A Control Method of High Impact Energy and Cosimulation in Powder High-Velocity Compaction

National Engineering Research Center of Near-Net-Shape Forming forMetallic Materials, South China University of Technology, Guangzhou 510640, China Metastable Materials Science and Technology State Key Laboratory, Yanshan University, Qinhuangdao 066004, China Guangdong Key Laboratory for Processing and Forming of Advanced Metallic Materials, South China University of Technology, Guangzhou 510640, China


Introduction
High-velocity compaction (HVC) is widely used in the powder metallurgy (PM) of titanium-, aluminum-, and ironbased alloys as well as magnets and other materials, for example [1][2][3][4].Compared with conventional compaction (CC), HVC improves the green density of metal powders and enhances the uniformity of the density distribution [5].
e advantages of HVC include high impact energy, low cost, low elasticity aftereffect, and small demolding force [6].In addition, in the consolidation of Cu-Al 2 O 3 alloys, compared with hot pressing (HP) and hot extrusion (HE), HVC compacts exhibit high softening temperatures and good mechanical properties at high temperatures [7].Moreover, combining other methods, green density can be further enhanced in HVC.Zhang et al. [2] enhanced the green density (0.11-0.25 g/cm 3 ) using the annealed powder in iron-based alloy HVC.Zhang et al. [8] utilized warm die HVC to enhance the green density of an iron-based alloy (0.09-0.27 g/cm 3 ).Park et al. [9] found that the density of the compact increased under multiple pressures in the magnetic pulsed compaction of Al-Si powders.Jiang et al. [10] studied the high-temperature HVC (HTHVC) of W85-Cu heat sinks and concluded that the HTHVC process significantly increases the density of the tungsten skeleton compact.
During the HVC process, the strong impact stress waves or shock waves generated by the dynamic pressure on the hammer are transmitted into the powder.As a result, the powder rapidly forms and densifies within a period of 0.02 s.Following the application of a high-frequency impact stress wave with an interval of 0.3 s, the powder's relative density can be further improved.As a result, the mechanical properties of the metal powder product can be enhanced [2,5,8].Shoaib and Kari [11] simulated nonlinear elastoplastic shock waves in particle systems subjected to HVC using the discrete element method.Li et al. [12] analyzed the shock waves and green density and explored the HVC mechanism of the metal powder based on a mesoscopic approach using the multispeed lattice Boltzmann method.Wang et al. [13] simulated pressure propagation in the HVC process based on the discrete element method; the results revealed a delay phenomenon and serrated waves with different gradients in the loading and unloading processes.
e impact velocity and energy have a critical influence on compact densification during HVC.e impact velocity during HVC is two to three orders of magnitude higher than that of the conventional compaction process [14].e impact energy during HVC depends on the impact velocity and the weight of the hammer.Yuan et al. [15] analyzed in detail the influence of the impact energy on the maximum impact force, green density, ejection force, spring back, hardness, and bending strength of the compacts in aluminum alloy powder HVC.On this basis, Ti-6Al-4 V powder [16] and Ti-10Mo alloy powder [17] were used to conduct similar studies.Wang et al. [18] investigated the relationships among the impact velocity, the green density, the sintered density, the bending strength, and the tensile strength of HVC-processed iron powder and noted that, with increasing impact velocity, the green density and the bending strength significantly increased.Moreover, Li et al. [19] obtained similar results in the HVC of 0.9Al 2 O 3 /Cu composite powders.Deng et al. [20] analyzed the influence of the impact energy and velocity on the density and magnetic properties of NdFeB powders and HVC magnets.In addition, Deng et al. [21] prepared the magnets under various conditions, including impact energy, filling weight, mold dimension, and plasticity.
e results of both studies revealed that the density of the as-compacted NdFeB magnets increased with increasing impact energy.Yan et al. [14] prepared the ring and the cylindrical samples by Ti powder HVC and found that the green density increased with increasing impact energy, in contrast to decreasing with increasing filling weight.Yan et al. [22] further studied the influence of particle size on the green density.e authors believed that the green density of compacts is mainly determined by the particle size of the powders at relatively larger impact energies.Subsequently, the pure Ti powder was replaced by Ti-6Al-4 V [23] and Ti-4.5Al-6.8Mo-1.5Fe[24] powder, and similar results were obtained.Eriksson et al. [25] investigated the influence of different impact energies on HVC behavior in the formation of a dental coping made from titanium powder.
Many energy storage methods, such as gravity energy storage, hydraulic energy storage, and chemical energy storage, can produce the high speed required for pressing.Sethi et al. [5] listed four types of dynamic compaction equipment of various configurations, namely, guns, rams, electrical impulse, and explosive units, used to produce high impact energy and the corresponding operating parameters.Vivek et al. [3] used a variation of electrically driven vaporizing foil actuators for the dynamic compaction of Ti-based alloy powders.Babaei et al. [4] utilized the gas mixture detonation method to study experimentally the HVC of aluminum powders.Gustafsson et al. [26] employed a projectile accelerated inside an air gun to generate elasticwave propagation and achieved impact loading.Shoaib et al. [27] incorporated a relaxation assist device into a piston die assembly to better lock the particles during the compaction process and convert the higher kinetic energy of the hammer into particle deformation.Khan et al. [28] studied the influence of the upper relaxation assist device on green density, spring back, green strength, and hardness in the powder HVC of pure iron.
Recently, with the progress of HVC technology, many industrial HVC machines have been developed.Hydropulsor, SKF, and other companies now manufacture a series of industrial hydraulic presses [29,30].Doremus et al. [6] developed an industrial hydraulic press with an impact energy of 18 kJ and impact velocity of 10 m/s.However, the application of these industrial setups is limited by the high impact velocity that must be promoted, their high cost, and their lack of a built-in heating device [30].Guan et al. [31] developed a mechanical energy storing HVC laboratory machine with the maximum impact energy as great as 2035 J.
e impact energy is produced by the impulse of the hydraulically driven spring on the hammer.
e press is employed to consolidate NdFeB powders into nanocrystalline bulk magnets [1,20,21].However, its impact energy requires further improvement, and this method is difficult to implement in industrial automated production lines.Moreover, the energy storage element, cylindrical spiral spring, suffers from several defects, including small energy storage, poor stiffness stability, and elastic relaxation following long-term usage.Furthermore, energy control is a significant aspect of HVC technology.Sethi et al. [5] believed that once the critical limit of the speed of sound is reached, energy, not velocity, is the critical parameter that controls the shock wave phenomenon for easily compressible materials.At higher energy levels, the velocity has even minor negative effect on the densification.
Currently, mechanical-hydraulic control cosimulation is widely used in mechanical design.A mechanical system can be evaluated and optimized using a multidisciplinary cosimulation platform that considers the structural kinematics and dynamics, hydraulic system, structural strength, control system, and other aspects [32][33][34][35][36][37][38][39].Zhao et al. [32] proposed a consensus predictive control protocol and a simplified hydraulic mechanism of a 360 MN extrusion machine and illustrated their validity with an ADAMS-EASY5 cosimulation platform.Ye et al. [33] developed a cosimulation platform by using AMESim and MATLAB/Simulink to evaluate the performance of the proposed PID tuning method of a valve-controlled cylinder system employed in a hydraulic excavator.Zhang et al. [34] built a cosimulation model using MATLAB/Simulink and ADAMS to verify the proposed control strategy for a double shaking table system.Zeng et al. [35] used LS-DYNA, ADAMS, and AMESim software packages to construct the drum cutting coal model, the gear transmission model, and the hydraulic system model of the cutting unit of a mining shearer, respectively.

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Advances in Materials Science and Engineering Data transmission and cosimulation of these three models were implemented with MATLAB.In this study, impact energy is enhanced by modifying the energy storage method of the existing HVC machine [31] using combination disc springs.Subsequently, a green compact with a 98% relative density is produced using pure iron powders to verify the method of the energy storage and enhancement.Moreover, the automatic control method of the impact energy is presented and validated via HVC experiments and cosimulation.
e presented method and equipment provide a foundation for HVC industrial application to large powder metallurgy parts.

Implementation of High Impact Energy
e design objective is as follows: pack 14 g of iron powder into a die with a diameter of 20 mm and develop the necessary test equipment to produce green compacts with relative densities as great as 98%.According to (1) [40], the maximum impact energy is 2323 J. Assuming that 80% of the energy stored in the spring can be converted into impact energy, the spring energy storage is at least 2903 J. Consequently, 3000 J of stored energy is chosen as the design parameter.ln φ � 65.5 exp 0.119 where φ is the green porosity; P is the energy density; and ΔH L is the latent heat of powder melting.

Mathematical Model of Energy and Velocity.
e mechanical energy storing HVC press compresses the springs through hydraulic pressure and then releases the energy via spring deformation restoration, pushing the hammer with a high-speed movement.e kinetic energy of the hammer is mainly determined by the energy stored via spring deformation.In the initial condition, the mathematical model of the impact energy can be expressed as where E is the total impact energy; E p is the potential energy of the mechanism; E k is the kinetic energy of the mechanism, with E k � 0 in the initial condition; k is the average stiffness of the springs; and x is the initial deformation of the springs.When the compression in the springs is released, the mathematical model of the total kinetic energy of the spring system at any time in the ideal state of motion, that is, without friction or damping, can be expressed as where E K1 is the kinetic energy of the hammer; E K2 is the kinetic energy of the springs; M is the quality of the hammer; m is the quality of the springs; and v is the velocity of the hammer.
Because the length of the impact stroke is small, the value of the gravitational potential energy of the hammer is negligible compared to that of the kinetic energy.erefore, when the springs are completely released, their deformation energy is transformed almost entirely into the kinetic energy of the impact mechanism.According to (2) and ( 3), the relationship between the impact velocity and spring deformation can be expressed by the following equation: Moreover, because of these advantages, this test system is better suited for mass production in industrial applications.
Figure 1 shows the overall structure of the modified machine, which consists of an energy storage system, an energy control system, and a hydraulic control system.
Figure 2 represents the components associated with energy control.Spring compression is controlled by the designed hollow hydraulic cylinder, in which the sensors are installed at the entrance and exit positions to measure the oil pressure.When the hydraulic cylinder is in operation, the signal of the spring deformation measured by the displacement sensor is accumulated together with the signals from the oil pressure sensor on the programmable logic controller (PLC) to obtain the real-time spring energy storage.Compared with the set value of the energy storage, the value of the real-time energy storage is updated to meet the set value by adjusting the spring deformation and the oil pressure.

Design of the Disc Spring.
To reduce the modifications to the existing machine, the inner diameter of the disc spring is selected as d > 100 mm and the outer diameter is selected as D < 250 mm to match the diameter of the original impact rod (100 mm).e disc spring is made of 60Si2MnA spring steel.
e mathematical model of the axial force of the disc spring can be derived as follows: where E is the elastic modulus of the disc spring; μ is the Poisson ratio; t is the monolithic spring thickness; D is the spring outer diameter; f is the deformation; h 0 is the deformation when the spring is planished; and K 1 is the calculation coefficient, which is expressed as follows: where c � D/d and d � 102 mm is set according to the disk spring design manual [41].e structure of the monolithic disc spring is shown in Figure 3.

Advances in Materials Science and Engineering
e involution combination structure is adopted to ensure that the spring can withstand greater load in the same compression [42].
e parameters are as follows: E 2.06 × 10 5 N/mm 2 , μ 0.3, and c D/d 2. K 1 is calculated using (6).According to the disc spring design manual [41], we take F 1 D/d 2; by checking the characteristic curve of the disc spring, the deformation f 4.4198 mm is obtained.
e energy storage of the monolithic disc spring is as follows: To meet the requirements of the impact energy of 3000 J, the number of disc springs is i 32.us, the total energy is U z i × U 3000 J, the total deformation is f z i × f 141 mm, and the spring height is 259 mm after loading.In brief, the spring can reach 3000 J when the deformation is approximately 141 mm.
In summary, the design parameters of the disc spring are as follows: the disc spring is made of 60Si2MnA steel, the outer diameter is D 200 mm, the inner diameter is d 102 mm, the free height of the monolithic spring is 12.5 mm, the total    Advances in Materials Science and Engineering number of pieces of the spring is 32, and the free height of the combination is 400 mm.

Hydraulic Control System for Spring Energy Storage
A method for the hydraulic control of the spring system's compression is developed to indirectly control the spring's energy storage.e hydraulic control system mainly consists of three hydraulic cylinders, three reversing valves, an overflow valve, a three-phase asynchronous motor, and a single couplet vane pump.Eight buttons are used to control the movement of the three hydraulic cylinders and the start and stop of the main engine.e maximum oil pressure and the maximum thrust of the hydraulic system are up to 20 MPa and 62439 N, respectively, which meet the requirements of the maximum compression stroke of the springs.e hydraulic control system frame shown in Figure 4 describes a closed-loop control system.e pump provides power to the valves and the cylinders.After setting the parameters in the PLC, the signals coming from the pressure sensor and the displacement sensor are amplified by the PLC and transmitted to the reversing valve.e oil flow in the cylinder is adjusted via changing the opening size of the reversing valve core.In this manner, the spring displacement can be controlled.
e spring compression is measured by the displacement sensor installed on the hydraulic cylinder, as shown in Figure 5(a).A roller installed on the head of the encoder is connected with the welding bolt and is attached to the flange of the hollow piston rod by a fine wire rope.
e roller rotates one circle for 10,000 pulses of the encoder.When compressing the springs, the encoder pulse signal corresponding to the moving distance of the wire rope is converted and amplified to the PLC.e real-time load signal is read by the pressure sensor installed on the oil inlet of the hollow hydraulic cylinder and then is transmitted to the PLC, as shown in Figure 5(b).e control program is completed using the ladder diagram in GX Developer of the MELSOFT software to drive the three reversing valves.
e MITSUBISHI FX1N-40MR controller and the MITSUBISHI GT1 150 touch screen are selected as the PLC and the operation panel, respectively.
e communication between the two components is implemented through programming in the GT Designer3 and the transparent transfer function of the bus connection GOT.

Cosimulation of Energy Control for the HVC Machine
e control system model, hydraulic system model, and mechanical model are built in LabVIEW, AMESim, and ADAMS software packages, respectively.e hydraulic interaction control system is established using the LabVIEWoriented interface pattern in LabVIEW and AMESim cosimulation.rough the ADAMS software interface, the mechanical-hydraulic system is combined in AMESim to allow the LabVIEW simulation platform to interactively control the ADAMS mechanical system.

LabVIEW Simulation Control Panel.
In LabVIEW, three functional areas, namely, the input signal control area, the output signal monitoring area, and the debug monitoring area, are designed in the control panel.e operating interface is shown in Figure 6.A virtual button is used to enter the preset spring energy, and a virtual oscilloscope is used to show each of the following curves: spring compression, spring elasticity, and spring energy.

Cosimulation Modeling.
In mechanical system modeling, the three-dimensional model of the combined disc spring established by SolidWorks software is imported into the finite element software to perform the dynamic modal analysis used to build the flexible body of the spring.Subsequently, the MNF file is imported into the ADAMS software to replace the rigid body of the spring group.Next, a rigid-flexible coupling simulation system is built.e assembly constraints of virtual equipment, the spring compression, and the state variables of the spring constraint force are applied based on the forming process.
Regarding the hydraulic system modeling, the components of the hollow double piston rod hydraulic cylinder are modeled by the component library HCD of the AMESim software.
e cosimulation model of mechanical-hydraulic control is shown in Figure 7.
e LabVIEW module port is connected to the AMESim model input signal port.In the cosimulation model, the displacement and force proportional elements are used to modify the differences between the unit systems in AMESim and ADAMS.e spring energy storage proportional element is used to modify the relationship of the integral accumulation equation between the spring compression and the spring force.
LabVIEW controls the AMESim hydraulic system to adjust the spring compression and the spring constraint reaction in the ADAMS mechanical system to achieve the given energy value that is imputed in the LabVIEW control panel.e spring compression, the spring constraint reaction, and the spring energy storage are presented on the virtual oscilloscopes.
e cosimulation interactive control program is composed of three main modules: the initialization module, main module, and termination module.

Results of Cosimulation.
e HVC process simulation with a given impact energy of 3000 J was conducted in the proposed cosimulation platform, as shown in the screen shot of the cosimulation running in Figure 6.In cosimulation, the variables for the spring compression, the spring constraint reaction, and the spring energy in ADAMS and AMESim can be shown on the control panel.With the agreement of the three software results, the software interface, the spring energy automatic control, and the data Advances in Materials Science and Engineering real-time interaction of the cosimulation platform are validated.
e spring energy, compression, and reaction data extracted from AMESim are shown in Figure 8, Figure 9, and Figure 10, respectively.Figure 8 shows that the spring energy reaches the setting value of 3000 J within 2 s.In Figure 9, the maximum spring compression is 109.5 mm. e spring maximum reaction value is 5.484 × 10 4 N as shown in Figure 10.In summary, the simulation results basically coincide with the theoretical results.

HVC Experiment.
e developed industrial prototype machine is shown in Figure 11.e disc springs are manufactured according to the design parameters presented in section 2.3, and the stiffness test is conducted on the 20,000 N spring tensile test machine.Water-atomized iron powders, with a theoretical density of 7.86 g/cm 3 , are used in the experiment.e die (ϕ 20 mm inner diameter) is filled with 14 g of powder.Lithium stearate anhydrous ethanol suspension (1%) is used as the lubrication, which is uniformly applied on the inner wall of the die and the surface of the upper and lower punches.
Two groups of experiments are conducted: one is the spring energy test, in which the energy values are set to 200 J, 500 J, 800 J, 1100 J, 1400 J, 1700 J, 2000 J, 2300 J, 2600 J, 2900 J, and 3200 J, and the other is the spring displacement test, in which the displacement values are 40 mm, 50 mm, 60 mm, 70 mm, 80 mm, 90 mm, 100 mm, 110 mm, 120 mm, 130 mm, and 140 mm.Two green compacts are produced for each different energy value or displacement value.e impact velocity is measured using a photoelectric sensor.e green density is measured and calculated by the wax sealing method.

Veri cation of the Impact Energy Control of the Modi ed Machine.
e experimental results for energy storage are shown in Figure 13.e experimental results are found to be in good agreement with the set values in the low energy condition, with a minimum error of 0.7%.However, in the higher energy condition, the maximum error is 7.2% because of hydraulic uctuation in the system control, shooting time delay, the complexity of the testing environment, the maximum sampling frequency limit of the data acquisition card, and other factors.
e experimental results demonstrate that the disc spring combination can improve the energy storage.Moreover, the agreement among the set values, the screen display results, and the experimental results indicates the rationality of the hydraulic automatic control scheme.

Energy Comparison between the Modi ed and Existing
Machines.Compared with the cylindrical spiral spring of the existing machine, the disc spring energy storage method presented in this study reduced the height of the machine by 33% and e ectively enhanced the spring energy storage value.Figure 14 shows the relationship between the energy storage value and the deformation of the modi ed and existing machine with di erent springs.e energy storage  8 Advances in Materials Science and Engineering capacity of the springs is observed to be enhanced with increasing spring compression.Moreover, at the same compression, the energy storage capacity of the disc spring group is higher.e calculated energy of the disc spring is approximately 3000 J when the compression is 141 mm.

Compact Density of the Powder Forming Experiment.
Figure 15 shows the green compact density of the powder forming experiment.e results indicate that the modi ed machine has great ability to form powder compactions.e green density is enhanced with the increase of spring compression.When the spring compression increases from 40 mm to 50 mm, the green density increases from 5.79 g/cm 3 to 6.17 g/cm 3 slowly; when it increases from 50 mm to 60 mm, the green density increases from 6.17 g/cm 3 to 7.04 g/cm 3 rapidly, with an overall increase of 14.1%; and when it increases from 90 mm to 120 mm, the green density increases from 7.71 g/cm 3 to 7.75 g/cm 3 , with an overall increase of 0.5%. is phenomenon is consistent with the HVC mechanism.When the spring compression reaches 140 mm, the compact density is approximately 7.76 g/cm 3 and the relative density is 98.7%.e density is higher than the value of 7.70 g/cm 3 of the compact made by combining powder annealing with the HVC method.

Conclusions
(1) e impact energy storage of the HVC machine was developed by using the combination disc springs to modify the existing machine.e design indicator of 3000 J was reached in the developed industrial prototype machine.(2) e hydraulic control method was presented to automatically control the impact energy of the   Experimental results Advances in Materials Science and Engineering machine via controlling the spring's compression.e communication between the PLC controller and the touch screen was implemented by the developed program.

Theoretical calculation results
(3) A human-computer interactive control simulation platform was created.By using the interface of LabVIEW and AMESim, a controllable mechanicalhydraulic cosimulation platform was established, and then, an ADAMS virtual prototype of the test machine was controlled by LabVIEW.(4) Using the experimental research of the iron powder HVC, the presented mathematical model of energy storage was verified.Furthermore, the corresponding relations among spring compression, spring energy, and green density were analyzed, and the relative density of the green compact was found to be improved.

Data Availability
e datasets used to support this study cannot be made freely available at this time as the data also form part of an ongoing study.Access to these data will be considered by the corresponding author upon request.

Figure 6 :
Figure 6: Control panel for cosimulation of energy control.

Figure 13 :
Figure 13: Comparison among the set, display, and experiment results.

Figure 14 :
Figure 14: Energy storage values of two types of springs.

Figure 12 :
Figure 12: Comparison between the theoretical calculation of the velocity and the measured velocity as a function of spring compression.