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Dynamic Characteristics of Vibrating Flip-Flow Screens Considering Material Impact Force
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Boyu Wu1, 2, 3, Shuqian Cao1, 2, 3, Qingquan Luo1, 2, 3
International Journal of Mechanical System Dynamics | 2025, 5(3) : 518 - 534
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International Journal of Mechanical System Dynamics | 2025, 5(3): 518-534
• RESEARCH ARTICLE •
Dynamic Characteristics of Vibrating Flip-Flow Screens Considering Material Impact Force
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Boyu Wu1, 2, 3, Shuqian Cao1, 2, 3, Qingquan Luo1, 2, 3
Affiliations
  • 1School of Mechanical Engineering, Tianjin University, Tianjin, China
  • 2Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, China
  • 3National Key Laboratory of Vehicle Power System, Tianjin, China
doi: 10.1002/msd2.70010
Outline
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Vibrating flip-flow screens are widely used in the field of screening; its actual operation is affected by the impact force of materials, but existing research usually ignores this effect. Based on this background, considering the influence of material impact force and moment on vibrating flip-flow screens, this paper develops a dynamic model and a vibration differential equation of a vibrating flip-flow screen, performs the analysis of material movement and calculation of the material impact force, and includes the material impact force in the dynamic characteristic analysis of a vibrating flip-flow screen. The results indicate the following: (1) The impact forces and account for 29% and 57.58% of the excitation force amplitude, respectively, indicating that they are of the same magnitude as the excitation force. Material impact increases the vibration amplitudes of the main and floating frames, and therefore, cannot be ignored in vibrating flip-flow screen design. (2) By comparing the vibrating flip-flow screen's responses with and without the impact, it is found that impact force significantly influences the system response, causing the displacement curve to shift and the amplitude–frequency curve to have periodic fluctuations and peak values. (3) The effects of impact parameters on the dynamic characteristics of a vibrating flip-flow screen are studied. The results show that increases in material mass and material binding coefficient lead to a decrease in the system natural frequencies. Due to the impact force, the amplitude–frequency curve of the main frame peaks at a frequency lower than the first order of the natural frequency, and the amplitude–frequency curve of the floating frame peaks in the intervals of 5–10 Hz and 20–25 Hz. The results provide a theoretical reference for the design of vibrating flip-flow screens. The operating frequency of vibrating flip-flow screens should be selected to avoid the peak value due to the impact force, which helps extend the working life.

dynamic characteristics  /  impact force  /  material motion  /  vibrating flip-flow screen
Boyu Wu, Shuqian Cao, Qingquan Luo. Dynamic Characteristics of Vibrating Flip-Flow Screens Considering Material Impact Force[J]. International Journal of Mechanical System Dynamics, 2025 , 5 (3) : 518 -534 . DOI: 10.1002/msd2.70010
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1 | Introduction
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In screening operations, the wet fine-grained material sticks easily and difficult to screen because of its high water content and small particle size. Due to the periodic motion of the elastic screen, the acceleration of a vibrating flip-flow screen is much higher than that of an ordinary vibrating screen, and the projectile acceleration of the screen can reach 30–50 times the gravitational acceleration. The material bounces on the screen after making contact with the screen, which can effectively prevent the retention and adhesion of the material onto the screen or material blocking the screen mesh. Therefore, the screening problem of wet fine-grained materials can be better solved with the use of a flip-flow screen [1, 2].
Material is an important factor that cannot be ignored when studying the dynamic characteristics of a vibrating flip-flow screen. Due to the complexity of the movement of the material on the screen, the material is often ignored in many studies or is considered as the equivalent mass for system dynamics analysis [3-6]. However, in the work of a vibrating flip-flow screen, the material has an impact on the screen surface due to the throwing motion of the vibrating flip-flow screen and has obvious nonlinear characteristics, so it has an important influence on the dynamic characteristics of the vibrating flip-flow screen.
Some scholars have conducted relevant research on the impact force produced by materials. He et al. [7] developed a coupling analysis model of vibration system dynamics and particle dynamics, taking into account the throwing effect of the screen body on the material, and studied the change law of the material impact force with the main parameters of the vibrating screen. The relationships between the screen surface area, the screen length, the screen surface inclination angle, and the vibration direction angle and material impact force are determined. Wang et al. [8] designed the orthogonal test, used range and variance analysis to determine the impact of vibration parameters on the impact force, and used the discrete finite element method to study the structural response of the screen under the impact of materials. Zhou et al. [9] analyzed the nonlinear force acting on the screen surface when the material is thrown on the large linear screen, and on this basis, determined the formula for calculating the equivalent mass and equivalent damping of the material. Manuel Moncada et al. [10] developed a 3DOF model of a vibrating screen and found that the amplitude calculated without considering the impact force of the material was inaccurate.
Many scholars have conducted relevant studies on the effect of material impact force on various aspects of vibrating screens [11, 12]. Hou et al. [13] proposed a simplified mechanical model considering material impact for a self-synchronous vibration system driven by two eccentric rotors and obtained the change law of phase difference affected by material impact. Jiao et al. [14] studied the influence of material impact force on a double-mass vibrating screen and analyzed the amplitude–frequency response of the upper and lower bodies. Ma [15] considered the influence of friction force and impact force of materials on a double-mass linear vibrating screen and found that the amplitude of the upper body decreases while that of the lower body increases when the impact force of materials is considered. Xia et al. [16] studied the dynamic response of linear screens under material impact by developing a discrete element method-multi body kinematics coupling model. Li et al. [17] developed a time-varying piece-based nonlinear dynamic model of an elliptical vibrating screen based on the force analysis of the material under sliding and throwing motion and obtained an approximate steady-state analytical solution of the system using the incremental harmonic balance method. Lin et al. [18] studied the influence of materials on the equivalent stiffness and equivalent damping of screens by dynamic tests. Peng et al. [19] tested and analyzed the vibration and strain signals of the screen, studied the dynamic influence of coal on a vibrating screen, analyzed the mechanical characteristics of the load-bearing beam, and found that the structural strain increased by 14.79% after considering the influence of materials. It has been observed that the material in practical engineering has a significant effect on the vibrating screen, and if such an effect is not considered, the numerical and experimental results deviate significantly.
Based on this background, the effect of the impact force generated by the material on a vibrating screen is clear. At present, more attention is paid to the effect of the material impact force on the linear screen, while there is a lack of relevant research on vibrating flip-flow screens due to the complexity of their material movement. Moreover, most of the previous studies focus on the effect of vibration parameters on the impact force and the structural response of the impact force on the screen, and there is a lack of research on the dynamic characteristics of vibrating flip-flow screens. In this paper, a dynamic model of a vibrating flip-flow screen considering the impact force of the material is developed, the impact force and impact moment generated by the material on the vibrating flip-flow screen are determined, and the effects of the impact parameters on the dynamic characteristics of the vibrating flip-flow screen are analyzed, which can make the dynamic model closer to the actual system and help to guide the design and improvement of vibrating flip-flow screens.
2 | Model of a Vibrating Flip-Flow Screen
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In the dynamic analysis modeling of a vibrating flip-flow screen, the displacement in the compression direction of the shear spring between the floating frame and the main frame is usually ignored, and only its displacement along the moving direction of the floating frame is studied. However, the compression direction of the shear spring should not be ignored in the actual analysis. Therefore, taking shear rubber springs with Shore hardness of 50HS as an example, the analysis is as follows:
The relationship between the tensile modulus and the shear modulus of the rubber spring and Shore hardness are expressed, respectively, [20] as follows:
The three-dimensional model and dimensions of the shear spring are shown in Figure 1.
For a rectangular section, when the shear deformation direction is parallel to the longitudinal side, the shear shape coefficient is given by
where denotes the length of the rubber spring and is the height of the rubber spring.
Without considering the effects of cross-sectional area variations and bending deformation, the stiffness in the shear direction of the shear rubber spring is determined using the following approximate formula:
where is the shear force, is the cross-sectional area, is the deformation of the rubber spring in the direction of the shear force, and is the shear shape coefficient.
The stiffness in the compression direction of the shear rubber spring is determined as follows: Under compression conditions, the elastic modulus of the rubber spring is influenced by its shape, size, and the combination state of the supporting surface of the attachment. Consequently, the elastic modulus of the rubber spring differs from that of the rubber material itself. Direct use of the elastic modulus of the rubber material would result in significant errors. The elastic modulus of the rubber spring is related to the elastic modulus of the rubber material as follows [21]:
where is the compression shape factor of the spring.
For a rectangular rubber spring, the compression shape coefficient is defined as
where is the area ratio
where represents the width of the rubber spring, is the height of the rubber spring, and is the free area of the side surface of the rubber spring. Therefore, the compression stiffness of the shear rubber spring can be determined from
In the case of small deformation, the elastic force is approximately linear, and an approximate spring stiffness formula can be written as
In this paper, the shear spring parameters are as follows: a = 240 mm, b = 80 mm, h = 40 mm, E = 1.8 MPa, and G = 0.6 MPa. According to Equations (4), (6), (7), and (9), shear stiffness of the shear spring = 296.68 kN/m and compression stiffness = 2529.2 kN/m can be obtained.
By comparing the shear stiffness and the compression stiffness of the shear spring, it can be seen that the compression stiffness of the shear spring is only 8.525 times that of the shear stiffness, which means that they are of the same order. Therefore, the vertical and parallel motion of the floating frame relative to the main frame should be considered in the dynamic modeling analysis of the vibrating flip-flow screen.
The dynamic model of the vibrating flip-flow screen used in this study is shown in Figure 2. The vibrating flip-flow screen is composed of the main frame , the floating frame , and two eccentric rotors with mass . The main frame is connected to the frame mounted on the ground by vibration isolation springs and the floating frame is connected to the main frame by rubber shear spring and flip-flow screen panels. A pair of eccentric rotors driven by the motor is symmetrically mounted on the main frame; is the distance of the line of action of the excitation force generated by the rotors from the centroid of the main frame and represents the horizontal distance from the center of the main frame to the isolation spring at one end. The dispersed impact force of the material is considered as the concentrated force acting on the center of mass of the floating frame and the moment acting on the center of mass of the main frame.
The displacement of the main frame along the horizontal direction is , the displacement of the main frame perpendicular to the flip-flow screen panel upward is , the angle of rotation about the axis through the center of mass perpendicular to the side plate is , and the displacement of the floating frame relative to the main frame along the horizontal direction is . The displacement of the floating frame relative to the main frame perpendicular to the horizontal direction is . That is, is the vector of generalized coordinates of the system.
The total kinetic energy of the vibrating flip-flow screen system can be expressed as
where represents the mass of the main frame, is the mass of the floating frame, and denotes the moment of inertia of the screen body around the axis perpendicular to .
The total elastic potential energy of the vibration system is as follows:
where is the equivalent stiffness of the isolation spring along the direction, is the equivalent stiffness of the isolation spring along the direction, represents the shear stiffness of the shear spring along the direction, indicates the compression stiffness of the shear spring along the direction, is the horizontal stiffness of the isolation spring, and denotes the vertical stiffness of the isolation spring.
The dissipated energy of the vibration system is given by
where and represent the damping coefficients of the isolation spring along the and directions, respectively, and are the damping coefficients of the shear spring along the and directions, respectively, and is the damping coefficient of flip-flow screen panels.
The excitation force generated by the eccentric block group driven by the motor in reverse operation is represented as
where is the amplitude of the excitation force and is the circular frequency of the excitation force.
By substituting the kinetic energy, potential energy, and dissipative energy of the system into a Lagrange equation, the dynamic equations of the system can be written as
where , , , and are the system-generalized mass matrix, the damping matrix, the stiffness matrix, and the generalized force vector, respectively, defined as follows:
where is the total stiffness of flip-flow screen panels and and represent the components of the material impact force in the and directions, respectively. is the impact torque of the material on the floating frame of the vibrating flip-flow screen.
3 | Analysis of Material Motion on the Screen
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The motion of the material on the screen exists in various forms, such as throwing motion, relative stationary motion, forward sliding, and reverse sliding. The main motion of the material is the throwing motion. Csizmadia et al. [22] simulated the throwing motion of the material on the screen using a single spherical material.
3.1 | Calculation of the Initial Material Speed
In the absolute coordinate system , the absolute coordinate system axis is parallel to the ground and axis is perpendicular to the ground. By analyzing the actual motion of the vibrating flip-flow screen, it can be seen that the initial velocity of the material on the screen is divided into two parts, namely, the velocity of the floating frame and the velocity generated by the flip-flow screen panel, as shown in Figure 3.
The displacement formula of the floating frame is as follows:
where is the amplitude of the displacement curve of the floating frame and represents the time. The velocity of the floating frame along the direction of the excitation force can be obtained from the equation
The velocity of the material at the beginning of the throwing motion can be obtained from
where is the angle between and the horizontal plane and is the angle between and the vertical plane.
The acceleration of throwing motion is caused by the flip-flow screen panel. This acceleration is driven by the periodic bending motion of the beam on the screen frame. The motion of each screen panel is similar, and, therefore, the motion of the entire screen surface can be derived by studying a single screen panel. Taking one unit of the screen surface in the screen panel, simplifying it as a movable end and a fixed end of a simply supported beam, and assuming that the length of the screen surface is independent of the bending radius and in the no-load condition, the screen surface deflection curve can be replaced by three consecutive arcs, as shown in Figure 4.
Therefore, when any screen panel is simplified into a simply supported beam, the expressions of displacement, velocity, and acceleration at the center point of the screen panel can be given by [23, 24]
where represents eccentricity and denotes the screen panel length.
The focus of this study is on the whole vibrating flip-flow screen, so the acceleration at the middle point of the screen panel is considered as the peak acceleration of screen panels. The acceleration at the middle point of the screen panel presents a cosine distribution with time and the screen panel force on the material is always perpendicular to the sieve plate upward. Therefore, the material acceleration is simplified as follows:
where is the amplitude of acceleration at the middle point of the screen panel.
Thus, the velocity provided to the material by the screen panel is given by
where is the single working time of the flip-flow screen panel.
The angle between the initial velocity of the material throwing motion and the horizontal direction can be calculated using the following formula:
The velocity of the floating frame to the material on the screen changes little with time compared with the velocity of the screen surface, so only the change of angle caused by is considered. The angle between the initial velocity of the material slant motion and the horizontal direction changes with time t, as shown in Figure 5.
3.2 | Analysis of the Material Throwing Process
The discharge end of the floating frame is tangential to the horizontal plane, and the angle between the material movement direction and the horizontal plane is . The object coordinate system is with axis tangential to the screen plane and axis perpendicular to the section plane. The angle between the absolute coordinate system and the object coordinate system is , as shown in Figure 6.
The material begins to move at an initial velocity of relative to the ground and falls to point . Therefore, the motion of the material can be decomposed in the absolute coordinate system and the object coordinate system, respectively, as
Assuming that the throwing time of the material is , the displacement of the material in the absolute coordinate system is in the axis direction and in the axis direction. The displacement of the material in the object coordinate system axis direction is and the displacement in the axis direction is . When analyzed separately in the absolute coordinate system and the object coordinate system, the following formula can be obtained:
where and . The simultaneous solution yields the material throwing time .
3.3 | Calculation of Material Impact Force and Impact Moment
During the throwing process, the material binding mass can be regarded as the material binding mass remaining on the screen during the material movement time. Therefore, when the impact force of the material on the screen panel is considered, the material binding mass can be obtained as
where represents the screen processing capacity, is the time for which the material remains on the screen surface from the feed end to the discharge end, and denote the proportions of coarse and fine particles in the feed, respectively, and are the placement efficiencies of the coarse and fine particles, respectively, and is the screening efficiency.
Because it is not easy to measure the thickness of the material on the screen, its average thickness is considered as the approximate thickness. The screen surface of the vibrating flip-flow screen is curved, so the material on the screen is differentiated by the angle of the screen face to facilitate calculation. Thus, the mass of the microelement material block is given by
where is the material mass on the screen surface and is the angle between the feed end and the discharge end of the vibrating flip-flow screen.
Assuming that the collision between the material and the screen surface is inelastic and the collision time is very short, the impact force of the microelement material block on the screen at the end of the throwing motion can be obtained from the theorem of momentum.
where denotes the time of the material impact screen surface process, in most actual cases s [25-27]. and represent the velocity change values of the micro material in the axis direction and on the absolute coordinate system, respectively. When the material impacts the floating frame, its speed becomes the moving speed of the floating frame at that moment, and the change in the material speed can be calculated using the following equation:
The rotation of the floating frame around its center of mass is small, so the rotation of the vibrating flip-flow screen around the center of mass is considered. Then, the impact force of the material uniformly distributed on the screen surface produces a torque at the center of the screen body. Taking any point on the screen surface as an example, the torque is calculated as follows:
where is the distance from the horizontal force to the center of mass and is the distance from the vertical force to the center of mass.
As shown in Figure 7, since the screen has an approximately circular arc shape, SolidWorks can be used to find the center of mass location of the vibrating flip-flow screen , the angle between the line connecting the center of mass to the discharge end and the center of the circle, and the radius of the center of mass.
The position relationship between the center of mass of the vibrating flip-flow screen and the impact point of the material is shown in Figure 8.
In Figure 8, represents the centroid position of the vibrating flip-flow screen, is the center of the circle of the screen, is the arc radius of the floating frame, and is the distance from the position of the centroid of the vibrating flip-flow screen to . denotes the angle formed by the force application point and the line connecting the discharge end to the circle center and is the angle between the centroid position and the line connecting the discharge end to the circle center.
The distance between the impact force point and the center of mass can be calculated from
The impact force and the impact moment of the material can be calculated as follows:
Since the above equations are only the impact force and moment of a single microelement material block, in order to find the effect of the whole material on the floating frame, the differential impact force and differential moment need to be integrated, and the components of the impact force , and and impact moment , and of the material can be obtained using the equations
where is the angle corresponding to the line between the inlet and the outlet end of the vibrating flip-flow screen and the center of the circle.
4 | Simulation of the Vibrating Flip-Flow Screen System Considering the Material Impact Force
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As previously mentioned, the coordinate system xoy is defined on the screen. The x direction is the working direction of the screen panel and the y direction is perpendicular to the working face. The material impact force in this coordinate system has the following components:
where is the installation angle of the vibrating flip-flow screen. The torque caused by the impact of the material on the system is given by
Parameters of the vibrating flip-flow screen system are shown in Table 1.
, , and can be calculated as shown in Figure 9.
The impact force , and impact moment generated by material movement have periodicity. The maximum and values of the material impact force are 29% and 57.58%, respectively, compared with the amplitude of the excitation force of the vibrating flip-flow screen. It can be seen that the impact force generated by the material should be considered in the analysis and design process of the vibrating flip-flow screen.
The floating frame and the fixed beam of the main frame are alternately arranged and connected by screen panels, and therefore, the material impact force affects both. The material impact force is assumed to be equally distributed among them. Therefore, the generalized force F of the 5DOF vibration system of the vibrating flip-flow screen affected by the material impact force is expressed as
In order to further analyze the influence of material impact force on the dynamic characteristics of the vibrating flip-flow screen, the Runge–Kutta method is used to numerically integrate the dynamic equation. The curves of the displacement of the vibrating flip-flow screen and the overall rotation angle as a function of time with or without the material impact force are given. The displacements of the main frame are shown in Figure 10.
As shown in Figure 10, comparing the displacement of the main frame, it can be found that the steady-state amplitude of the main frame is 2.30 mm when the effect of the material impact force is not considered. When the effect of the material impact force is considered, the vibration curve of the main frame shifts 7.94 mm in the positive direction of due to the continuous impact force. The maximum and minimum displacement values of the main frame are 10.47 and 5.41 mm, respectively. The vibration amplitude is 2.53 mm, which increases by 10% compared with that without the impact force. Compared with the displacement , it can be found that when the impact force is considered, the deviation of the vibration curve in the negative direction is 12.65 mm, the maximum and minimum values of the main frame are—18.23 and −7.07 mm, respectively, and the vibration amplitude is 5.58 mm, which increases by 2.95% compared with the case without material impact.
It can be found that the effect of material impact force in the direction of is significantly greater than that in the direction of . When the impact force is considered, the vibration of the main frame in the direction is more intense and unstable in the transient response stage and the vibration amplitude in the direction is less affected by the impact force, but more stable in the transient response stage. The material impact force will cause the vibration curve to offset, and therefore, the actual design should take into account the material impact force caused by the main frame at the initial stage of larger vibration amplitude and offset, to improve system durability and avoid damage (Figure 11).
The displacement of the floating frame affected by the impact force of the material increases 48.85% compared with that without the impact force, and an upward offset of 0.93 mm is generated. The displacement of the floating frame also produced a negative orientation offset of 0.44 mm, and its amplitude is 0.92 mm, which represents an increase of 84% over the unaffected value. At the same time, the cyclical peak caused by smaller shocks appears on the curve, which is 39.09% of the amplitude.
It can be seen that the material impact has a significant effect on the floating frame, which causes the floating frame to produce a large vibration amplitude in the transient response stage and the offset in the running stage. Displacements and of the floating frame are important parameters in the design of the vibrating flip-flow screen. In order to prevent large displacement caused by material impact, the stiffness of the shear spring should be appropriately increased.
To understand the motion state of the main frame and the floating frame more clearly, the centroids of the main frame and the floating frame are selected as feature points, and the motion trajectories of feature points in the stable state of the vibrating flip-flow screen system are given, when the material impact force is considered, as shown in Figure 12.
The influence of material impact force on the overall rotation angle of the vibrating flip-flow screen is shown in Figure 13. When impacted by the material, the overall shift is −3.386 10−2 rad. The maximum and minimum of rotation angle are 3.386 10−2 rad and −3.915 10−2 rad, respectively, with a 346.7% increase in amplitude.
5 | Influence of Impact Parameters on Dynamic Characteristics
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The dynamic characteristics of the vibrating flip-flow screen are affected by many factors [28-30], and the change of parameters in the working process leads to a change in the amplitude of the screen body, which may lead abnormal behavior. Therefore, it is necessary to analyze the dynamic characteristics of the vibrating flip-flow screen when various system parameters change, so as to avoid instability or even damage caused by changes in system parameters during operation. In the following subsection, the effect of different parameters is examined.
5.1 | Effect of Material Mass Variations on System Characteristics
When screening wet or fine-grained materials, there may be accumulation of materials during operation, which causes the mass of the material of the vibrating flip-flow screen system to increase, and the impact force generated by the material will change. Stopping the feed will lead to a reduction in the material on the screen, thus reducing the vibration mass. These conditions will have an effect on the dynamic characteristics of the vibrating flip-flow screen system, and for this reason, the material mass changes are analyzed as follows:
When the mass m of the material is 5000, 6000, and 7000 kg, respectively, the frequency–amplitude curves of the main frame and the floating frame are shown in Figure 14.
The amplitude of the floating frame is significantly affected by impact force before the first natural frequency, and its amplitude is much larger than that without considering impact force, while the main frame is less affected by material impact force. With an increase of the material mass on the screen, the amplitudes of the main frame and the floating frame increase, and the second natural frequency of the amplitude–frequency curve in the x1 direction of the main frame and the x2 direction of the floating frame decreases significantly compared with the first natural frequency.
Taking the operating frequency of the screen as a reference, the changes of the displacement x1 of the main frame are 11.64%, 13.04%, and 14.34%, respectively, when the material impact is considered and the mass is 5000, 6000, and 7000 kg, respectively. The changes of displacement of the main frame are 6.49%, 7.03%, and 8.95%. The changes of displacement of the floating frame are 19.29%, 32.39%, and 46.16%. The changes of displacement of the floating screen frame are 85.46%, 111.21%, and 137.13%. It can be seen that with the change of material mass, the sensitivities are , , , and from small to large, respectively. The displacement of the floating frame with respect to the main frame is affected the most.
5.2 | Effect of Variations in the Material Binding Coefficient on System Characteristics
In actual conditions, various factors, such as material properties, angle of the screen, material thickness, and material shape, cause the material on the screen to have different material binding coefficients [31]. This, in turn, affects the vibration mass of the material and the impact force that it exerts. Figure 15 illustrates the influence of different material binding coefficients on the characteristics of the system considering the material impact force.
With an increase in the material binding coefficient, the amplitudes of all degrees of freedom of the vibrating flip-flow screen increase. The first-order natural frequency of the amplitude–frequency curve is less affected and the second-order natural frequency of and decreases with an increase of the material binding coefficient.
Consider the operating frequency as the reference when the material binding coefficient is 0.2, 0.3, and 0.4. The changes of and are 13.04%, 22.02%, and 35.78%, and 7.03%, 9.97%, and 15.17%, respectively. The changes of and of the floating frame displacement are 32.39%, 77.08%, 131.43%, and 111.21%, 188.62%, and 270.58%, respectively. It can be found that the sensitivities are , , , and from small to large when the material binding coefficient is changed, and the floating frame displacement is mostly affected.
5.3 | Effect of Material Acceleration on System Characteristics
The initial acceleration of the material is provided by both the movement of the screen body and the flip-flow motion of flip-flow screen panels, with the flip-flow motion serving as the primary contributing factor. It is influenced by both the physical parameters of the screen panels as well as factors such as material properties and layer thickness. Hence, an analysis of the system characteristics, taking into account the material impact force under varying material acceleration scenarios, is performed, and the results are shown in Figure 16.
An examination of the results of Figure 16 indicates that an increase in material acceleration results in significant amplification of the amplitudes, particularly at lower frequencies, across the various degrees of freedom of the flip-flow screen. At the operating frequency of the flip-flow screen, the percentage changes in the displacement of the main frame are 10.63%, 13.04%, and 18.69%. The percentage changes in the displacement are 6.41%, 7.05%, and 13.02%. Similarly, the percentage changes in the displacement of the floating frame are 18.15%, 32.39%, and 47.84% and the percentage changes in the displacement are 74.08%, 111.21%, and 151.31%.
In summary, the analysis indicates that the sensitivity of the degrees of freedom of the flip-flow screen to different impact parameters, in descending order, is as follows: material binding coefficient, material acceleration, and material mass. When the impact parameters of the flip-flow screen change, the amplitude of the displacement of the floating frame relative to the main frame in the direction perpendicular to the working direction is most significantly affected. Therefore, when designing the flip-flow screen, the effect of changes in impact parameters should be considered, and attention should be paid to whether the displacement of the floating frame relative to the main frame in the direction perpendicular to the working direction exceeds the design requirements as a result. Additionally, it has been observed that variations in the material mass and the material binding coefficient can lead to changes in the system natural frequencies, resulting in significant amplitude fluctuations not only before the first natural frequency of the main frame but also within the frequency ranges of 5–10 Hz and 20–25 Hz for the floating frame. When selecting the operating frequency, it is important to avoid these peak values to prevent adverse impacts on the working efficiency and lifespan of the flip-flow screen.
6 | Conclusion
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This paper conducted a dynamic characteristic analysis of the vibrating flip-flow screen, considering the impact force of the material. A dynamic model of the vibrating flip-flow screen that incorporates the impact force of the material was developed. The motion of the material on the screen was analyzed, and calculations of the material impact force and impact moment were carried out. The effects of different parameters on the dynamic characteristics of the vibrating flip-flow screen were also analyzed. The main conclusions are as follows:
1.

After calculating and comparing the compressive stiffness and the shear stiffness of the shear springs in the vibrating flip-flow screen, it was found that the compressive stiffness of the shear springs is only 8.525 times that of its shear stiffness. Therefore, when developing the dynamic model of the vibrating flip-flow screen, the vertical displacement of the floating frame relative to the main frame should be taken into consideration.

2.

An analysis was conducted on the material motion on the vibrating flip-flow screen, during which the initial velocity of the material was calculated. Furthermore, the impact forces and moments exerted by the material on the vibrating flip-flow screen were derived and their time-varying curves were plotted. The results revealed that the material impact forces and account for 29% and 57.58% of the amplitude of the excitation force, respectively, indicating that they are of the same order of magnitude as the excitation force. Therefore, the influence of material impact forces should not be neglected in the design and calculation of flip-flow screens.

3.

Based on the impact forces, a dynamic characteristic analysis of the vibrating flip-flow screen was conducted. A comparative analysis was performed between two scenarios: one considering the impact forces and the other neglecting these. The findings indicated that the material impacts result in increased displacements across all degrees of freedom of the vibrating flip-flow screen. Additionally, the displacement curves of both the main frame and the floating frame showed shifts. Notably, the material impact forces have a relatively significant influence on the amplitude and the relative amplitude of the floating frame.

4.

The degree of influence of different parameters on the degrees of freedom of the vibrating flip-flow screen, from the greatest to the least, is the material binding coefficient, material acceleration, and material mass. The greatest impact due to all parameters in terms of perpendicularity to the working direction occurs in the floating frame relative to the main frame. The increase in both the material mass and the material binding coefficient leads to a decrease in the natural frequencies of the system. The amplitude–frequency curve of the main frame peaks before the first order of the intrinsic frequency and the amplitude–frequency curve of the floating frame peaks at intervals of 5–10 Hz and 20–25 Hz. The actual force situation of the vibrating flip-flow screen is more complicated; future research can consider the friction of the material and the impact force generated during material conveying and other comprehensive force scenarios to develop a more detailed dynamic model and further study the dynamic characteristics of vibrating flip-flow screens.

Funding
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  • National Natural Science Foundation of China(12272259)
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Article Info
doi: 10.1002/msd2.70010
  • Receive Date：2024-12-27
  • Online Date：2026-03-24
Article Data
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History
  • Received：2024-12-27
  • Revised：2025-02-17
  • Accepted：2025-03-01
Funding
National Natural Science Foundation of China(12272259)
Affiliations
    1School of Mechanical Engineering, Tianjin University, Tianjin, China
    2Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, China
    3National Key Laboratory of Vehicle Power System, Tianjin, China

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Shuqian Cao ()
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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