tribological system, the following conclusions can be summed up from the present studies: (1) The FIV is closely related to the friction state. The extracted ‘‘strong contact-induced vibration response” in FIV signal can reflect the contact condition between the surfaces of friction pair; the extracted ‘‘weak contact-induced vibration response” in FIV signal can reflect the friction condition between the surfaces of friction pair. (2) The identification of friction state can be achieved by measuring extracted ‘‘strong contact-induced vibration response” and ‘‘weak contact-induced vibration response” simultaneously. In this research, it is found that the FIV with two different amplitude-frequency characteristics can be simultaneously excited under different friction state, but their driving mechanism needs to be further researched. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This present project is supported by the National Natural Science Foundation of China (Grant No. 51879020 and 51679022).
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