Browse Topic: Mufflers

Items (51)
Multi-Physics and CFD Analysis of an Enclosed Coaxial Carbon Nanotube Speaker for Automotive Exhaust Noise Cancellation2019-01-15696/5/2019
Automotive exhaust noise is one of the major sources of noise pollution and it is controlled by passive control system (mufflers) and active control system (loudspeakers and active control algorithm). Mufflers are heavy, bulky and large in size while loudspeakers have a working temperature limitation. Carbon nanotube (CNT) speakers generate sound due to the thermoacoustic effect. CNT speakers are also lightweight, flexible, have acoustic and light transparency as well as high operating temperature. These properties make them ideal to overcome the limitations of the current exhaust noise control systems. An enclosed, coaxial CNT speaker is designed for exhaust noise cancellation application. The development of a 3D multi-physics (coupling of electrical, thermal and acoustical domains) model, for the coaxial speaker is discussed in this paper. The model is used to simulate the sound pressure level, input power versus ambient temperature and efficiency. The 3D model provides accurate results of the temperature profile and heat flow as compared to a 2D model. Also, the flow of exhaust gases can be efficiently modeled using a 3D model. The flow analysis would help understand any flow penetration into the speaker as well as the effect of heat transfer due to the flow. The model is validated by comparing the experimental results with the simulation results. Along with multi-physics simulation, CFD analysis of the coaxial speaker is also studied in this paper. The CFD analysis is focused on the backpressure generated by the speaker and the flow path of the exhaust gases inside the CNT speaker.
Prabhu, Suraj MadhavBarnard, AndrewSenczyszyn, Steven
Modelling and Optimization of Plug Flow Mufflers in Emission Control Systems2017-01-17826/5/2017
Large-scale emergency or off-grid power generation is typically achieved through diesel or natural gas generators. To meet governmental emission requirements, emission control systems (ECS) are required. In operation, effective control over the generator’s acoustic emission is also necessary, and can be accomplished within the ECS system. Plug flow mufflers are commonly used, as they provide a sufficient level of noise attenuation in a compact structure. The key design parameter is the transmission loss of the muffler, as this dictates the level of attenuation at a given frequency. This work implements an analytically decoupled solution, using multiple perforate impedance models, through the transfer matrix method (TMM) to predict the transmission loss based on the muffler geometry. An equivalent finite element model is implemented for numerical simulation. The analytical results and numerical results are then evaluated against experimental data from literature. The transmission loss required in each application of the ECS system will vary depending on the noise profile of the generator in question; therefore, it is necessary to have an effective method of redesigning the muffler to meet the design requirements. Prior work on TMM-based muffler shape optimization utilized complex algorithms such as neural networks and simulated annealing. The present study simplifies the process by using the bounded, limited-memory implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm in a multi-start framework for shape optimization to achieve the desired transmission loss. By constraining the multi-start method with appropriate design limits, the algorithm is initialized at multiple random points within the design space, ensuring that the solution approaches the global optimum when using a sufficiently large number of initializations.
Puthuparampil, JobinPong, HenrySullivan, Pierre
Measurement of Flow-Generated Noise inside Mufflers2017-01-17956/5/2017
Flow-generated noise has recently received a lot of attention within the process of designing exhaust and intake systems. Flow-generated noise can limit the amount of sound reduction a muffler can introduce inside ducts. This is more important in the modern system design where mufflers are compact and the flow speeds become higher in different sections inside the muffler. In this paper, three measurement techniques are used to measure the flow-generated noise from a duct element. The first is based on calculating the sound power levels inside a reverberation room according to ISO 3741. The radiated noise is measured from the muffler body as a source of noise, then from the tail pipe as an active one-port source. The second is based on sound power measurements inside the ducts using the active two-port theory. The third is measuring the sound pressure radiation inside an anechoic room. There has been a lot of work done to calculate the flow generated noise from simple duct elements but little has been published on full mufflers. In this paper, a compact muffler was studied. A 1D model based on the two-port theory was built for this muffler and whereas the flow-generation mechanisms were included in the active two-port formulation, and calculated using different scaling laws from literature for different duct elements such as orifices, pipes and open ends. Comparisons between simulations and measurements were performed to prove the reliability of the flow noise simulation technique.
Abosrea, AhmadElnady, Tamer
Active Cancellation of Exhaust Noise over Broad RPM Range with Simultaneous Exhaust Sound Enhancement2017-01-17536/5/2017
Demands for engines to operate at low-frequency firing order are increasing in the automotive market. This requirement is driven by consumer and regulatory demand for vehicles which are more efficient in the use of fuel. As a result, engine and transmission technologies have been developed which permit operation of engines with fewer cylinders at increasingly low RPM’s. The resulting low frequency exhaust noise is more difficult to attenuate than in vehicles in years past. At the same time, vehicles often have less packaging space for mufflers, when larger volume would otherwise be needed to attenuate at lower frequencies. A further challenge is the demand for increasingly refined performance sounds from the exhaust systems of premium cars despite the technical obstacles involved in even maintaining sound quality. Finally, legally permissible sound levels are decreasing in some markets. These market and regulatory demands require new solutions. Technology has been demonstrated using an ANC system. The system uses the operating principle of ANC, using a feed-forward control mechanism. This system has now been demonstrated to attenuate multiple firing orders by sound cancellation down to 1000 RPM on a 4 cylinder gasoline turbocharged engine. It has also been demonstrated to simultaneously attenuate undesirable orders and accentuate desirable orders. This has been demonstrated in a vehicle with a 4 cylinder TC engine and also in a V8 application operating in 4 cylinder mode, where such desired engine order sounds could not be expected typically.
Riddle, Jack HallBemman, Ya-JuanFrei, TomWu, SihuiPadalkar, Ishang
Modeling the Sound Pressure Loss of an Electromechanical Active Helmholtz Resonator2017-01-18276/5/2017
A muffler attached to an engine attenuates sound over a dedicated frequency range. This research involves the development of an active muffler that is keyed to the revolutions per minute (rpm) of the engine and suppresses the fundamental frequency being exhausted through the tailpipe. The active muffler consists of a tracking side-branch resonator terminated with a composite piezoelectric transducer. The use of an exponential horn as a resonating cavity and terminated with a composite piezoelectric transducer is presented. This would create Electromechanical Active Helmholtz Resonator (EMAHR) creates a notch that can be moved between 200-1000 Hz. The use of acoustical-to-mechanical, mechanical-to-electrical, and analog-to-digital transformations to develop a system model for the active muffler are presented. These transforms will be presented as two-port network parameters. The use of two-port networks to model the electroacoustic system are a defining factor in the analysis. The two-port network parameters for the pipe, horn and piezoelectric transducer are discussed. Using the developed electroacoustic model in simulation the system can be further developed, specifically the load on the composite piezoelectric transducer. The load can be produced with analog-to-digital, digital, and digital-to-analog circuitry. A microcontroller can be used to perform filtering to produce the desired current from the voltage input, or response of an electrical impedance. This impedance generation with a microcontroller is briefly discussed. The sound pressure level results of the modeling are shown over the frequency range of 200-1000 Hz. The maximum sound pressure loss at these frequencies is characterized by the model for the EMAHR.
Santora, Michael J.Ige, Cyril GbengaOtto, JeffEgolf, David
Experimental Acoustic Analysis of a Motorcycle Dissipative Muffler in Presence of Mean Flow2016-32-003911/8/2016
In recent years, the motorcycle muffler design is moving to dissipative silencer architectures. Due to the increased of restrictions on noise emissions, both dissipative and coupled reactive-dissipative mufflers have substituted the most widely used reactive silencers. This led to higher noise efficiency of the muffler and size reduction. A dissipative muffler is composed by a perforated pipe that crosses a cavity volume filled by a fibrous porous material. The acoustic performance of this kind of muffler are strictly dependent on the porosity of the perforated pipe and the flow resistivity characteristic of the porous material. However, while the acoustic performance of a reactive muffler is almost independent from the presence of a mean flow for typical Mach numbers of exhaust gases, in a dissipative muffler the acoustic behaviour is strictly linked to the mass flow rate intensity. In this paper, an experimental analysis on a commercial dissipative muffler for motorcycles is presented. More in details, the acoustic performance of the silencer is determined by using a test rig that is based on the multi-microphone technique and the two source method. The acoustic test rig used allows carrying out the measurements in presence of mean flow in order to evaluate the influence of the mean flow on the muffler acoustic performance. The possibility to study the muffler behaviour in presence of mean flow makes the experimental conditions closer to the real operating ones. The aim of the present work is to determine how the acoustic response of a dissipative muffler is influenced by the fluid-dynamic interaction between the mean flow and the flow resistivity chamber.
Fioravanti, AndreaVichi, GiovanniStiaccini, IsaccoFerrara, GiovanniFerrari, Lorenzo
Research on Integration of Automotive Exhaust-Based Thermoelectric Generator with Front Muffler2016-01-02034/5/2016
In order to make full use of engine exhaust heat, the thermoelectric module been used to contribute to thermoelectric power generation in the automotive. At present, the thermoelectric generators (TEGs) have been developing with continuously advances in thermoelectric technology. And almost all of the existing thermoelectric technologies are adding a gas tank to the vehicle exhaust system which increases the exhaust back pressure and occupying excessive space of the vehicle chassis. In this study, a new TEG integrated with a front silencer muffler (FMTEG) is proposed. The muffler is reshaped as the heat exchanger which has a hexagon cross-section. The water tank and clamping mechanism have been redesigned for the new heat exchanger. The FMTEG system’s dimensions are small that can well meet the installation requirements and has a good compatibility with the vehicle exhaust system. The multi-dimensional computational fluid dynamics (CFD) models have been built to simulate the transmission loss (TL) of the noise, thermal field, pressure field of the integrated heat exchanger. The maximum output power has been calculated. The simulation and calculation results show that FMTEG have a better thermal performance and output power performance than the hollow structure. It has a lower back pressure about 250pa. Meanwhile, the average transmission loss of the FMTEG is about 15dB. The FMTEG’s acoustic performance has been proved that it can meet the requirements of the vehicle. Consequently, the use of the FMTEG with better performance could be effectively achieved.
Deng, YadongLiu, ChunhuaChu, Panqi
Research on Acoustic Performance of Automotive Exhaust Thermoelectric Generator2016-01-02204/5/2016
With great development of thermoelectric exhaust heat recovery technology, more and more attention has been paid to optimization of automotive thermoelectric generators (ATEGs). A lot of work has been done on optimization of flow field and thermal analysis. However, investigation on acoustic optimization is rather limited. In this paper, efforts have been paid to study the acoustic performance of a flat-plate TEG, and the feasibility of integration of automotive exhaust thermoelectric generator with muffler was discussed. The internal configuration of heat exchanger looks like “fishbone”. Four factors have been taken into consideration: the spacing of two fins, angle of the fins, the diameter of inlet and outlet of exchanger; and filling sound absorbing material in heat exchanger chamber. Based on these four factors, acoustic analysis was carried out. LMS Virtual.Lab was used to compute the acoustic performance of exhaust-based heat exchanger, and transmission loss (TL) is regarded as the evaluation index for acoustic performance. GT-Suite simulations were used to obtain the pressure drop of TEGs. Results indicate that changing the spacing of two fins and angle of fins have a negligible effect on improving the overall TL of a heat exchanger, decreasing the diameter of inlet and outlet of heat exchanger and filling up the heat exchanger chamber with sound absorbing material improves overall acoustic performance.
Gu, BanYuan, Xiaohong
Coupled CFD and Vibro-Acoustic Modeling of Complex-Shaped Mufflers Accounting for Non-Uniform Mean Flow Effects2015-01-23136/15/2015
Flow strongly affects the propagation of acoustics wave transmission within a duct and this must be addressed by the vibro-acoustic modelling of duct systems subject to non-uniform flow. Flow impacts both the effective sound propagation speed in a duct and refracts the sound towards or away from the duct walls depending on whether the acoustic waves are propagating in the direction of the flow or against the flow. Accurate modeling of the acoustic propagation within a duct is crucial for design and “tuning” of muffler systems that need to strongly attenuate narrowband acoustic sources from the engine. Muffler systems that may avoid matching acoustic resonances to engine narrowband sources when no flow is present may experience shifting of resonances to frequencies that match engine sources and cause problems when the flow during a real operating condition is present. Therefore accounting for detailed flow effects on the acoustic propagation and the modal characteristics of the muffler system is essential for effective design. However, for real-life, complex geometries, flow patterns have no analytical solution and have to be determined by means of computational fluid dynamics (CFD). This paper describes an automated process for coupling acoustic finite element (FE) muffler vibro-acoustic design to an open source computational fluid dynamics (CFD) solver whose predicted results are automatically returned and used to generate muffler noise attenuation predictions accounting for flow effects. A validation case study showing the ability for a non-CFD expert modeler to obtain accurate muffler predictions for cases of non-uniform flow is presented. This approach can support a broad range of muffler designs and can represent a significant savings of testing and development time. Limitations and future steps for this modeling approach are discussed.
Gardner, BryceMejdi, AbderrazakMusser, ChadwyckChaigne, SébastienDe Campos Macarios, Tiago
Measurement and Simulation of Two-Inlet Single-Outlet Mufflers2015-01-23166/15/2015
In several applications, two-inlet single-outlet mufflers are possible to encounter in exhaust systems. They are usually used to merge two exhaust streams from two similar engines or from two sides of an engine. They have an advantage of reducing the back pressure on the engine(s). There is a lot of published research on the analysis of single-inlet single-outlet mufflers acting as a two-port. On the other hand, there are a few publications on the analysis of two-inlet single-outlet mufflers due to their complexity representing a three-port. A three-port is characterized by a 3×3 Scattering Matrix. The nine elements of this matrix represent the 3 reflection coefficients at each port, and the 6 transmission coefficients between the 3 ports in both directions. In this work, a two-inlet single-outlet muffler is studied. The elements of the scattering matrix were measured using the two-source two-microphone technique with and without flow. These elements were also calculated from 1D simulation using a set of two-port elements representing the internal dimensions of the muffler, and compared to those obtained from the measurement. A similar 1D simulation was performed using Flow two-ports in order to analyze the flow distribution inside the muffler and the pressure drop across both flow paths. The flow distribution is crucial to obtain accurate acoustic predictions. For all cases, there was a very good agreement between the measurement and the simulations.
Elsahar, WeamElnady, Tamer
Exhaust and Muffler Aeroacoustics Predictions using Lattice Boltzmann Method2015-01-23146/15/2015
Exhaust and muffler noise is a challenging problem in the transport industry. While the main purpose of the system is to reduce the intensity of the acoustic pulses originating from the engine exhaust valves, the back pressure induced by these systems must be kept to a minimum to guarantee maximum performance of the engine. Emitted noise levels have to ensure comfort of the passengers and must respect community noise regulations. In addition, the exhaust noise plays an important role in the brand image of vehicles, especially with sports car where it must be tuned to be “musical”. However, to achieve such performances, muffler and exhaust designs have become quite complex, often leading to the rise of undesired self-induced noise. Traditional purely acoustic solvers, like Boundary Element Methods (BEM), have been applied quite successfully to achieve the required acoustic tuning. However, they fail at predicting all of flow-induced noise, as well as non-linear noise dissipation mechanisms. A natural candidate for this type of problem is the use of a Lattice-Boltzmann Method (LBM) solver as a CFD tool. It has already been successfully applied and validated to quantify self-induced noise of mufflers as well as complex acoustic devices performance like acoustic liners. In this paper, a muffler baseline geometry self-induced noise is assessed using the commercial LBM solver PowerFLOW. Noise generation mechanisms are identified and design modifications are proposed to atone it. The given baseline and iterations designs noise mechanisms are analyzed and the obtained noise reductions are compared and discussed.
Mann, AdrienKim, Min-SukNeuhierl, BarbaraPerot, FranckPowell, RobertRose, ThomasKrueger, Jan
Managing the acoustic signature of military vehicles can play a critical role in the safety of soldiers. Low-frequency sounds propagate through the atmosphere, resulting in unacceptable acoustic vehicle detection ranges, requiring relatively large silencer structures to mitigate. Currently, these requirements are met by using a custom muffler that is hand-assembled using low-volume prototyping manufacturing techniques. This method results in significant engineering and manufacturing time.
Application of the Fourier Amplitude Sensitivity Test (FAST) to Analyze Thermal Performance of Vehicle Underbody Components2015-01-04384/14/2015
This paper describes the application of the Fourier Amplitude Sensitivity Test (FAST) method [1] to investigate the effect of uncertainty in design parameters on the thermal system performance of vehicle underbody components. The results from this study will pinpoint the design parameters which offer the greatest opportunity for improvement of thermal system performance and reliability. In turn, this method can save engineering time and resources. An analytical model was developed for a vehicle underbody system consisting of a muffler, heat shield, and spare tire tub. The output from this model was defined as the temperature of the spare tire tub. The majority of the input parameters in this model deviate from their nominal values due to environmental factors, wear and ageing, and/or variation in the manufacturing process. Using MATLAB software package, the model was simulated with input parameters which were simultaneously and sinusoidally varied at distinct frequencies over their respective uncertainty ranges. Finally, the Fourier transform was applied to the output of the model to convert the response into the frequency domain to allow the amplitude of each of the distinct frequencies to be recognized. The amplitude of each frequency was used as an indication of the effect of the corresponding parameter's variation on the temperature of the spare tire tub. Reducing the amount of variation in the most influential parameters and/or reducing the system sensitivity to these parameters will have the greatest improvement on the overall thermal performance of the system.
Lehman, AshleyStoilov, VesselinSobiesiak, Andrzej
Assessment and Experimental Validation of a 3D Acoustic Model of a Motorcycle Muffler2014-32-012211/11/2014
The intake and exhaust lines provide the main abatement of the acoustic emissions of an Internal Combustion Engine (ICE). Many different numerical approaches can be used to evaluate the acoustic attenuation, which is commonly expressed by the Transmission Loss. One-dimensional (1D) and three-dimensional (3D) simulations are conventionally carried out only considering the acoustic domain of the muffler or of the air-box. The walls of the acoustic filter are considered fully rigid and the interaction between the acoustic waves and the structure is consequently negligible. Moreover, the effect of the manufacturing characteristics and the attenuation of the acoustic waves due to the fluid viscous-thermal effects are also commonly disregarded in the numerical analysis of the filters. In addition, the presence of a catalytic converter or a filter cartridge may have an influence on the numerical results. All these aspects, however, can remarkably affect the matching between simulations and experiments both at high frequencies and at medium-low ones. In the present study, the effect of the aforementioned issues on the prediction capabilities of a 3D FEM model are analysed, with particular attention to the prediction of the acoustic attenuation of a commercial muffler. In detail, simplified models were developed in order to include the manufacturing features into acoustic simulations with almost negligible increase of the computational time. Numerical models were applied to a commercial motorcycle muffler featuring three chambers and a catalytic converter, and then validated by means of a specific experimental campaign that was carried out on an acoustic test rig. The tests were run at ambient temperature and no-flow conditions, obtaining good agreement between theory and experiments.
Fioravanti, AndreaLenzi, GiulioVichi, GiovanniFerrara, GiovanniRicci, StefanoBagnoli, Leonardo
Investigation of the Urea Evaporation and Mixing with Various Temperatures and Injector and Injection Angles in the Catalytic Muffler2013-01-10784/8/2013
Diesel engine is being used widely in many industrial fields, as it provides merits in the aspects of higher thermal efficiency and less CO₂ emission. However, NOx regulations for diesel engines are being strengthened and it is impossible to meet the emission standard without aftertreatment systems such as SCR (Selective catalytic reduction), LNC (Lean NOx catalyst), and LNT (Lean NOx trap). Among the NOx reduction aftertreatments, Urea-SCR system is known as the most stable and efficient method to solve the problem of NOx emission. But this device has some issues associated with the ammonia slip phenomenon which is occurred by shortage of evaporation and thermolysis time, and that makes it difficult to achieve uniform distribution of the injected urea. Therefore, this study has focused on the mixing enhancement between urea and exhaust gases to enhance the efficiency of the SCR equipped in catalytic muffler by changing injector angle to improve the spray uniformity of the urea water solution. Finally, it can be found that various parameters such as the injector and injection angles and an exhaust gas temperature significantly affect the urea evaporation and mixing with exhaust gases, and therefore, optimization of these parameters are required.
An, Tae HyunKim, Man YoungJung, Hak SupKim, HongsukCho, Gyubaek
Improving the Simulation of the Acoustic Performance of Complex Silencers for ICE by a Multi-Dimensional Non-Linear Approach2012-01-08284/16/2012
In this paper a three-dimensional time-domain CFD approach has been employed to predict and analyze the acoustic attenuation performance of complex perforated muffler geometries, where strong 3D effects limit the validity of the use of one-dimensional models. A pressure pulse has been imposed at the inlet to excite the wave motion, while unsteady flow computation have been performed to acquire the time histories of the pressures upstream and downstream of the silencer. Pressures in the time domain have been then transformed to acoustic pressures in the frequency domain, to predict the transmission loss. In order to achieve reliable predictions of the acoustic attenuation, especially above the plane wave cut-off frequency, an advanced non-reflecting boundary condition to model the anechoic termination, based on the NSCBC characteristic theory, has been implemented in a multidimensional open-source CFD code and it has been used together with a time dependent compressible Navier Stokes equation solver. The original local one dimensional inviscid relations (LODI) in Cartesian coordinates presented in [1] have been extended to local coordinates and have been applied for unsteady calculations in a multistage time stepping scheme. Numerical results show that the agreement between simulations and experiments strongly improves at high frequency when the novel boundary condition is applied. A comparative study with a 1D non-linear model for unsteady compressible flows is shown on four different configuration of reverse flow chambers and on a single-plug perforated muffler for internal combustion engine applications. Advantages and drawbacks of the proposed approach are discussed.
Piscaglia, FedericoMontorfano, AndreaOnorati, Angelo
Acoustic Characterization of Automotive Mufflers - Part II: Validation of the Numerical Models by Means of Experimental Data2012-01-08014/16/2012
Increasing interest is being paid to noise pollution of internal combustion engines and as a result, recent international standards imposed more severe limitations to acoustic emissions on engine manufacturers. In particular, the noise coming from gas-dynamic interactions has an important influence in determining the final noise level of the engine; as a consequence, the muffler design is currently being considered as one of the most important research threads for engine companies. Within this context, the 1D approach to numerical simulations, which has been successfully applied by industrial designers to the fluid-dynamic design of the engine, is considered to be inaccurate in the evaluation of the acoustic behavior of the muffler for medium-high frequencies. On the other hand, an extension of the applicability of these codes in the medium-high frequencies would be desirable. The direct advantage would be the use of the same software for the simulation of both the fluid-dynamic and acoustic performance of the engine. On these bases, a commercial 1D numerical code was primarily analyzed in terms of accuracy, computational cost and modeling capability of mufflers from the acoustic point of view. As a second step, two non-conventional approaches were developed in order to improve the prediction capabilities of the 1D code and to widen its frequency range of validity, as well. The base scheme of these new approaches was to extend the application of the traditional 1D nonlinear equations not only in the axial direction but also in perpendicular directions within the cross-section of the muffler, achieving a simplified description of the acoustic phenomena in the whole volume. The 1D predictions using these new approaches were compared both with several sets of experimental data collected on a purposefully developed test rig and specific 3D simulations; as a result, their limits in terms of accuracy were highlighted. Moreover, the introduction of the new sub-models increased the accuracy of the simulations and the frequency range of validity, leading to notable results with respect to traditional formulations of the problem.
Ferrara, Giovanniferrari, LorenzoVichi, GiovanniLenzi, GiulioBiliotti, Davide
The numerical analysis and technique development on light truck muffler bracket forming2000-05-02196/12/2000
The light truck muffler bracket is a kind of deep and complicated stamping part which has curve flange. It is formed by once drawing with 3 mm thick 08TIL sheet. Since it is difficult to design good technique for the workpiece, after the muffler bracket was put into production, problems such as cracks at the bottom projecting corner and wrinkles at the curved flange corner often occurred. This led to high waste product ratio of 15 (and high substandard product ratio of 30). Therefore the part quality was heavily influenced, the production cost kept at high state for long term. In this paper, the geometry model of forming process part is built with the software Euclid3, the forming process of muffler bracket is numerically analyzed with the software LS-DYNA3D. The metal flow law and deformation character under the curve blankholding surface is revealed, in the meantime, the main reason of cracks and wrinkles appearing in the part during the forming process is studied, the direct reason of cracks at the projecting corner of muffler bracket bottom is verified as the metal flow resistance is too large at the preformed flange corner. The new technique that the preformation is finished by punch and die, the formation is finished by punch, die and binder have been developed. The waste product ratio and substandard product ratio have been descended below 0.05. Thus the quality problem which has puzzled production for a long time is successfully solved by using numerical simulation technology, theory bases are offered for the designing of stamping and die of similar workpieces.
Xu, Cheng LinZhu, Wei Cheng
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