The object of this paper is the changing process of damping force as the falling weight impacting the elastomer buffer. The whole mechanical system is built up through practical test and simulation. According to the type of elastomer buffer and the experimental process in shock environment, velocity damping force identification model was established. Wavelet denoising and least square method were used for parameter identification of damping force. Considering the data saturation problem in the traditional least square method, the limited memory least square method was obtained to improve the identification method. The results of parameter identification of damping force based on limited memory method proved that the limited memory method was superior to least square method. The numerical results demonstrate the effectiveness of the identification model

Qiang Chen

Shuyun Chen

Xiaoya Gao

Yingjun Wang

English

Vibroengineering PROCEDIA

  © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 155 
Research on damping parameter identification of 
elastomer buffer 
Shuyun Chen1, Qiang Chen2, Xiaoya Gao3, Yingjun Wang4 
1, 2, 4Control and Science Engineering, School of Mechanical Engineering,  
Nanjing University, 210093, Nanjing, P. R. China 
3Information Center of China North Industries Group Corporation, 100089, Beijing, P. R. China 
2Corresponding author 
E-mail: 1chenshuyunok@163.com, 2chenqia0772@vip.sina.com, 3xiaoyagaobj@163.com, 
4wangyingjun13@126.com 
(Accepted 29 August 2014) 
Abstract. The object of this paper is the changing process of damping force as the falling weight 
impacting the elastomer buffer. The whole mechanical system is built up through practical test 
and simulation. According to the type of elastomer buffer and the experimental process in shock 
environment, velocity damping force identification model was established. Wavelet denoising and 
least square method were used for parameter identification of damping force. Considering the data 
saturation problem in the traditional least square method, the limited memory least square method 
was obtained to improve the identification method. The results of parameter identification of 
damping force based on limited memory method proved that the limited memory method was 
superior to least square method. The numerical results demonstrate the effectiveness of the 
identification model. 
Keywords: elastomer buffer, damping force, limited memory method, parameter identification. 
1. Introduction 
Elastomer buffer has great application in various fields, which has the advantages of large 
capacity, stability, and simple structure. Over the years, the analysis and exploration of the 
damping process of elastomer buffer has been a hot research. For different application fields of 
elastomer buffer, accurate modeling of damping process is very meaningful to the study of 
mechanical system and noise reduction. 
When the types of elastomer buffer and experimental environment are different, the damping 
parameter identification model is different. Accurate experimental subjects and establishing a 
right identification model directly determine the feasibility of damping parameter identification. 
The experimental object in this paper is a vertical impact process. According to the experiment, 
velocity-damping identification model was established. In the simulation phase, the wavelet 
denoising was used to filtering the experimental data. Aiming at the defects of the traditional least 
square method, the limited memory method was used to solve the problem of data saturation, 
which ensured that the algorithm has better precision of fitting. 
2. Identification model 
2.1. Elastomer buffer 
At present, the most widely used elastomer buffer for practical application is shown in Fig. 1. 
It is a single rod elastomer buffer. This kind of damper has a closed chamber, which is filled with 
viscoelastic fluid damping materials. When elastomer is impacted by external load, the buffer 
piston rod is pressed into the cavity. The damping material flows through the annular gap formed 
by piston and cylinder wall. The damping medium in cavity is compressed and the internal 
pressure increases, that caused the elastic force to the piston rod. At the same time, the piston head 
and damping structure produce great friction with the viscous damping medium. When the speed 
is higher, more viscous resistance will be produced. The impact kinetic energy can be turned into 
heat energy and elastic potential energy, which can be released in a very short time to achieve the 
RESEARCH ON DAMPING PARAMETER IDENTIFICATION OF ELASTOMER BUFFER.  
SHUYUN CHEN, QIANG CHEN, XIAOYA GAO, YINGJUN WANG 
156 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
effect of energy absorption. The elastomer also has good elasticity, that means, the volume will 
shrink under great external force. When the external pressure is up to 500 MPa, the compression 
ratio is not less than 17 % of the initial volume. When the external force is removed, the elastomers 
will automatic reset and release energy storage. And from Fig. 1, the numbers 1 to 5 represent 
piston rod, cylinder head, piston, resilient rubber and cylinder block. 
 
Fig. 1. Schematic diagram of elastomer buffer structure 
2.2. Identification model 
Energy buffer device can be manufactured according to different materials, energy dissipation 
mechanisms and structures. The experiment in this paper was performed in the shock environment. 
Speed-damping model is widely used for elastomer buffer in shock environment, which is shown 
as Eq. (1): 
ܨ = ܥݒ௡, (1)
where ܨ is damping force, ܥ is damping coefficient, ݒ is the relative velocity of the piston and 
cylinder body and ݊ is velocity correlation coefficient (the larger its value, the smaller buffer’s 
nonlinear degree). 
The model Eq. (1) shows is nonlinear. The complexity of nonlinear model is higher than that 
of linear model in the process of fitting. If it can be transformed into linear model, the fitting effect 
will be better. In order to linear fitting, logarithm was used on both sides of the formula which is 
shown as Eq. (2): 
lnܨ = lnܥ + ݊ ⋅ lnݒ. (2)
After the transformation above, the parameters need to be identified are linear parameters lnܥ 
and ݊. The data lnܨ and lnݒ can be obtained by the calculation of the damping force and velocity. 
3. Identification algorithms 
3.1. Least square method (LSM) 
The least square method is a relatively mature algorithm. It has been widely used in scientific 
experiments and engineering technology. With the development and popularization of modern 
computer, LSM shows more powerful vitality. LSM is used for solving the problem of how to 
find reliable value from a set of measurements. Its basic principle is: a group of data (ݔ௜ , ݕ௜ ,  
݅ = 1, 2,…, ݊) are obtained, and try to find a best fitting curve in which the difference quadratic 
sum of the value of each point on the curve and measured value is minimum. 
In the design of experiments, in order to reduce the error, multiple point measurement is 
performed. The number of the equations is far more than that of undetermined parameters. These 
equations are called inconsistent equation group. The equations transformed by LSM are called 
the normal equations (here the number of equations is equal to the number of undetermined 
parameters). The undetermined parameters can be calculated by the normal equations. 
3.2. Limited memory method (LMM) 
The LSM is simple and practical, and its recursive algorithm is convergence and reliable. 
RESEARCH ON DAMPING PARAMETER IDENTIFICATION OF ELASTOMER BUFFER.  
SHUYUN CHEN, QIANG CHEN, XIAOYA GAO, YINGJUN WANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 157 
When the noise is white noise, the estimates can be unbiased, consistent and efficient. But with 
the growth of data, LSM will show the phenomenon of data saturation so that the recursive 
algorithm loses correction ability slowly. In that case, limited memory was introduced to LSM 
and the recursive algorithm called limited memory method was obtained. LMM can solve the 
problem of data saturation caused by LSM. 
4. Study case 
4.1. Experimental installation 
Before the experiment, the buffer is arranged on the base. The impact hammer with quality of 
30 kg was put in a suitable height. Then let the hammer fall free along the rail and impact the 
piston rod of buffer. The variation rule of displacement during the impact process was recorded 
by laser displacement sensor and data acquisition system. The actual installation of measuring 
equipment and buffer is shown in Fig. 2. And from Fig. 2, the numbers 1 to 5 represent impact 
hammer, acceleration sensor, laser displacement sensor, elastomer buffer and data acquisition 
equipment. 
 
Fig. 2. Schematic diagram of equipment 
4.2. Data processing 
 
Fig. 3. Acceleration-time curve of low speed 
 
Fig. 4. Acceleration-time curve of high speed 
During the falling process, displacement information of the hammer was collected by laser 
displacement sensor with sampling frequency of 10 KHz. After the displacement information was 
collected, acceleration information could be obtained by two differential operation of 
displacement. Combined with the quality of the hammer, the damping force time curve could be 
obtained. During the falling process, there would be noise and vibration interference. Therefore, 
the data need to filter so that the accuracy of data can be ensured. By adjusting the initial height 
RESEARCH ON DAMPING PARAMETER IDENTIFICATION OF ELASTOMER BUFFER.  
SHUYUN CHEN, QIANG CHEN, XIAOYA GAO, YINGJUN WANG 
158 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533  
of the hammer, displacement-time curves of different initial velocity can be obtained. Thus the 
damping force time curves of different initial velocity can also be gained. Two different initial 
heights, 300 mm and 700 mm were used to perform the low speed test and high speed test in this 
paper. The parameter identification of two sets of data was used to verify the validity of the 
identification model. 
The acceleration-time diagrams of low speed and high speed are shown in Fig. 3 and Fig. 4. 
Through the calculation, the damping force curves during the hammer impacting the buffer are 
shown in Fig. 5 and Fig. 6. 
 
Fig. 5. Damping force curve of low speed 
 
Fig. 6. Damping force curve of high speed 
4.3. LSM for parameter identification 
According to Eq. (2), parameter identification was performed with LSM respectively in low 
speed group and high speed group. The identification results were shown in Fig. 7, Fig. 8 and 
Table 1. 
 
Fig. 7. LSM result of low speed group 
 
Fig. 8. LSM result of high speed group 
 
Table 1. Identification result of LSM 
Speed type ܥ/ܰ∙(m/s)-1 ݊
Low speed group 263.34 0.4225 
High speed group 314.45 0.3965 
Table 2. Identification result of LMM 
Speed type ܥ/ܰ∙(m/s)-1 ݊ 
Low speed group 272.46 0.4352 
High speed group 282.56 0.4410 
4.4. LMM for parameter identification 
According to Eq. (2), parameter identification was performed with LMM respectively in low 
speed group and high speed group. The identification results were shown in Fig. 9, Fig. 10 and 
Table 2. 
RESEARCH ON DAMPING PARAMETER IDENTIFICATION OF ELASTOMER BUFFER.  
SHUYUN CHEN, QIANG CHEN, XIAOYA GAO, YINGJUN WANG 
 © JVE INTERNATIONAL LTD. VIBROENGINEERING PROCEDIA. NOVEMBER 2014. VOLUME 4. ISSN 2345-0533 159 
 
Fig. 9. LMM result of low speed group 
 
Fig. 10. LMM result of high speed group 
5. Conclusions 
The damping force model of elastomer buffer in shock environment is nonlinear. Through 
linearizing the nonlinear equation, the original parameters will be obtained by inverse logarithmic 
operation. This method can guarantee the accuracy of the premise and greatly improve the 
efficiency of the algorithm. By identifying the model parameters with LSM and LMM, the 
correctness of the model is confirmed. 
The traditional LSM has defects of data saturation. In the fitting process, the accurate 
parameter identification cannot be guaranteed with the growth of initial velocity. LMM can solve 
this problem and identification parameters can be also obtained accurately at high speed. 
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Research on damping parameter identification of elastomer buffer

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