Vibration and collision in the process of friction will cause large deviation of identification result with the actual situation. In this paper, friction process with the influence of vibration and collision as well as data collection of this process are implemented; to eliminate influence of vibration and collision in the aspect of the original data, sine filter is introduced into friction model according to the theory of Fourier series; ideas of simulated annealing is introduced into genetic algorithm to form hybrid algorithm, friction parameter can be identified combined with model and test data. The numerical results demonstrate the proposed method has effective identification results for friction process under the influence of the vibration and collision

Qiang Chen

Ying Chen

Yingjun Wang

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 145 
Research on friction parameter identification under the 
influence of vibration and collision 
Qiang Chen1, Yingjun Wang2, Ying Chen3 
1, 2Department of Control and System Engineering, Nanjing University, 210093, Nanjing, P. R. China 
3Department of Management Science and Engineering, Nanjing University, 210093, Nanjing, P. R. China 
2Corresponding author 
E-mail: 1chenqia0772@vip.sina.com, 2wangyingjun13@126.com, 3cheny@nju.edu.cn 
(Accepted 24 July 2015) 
Abstract. Vibration and collision in the process of friction will cause large deviation of 
identification result with the actual situation. In this paper, friction process with the influence of 
vibration and collision as well as data collection of this process are implemented; to eliminate 
influence of vibration and collision in the aspect of the original data, sine filter is introduced into 
friction model according to the theory of Fourier series; ideas of simulated annealing is introduced 
into genetic algorithm to form hybrid algorithm, friction parameter can be identified combined 
with model and test data. The numerical results demonstrate the proposed method has effective 
identification results for friction process under the influence of the vibration and collision. 
Keywords: friction parameters identification, vibration and collision, sine filter, hybrid algorithm. 
1. Introduction 
The existence of friction seriously restricts the performance of the mechanical system, so using 
appropriate method to identify friction parameter and to make friction compensation has vital 
significance. Friction process has obvious non-linear features, and it always includes the influence 
of additional factors such as vibration and collision. Vibration of the projectile and collision 
between projectile and channel in the process of pushing projectile is an example. This situation 
increases the recognition difficulty and reduces the precision of friction parameter identification 
to some extent. Thus, it has significant meaning for the improvement of precision of model 
parameter identification to use appropriate method to eliminate the additional effect of vibration 
and collision on friction process. 
Due to influence of additional factors, test data under vibration and collision cannot be directly 
applied to model parameter identification. Meanwhile, the traditional filtering methods always 
lead to the missing of useful information, which result in identification result cannot be well reflect 
the performance of the actual friction process. And it is very adverse for the subsequent friction 
compensation. Precision of model parameter identification determines the credibility in solving 
practical problems by using the model to a large degree, so choice of identification algorithm is 
also very important in addition to the model. Genetic algorithm and simulated annealing algorithm 
are two excellent intelligent algorithm in recent years. They both have a superior capacity to 
generate and search solution set, but they also have their own insurmountable defects which limit 
the application of algorithm. Fortunately, the complementarity in performance makes it possible 
to combine the two algorithms. Frictional experiment with vibration and collision is designed in 
this paper, and test data can be collected by high-speed photography technology and acceleration 
sensor. According to the theory of Fourier series, sine filter is introduced into the classical stribeck 
friction model to eliminate the influence of vibration and collision. At last, with friction model 
and test data, friction parameter can be identified by hybrid algorithm. The numerical results 
demonstrate the effectiveness of the identification method. 
RESEARCH ON FRICTION PARAMETER IDENTIFICATION UNDER THE INFLUENCE OF VIBRATION AND COLLISION.  
QIANG CHEN, YINGJUN WANG, YING CHEN 
146 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
2. Identification model 
2.1. Friction device  
Vibration and collision in process of friction will result in a large error in identification result. 
In order to further improve the precision of friction parameter identification under the impact of 
vibration and collision, friction process under the influence of vibration and collision is 
implemented in this paper based on friction mechanism. The experimental device is shown in 
Fig. 1. The numbers 1 to 3 respectively represent slippery course, slider and spring impact  
hammer. The spring impact hammer can release impact energy of 2 J, this energy can make the 
slider get an initial velocity, and then the slider will move alone the slippery course at a certain 
speed. In the process of moving, the slider gets not only friction force from slippery course, but 
also includes its own vibration and collision with the slippery course. In the moving process of 
the slider, a high speed camera and an acceleration sensor are used to record dynamic data 
information, after filtering and noise reduction, test data can be used to identify friction parameters 
in combination with friction model and intelligent algorithm. 
1
2
3
 
Fig. 1. Schematic diagram of friction device 
2.2. Identification model 
Friction model can be divided into static friction model and dynamic friction model. Static 
friction model recognize friction as function of relative velocity between two contact surfaces, 
which cam well reflect friction process with viscous effect, and it is also the basis of research on 
parameter identification of dynamic friction model. Stribeck friction model is one of the classic 
models, this model can reflect most of the friction phenomena, can be used to analyze complex 
friction phenomena, so it is used widely, which is shown as Eq. (1): 
݂ሺߥሻ = ௖݂ + ሺ ௦݂ − ௖݂ሻ݁൤ିቀ
ఔ
ఔೞቁ൨ + ௩݂ݒ, (1)
where ௖݂ is coulomb friction, ௦݂ is static friction, ௩݂ is viscous friction and ௦ܸ is stribeck velocity. 
Related studies have shown that when vibration and the collision are included into friction 
process, such as vibration of the projectile and collision between projectile and channel in the 
process of pushing projectile, classic friction model cannot be well reflect the dynamic 
performance and static performance of the actual friction process, and it is also very adverse for 
the subsequent friction compensation. According to the theory of Fourier series, sine filter is 
introduced into the classical stribeck friction model, in order to eliminate the additional influence 
of vibration and collision in the aspect of the original data. And then the model can be shown as 
Eq. (2): 
݂ሺߥሻ = ௖݂ + ሺ ௦݂ − ௖݂ሻ݁൤ିቀ
ఔ
ఔೞቁ൨ + ௩݂ݒ + ෍ ௜݂
௡
௜ୀଵ
sinሺ߱௜t + ߮௜ሻ. (2)
RESEARCH ON FRICTION PARAMETER IDENTIFICATION UNDER THE INFLUENCE OF VIBRATION AND COLLISION.  
QIANG CHEN, YINGJUN WANG, YING CHEN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 147 
A precise model is got when ݊ → ∞, considering the feasibility of calculation, set ݊ as 2. 
There are ten parameters need to be identified in Eq. (2). 
3. Identification algorithms 
3.1. Genetic algorithm (GA) and simulated annealing algorithm (SA) 
The theory basis for genetic algorithm is schemata theorem and building block hypothesis. 
Schemata theorem makes genetic algorithm has the possibility to find the global optimal solution, 
while building block hypothesis points out that the specific pattern can generate the global optimal 
solution under the effect of genetic operators. High robustness of genetic algorithm make it 
becomes a new way to solve nonlinear optimization problem. 
Simulated annealing algorithm simulates the process of solid annealing. Because of design and 
application of Metropolis rule, SA can accept worse solution in the process of iterations at a certain 
probability to avoid SA is trapped into local optimal solution. And this makes sure that SA can 
obtain the optimal solution at a great possibility when to solve combinatorial optimization, system 
identification and other issues. 
3.2. Simulated annealing genetic algorithm (SGA) 
Genetic algorithm and simulated annealing algorithm has attracted much attention in recent 
years, and has been widely used in various fields. However, single intelligent algorithm always 
has its own limitations, such as the convergence speed of genetic algorithm is slow and its local 
search ability is not very good; at the same time, optimization time of simulated annealing 
algorithm is always very long. Anyway, these two intelligent algorithms are important but not 
powerful search methods. 
Genetic algorithm and simulated annealing algorithm are complementary in optimize 
performance, and simulated annealing genetic algorithm is a hybrid algorithm which combined 
with that two intelligent algorithms. The performance of that hybrid algorithm gets a big 
promotion because of it possesses advantages of both that two algorithms, and just because of this, 
that hybrid algorithm is widely used in various fields such as system identification. Hybrid 
algorithm introduces ideas of simulated annealing while sets genetic algorithm as basic  
framework, which flowchart is shown in Fig. 2. 
 
Fig. 2. Simulated annealing genetic algorithm flowchart 
RESEARCH ON FRICTION PARAMETER IDENTIFICATION UNDER THE INFLUENCE OF VIBRATION AND COLLISION.  
QIANG CHEN, YINGJUN WANG, YING CHEN 
148 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
4. Case study 
4.1. Experimental installation 
In this study, a spring shock device is adopted to simulate the friction process under influence 
of vibration and collision, which is shown in Fig. 1. The spring impact hammer with impact energy 
of 2 J is put in initial position. Then the slider is driven by the spring impact hammer and moves 
alone the slippery course at a certain speed. The variation rule of acceleration of the slider during 
the friction process was recorded by acceleration sensor and data acquisition system, while the 
displacement data and velocity information is measured by a high speed camera. In addition, a 
LED cold light source is used to solve the problem of illumination compensation. The actual 
installation of measuring equipment is shown in Fig. 3. 
 
Fig. 3. Schematic diagram of equipment 
4.2. Data processing 
During the friction process, displacement information of the slider is recorded by a high speed 
camera while the sampling frequency is set at about 4 K Hz. The information what we are 
concerned is velocity single and acceleration single, however, the high speed camera can only get 
displacement information, so two differential operation of displacement need to be executed to 
obtain single of velocity and acceleration. Then, the friction force time curve can be obtained 
combining with the quality of the solider. During the experiment, there would be noise 
interference which can easily cause data distortion, thus low-pass filter is taken to filter the original 
data before differential operation so that high frequency noise can be restrained effectively and 
accuracy of data can be ensured. 
The velocity curve and acceleration-time diagram during the solider moving alone the slippery 
course are respectively shown in Fig. 4 and Fig. 5. 
 
Fig. 4. Velocity curve of solider 
 
Fig. 5. Acceleration-time diagram of solider 
0.00 0.01 0.02 0.03 0.04 0.05 0.06
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Ve
loc
ity
 (m
/s)
Time (s)
0.00 0.01 0.02 0.03 0.04 0.05 0.06
15
20
25
30
35
40
45
50
55
Ac
ce
ler
ati
on
 (m
/s2
)
Time (s)
RESEARCH ON FRICTION PARAMETER IDENTIFICATION UNDER THE INFLUENCE OF VIBRATION AND COLLISION.  
QIANG CHEN, YINGJUN WANG, YING CHEN 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533 149 
4.3. Parameter identification without sine filter 
Parameter identification can be performed with simulated annealing genetic algorithm, and the 
identification results are shown in Fig. 6 and Table 1. 
 
Fig. 6. Actual friction and theory friction comparison 
Table 1. Identification result without sine filter 
Friction (N) ܨ௖ ܨ௦ ܨ௩ ௦ܸ
Identified value 10.0000 17.8104 5.0000 0.2512 
4.4. Parameter identification with sine filter  
Parameter identification can be performed with simulated annealing genetic algorithm, and the 
identification results are shown in Fig. 7 and Table 2. 
 
Fig. 7. Actual friction and theory friction comparison 
Table 2. Identification result without sine filter  
Items ܨ௖ (N) ܨ௦ (N) ܨ௩ (N∙m/s) ௦ܸ (m/s) ܨ௔ (N) 
Value 4.0266 12.7125 14.7817 1.9551 1.5971 
Items ܨ௕ (N) Ω௔ (rad/s) Ω௕ (rad/s) Φ௔ (rad/s) Φ௕ (rad/s) 
Value 0.2665 2.8556 0.7038 0.3363 0.8242 
5. Conclusions 
Sine filter is included into classic friction model in this paper, which can express additional 
interference signal to some extent. And it can be used to eliminate the influence of interference 
signal in the aspect of the original data, which can avoid information distortion caused by the 
0.00 0.01 0.02 0.03 0.04 0.05 0.06
12
14
16
18
20
22
24
Fr
ict
ion
 (N
)
Time (s)
 real value
 identified value
0.00 0.01 0.02 0.03 0.04 0.05 0.06
12
14
16
18
20
22
24
Fr
ict
ion
 (N
)
Time (s)
 real value
 identified value
RESEARCH ON FRICTION PARAMETER IDENTIFICATION UNDER THE INFLUENCE OF VIBRATION AND COLLISION.  
QIANG CHEN, YINGJUN WANG, YING CHEN 
150 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. SEP 2015, VOLUME 5. ISSN 2345-0533  
traditional filtering method. The introduction of sine filter can improve precision of parameter 
identification, and the effectiveness of this method is confirmed by identifying the model 
parameters with SGA. However, the hybrid algorithm also has its disadvantage such as long 
execution time, thus further work of this study would do more research to improve algorithm 
efficiency. 
Acknowledgement 
This is supported by the National Key Scientific Instrument Development Projects, 
No. 2013YQ470765. 
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