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Design of a centrifugal linear vibrating feeder driven by an eccentric motor
Journal: Transactions of the Canadian Society for Mechanical Engineering
Manuscript ID TCSME-2018-0244.R1
Manuscript Type: Article
Date Submitted by the Author: 11-Mar-2019
Complete List of Authors: Niu, Ruikun; Nanjing University of Aeronautics and Astronautics, State Key Laboratory of Mechanics and Control of Mechanical StructuresHua, Zhu; Nanjing University of Aeronautics and Astronautics
Keywords: linear feeder, eccentric motor, simulation test, performance
Is the invited manuscript for consideration in a Special
Issue? :Not applicable (regular submission)
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Design of a centrifugal linear vibrating feeder driven by an
eccentric motor
Niu Ruikun, Zhu Hua1
(State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing
University of Aeronautics and Astronautics, Nanjing; 210016, China)
The research is funded by The National Basic Research Program of China (973 Program, Grant
No. 2015CB057501).
About the author: Niu Ruikun, Doctoral student, Nanjing University of Aeronautics and
Astronautics, Nanjing, China. E-mail: [email protected]
Zhu Hua (communication author), Associate Professor, E-mail: [email protected]
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Abstract: In this paper, a novel linear vibrating feeder is designed that uses the
centrifugal motion of an eccentric motor as the driving source. Firstly, the working
principle of the linear vibrating feeder is theoretically analyzed and the dynamic
model is established. Subsequently, a dynamic simulation of the system is carried out
using the ANSYS software. The relationship between the displacement amplitude,
vibration speed, and frequency of the linear vibrating feeder prototype is tested using
a three-dimensional vibrometer, with an OT-10A copper terminal used to test the
prototype. The experimental results indicate that, at a vibration frequency of 125 Hz,
maximum vibration speeds of 1.23 mm/s and 1.70 mm/s are reached in the X- and
Z-directions, respectively. The corresponding maximum amplitudes are 0.7 mm and
0.99 mm, and the material feeding speed reaches a maximum value of 123 mm/s.
Compared with similar piezoelectric and electromagnetic vibrating feeders, the total
weight of the prototype is reduced by a third, the noise is reduced by more than 20 dB,
and the driving voltage is only 3.6 V. Hence, the performance of the linear vibrating
feeder has been successfully demonstrated.
Keywords: linear feeder, eccentric motor, simulation test, performance
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1. Introduction
Linear vibrating feeders are major components of automatic production lines and
have a wide range of applications in the medical and military fields, and in the
manufacturing of precision instruments. Conventional linear vibratory feeders are
classified into electromagnetic and piezoelectric varieties, Maul G P (2005) and Zhan
Qixian (1997). Electromagnetic vibrating feeders generate an adsorption force and
vibration by energization of an electromagnetic coil. They are characterized by large
amplitude vibrations, high conveying speed, and low cost. Compared with
piezoelectric driving sources, the noise and energy consumption are large, while the
output performance is relatively poor, Su Jiang (2010), Choi S B (2004), Ting Y et al
(2005), Jiao Qiwei (2001). Piezoelectric feeders use piezoelectric bimorph as the
driving source, which have the advantages of simple structure, low noise, and good
stability, while the electromagnetic production cost is relatively high. In recent times,
Japan has formed a world monopoly on piezoelectric vibrating feeders, Jeffrey
Boothroyd (2009), SU Jiang et al (2013), Tian Zongjing, Wu Wenfu (2011). In the
1990s, China began to study vibrating feeders. Although some achievements were
made with the piezoelectric design, the structure was not innovative enough, the
technology was not mature enough, and the products were not widely promoted, Paul
C P at el (2007), Liang Yanfei and Tan Weiming (2008), Jiang Bin (2008). The output
stability of the electromagnetic feeder is lower than that of the piezoelectric type, but
its efficiency is high, and its production cost and market price are low. As a result,
electromagnetic vibrating feeders have been heavily promoted, and occupy a large
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portion of the Chinese market.
As early as 1981, SINFONIA Co., Ltd. used two symmetrical feeding grooves in
the electromagnetic vibrating feeder in order to generate reciprocating vibration by
eliminating the interaction force produced during chute vibration. In 2010, the NTN
Corporation of Japan proposed the reduction of the vibration amplitude in the vertical
direction due to the vibration in the horizontal direction of the groove. In 2011,
SHINKO Co., Ltd. of Japan further proposed a vibration transmission device that
separately provided an amplitude adjustment circuit and a phase adjustment circuit,
able to adjust the vibration frequency and vibration amplitude.
In 1977, Japan Special Ceramics Co., Ltd. was the first to propose a "piezoelectric
vibration transfer device" using piezoelectric ceramics as the driving source, and
applied for a patent, Special Ceramics Co., Ltd(1977). In November 2002, SHINKO
Co., Ltd. of Japan applied for a patent on the piezoelectric vibrating feeder, Its
working method combines piezoelectric drive and inertial drive, Kato Ichi at el
(2013). In the same year, Yung and coworkers from the Chung Yuan Christian
University in Taiwan proposed a closed-loop control method. The feeder was
optimized to improve the conveying speed of the material. The acceleration and force
of the vibration platform were experimentally measured, Yung T at el (2002). In
2010, Tan et al. of the Dalian Jiaotong University designed a lateral diagonal tensile
piezoelectric vibrating feeder, where the piezoelectric bimorph adopts an inclined
arrangement at a certain angle with the central axis of the feeder to transfer materials,
TAN X D at el (2011). In 2013, Su Jiang et al. of the Jilin University designed and
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developed a designed and developed a vertical drive and inertial drive piezoelectric
vibratory feeder. These two structures are driven by a ring-shaped piezoelectric
vibrator and an combined piezoelectric vibrator, respectively. In order to obtain the
conveying effect, the top plate acquires upper, lower, front, and rear composite
vibrations, SU Jiang(2013).
In the current paper, a novel variation of a linear vibrating feeder is designed. The
mechanism uses an eccentric motor as the excitation source and transmits power
through the supporting spring piece. Subsequently, complementary dynamic
simulations and experimental tests of the device are conducted and analyzed.
2. Working principle and structural design
2.1. Working principle
The centrifugal linear feeder is composed of five components: a top plate, an
eccentric motor, a supporting spring piece, a base plate, and shock-absorbing feet. The
complete structure is shown in Fig. 1. The eccentric motor is attached to the center of
the top plate by epoxy resin. When the motor is powered using forward DC current, it
rotates clockwise and the centrifugal force, generated by the rotation of the eccentric
shaft, drives the top plate in the upward-downward direction and the
forward-backward direction in a reciprocal manner. At the same time, the top plate
transmits the force to the supporting spring piece. The role of the supporting spring
piece is to amplify the displacement of the top plate. The mechanism enables the
feeder to achieve large-amplitude vibrations and large output forces. When the
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rotational frequency of the motor is equal to the natural frequency of the system, the
entire device reaches a state of resonance. At this time, the motion amplitudes of the
top plate in the upward-downward and forward-backward directions, reach a
maximum value. This cycle is repeated such that the top plate has the capability to
transfer material. The stiffness and inclination angle of the spring piece have high
influence on the displacement amplitude of the enlarged top plate. During
experiments, the effects of different kinds of materials can be investigated by altering
the rigidity of the supporting spring piece and the inclination angle.
2.2. Kinetic model
Using the mechanical vibration theory, the linear vibration feeder system, driven
by an eccentric motor, is simplified to the dynamic model shown in Fig. 2, where m1
is the mass of the top plate and the motor, m2 the mass of the base and the supporting
spring piece, k1 the stiffness of the supporting spring piece, k2 the stiffness of the
rubber base, c the damping of the supporting spring piece, and F the initial excitation
force, which is the centrifugal force generated by the eccentric motor to induce
motion, . 𝐹 = 𝑚𝑤2𝑅
During feeder vibration, the x1 and x2 displacements of masses m1 and m2 are
given relative to their respective static equilibrium positions for any time t. Using
Newton's second law, the dynamic differential equation is:
(1) {𝑚1𝑥1 + 𝑐1(𝑥1 ― 𝑥2) + 𝑘1(𝑥1 ― 𝑥2) = 𝐹𝑠𝑖𝑛(𝑤𝑡)𝑚2𝑥2 + 𝑘2𝑥2 ― 𝑐1(𝑥1 ― 𝑥2) ― 𝑘1(𝑥1 ― 𝑥2) = 0
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Let the solution of the differential equation be:
(2) {𝑥1 = 𝐴1sin (𝑤𝑡)𝑥2 = 𝐴2sin (𝑤𝑡)
where A1 and A2 are the displacement amplitudes of the top and base plates,
respectively. If damping is neglected (i.e. c=0), Equation 2 may be inserted into
Equation 1 and give after simplification:
(3) { ― 𝑚1𝑤2𝐴1 + 𝑘1(𝐴1 ― 𝐴2) = 𝐹― 𝑚2𝑤2𝐴2 + 𝑘2𝐴2 ― 𝑘1(𝐴1 ― 𝐴2) = 0
Since k1 is assumed to be much larger than k2, the natural frequency of the system
is:
(4) 𝑤𝑛 =𝑘1(𝑚1 +𝑚2)
𝑚1𝑚2
The vibration system with two degrees of freedom is simplified to a single degree
of freedom forced vibration system, shown in Fig. 3, with equivalent mass defined as
. The differential equation of the system is now:𝑚 =𝑚1 +𝑚2
𝑚1𝑚2
(5) 𝑚𝑥 +𝑐𝑥 + 𝑘1𝑥 = 𝐹𝑠𝑖𝑛(𝑤𝑡)
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where m is the equivalent mass, c the damping of the system, and k the stiffness of the
supporting spring.
The frequency and damping ratios are and = , respectively. 𝜆 = 𝑤/𝑤𝑛 ζ 𝑐/𝑐0
The displacement amplitude ratio is β=X/X0 and the static deflection of the vibration
system under the action of constant force F0 is X0=F/k. The displacement amplitude of
the forced vibration is:
(6) 𝑋 =𝐹
(𝑘 ― 𝑚𝑤2)2 + (𝑐𝑤)2
and the displacement amplitude ratio is given by:
(7) β =𝑋𝑋0
=1
(1 ― 𝜆2)2 + (2𝜍𝜆)2
If , the amplitude ratio has its maximum value. Moreover, the 𝑤 = 𝑤𝑛 1 ― 2ζ2
amplification factor is at a maximum, and the excitation frequency is slightly smaller
than the resonance frequency.
2.3. Simulation analysis
In order to determine a suitable mode of vibration for the vibrating feeder, the
ANSYS software is used to perform modal analysis and determine the harmonic
response of the whole system. Fig. 4 shows the first four orders of modal
displacement of the system. For the first-order mode, it can be seen that the top plate
of the feeder vibrates left and right, and up and down with the supporting spring
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piece. For the second-order mode, the top plate oscillates with the support spring
piece in the forward-backward direction. The third-order mode is characterized by
symmetrical vibration of the supporting spring piece in the left and right direction. For
the fourth-order mode, the supporting spring piece vibrates also in the left-right
direction. It is concluded that the first-order mode of vibration encapsulates the
desired behavior.
The harmonic response of the linear vibrating feeder is analyzed when the
centrifugal force F is applied to the top plate. For the first harmonic of the resonance
frequency of 121 Hz, the centrifugal force F is calculated to be 2.3 N. The
relationship between frequency and amplitude is obtained from the simulations, as
shown in Fig. 5. When the motor frequency is 127 Hz, the displacement amplitudes of
the system in the X- and Z-directions reach the maximum values of 1.85 mm and 1.05
mm, respectively.
3. Experimental setup
3.1. Prototype size
The current section describes the design of a linear vibration feeder prototype,
driven by an eccentric motor. The top plate is machined from aluminum alloy, with a
length and width of 84 mm and 27 mm, respectively. The dimensions of the
supporting spring piece are 95 mm × 24 mm × 1 mm, and its material is 65Mn. The
supporting spring piece has an inclination angle of 75°. The dimensions of the cast
iron base plate are 110 mm × 40 mm × 20 mm. The shock-absorbing feet are made
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from silicone rubber with a diameter of 10 mm and a height of 10 mm. The basic
dimensions of the M20 eccentric motor are shown in Fig. 6. The motor size is 10 mm
× 15 mm. A voltage is applied to the motor using a DC power supply. An image of
the experimental setup is shown in Fig. 7.
3.2. Performance simulations
The motor voltage is varied to investigate the relationship between voltage and
frequency. A Doppler 3D laser vibrometer (SPV-300) is used to test the vibration of
the linear vibrating feeder, as shown in Fig. 8. The relationship between frequency
and amplitude is obtained by varying the frequency. The relationship of frequency
with displacement amplitude and velocity is measured as a function of frequency. An
OT-10A copper terminal is used as the conveying material, and the influence of the
frequency, voltage, and feeding speed is investigated.
4. Experimental analysis
4.1 Test results
Firstly, the voltage is adjusted from 0.4 to 8 V, and a three-dimensional
vibrometer is used to scan the vibration of the linear vibrating feeder. The relationship
between the horizontal and vertical frequencies and the amplitude is shown in Fig.
9(a). From the relationship between frequency and vibration speed, plotted in Fig.
9(b), it can be observed that the displacement amplitude and vibration speed increase
with increasing frequency. At 125 Hz, resonance occurs and the displacement
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amplitude and vibration speed reach their maximum values. The maximum
amplitudes in the horizontal and vertical direction are 0.99 and 0.7 mm, respectively,
and the maximum vibration speeds are 1.677 and 1.229 mm/s, respectively. As the
vibration frequency further increases, the displacement amplitude and vibration speed
gradually decrease. The theoretical simulation has a resonance frequency of 127 Hz.
According to theoretical modeling, the actual excitation frequency is smaller than the
resonance frequency, and the newly-designed vibrating feeder operating frequency is
125 Hz, which is basically consistent with the theoretical simulation. The fact that the
actual amplitude of the feeder is inconsistent with the amplitude calculated by the
theoretical simulation can be attributed to: a) the equivalent simplification of the
stator structure during the simulation; b) an error in the machining and assembly of
the part. Therefore, the ideal state cannot be achieved.
The voltage is adjusted to 3.6 V to reach a resonance frequency of 125 Hz, and
the position of the top plate of the feeder prototype is measured with a
three-dimensional laser vibrometer. The vibration behavior is shown in Fig. 10, where
the black grid shows the initial horizontal position, and the red and green grids
indicate the positions at different times. The power supply applies a voltage, and the
top plate moves from its initial position to the position shown in Fig. 10(a).
Subsequently, the top plate moves to the position shown in Fig. 10(c) through the
position shown in Fig. 10(b). This simple harmonic motion cycle is repeated and
corresponds to the first-order mode of vibration, according to the dynamic simulations
results.
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Subsequently, the feeding speed of the vibrating feeder is tested. The motor voltage
is adjusted from 0.4 V to 7 V to generate different motor rotation speeds and
excitation frequencies, and the OT-10A copper terminal is used as the conveying
material to test the relationship between the feeding speed and the frequency of the
motor. The characteristic relationship between the feeding speed and the frequency is
shown in Fig. 11. It is observed that the feeding speed increases with the increase of
frequency in the range between 0 and 125 Hz. For frequencies greater than 90 Hz, the
feeding speed increases more substantially. At 125 Hz, the feeding speed reaches its
maximum value of 123 mm/s, and as the vibration frequency is further increased, the
feeding speed decreases.
4.2. Experimental tests
The frequency of the motor is adjusted such that the newly-designed vibrating
feeder operates under resonant conditions. The operating parameters of the linear
vibrating feeder are compared with similar piezoelectric and electromagnetic
vibrating feeders in Table 1.
In Table 1, it can be seen that at the same resonant state, the centrifugal vibrating
feeder has the lowest driving voltage of 3.6 V. The noise is 20 dB or lower, which is
smaller than those of the piezoelectric and electromagnetic vibrating feeders. Its total
weight is about one third of that of the other feeders. Compared to the other two
models, the centrifugal linear vibrating feeder has a lower feeding speed of 123 mm/s.
However, the difference in speed is small, and the output is stable.
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5 Conclusions
(1) In view of the high cost and complex structure of industrial vibrating feeders, a
new linear vibrating feeder has been designed using as the driving source an eccentric
motor. Compared to conventional electromagnetic and piezoelectric linear vibrating
feeders, the structure of the proposed feeder is simple, the power consumption is low,
the cost is low, and it has strong applicability. The dynamic model is established and a
modal analysis is carried out. It can be seen from the simulation results that the
first-order vibration mode is the left and right reciprocating motion, which is the
vibration mode desired in the design.
(2) The displacement amplitude and vibration speed were investigated using a
three-dimensional vibrometer. The speed of the motor is found to increase with the
increase of voltage. The displacement amplitude, vibration speed, and feeding speed
reached a maximum at 125 Hz. The maximum amplitudes of the feeder in the
horizontal and vertical directions are 0.99 mm and 0.7 mm, respectively, the
maximum vibration speeds are 1.677 mm/s and 1.229 mm/s, respectively, while the
maximum feeding rate was 123 mm/s.
(3) Compared to the electromagnetic and piezoelectric linear vibrating feeders, the
total weight of the newly-developed centrifugal feeder was found to be 30% that of
the electromagnetic feeder, and the noise is 45% that of the electromagnetic linear
vibrating feeder. The power consumption is slightly higher than that of the
piezoelectric vibrating feeder. The feeding speed is slightly lower than that of the
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other two models, and the conveying speed is higher.
References
Choi S B,Lee D H. 2004. Modal analysis and control of a bowlparts feeder activated by piezoelectric actuators. Journal of Sound and Vibration. Sci. 275(3): 452-457. Dio:10.1016/j.jsv.2003.10.008.Jiang Bin. LIU Xiaolun, YANG Zhigang. et el. 2008. Study on vertical dirve ultrasonic feeder. opt. Precision Eng. EI. 16(6): 1082-1086. Dio:10.3901/JME.2008.11.283.Jeffrey Busthroy. 2009. Assembly Automation and Product Design. Xiong Yongjia, translated. Mechanical Industry Press.Jiao Qiwei, Cui Wenhui, Sun Baoyuan, et al. 2001. Development of piezoelectric vibrating feeder. Sensor Technology. 20(4): 23-36. www.cnki.com.cn/Article/CJFDTotal-CGQJ200104006.htm [accessed 12 October 2017].Kato Ichi, Fujii Takara. 2002. Piezoelectric-driven feeder and piezoelectric element-driven feeder: China, cn1380234a. 11-20. www.sipo.gov.cn/ [accessed 05 October 2018].Liang Yanfei, Tan Weiming. 2008. Automatic Machinery and Automatic Production Line . Higher Education Press.Maul G P, Thomas M B. 1997. A system model and simula-tion of the vibratory bowl feeder. Journal of Manu-facturing Systems. Sci. 16(5): 309-314. Dio:10.1016/s0278-6125(97)88461-0.Paul C P, Chao, Chien-Yu Shen. 2007. Dynamic modeling and experimental verification of a piezoelectric part feeder in a structure with parallel bimorph beams. Ultrasonics. Sci. 46(3): 205-218. Dio:10.1016/j.ultras.2007.02.002.Special Ceramics Co., Ltd. 1997. Piezoelectric vibration transfer device: Japan, 52-61087. 05-04.SU Jiang. 2013. Application Research of Piezoelectric Vibrator on Linear Vibrating Feeder. Jilin University School of Mechanical Engineering Ph.D. thesis.Su Jiang.2010. Current status and development trends of vibration feeder.Machinery Design &Manufacture. EI. 4(7): 244-246. www.cqvip.com/Main/Detail.aspx?id=34570021 [accessed 15 October 2018].Su Jiang, Yang Zhigang, Tian Fengjun, et al. 2013. Inertial piezoelectric vibrating feeder. Journal of Agricultural Machinery. EI. 44(8): 281-286. Dio:10.6041/j.issn.1000-1298.2013.08.048.TAN X D, ZHAO Y S, LIU C B, et al. 2001. The Analysis and Experiment Study on a New Driving Structure of Piezoelectric Vibration Feeder. Advances in Mechanical Design. 199(2): 1107-1112. dio:10.4028/www.scientific.net/AMR.199-200.1107.Tian Zongjing, WU Wenfu. 2011. Research status and application of piezoelectric vibratory
feeder device. Machinery &Design Manufacture, 10(11): 54-56.
www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jxsjyzz201111022 [accessed 15 October 2018].Ting Y. Jar H C. Lin C Y. et al. 2005. A new type of parts feeder driven by bimorph piezo actuator. Ultrasonics. Sci. 43(7): 566-573. Dio: 10.1016/j.ultras.2004.11.007.Yung T, Shin MS, Chang HY. 2002. Proceeding of the ASME Design Engineering Technical
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Conference. Analysis and design of four-bar linkage type vibratory parts feeder driven by piezoelectric actuator. Sci. 43.Zhan Qixian. 1997. Automatic Mechanical Design. China Light Industry Press.
Table 1. Comparison of operating parameters of centrifugal, piezoelectric, and
electromagnetic linear vibrating feeders.
Type Total
mass (g)
Height
(mm)
Resonance
frequency
(Hz)
Drive
voltage (V)
Drive current
(mA)
Noise
(dB)
Feeding speed
(mm/s)
Eccentric 300 100 125 3.6 80 35 123
Piezoelectric 800 93 325 220 29 55 128
Electromagnetic 960 88 50 220 190 80 135
* Relative to the original result(total mass,height,drive voltage) obtained by the
instruction manual method.
Fig. 1. Structural diagram of the centrifugal linear feeder, consisting of (1) a top
plate, (2) an eccentric motor, (3) two supporting spring pieces, (4) a base plate,
and (5) 4 damping feet.
Fig. 2. Mechanical model of the linear vibration feeder.
Fig. 3. Simplified diagram of the mechanical model.Fig. 4. The first four orders of vibration mode of the system. [Color online.]Fig. 5. Displacement amplitude as a function of frequency derived from the simulations. [Color online.]Fig. 6. Eccentric motor dimension.
Fig. 7. Experimental setup, including the linear vibrating feeder and the power
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supply.
Fig. 8. Image of the 3D laser vibration experiment.
Fig. 9. (a) Displacement amplitude as a function of velocity. (b) Vibration speed
as a function of frequency. [Color online]
Fig. 10. Motion of the top plate of the linear vibrating feeder. [Color online.]
Fig. 11. Feeding speed as a function of frequency.
Table 1. Comparison of operating parameters of centrifugal, piezoelectric, and
electromagnetic linear vibrating feeders.
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Fig. 1. Structural diagram of the centrifugal linear feeder, consisting of (1) a top plate, (2) an eccentric motor, (3) two supporting spring pieces, (4) a base plate, and (5) 4 damping feet.
Fig. 2. Mechanical model of the linear vibration feeder.
Fig. 3. Simplified diagram of the mechanical model.
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Fig. 4. The first four orders of vibration mode of the system.First-order mode Second-order mode
Third-order mode Fourth-order mode
Fig. 5. Displacement amplitude as a function of frequency derived from the simulations.
60 80 100 120 140 160
0.0
0.5
1.0
1.5
2.0
Amplitude(mm)
Frequency(Hz)
X direction amplitude Z direction amplitude
0 2 4 6 8 10
0
2
4
6
8
10
Fig. 6. Eccentric motor dimension.
Fig. 7. Experimental setup, including the linear vibrating feeder and the power supply.
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Fig. 9. (a) Displacement amplitude as a function of velocity. (b) Vibration speed as a function of frequency.
0 50 100 150 200 250-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Amplitude(mm)
Voltage(Hz)
Z direction amplitude X direction amplitude
0 2 4 6 8 10
0
2
4
6
8
10
0 50 100 150 200 250-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Vibration speed(mm/s)
Frequency(Hz)
Z direction vibration speed X direction vibration speed
0 2 4 6 8 10
0
2
4
6
8
10
(a) (b)
Fig. 10. Motion of the top plate of the linear vibrating feeder.
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0 50 100 150 200 250
0
20
40
60
80
100
120
140
Feed speed(mm/s)
Frequency(Hz)
0 2 4 6 8 10
0
2
4
6
8
10
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