*Corr. Author’s Address: Wuhan University of Technology, Wuhan, China, zhaoxh@whut.edu.cn 445
Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457 Received for review: 2020-10-01
© 2021 Journal of Mechanical Engineering. All rights reserved.  Received revised form: 2021-01-04
DOI:10.5545/sv-jme.2020.6959 Original Scientific Paper Accepted for publication: 2021-01-07
Active Vibration Control of a Mechanical Servo High-speed  
Fine-Blanking Press
Liu, Y .X. – Shu, Y .W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
Yanxiong Liu
1,3
 – Yuwen Shu
1,3
 – Wentao Hu
1,3
 – Xinhao Zhao
1,2,*
 – Zhicheng Xu
1,3
1
Wuhan University of Technology, Hubei Key Laboratory of Advanced Technology of Automotive Components, China 
2
Wuhan University of Technology, School of Materials Science and Engineering, China 
3
Wuhan University of Technology, Hubei Collaborative Innovation Center for Automotive Components Technology, China
The fine-blanking process as an advanced sheet metal forming process has been widely applied in industry. However, specially designed 
equipment is required for this process. In this paper, a novel mechanical servo high-speed fine-blanking press with the capacity of 3200 kN 
is proposed, and the vibration control for this machine is researched to achieve the requirement of fine-blanked parts of high dimensional 
accuracy, since the vibration of the fine-blanking machine will cause the machining displacement error and reduce the machining accuracy. 
Self-adaptive feed-forward control is used to simulate the active vibration control of the mechanical fine-blanking machine. The vibration 
control principle of the fine-blanking machine is described, and the control algorithm is established. At the same time, the mechanical 
vibration model of the fine-blanking machine as the controlled object is established, and the parameters of the excitation input and the 
mechanical model are obtained by the fine-blanking finite element simulation and the experiments of the vibration measurement of the press. 
Finally, the numerical simulation and analysis of active vibration control based on MATLAB are carried out. The results show that the control 
effect is good, and the vibration response is effectively reduced, thus greatly increasing the processing accuracy, saving a significant amount 
of energy, and reducing the energy consumption and defective rate.
Keywords: active vibration control; mechanical vibration model; mechanical servo high-speed fine-blanking press; self-adaptive feed-
forward control
Highlights
• 	 The mechanical vibration model of the fine-blanking machine tool is established.
• 	 The dynamic model parameters of the mechanical fine-blanking machine are obtained by using finite element analysis and 
empirical formula.
• 	 An adaptive feed-forward vibration controller for the fine-blanking machine is designed and applied to active vibration control of 
the fine-blanking machine.
• 	 The vibration response of the whole machine has been effectively reduced when the active control is applied, in which the 
time-domain vibration response has been reduced by more than 95 %, and the frequency-domain vibration response has been 
reduced by more than 80 %, which means that the vibration reduction effect is obvious.
0  INTRODUCTION
The fine-blanking (FB) process as an advanced net 
shape or near-net shape plastic forming process 
has been widely applied in industry because of the 
advantages of high efficiency and high parts quality 
[1] and [2]. Many mid-thick sheet metal components 
with complicated shapes and high dimensional 
accuracy can be fabricated with the FB process in 
one operation, as shown in Fig. 1a. Compared with 
the conventional blanking process, a special designed 
fine-blanking press was required for this process, 
providing at least three separate forces: blanking 
force, blank holder force, and counter punch force [3]. 
Now, almost all FB presses are hydraulic machines 
with the capacity of 3200 kN to 12000 kN [4], and the 
forming efficiency is about 30 to 70 times per minute 
with a punch stroke of 40 mm. With the increasingly 
huge market demand for the mid-thick sheet metal 
parts, the FB efficiency should be further improved; 
the target is about 200 times per minute or higher.
A mechanical servo high-speed FB press was 
designed and fabricated by our research group and 
Huangshi Huali Co., Ltd., and the forming efficiency 
can reach up to 220 times per minute and the maximum 
forming capacity is 3200 kN. The mechanical 
construction of the main driving system is shown 
in Fig. 1b, and the main slide block can achieve the 
trajectory shown in Fig. 1c. With the increasing punch 
frequency, the vibration of the FB press will become 
increasingly severe. It is known that the vibration of 
the press not only affects the parts’ quality, such as 
causing the crack on the cutting surface and reducing 
the dimensional accuracy but also reducing the service 
life of the machine. Moreover, the noise caused by 
the machine vibration will adversely affect working 
conditions and human health. Therefore, vibration 
control for the high-speed fine blanking press is 
urgently required.  

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
446 Liu, Y.X. – Shu, Y.W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
a) 
b) 
c) 
Fig. 1.  a) The mid-thick sheet metal parts fabricated by FB 
process, b) the mechanical construction of the main driving system 
of the high-speed FB press, and c) the slide block stroke diagram
In general, the passive control method was 
applied for the vibration control of the traditional 
press, such as increasing the stiffness of the frame 
and adding the vibration isolation system, and the 
vibration control effort for the excitation source of 
the press is very rare. For the high-speed FB press 
proposed in this paper, except for the passive control 
method, the active vibration control method was also 
applied to restrain the vibration of the whole machine 
caused by the elastic restoring force produced by the 
FB process. Therefore, the low-frequency vibration 
can be effectively suppressed, so as to reduce the 
vibration of the mechanical servo high-speed FB press 
to the greatest extent. 
For the research of the active control by Lueg, 
Guicking [5] submitted, early in 1933, a patent 
application describing for the first time the principle of 
active noise cancellation. The basic idea is that using 
the active control wave with the same amplitude of the 
noise to counteract the original noise. In 1953, Olson 
and May [6] invented the electronic sound absorption 
equipment, which proved the practical feasibility of 
the active vibration and noise control theory through 
experiments. Since then, active vibration control 
technology has been gradually applied to engineering 
machines. Winberg et al. [7] and Daley et al. [8] 
applied the active vibration control for the marine 
applications.
In recent years, many new active vibration 
control theories have been developed. Shao et al. 
[9] created the finite element (FE) active vibration 
control model of the piezoelectric flexible linkage 
by using the mixed Hamilton principle. Based on the 
complex mode theory, a hybrid independent mode 
controller, which consisted of the state feedback and 
disturbance feed-forward control, was developed. 
The results showed that the vibration was effectively 
suppressed for the flexible four-bar linkage. Li [10] 
studied the active control of submarine vibration 
system, and a corresponding adaptive control method 
was put forward. A good control effect of the vibration 
system by applying the periodic excitation force was 
obtained. Zhu et al. [11] proposed the active vibration 
control process for the marine diesel engine, and the 
x-LMS algorithm based on the off-line identification 
of error channel was used for the active vibration 
control. Belyi and Gan [12] studied and brought 
forward a combined bilateral and binaural active noise 
control algorithm for closed-back headphones. Soni 
et al. [13] published about the active vibration control 
of a ship-mounted flexible rotor-shaft-bearing system. 
Teo and Fleming [14] published optimal integral force 
feedback for active vibration control in 2015. Park 
and Kim [15] studied semi-active vibration control 
of space truss structures by friction damper for the 
maximization of modal damping ratio in 2013. 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
447 Active Vibration Control of a Mechanical Servo High-speed Fine-Blanking Press 
Through the inspiration of the active vibration 
control method mentioned above, the active vibration 
control strategy was researched for the mechanical 
servo high-speed FB press to suppress the periodic 
low-frequency vibration of the machine. The active 
vibration control principle of the high-speed FB press 
was analyzed, and the adaptive vibration controller 
was created. According to test results of the FB press 
vibration, the input parameters for the control model 
were obtained, and the active vibration control effect 
was predicted by using MATLAB software.
1  ADAPTIVE VIBRATION CONTROLLER DESIGN
1.1  Active Vibration Control System
The active vibration control system of a mechanical 
servo FB press is mainly composed of the following 
parts, as shown in Fig. 2.
(1) Controlled object. In this paper, the controlled 
object is the mechanical servo FB press. The 
main drive system of the press is the excitation 
source of the controlled object; the excitation 
force acts on the frame and then transfers to the 
whole machine. Since the elastic restoring force 
is mainly acted on in the vertical direction, the 
mathematical model of the controlled object is 
primarily focused on the vertical deformation.
(2) Measuring mechanics. The core component 
of the measuring mechanics is the sensor. An 
acceleration sensor is often used in the data 
acquisition of vibration response. The vibration 
signal of the whole machine measured by the 
acceleration sensor is transmitted to the control 
system through signal amplification and filtering, 
which is used as the input parameter of the active 
vibration control.
(3) Electric actuator. According to the command of 
the controller, the actuator applies the specified 
force or torque on the frame of the press and 
feeds back the action effect to the controller.
(4) Controller. The controller is the core part of 
the active vibration control system, which can 
provide the command and control rate of the 
actuator. Because the main driving system is 
motorial during the forming process, the adaptive 
controller which can adjust the parameters of the 
control system applied in this paper.
(5) Energy and auxiliaries. The external energy 
supplies the input energy of the actuator for the 
active vibration control system of the FB press.
Fig. 2.  Schematic diagram of the active vibration control system for FB press
1.2  Adaptive Vibration Control Algorithm
The selection and design of the algorithm play an 
important role in the adaptive vibration controller. 
Among many adaptive control methods, the least 
mean square (LMS) adaptive algorithm [16] has been 
widely used, in which the gradient search method 
is used, the convergence solution can be obtained 
quickly, and the implementation is relatively simple.
The LMS algorithm can be expressed by Eq. (1):
 
Fenn Ee n
Ed nd nyny n
(()) () (( ))
() ()() ().

  




2
22
2 (1)

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
448 Liu, Y.X. – Shu, Y.W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
The filter of the adaptive active vibration 
controller adopts the finite impulse response (FIR) 
structure, and its structure diagram is shown in Fig. 3.
Fig. 3.  Adaptive FIR filter
In Fig. 3 x(n) represent the input of the adaptive 
active vibration control filter, y(n) is the output of the 
adaptive active vibration control filter, w(n) is the 
impulse response, w(n) = {w(0), w(1), ..., w(n – 1)},  
then:
 yn nn wnxn i
i
i
N
() () () ()( ). 



WX
T
0
1
 (2)
For the filter with transverse structure, substitute 
the expression of  into Eq. (1):
    En nn n (( )) () () (), dW RW WP
2
2
TT
 (3)
where where R = E [X(n) X
T
(n)] is the autocorrelation 
matrix of N×N, is the cross-correlation vector for 
N×1, which represents the correlation between the 
ideal signal d(n) and the input vector.
Because the gradient descent method is adopted 
for the optimization process, so:
 






W()
.
()
n
wn w
0 (4)
When the mean square error  reaches to the 
minimum value, the optimal weight coefficient can be 
obtained.
If the R matrix is full rank, the best value of the 
weight coefficient should be satisfied with W
*
 = R
–1
 P, 
namely:
w
w
w
n
n
xx x
xx
0
1
1
01 1
10























()
() () ()
() ()
 
  
 


x
xx x
xd
xd
n
nn
()
()() ()
()
() 














2
12 0
0
1
1
 



xd
n ()
,













1
 (5)
where, ϕ
x
 (m) = E[x(n) x(n – m)] shows the 
autocorrelation value of x(n), ϕ
xd
 (k) = E[x(n) d(n – k)] 
represents the cross-correlation value between x(n) 
and d(n).
In practical applications, it is difficult to obtain 
the autocorrelation and cross-correlation values of 
signals. Therefore, gradient estimation value can be 
used, that is:
 
gn dnxn xnxn wn
xn dn xn wn
w

() ()() () ()()
() (( )( )()).
 
 
22
2
T
T
 (6)
Using the gradient estimation value to replace the 
real values, then:
 wn wn enxn ()() ()() .   12  (7)
This is the iterative equation of the LMS 
algorithm. In practical application, the step size is 
fixed, and the value of will affect the performance of 
the algorithm, resulting in the change of convergence 
speed, jump tracking ability and steady-state 
imbalance of the algorithm. Since the most appropriate  
value is very difficult to obtain, the variable step size 
normalized LMS algorithm is usually applied, which 
can be expressed as:
 wn wn enxn wn wn
n
()() ()() () () .    12  (8)
According to the expression of the instantaneous 
square error of the LMS algorithm, the instantaneous 
square error of variable step size normalized LMS 
algorithm can be expressed as:
 
 en en wn xnxn wn
wn xnxn wn dn
22
2
2
() () ()() ()()
()() ()() (
 
 
TT
TT
) ) ()() , wn xn
T
 (9)
then:
 



en en en
wn xnen
wn xnxn wn
22 2
2
() () ()
()()()
()() ()() .

T
TT
 (10)
From Δw(n) = 2μ
n
 e(n) x(n), we can get:
 
 
 



en en xn xn
enxn xn
n
n
22
2
2
4
4
() () ()()
() ()() .


T
T
 (11)
To minimize Δe
2
 (n), which makes the 
instantaneous square error close to the square error, 
we can take 
den
d
n

2
0
()

 , then,
 
n
xn xn

1
2
T
()()
. (12)
In order to avoid the steady-state imbalance, a 
fixed numerical convergence factor μ
k
 is introduced 
to avoid a large step size when the denominator is 
very small during the iteration process. At the same 
time, another parameter γ is introduced to adjust the 
denominator. Then the updated iterative equation of 
the new variable step size normalized LMS algorithm 
is:

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
449 Active Vibration Control of a Mechanical Servo High-speed Fine-Blanking Press 
 wn wn
xn xn
enxn
k
()()
()()
()() .  

1


T
 (13)
1.3  Adaptive Feedforward Active Vibration Control of the 
Fine-Blanking Press
As mentioned in Section 1.1, the main drive system of 
the press applies vertical excitation force to the whole 
machine, including the frame. The actuator is installed 
on the frame, which can exert a controllable force 
with the opposite direction of the excitation force of 
the main drive system to offset the original vibration 
and realize active vibration reduction.
Because the vibration on the frame is easy to 
measure, the upper and lower cross-beams of the 
frame are selected as the vibration observation parts 
of the control system. The excitation force  generated 
by the main drive system is transmitted to the frame 
through the primary channel to generate the vibration 
response, which can be used as the reference input of 
the adaptive active vibration control.  is the control 
input, and the value is the estimated value of the 
excitation force. By adjusting the  with the adaptive 
feed-forward control method, the vibration response 
of the frame can be reduced, and the effect of reducing 
the vibration of the whole machine can be achieved. 
The control block diagram is shown in Fig. 4. 
Fig. 4.  Active vibration control block diagram of the FB press
In Fig. 4, F(n) is the excitation force generated 
by the main drive system, d(n) is the excitation force 
response used as the reference input, e(n) is the 
control system error and also used as the controlled 
output when the control system is stable, W(z) is the 
adaptive controller, R(n) is the estimated value of the 
excitation force, G(n) is the transfer function which 
reflects the excitation force transferred to the frame,  
S(n) is the transfer function which reflects the control 
force transferred to the frame. The FIR filter described 
above is adopted as the filter.
Based on the above control block diagram, the 
mean square error of the whole control system can be 
expressed as Eq. (1).
Then the control output y(n) of the n
th
 order filter 
is equal to the convolution operation:
 
yn Sn wnRn
Sn wR
i
N
i
N
() () ()()
() (( )( )),

 




 
0
 (14)
then the gradient value of the mean square error can 
be calculated as:
 g
dE en
dw
Ee nSnRn
w





 
2
2
()
()()(). (15)
According to the variable step-size normalized 
LMS algorithm, the variable step-size factor μ needs 
to be transformed, that is:
  
1
2( ()() )(()() )
,
SnRn SnRn
T
 (16)
then the iterative equation of the weight updating of 
the adaptive control algorithm can be obtained:
 wn wn
xn xn
enxn
n
()()
()()
()() ,  

1


T
 (17)
where, X(n) = S(n) R(n).
2  VIBRATION MECHANICAL MODEL DESIGN
2.1  Vibration Mechanical Model of the Fine Blanking Press
For the adaptive active vibration control system of the 
fine blanking machine, establishing the mechanical 
vibration model of the controlled object and obtaining 
the transfer function of the control system are 
required. It is assumed that the material distribution 
before each blanking process can be restored, and the 
material penetration is not considered. The punching 
force is located in the vertical direction, so the vertical 
direction, which has the maximum deformation, is 
mainly considered. Therefore, the structure of the 
FB press can be expressed as a combination of linear 
spring dampers.
Then the mechanical vibration model as shown in 
Fig. 5 can be established, and the motion equation for 
each mass block can be expressed as follows.
 mx FF
ii i
imp
i
el
 
 
, (18)
where F
i
imp
 is the sum of the impact forces exerted on 
the mass m
i
, F
i
el
 is the sum of the elastic forces 
applied to the mass m
i
.
The excitation source of the whole press comes 
from the main drive system. The excitation force 

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
450 Liu, Y.X. – Shu, Y.W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
acting on the main drive system is mainly composed 
of two parts. One part is the unbalanced inertia force 
F
y
, generated by the main drive system itself. The 
other part mainly is the elastic restoring force from 
the main drive system at the ending of the FB process, 
which is relatively difficult to obtain; this can be done 
so with the FE simulation of the FB process. The FB 
FE model is shown in Fig. 5. The material for this 
simulation is TC4 titanium alloy with a thickness of 5 
mm. The diameter of the fine-blanked part is 20 mm, 
and the FB speed is 5 mm/s. The relationship between 
the FB force and the time can be obtained, as shown 
in Fig. 6. When the punch force acts on the workpiece, 
the reaction force exerts on the main drive system in 
the opposite direction, which reflects the changing of 
the impact load acting on the main drive system.
Fig. 5.  The FE model of the FB process
Fig. 6.  The relationship between the fine-blanking force and the 
time
According to the mechanical vibration model, as 
shown in Fig. 7, the vibration equations of each mass 
block can be expressed by:
 
mx cx x
kx xF F
mx cx xc
imp
y
77 77 8
77 8
88 88 97
 
 

 
 
()
()
() ( 
  
xx
kx xk xx
mx cx cx x
k
87
88 97 87
99 99 89 8
9
0

  
 

)
() ()
()
x xk xx
98 98
0  











()
, (19)
where m
7
, k
7
, c
7
, and x
7
 represent the mass, equivalent 
stiffness, equivalent damping and displacement of the 
main drive, respectively. m
8
, k
8
, c
8
, and x
8
 represent 
the mass, equivalent stiffness, equivalent damping and 
displacement of the frame, respectively. m
9
, k
9
, c
9
, and 
x
9
 represent the mass, equivalent stiffness, equivalent 
damping and displacement of the embedded footings, 
respectively. k
10
 and c
10
 represent the equivalent 
stiffness and damping of the upper worktable. 
  xx
jj
and (  j = 6, 7, 8) represent the acceleration and 
velocity of the mass block.
Fig. 7.  Vibration mechanical model of the FB press
2.2  Parameters Determination of the Vibration Mechanical 
Equation
In order to solve the mechanical vibration equation, 
the parameters, such as the equivalent mass, 
equivalent stiffness, equivalent damping value and 
similar parameters, should be determined firstly based 
on the FB press structure.
2.2.1  Embedded Footings System 
Fig. 8 shows the foundation installation system for 
the FB press. For the embedded foundation in the 
deep homogeneous layer, we can use the formulas 
presented in [17] and [18] to calculate the stiffness and 
damping value. That is:

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
451 Active Vibration Control of a Mechanical Servo High-speed Fine-Blanking Press 
Fig. 8.  Foundation installation design  
of mechanical fine blanking machine
 
kG rC
G
G
l
r
S
cr GC S
l
r
G
G
v
S
v
vv
SS









01
0
1
0
2
22
0
()
()
,



 (20)
where G is the shear modulus of the soil, r
0
 is the 
radius of circular foundation or the equivalent radius 
of non-circular foundation. ρ is the density of the soil, 
l is the depth of embedment, G
S
 and ρ
S
 are the shear 
modulus and density of the backfill side layer, 
respectively. Dimensionless stiffness and damping 
parameters CC
v
v
1
2 and depend on the dimensionless 
frequency. SS
v
v
1
2 and are the dimensionless 
stiffness and damping parameter of the side layer. 
Novak [19] provided the C
v1
, CC
v
v
1
2 and , SS
v
v
1
2 and for 
most stamping equipment, as shown in Table 1.
Table 1.  Reference values of stiffness and damping for foundation 
installation system
soil
Half-space Side layer
C
v1 CC
v
v
1
2 and
S
v1 SS
v
v
1
2 and
Cohesive soil 7.5 6.8 2.7 6.7
Granular soil 5.2 5.0
Based on the installation conditions of the 
mechanical servo FB press, the average shear wave 
velocity of soil is 150 m/s, and the density is 1900 
kg/m³. The total mass of the foundation system 
is taken as 400,000 kg. The average shear wave 
velocity of backfill material is 120 m/s, and the mass 
density is 2400 kg/m³. The shear modulus of soil can 
be evaluated by G = ρV
S
2
, and it is 42.75 MPa for 
footing and 25.9 MPa for the side layer. Therefore, 
the stiffness and damping constants of the foundation 
installation system can be calculated by Eq. (21), 
which is k = 8.1×10
8
 N/m and c = 1.1×10
7
 (N/m)/s.
2.2.2  Frame Part
Because of the complexity of the frame structure, the 
FE method is usually used to obtain the equivalent 
stiffness of the frame mass. As shown in Fig. 9, the 
bottom surface is fixed by four points, and the upper 
cross-beam is applied with 200 N uniform force to 
get the deformation of the frame. According to the 
simulation results, the maximum deformation of the 
frame is 6.7324 × 10
–8
 m. Therefore, the equivalent 
stiffness of the frame can be calculated with:
 
k
F
l
f
f

 

 

=
200
6.7324 10
N/m
N/m
8
9
2971 10 .. (21)
Fig. 9.  Frame deformation under the action of the constant load

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
452 Liu, Y.X. – Shu, Y.W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
Fig. 10.  Acceleration and velocity attenuation on the frame under 
the impact load; a) acceleration, and b) velocity
2.2.3  Main Drive System
For the main drive system, the equivalent stiffness 
and damping can be obtained with the same method 
applied for the frame part. The FE model for the main 
drive system was created as shown in Fig. 11, in 
which the support constraint is applied to the bearing 
pedestal at the bottom of the main drive system, 
and the horizontal displacement of the slide block 
is constrained. The deformation of the main drive 
system can be obtained by applying 200 N uniform 
force load on the top of the slider, as shown in Fig. 11.
Based on the plots in Fig. 10 that the maximum 
deformation of the main drive system under the 
constant load is 6.0265×10
–7
. Then, the equivalent 
rigidity of the main drive system can be obtained by 
Eq. (25):
 k
F
l
T
T




 

200
60265 10
3321 0
7
8
.
.. N/m (25)
In order to obtain the equivalent damping of the 
main drive system, the 10
5
 N impact is applied to the 
top surface of the slider for 0.02 s. The maximum 
acceleration and velocity changing point on the main 
It is somewhat difficult to calculate the equivalent 
damping value of the frame. In general, it is required 
to calculate the logarithmic decrement rate δ of the 
system response under the impact vibration. The 
relationship between the logarithmic decrement rate 
and the structural damping ratio is shown in Eq. (22):
 



 
In
x
x
i
iT
2
1
2
, (22)
where ξ is the damping ratio of the frame, x
i
 is the 
displacement, velocity or acceleration amplitude on 
the frame at the time of t
i
, x
i+T 
is the displacement, 
velocity or acceleration amplitude on the same 
location at the time of t
i+T
.
Because the value of ξ is very small, it can 
be ignored after the square. Then, Eq. (22) can be 
simplified as:
   

In
x
x
n
i
it
2. (23)
Based on Eq. (23), once the logarithmic 
decrement rate δ is determined, the damping ratio ξ of 
the frame can be obtained.
 cm k  2 . (24)
Therefore, to obtain the equivalent damping 
of the frame, the logarithmic decrement rate of the 
vibration amplitude of the system under the impact 
load should be calculated first. Based on the above 
FE model, 1 MN impact force is applied to the frame 
workbench and the bearing seat hole with a time 
of 0.02 s. According to the simulation result, the 
maximum acceleration and velocity changing point on 
the frame can be obtained, as shown in Fig. 10. 
Based on the plots in Fig. 10, the following 
equivalent damping parameters can be obtained and 
summarized in Table 2.
Table 2.  Equivalent damping parameters of the frame
Value
Logarithmic 
decrement rate
Damping ratio 
of frame
t
i
t
i+T
δ ξ
Velocity v
7
0.272 0.103 0.971 0.154
Acceleration a
7
6.691 2.731 0.896 0.143
Based on the numbers in Table 2, it can be seen 
that the damping ratio of the frame is near 0.15. 
Therefore, it can be taken as 0.15. It is also known that 
the total mass of the frame is 12,314 kg. According to 
Eqs. (22) to (24), the equivalent damping value of the 
frame can be obtained as c
7
 = 1.81×10
6
.

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
453 Active Vibration Control of a Mechanical Servo High-speed Fine-Blanking Press 
drive system can be obtained from the simulation 
results as shown in Fig. 12.
Fig. 11.  Deformation of the main drive system  
under the constant load
Fig. 12.   Acceleration and velocity attenuation of the main drive 
system under the impact load; a) acceleration, and b) velocity
Based on the plots in Fig. 12, the following 
equivalent damping parameters can be obtained and 
summarized in Table 3.
Table 3.  Equivalent damping parameters of the main drive system
Value
Logarithmic 
decrement rate
Damping ratio 
of frame
t
i
t
i+T
δ ξ
Velocity v
6
1.601 1.038 0.433 0.069
Acceleration a
6
4.689 2.773 0.436 0.069
According to the parameters obtained in Table 
3, the value of the damping ratio of the main drive 
system is approximately 0.069. It is also known that 
the total mass of the main drive system is 2,592 kg. 
According to Eqs. (23) to (25), the equivalent damping 
value of the main drive system can be obtained as 
c
6
 = 1.28 × 10
5
.
After obtaining the parameters of each part, the 
mechanical vibration model of the controlled object 
can be finally established and used in the active 
vibration control simulation.
3  NUMERICAL SIMULATION AND DISCUSSION
3.1  Analog Excitation Input
Because the effect of the vertical excitation force 
on the forming accuracy is the most direct and the 
largest, the reference excitation force input of the 
active vibration control can be composed of the 
blanking force excitation during the FB process and 
the unbalanced inertia force excitation during the non-
working process. In order to simulate the error during 
the active vibration control process, the random 
vibration interference is added to the reference 
excitation input, which is shown in Fig. 13.
Fig. 13.  Reference excitation force input

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
454 Liu, Y.X. – Shu, Y.W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
3.2  Reference Input Based on the Measured Vibration 
Response
3.2.1  Vibration Measurement Scheme of Fine-Blanking 
Machine
The composition of the vibration measurement system 
of the mechanical servo FB press can be depicted 
by the schematic diagram shown in Fig. 14. During 
the working process, the vibration at the working 
area is the most obvious, which has a direct impact 
on the forming accuracy. Therefore, the vibration in 
the working area needs to be measured. Meanwhile, 
the rigidity of the frame in the middle area is much 
smaller than that of the upper and lower cross-beams, 
and the guide rail of the slide block is arranged on 
the frame column in the middle area. Therefore, 
measuring points need to be arranged on the inner 
side of the stand column to reflect the vibration mode 
of the whole machine. Consequently, the measuring 
points arranged at the worktable area of the FB press 
are shown in Fig. 15, and 12 three-way acceleration 
sensors are even distributed at the working area.
3.2.2 Test Results of Measuring Points
During the test, the mechanical servo FB press works 
periodically with a speed of 87 times per minute under 
the no-load condition. In the movement process, the 
inertial load affects the lower cross-beam directly, 
and the vibration will be transmitted to the worktable, 
resulting in the forming error. The bottom of the lower 
cross-beam connected with the ground by installation 
system, the overall stiffness is very large. Therefore, 
the acceleration response of measuring points 1, 2, 
and 3 can reflect the overall response of the lower 
cross-beam, which is shown in Fig. 16.
Compared with the upper and lower cross-beams, 
the rigidity of the frame columns on the left and right 
sides in the middle is smaller, and the deformation will 
have a great impact on the whole press deformation. 
As the left and right columns are of symmetrical 
structure, the deformation situation is similar from the 
results, so the deformation situation on the right side 
is selected for the analysis. The response situations in 
time domain and frequency domain are shown in Fig. 
17.
       
Fig. 15.  Measuring points distribution at the working area
Fig. 14.  Vibration measurement schematic diagram

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
455 Active Vibration Control of a Mechanical Servo High-speed Fine-Blanking Press 
Based on the plots in Figs. 16 and 17, when the 
frequency is about 200 Hz, points of 4, 5 and 6 have 
a stronger frequency response than the points of 1, 2 
and 3. 
The overall rigidity of the upper cross-beam is 
very large. Because the upper cross-beam is far from 
the frame installation system, it is easy to produce 
large vibration response. The response situations in 
the time and frequency domain are shown in Fig. 18.
Based on the plots in Figs. 16 to 18, points of 7, 
8 and 9 have a stronger frequency response when the 
frequency is about 150 Hz than points of 1, 2, 3, 4, 5 
and 6. But have a weaker frequency response when 
the frequency is about 200 Hz.
3.3  Numerical Simulation Results
According to the self-adaptive vibration feed-forward 
control method, as described in Section 2, the control 
system simulation process is programmed in the 
MATLAB software platform, and the value of μ
k 
is 
0.005, γ is 10
–5
. Combined with the mechanical model 
of the controlled object, the time-domain vibration 
response of each observation point with and without 
control can be obtained, as shown in Fig. 19a. The 
simulation results show that the control effect of all 
measuring points is very good, so we use measuring 
point 2 to show. The frequency domain vibration 
response of observation point 2 with and without 
control can be obtained, as shown in Fig. 19b. 
In Fig. 19, the blue line represents the vibration 
response output without control, and the red line 
represents the vibration response output adding active 
control. It can be seen from Fig. 19 that the vibration 
response of the press with the active vibration control 
is effectively reduced. The time-domain vibration 
response quickly achieves stability when the active 
control applied and the convergence speed is very 
fast, which means that it has a stable control effect at 
that time. It can be seen that the vibration of the frame 
               
Fig. 16.  Response of Z-direction time domain and frequency domain of measuring points at the lower cross-beam area  
(measuring points of 1, 2 and 3); a) time domain response diagram, and b) frequency domain response diagram
             
Fig. 17.  Response of Z-direction time domain and frequency domain of measuring point at frame column area  
(measuring points of 4, 5 and 6); a) time domain response diagram, and b) frequency domain response diagram

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
456 Liu, Y.X. – Shu, Y.W. – Hu, W.T. – Zhao, X.H. – Xu, Z.C.
has been significantly suppressed, and the maximum 
value of the vibration response has been reduced 
by more than 95 %; the amplitude variation of the 
vibration response is maintained within the range of  
m.
For the frequency domain control effect, it can 
be seen that after controlling the corresponding 
response of the first three modes, the vibration 
response amplitude reaches stability very fast, and the 
maximum value of the vibration response is reduced 
by more than 80 %. At the same time, the convergence 
speed of the system is very fast after the application of 
active vibration control. 
From the simulation results, it can be seen that the 
active vibration control applied to the FB press does 
not suppress the vibration completely. However, the 
effect of vibration control is very significant, which 
shows a promising future for the application of the 
active vibration control method on the FB press.
4  CONCLUSION
In this paper, the mechanical vibration model of 
the fine-blanking press as the controlled object is 
established, the dynamic model parameters of a 
mechanical fine-blanking machine are obtained by 
using finite element analysis and empirical formula. 
The principle of vibration control of fine blanking 
press is described, the control algorithm is established, 
and the adaptive vibration control block diagram of 
fine blanking press is established.
The self-adaptive feed-forward control is used to 
simulate the vibration control of the mechanical FB 
press. The simulation results show that the vibration 
control effect is good, and the conclusion can be 
obtained as follows.
The vibration response of the whole machine 
has been effectively reduced when the active control 
is applied, in which the time-domain vibration 
response has been reduced by more than 95 %, and 
the frequency-domain vibration response has been 
              
Fig. 18.  Response of Z-direction time domain and frequency domain of measurement point at upper cross-beam area  
(measuring points of 7, 8 and 9); a) time domain response diagram, and b) frequency domain response diagram
           
Fig. 19.  a) Time domain, and b) frequency domain vibration response with and without control

Strojniški vestnik - Journal of Mechanical Engineering 67(2021)9, 445-457
457 Active Vibration Control of a Mechanical Servo High-speed Fine-Blanking Press 
reduced by more than 80 %, which means that the 
vibration reduction effect is obvious. Effectively 
reducing the vibration effect of fine-blanking machine 
greatly increases the processing accuracy, saves 
significant amounts of energy, and reduces the energy 
consumption and defect rate.
5  ACKNOWLEDGEMENTS
The authors would like to thank the Fundamental 
Research Funds for the Central Universities (WUT: 
2019Ⅲ117CG), 111 Project (B17034) and Innovative 
Research Team Development Program of Ministry of 
Education of China (No. IRT_17R83) for the supports 
given to this research and the Huangshi Huali Metal 
Forming Machine Tool Co., Ltd. for their supports 
given to experiments.
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