In order to study the vibration behavior of rotating manipulator in the process of scramming, an experimental test is conducted on the vibration behavior during the process on different initial and measuring conditions. Through the experimental test, the vibration behavior exists two impact phenomena, which are found in the scramming process, and the feature extraction of the two impact phenomena is investigated. The dynamics parameters of the rotating manipulator are identified and hammer experiment is done to verify the dynamics parameters. With these parameters, an envelope model of the second impact response is established, and the applicability of the model is validated by experiments. The method of pasting damping layer on the surface of manipulator is employed to inhibit the vibration which is caused by the first impact. Via the experimental verification, the damping layer takes a certain effect on the vibration elimination

Changshuai Yu

Guangkai Chen

Yunpeng Zhu

Zhong Luo

Journal of Measurements in Engineering

Luo, Zhong

Yu, Changshuai

Zhu, Yunpeng

Chen, Guangkai

Journal of Mechatronics and Artificial Intelligence in Engineering

 8 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  36. Experimental study on vibration behavior of rotating manipulator in the process of scramming Zhong Luo1, Changshuai Yu2, Yunpeng Zhu3, Guangkai Chen4 School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China 1Corresponding author E-mail: 1zhluo@mail.neu.edu.cn, 2yu.chang.shuai@163.com, 3270641532@qq.com, 41148564928@qq.com (Received 12 January 2014; received in revised form 17 January 2014; accepted 22 January 2014) Abstract. In order to study the vibration behavior of rotating manipulator in the process of scramming, an experimental test is conducted on the vibration behavior during the process on different initial and measuring conditions. Through the experimental test, the vibration behavior exists two impact phenomena, which are found in the scramming process, and the feature extraction of the two impact phenomena is investigated. The dynamics parameters of the rotating manipulator are identified and hammer experiment is done to verify the dynamics parameters. With these parameters, an envelope model of the second impact response is established, and the applicability of the model is validated by experiments. The method of pasting damping layer on the surface of manipulator is employed to inhibit the vibration which is caused by the first impact. Via the experimental verification, the damping layer takes a certain effect on the vibration elimination. Keywords: manipulator, vibration behavior, hammer test, vibration elimination. 1. Introduction Manipulator is one of the most important and commonly used facilities in a variety of engineering applications. For example, the United States Robonaut, Ranger space manipulators can perform complex repair and assembly work on faulty satellites [1-2]. Because of the specificity of the space environment, vibration problem of space manipulator causes the task not being completed, and brings a great loss [3]. Therefore, the vibration behavior of manipulator has a very important effect on the manipulator’s work. Suppressing the vibration has been one of the significant problems to be solved urgently in the engineering field. A huge amount of research efforts have been devoted to the vibration elimination of manipulator in the literature. Dickerson [4] and Alberts [5] use the passive vibration control method of pasting elasticity damping materials to inhibit the manipulator structural vibration. Book [8] adopts pole assignment technique to design the state feedback controller in order to reduce the vibration of the flexible robot response. Sakawa [6] uses the linear quadratic optimal control theory to define the state feedback gain, and suppress elastic deformation and vibration of flexible robot. Bailey [7] and Plump J. M. [8] completes groundbreaking experiments that organically combine passive vibration control and active vibration control with using piezoelectric materials. There is not any work on the vibration behavior of manipulator during the rotating and scramming process. This paper presents an experimental study on the vibration behavior of rotating manipulator, and the manipulator’s vibration is restrained by pasting a damping layer. Through the experimental test, repeated impact phenomenon is found in the scramming process of manipulator. Via the feature extraction of repeated impact, the dynamics parameters of rotating manipulator are identified and an envelope model of the second impact response is established. 2. Experimental details and results An aluminum tube with the length of 73 mm, the width of 25 mm, the height of 500 mm and the wall thickness of 1 mm is fixed on a rotating module, which acts as a rotating manipulator 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN  © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 9 (Fig. 1). The measuring points and the direction of the manipulator’s rotation are shown in Fig. 1.  Fig. 1. The manipulator Three acceleration sensors are attached to the three points of the manipulator respectively. The manipulator is controlled under the rotational speed of five working conditions shown in Table 1. Under the five working conditions, the vibration behaviors of the three measuring points are tested. Table 1. The rotational speed of five working conditions Conditions 1 2 3 4 5 Rotational speed (rad/s) 1.57 0.785 0.523 0.392 0.314 According to the experimental test, the vibration behavior exists repeated impact phenomena. Repeated impact phenomenon is found in the scramming process of the manipulator (Fig. 2), including the first impact and the second impact.  Fig. 2. The vibration behavior of the manipulator Fig. 2 is obtained from the vibration signal acquisition. The phenomenon of emerging repeated impact happens in the process of manipulator scramming, and the responses of repeated impact are free vibration. 3. The principle of envelope method for free vibration attenuation to identify dynamics parameters Envelope method for free vibration attenuation is a commonly used method of measuring dynamics parameters [8]. Following the case of single degree of freedom, the principle of envelope method for free vibration attenuation to identify dynamics parameters is explained. 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 10 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  Attenuation response for a damping system of single degree of degree can be expressed as: = sin 1 − + , (1)where  is amplitude,  is natural frequency,  is time of free vibration,  is phase difference angle and  is damping ratio of the system. According to Eq. (1), envelope curve equation for displacement attenuation of single-degree-of-freedom vibration is Eq. (2): = . (2)Eq. (1) is displacement response, because of different types of vibration picking sensors, time-domain signal of attenuation response of velocity or acceleration may be obtained. Equations of velocity and acceleration are shown as Eq. (3) and Eq. (4): = sin 1 − + , (3)= sin 1 − + , (4)where  and  are amplitudes of velocity and acceleration attenuation response respectively. And  and  are the phase difference angles of velocity and acceleration attenuation response respectively. Eq. (4) and Eq. (1) have the same type, so acceleration response curve of single-degree-of-freedom vibration have the same envelope curve with displacement response, and the response curve is shown in Fig. 3.  Fig. 3. Time domain response curve of single degree freedom system In Fig. 3, damping makes the amplitude of system vibration decrease by geometric attenuation. The ratio of two adjacent amplitude is shown in Eq. (5): = = ( ) = , (5)where ,  are the values of two adjacent amplitude,  is the time of the first amplitude,  is called damping coefficient [9] and  is vibration period: = 11 − . (6)Based on Eq. (6), amplitude reduces to the initial value 1⁄  multiple every vibration 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN  © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 11 period. In fact, in order to avoid inconvenience of taking the index value. Common logarithm damping  replaces damping coefficient  shown in Eq. (7): = ln = ln = = 1 − . (7)According to Eq. (6) and Eq. (7), equations of damping ratios and natural frequency is shown as follows: = (2π) + , (8)= 11 − . (9)4. Experimental analysis 4.1. Dynamic parameters recognition of the manipulator Due to the influence of noise, de-noising method [11] is used to the first impact response of measuring point 1 on condition 1. The first impact response after de-noising processing is shown in Fig. 4, and -axis represents time and -axis represents acceleration value.  Fig. 4. The first impact after de-noising processing P1, P2 in vibration waveform (Fig. 4) are the first and the second peak points, and coordinate values of the two peaks are P1(1.55, 125.4), P2(1.57, 55.15). That means = 125.4 m/s2 and = 55.15 m/s2.  Under other conditions,  and  can be obtained by the same analysis (Table 2). Table 2. Peak points’ value of  and  (m/s2)  Measuring point 1 Measuring point 2 Measuring point 3       Condition 1 125.4 55.15 72.46 30.53 26.15 9.11 Condition 2 45.19 18.74 26.37 9.35 8.92 2.44 Condition 3 17.34 8.39 11.24 4.18 5.17 1.17 Condition 4 14.64 4.73 8.76 2.57 0.74 0.2 Condition 5 14.77 5.50 8.52 2.98 3.04 0.97 According to the data of Table 2, Eqs. (7)-(9), damping ratios (Table 2) and natural frequencies 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 12 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  (Table 3) can be obtained in different measuring points of different conditions. Table 3. Damping ratios  Measuring point 1 Measuring point 2 Measuring point 3 Condition 1 0.131 0.149 0.164 Condition 2 0.156 0.163 0.203 Condition 3 0.174 0.182 0.223 Condition 4 0.181 0.192 0.228 Condition 5 0.162 0.169 0.183 Table 4. Natural frequencies (Hz)  Measuring point 1 Measuring point 2 Measuring point 3 Condition 1 52.82 50.56 50.68 Condition 2 50.62 50.68 51.06 Condition 3 50.77 50.85 48.85 Condition 4 50.84 50.95 51.35 Condition 5 48.26 53.39 53.53 The average of damping ratios in Table 3 and natural frequencies in Table 4 are 0.177 and 50.86 Hz respectively. Therefore, = 0.177 and = 50.86 Hz can evaluate the damping ratio and the natural frequency. 4.2. Hammer experiment  Using hammer experiment [12] verifies the natural frequency (Fig. 5).  Fig. 5. Hammer experiment Natural frequencies got from hammer experiment are shown in Table 5. Table 5. Natural frequencies obtained by hammer experiment (Hz)  First-order Second-order Third-order Fourth-order Fifth-order Natural frequencies 52.61 308.41 350.40 429.31 609.18 According to Table 5, first-order natural frequency got from hammer experiment is 52.61 Hz, which is very close to the natural frequency 50.86 Hz got from the first impact of the manipulator (the error is 3.33 %), and proves the value of natural frequency 50.86 Hz is correct. 4.3. Establishing an envelope model of the second impact response According to these dynamics parameters got from the first impact, an envelope model of the second impact response is established as follows: 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN  © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 13 = ± ( ), (10)where  is the acceleration of vibration,  is the initial acceleration value of the second impact;  is multivariate time and  is the initial time. Besides,  is 0.177 and  is 50.86 Hz. The envelope model is verified by experiment. Fig. 6(a)-(e) respectively represent the second impact response of condition 1 to condition 5.  a) Condition 1  b) Condition 2  c) Condition 3  d) Condition 4  e) Condition 5 Fig. 6. The second impact and the envelope model Where the solid line represents the second impact response and the dotted line represents the envelope model. According to the comparisons, good agreement is observed, which proves that the dynamics parameters got from the first impact is correct and the envelope model is applicable. 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 14 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  5. Adding a damping layer to restrain the vibration of manipulator A sharp spike of acceleration arises in the first impact (Fig. 7). In order to restrain the vibration, a damping layer is added to the surface of the manipulator [13] (Fig. 8). The manipulator is controlled at the rotational speed on five working conditions as shown in Table 1 to do the experimental test. Fig. 7. Existing a sharp spike  Fig. 8. The manipulator with a damping layer The sharp spikes of manipulator with a damping layer and without a damping layer are compared in different measuring points under different conditions (as shown in Fig. 9). -axis represents rotational speed and -axis represents acceleration value.  Fig. 9. Comparing the sharp spikes Where the first black line represent the sharp spikes of measuring point 1 without a damping layer in different rotating speed, the second black line represents measuring point 1 with a damping layer and the two lines make a comparison. Similarly, the two red lines make the comparison of measuring point 2 without a damping layer and with a damping layer and the two blue lines make the comparison of measuring point 3. Therefore, a conclusion can be obtained that adding a damping layer can suppress the vibration of the manipulator through the above comparisons. 6. Conclusions Experimental study on the vibration behavior of a rotating manipulator during rotating and 36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN  © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 15 scamming process has been made. Repeated impact phenomenon is found in the scramming process of the manipulator. Conclusions obtained are as follow: (1) Dynamics parameters of the rotating manipulator are identified by the feature extraction of the first impact; (2) Using hammer experiment verifies the natural frequency correct; (3) Based on these dynamics parameters, an envelope model of the second impact response is established, and the applicability of the model is validated by experiments; (4) A sharp spike of acceleration arises in the first impact. A damping layer added to the surface of the manipulator is used to suppress the vibration, and via the experimental verification, the damping layer takes a certain effect on the vibration elimination. Acknowledgements This work was supported by the National Science Foundation of China (Grant No. 51105064); the National Program on Key Basic Research Project (Grant No. 2012CB026000); and the Natural Science Foundation of Liaoning Province (Grant No. 201202056). References [1] Lovchik C. S., Diftler M. A. The robonaut hand: a dexterous robot hand for space. IEEE International Conference on Robotics and Automation, Vol. 2, 1999, p. 907-912. [2] Parrish J. C. The ranger telerobotic flight experiment: a teleservicing system for on-orbit spacecraft. Telemanipulator and Telepresence Technologies III, In Proceedings of the SPIE, 1996, p. 177-185. [3] Zizeng Pei The active vibration control of piezoelectric intelligent cantilever beam. Shanxi, Master’s thesis of Xi’an Electronic and Science University, 2011. [4] Lane J. S., Dickerson S. L. Contribution of passive damping to the control of flexible manipulators. Proceedings of the International Computers in Engineering Conference, 1984, p. 175-180. [5] Alberts T. E., Dickerson S. L., Book W. J. On the transfer function modeling of flexible structures with distributed damping. ASME, Vol. 3, 1986, p. 23-30. [6] Sakawa Y. Modeling and feedback control of flexible arm. Journal of Robotics System, Vol. 2, Issue 4, 1985, p. 453-472. [7] Bailey T. L., Hubbard J. E. Distributed piezoelectric-polymer active vibration control of a cantilever beam. Journal of Guidance, Control, and Dynamics, Vol. 8, Issue 5, 1985, p. 605-611. [8] Plump J. M., Hubbard J. E., Bailey J. T. Nonlinear control of a distributed system: simulation and experimental results. Journal of Dynamic Systems, Measurement and Control, Vol. 109, Issue 5, 1987, p. 133-139. [9] Wei Sun, Fei Qi, Qingkai Han Identify the damping characteristics of hard coating composite structure based on envelope method of free vibration signal attenuation. Vibration and Shock, Vol. 32, Issue 12, 2013, p. 50-54. [10] Yimin Zhang, He Li Fundamentals of mechanical vibration. Beijing, Higher Education Press, 2010, p. 19-25. [11] Xingwei Guo Research on filtering technology of accelerometer signal. Science and Technology Innovation Herald, Vol. 22, 2008, p. 004. [12] Yunpeng Cui, Hongxia Pan, Zhijun Wang Analysis and study of a machine gun’s experimental modal based on experimental bench. Machinery Design and Manufacture, Vol. 3, 2013, p. 146-148. [13] Zhiyi Ning, Shaohui Du, Qingkai Han Effectiveness research of simulating blade gas shock and coating damping. Aeroplane, Vol. 39, Issue 5, 2013, p. 14-17. 

Experimental study on vibration behavior of rotating manipulator in the process of scramming

 8 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  
36. Experimental study on vibration behavior of rotating 
manipulator in the process of scramming 
Zhong Luo1, Changshuai Yu2, Yunpeng Zhu3, Guangkai Chen4 
School of Mechanical Engineering and Automation, Northeastern University, Shenyang, China 
1Corresponding author 
E-mail: 1zhluo@mail.neu.edu.cn, 2yu.chang.shuai@163.com, 3270641532@qq.com, 
41148564928@qq.com 
(Received 12 January 2014; received in revised form 17 January 2014; accepted 22 January 2014) 
Abstract. In order to study the vibration behavior of rotating manipulator in the process of 
scramming, an experimental test is conducted on the vibration behavior during the process on 
different initial and measuring conditions. Through the experimental test, the vibration behavior 
exists two impact phenomena, which are found in the scramming process, and the feature 
extraction of the two impact phenomena is investigated. The dynamics parameters of the rotating 
manipulator are identified and hammer experiment is done to verify the dynamics parameters. 
With these parameters, an envelope model of the second impact response is established, and the 
applicability of the model is validated by experiments. The method of pasting damping layer on 
the surface of manipulator is employed to inhibit the vibration which is caused by the first impact. 
Via the experimental verification, the damping layer takes a certain effect on the vibration 
elimination. 
Keywords: manipulator, vibration behavior, hammer test, vibration elimination. 
1. Introduction 
Manipulator is one of the most important and commonly used facilities in a variety of 
engineering applications. For example, the United States Robonaut, Ranger space manipulators 
can perform complex repair and assembly work on faulty satellites [1-2]. Because of the 
specificity of the space environment, vibration problem of space manipulator causes the task not 
being completed, and brings a great loss [3]. Therefore, the vibration behavior of manipulator has 
a very important effect on the manipulator’s work. Suppressing the vibration has been one of the 
significant problems to be solved urgently in the engineering field. 
A huge amount of research efforts have been devoted to the vibration elimination of 
manipulator in the literature. Dickerson [4] and Alberts [5] use the passive vibration control 
method of pasting elasticity damping materials to inhibit the manipulator structural vibration. 
Book [8] adopts pole assignment technique to design the state feedback controller in order to 
reduce the vibration of the flexible robot response. Sakawa [6] uses the linear quadratic optimal 
control theory to define the state feedback gain, and suppress elastic deformation and vibration of 
flexible robot. Bailey [7] and Plump J. M. [8] completes groundbreaking experiments that 
organically combine passive vibration control and active vibration control with using piezoelectric 
materials. 
There is not any work on the vibration behavior of manipulator during the rotating and 
scramming process. This paper presents an experimental study on the vibration behavior of 
rotating manipulator, and the manipulator’s vibration is restrained by pasting a damping layer. 
Through the experimental test, repeated impact phenomenon is found in the scramming process 
of manipulator. Via the feature extraction of repeated impact, the dynamics parameters of rotating 
manipulator are identified and an envelope model of the second impact response is established. 
2. Experimental details and results 
An aluminum tube with the length of 73 mm, the width of 25 mm, the height of 500 mm and 
the wall thickness of 1 mm is fixed on a rotating module, which acts as a rotating manipulator 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
 © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 9 
(Fig. 1). The measuring points and the direction of the manipulator’s rotation are shown in Fig. 1. 
 
Fig. 1. The manipulator 
Three acceleration sensors are attached to the three points of the manipulator respectively. The 
manipulator is controlled under the rotational speed of five working conditions shown in Table 1. 
Under the five working conditions, the vibration behaviors of the three measuring points are tested. 
Table 1. The rotational speed of five working conditions 
Conditions 1 2 3 4 5 
Rotational speed (rad/s) 1.57 0.785 0.523 0.392 0.314 
According to the experimental test, the vibration behavior exists repeated impact phenomena. 
Repeated impact phenomenon is found in the scramming process of the manipulator (Fig. 2), 
including the first impact and the second impact. 
 
Fig. 2. The vibration behavior of the manipulator 
Fig. 2 is obtained from the vibration signal acquisition. The phenomenon of emerging repeated 
impact happens in the process of manipulator scramming, and the responses of repeated impact 
are free vibration. 
3. The principle of envelope method for free vibration attenuation to identify dynamics 
parameters 
Envelope method for free vibration attenuation is a commonly used method of measuring 
dynamics parameters [8]. Following the case of single degree of freedom, the principle of envelope 
method for free vibration attenuation to identify dynamics parameters is explained. 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
10 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  
Attenuation response for a damping system of single degree of degree can be expressed as: 
ݔ = ܥ݁ିచఠ೙௧sin ቀඥ1 − ߫ଶ߱௡ݐ + ߮ቁ, (1)
where ܥ is amplitude, ߱௡ is natural frequency, ݐ is time of free vibration, ߮ is phase difference 
angle and ߫ is damping ratio of the system. According to Eq. (1), envelope curve equation for 
displacement attenuation of single-degree-of-freedom vibration is Eq. (2): 
ݔ௘ = ܥ݁ିచఠ೙௧. (2)
Eq. (1) is displacement response, because of different types of vibration picking sensors, 
time-domain signal of attenuation response of velocity or acceleration may be obtained. Equations 
of velocity and acceleration are shown as Eq. (3) and Eq. (4): 
ݔሶ = ܤ݁ିచఠ೙௧sin ቀඥ1 − ߫ଶ߱௡ݐ + ߠቁ, (3)
ݔሷ = ܣ݁ିచఠ೙௧sin ቀඥ1 − ߫ଶ߱௡ݐ + ߚቁ, (4)
where ܤ and ܣ are amplitudes of velocity and acceleration attenuation response respectively. And 
ߠ  and ߚ  are the phase difference angles of velocity and acceleration attenuation response 
respectively. Eq. (4) and Eq. (1) have the same type, so acceleration response curve of 
single-degree-of-freedom vibration have the same envelope curve with displacement response, 
and the response curve is shown in Fig. 3. 
 
Fig. 3. Time domain response curve of single degree freedom system 
In Fig. 3, damping makes the amplitude of system vibration decrease by geometric attenuation. 
The ratio of two adjacent amplitude is shown in Eq. (5): 
ߟ = ܣଵܣଶ =
ܣ݁ିచఠ೙௧భ
ܣ݁ିచఠ೙(௧భା்೏) = ݁
చఠ೙்೏, (5)
where ܣଵ, ܣଶ are the values of two adjacent amplitude, ݐଵ is the time of the first amplitude, ߟ is 
called damping coefficient [9] and ௗܶ is vibration period: 
ௗܶ =
1
ඥ1 − ߫ଶ߱௡
. (6)
Based on Eq. (6), amplitude reduces to the initial value 1 ݁చఠ೙்೏⁄  multiple every vibration 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
 © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 11 
period. In fact, in order to avoid inconvenience of taking the index value. Common logarithm 
damping ߜ replaces damping coefficient ߟ shown in Eq. (7): 
ߜ = ln ܣଵܣଶ = ln݁
చఠ೙்೏ = ߫߱௡ ௗܶ =
߫
ඥ1 − ߫ଶ. (7)
According to Eq. (6) and Eq. (7), equations of damping ratios and natural frequency is shown 
as follows: 
߫ = ߜඥ(2π)ଶ + ߜଶ, (8)
߱௡ =
1
ඥ1 − ߫ଶ ௗܶ
. (9)
4. Experimental analysis 
4.1. Dynamic parameters recognition of the manipulator 
Due to the influence of noise, de-noising method [11] is used to the first impact response of 
measuring point 1 on condition 1. The first impact response after de-noising processing is shown 
in Fig. 4, and ݔ-axis represents time and ݕ-axis represents acceleration value. 
 
Fig. 4. The first impact after de-noising processing 
P1, P2 in vibration waveform (Fig. 4) are the first and the second peak points, and coordinate 
values of the two peaks are P1(1.55, 125.4), P2(1.57, 55.15). That means ܣଵ = 125.4 m/s2 and 
ܣଶ = 55.15 m/s2.  Under other conditions, ܣଵ  and ܣଶ  can be obtained by the same analysis 
(Table 2). 
Table 2. Peak points’ value of ܣଵ and ܣଶ (m/s2) 
 Measuring point 1 Measuring point 2 Measuring point 3 ܣଵ ܣଶ ܣଵ ܣଶ ܣଵ ܣଶ 
Condition 1 125.4 55.15 72.46 30.53 26.15 9.11 
Condition 2 45.19 18.74 26.37 9.35 8.92 2.44 
Condition 3 17.34 8.39 11.24 4.18 5.17 1.17 
Condition 4 14.64 4.73 8.76 2.57 0.74 0.2 
Condition 5 14.77 5.50 8.52 2.98 3.04 0.97 
According to the data of Table 2, Eqs. (7)-(9), damping ratios (Table 2) and natural frequencies 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
12 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  
(Table 3) can be obtained in different measuring points of different conditions. 
Table 3. Damping ratios 
 Measuring point 1 Measuring point 2 Measuring point 3 
Condition 1 0.131 0.149 0.164 
Condition 2 0.156 0.163 0.203 
Condition 3 0.174 0.182 0.223 
Condition 4 0.181 0.192 0.228 
Condition 5 0.162 0.169 0.183 
Table 4. Natural frequencies (Hz) 
 Measuring point 1 Measuring point 2 Measuring point 3 
Condition 1 52.82 50.56 50.68 
Condition 2 50.62 50.68 51.06 
Condition 3 50.77 50.85 48.85 
Condition 4 50.84 50.95 51.35 
Condition 5 48.26 53.39 53.53 
The average of damping ratios in Table 3 and natural frequencies in Table 4 are 0.177 and 
50.86 Hz respectively. Therefore, ߫ = 0.177 and ߱௡ = 50.86 Hz can evaluate the damping ratio 
and the natural frequency. 
4.2. Hammer experiment  
Using hammer experiment [12] verifies the natural frequency (Fig. 5). 
 
Fig. 5. Hammer experiment 
Natural frequencies got from hammer experiment are shown in Table 5. 
Table 5. Natural frequencies obtained by hammer experiment (Hz) 
 First-order Second-order Third-order Fourth-order Fifth-order 
Natural frequencies 52.61 308.41 350.40 429.31 609.18 
According to Table 5, first-order natural frequency got from hammer experiment is 52.61 Hz, 
which is very close to the natural frequency 50.86 Hz got from the first impact of the manipulator 
(the error is 3.33 %), and proves the value of natural frequency 50.86 Hz is correct. 
4.3. Establishing an envelope model of the second impact response 
According to these dynamics parameters got from the first impact, an envelope model of the 
second impact response is established as follows: 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
 © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 13 
ݔ = ±ܣ݁ିଶగచఠ೙(௧ି௧బ), (10)
where ݔ is the acceleration of vibration, ܣ is the initial acceleration value of the second impact; ݐ 
is multivariate time and ݐ଴ is the initial time. Besides, ߫ is 0.177 and ߱௡ is 50.86 Hz. 
The envelope model is verified by experiment. Fig. 6(a)-(e) respectively represent the second 
impact response of condition 1 to condition 5. 
 
a) Condition 1 
 
b) Condition 2 
 
c) Condition 3 
 
d) Condition 4 
 
e) Condition 5 
Fig. 6. The second impact and the envelope model 
Where the solid line represents the second impact response and the dotted line represents the 
envelope model. According to the comparisons, good agreement is observed, which proves that 
the dynamics parameters got from the first impact is correct and the envelope model is applicable. 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
14 JOURNAL OF MEASUREMENTS IN ENGINEERING. MARCH 2014, VOLUME 2, ISSUE 1  
5. Adding a damping layer to restrain the vibration of manipulator 
A sharp spike of acceleration arises in the first impact (Fig. 7). In order to restrain the vibration, 
a damping layer is added to the surface of the manipulator [13] (Fig. 8). The manipulator is 
controlled at the rotational speed on five working conditions as shown in Table 1 to do the 
experimental test. 
Fig. 7. Existing a sharp spike 
 
Fig. 8. The manipulator with a damping layer 
The sharp spikes of manipulator with a damping layer and without a damping layer are 
compared in different measuring points under different conditions (as shown in Fig. 9). ܺ-axis 
represents rotational speed and ݕ-axis represents acceleration value. 
 
Fig. 9. Comparing the sharp spikes 
Where the first black line represent the sharp spikes of measuring point 1 without a damping 
layer in different rotating speed, the second black line represents measuring point 1 with a damping 
layer and the two lines make a comparison. Similarly, the two red lines make the comparison of 
measuring point 2 without a damping layer and with a damping layer and the two blue lines make 
the comparison of measuring point 3. Therefore, a conclusion can be obtained that adding a 
damping layer can suppress the vibration of the manipulator through the above comparisons. 
6. Conclusions 
Experimental study on the vibration behavior of a rotating manipulator during rotating and 
36. EXPERIMENTAL STUDY ON VIBRATION BEHAVIOR OF ROTATING MANIPULATOR IN THE PROCESS OF SCRAMMING.  
ZHONG LUO, CHANGSHUAI YU, YUNPENG ZHU, GUANGKAI CHEN 
 © JVE INTERNATIONAL LTD. ISSN PRINT 2335-2124, ISSN ONLINE 2424-4635, KAUNAS, LITHUANIA 15 
scamming process has been made. Repeated impact phenomenon is found in the scramming 
process of the manipulator. Conclusions obtained are as follow: (1) Dynamics parameters of the 
rotating manipulator are identified by the feature extraction of the first impact; (2) Using hammer 
experiment verifies the natural frequency correct; (3) Based on these dynamics parameters, an 
envelope model of the second impact response is established, and the applicability of the model 
is validated by experiments; (4) A sharp spike of acceleration arises in the first impact. A damping 
layer added to the surface of the manipulator is used to suppress the vibration, and via the 
experimental verification, the damping layer takes a certain effect on the vibration elimination. 
Acknowledgements 
This work was supported by the National Science Foundation of China (Grant No. 51105064); 
the National Program on Key Basic Research Project (Grant No. 2012CB026000); and the Natural 
Science Foundation of Liaoning Province (Grant No. 201202056). 
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Experimental study on vibration behavior of rotating manipulator in the process of scramming

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