Equivalent Stiffness Research Articles

Practical Method for Identifying Model Parameters for Machining Error Simulation in End Milling Through Sensor-Less Monitoring and On-Machine Measurement

Depending on cutting conditions, unacceptable machining errors are caused by tool deflection in end milling operations. Many studies have proposed methods for predicting the machining error owing to the tool deflection to achieve the theoretical optimization of the cutting conditions. However, the conventional machining error simulation is not practically utilized to determine the optimal cutting conditions. Tool system stiffness parameters and cutting coefficients must be identified in advance to simulate machining errors. However, dynamometers and displacement sensors are required for parameter identification. Therefore, it is impossible to identify the required parameters in typical factories, which do not possess such special equipment. In this study, a practical method was developed to identify the stiffness parameters that can be determined in factories. The proposed method employs on-machine measurement and sensor-less cutting force monitoring to achieve practical parameter identification. In the proposed method, the profile milling is first conducted. During the milling operation, the cutting force and cutting torque are monitored through a controller based on the sensor-less monitoring technique. After the operation, the machining error distribution on the machined surface is measured on machine using a touch probe. The required parameters are identified by minimizing the differences between the measured and theoretical forces, torques, and machining error distributions.

Interclonal variability in sensitivity to wind breakage: Comparative analysis of the mechanical behaviour of stems of two Hevea clones

The rubber tree (Hevea brasiliensis) is the main source of natural rubber production, with more than 14 million tonnes produced each year. Unfortunately, throughout their economic lifespan on the plantation (between 35 and 40 years), heveas trees are sensitive to wind damage, especially trunk breakage. Over a 30-year period, it is estimated that losses due to the wind breakage of tree stems reach nearly 40%. Industrial hevea plantations are organized in monoclonal plots. Clones are selected based on their productivity, disease resistance, etc., but not for their mechanical behaviour or sensitivity to wind-induced breakage, as breeders lack the appropriate tools to assess these criteria. Field observations highlight variations among clones in their susceptibility to wind breakage, underscoring the increased importance of evaluating mechanical criteria. Among the known causes of these differences in Hevea trees are competition between latex production and growth, crown shape and the presence of tension wood. In this article, we investigated the mechanical behaviour of the stems of two Hevea clones. One, IRCA825, is recognized as very sensitive, while the other, IRCA41, is known for its resistance to wind breakage. We measured biomechanical parameters such as trunk bending stiffness (EI), green wood stiffness (E) and modulus of rupture (MOR). To assess these parameters, we performed bending tests until breakage on standing trees of clonal fields in Ivory Coast, followed by wood characterisation tests in laboratory. A comparative analysis of the bending tests revealed that clones IRC825 and IRCA41 exhibit equivalent trunk bending stiffness. Nevertheless, IRCA41 differs from IRCA825 by having higher green wood stiffness and breaking strength, attributes that mainly explains its higher wind resistance. Comparative analysis of the wood structure indicated that the differences in wood stiffness and breaking strength are mainly attributed to the higher wood density in IRCA41 compared to IRCA825, with no discernible differences in microfibril angle and specific modulus.

Influence of soundboard modelling approaches on piano string vibration.

This work explores the influence of the dynamics of the piano soundboard on string vibration and on the force acting between the vibrating string and the bridge. Four different soundboard representations of different complexities are considered: (i) a finite element model that considers the complete dynamic behavior of the soundboard at the connection point with the string within the frequency range of interest, (ii) a reduced modal model containing only five modes, (iii) a Kelvin-Voigt system characterized by an equivalent stiffness and damping, and (iv) a rigid soundboard represented by a simply supported boundary condition. The connection between the string and the soundboard is modelled by coupling a simply supported stiff string model with the different representations of the soundboard through a contact stiffness. As well as directly accounting for the string-soundboard coupling, this approach also includes the duplex scaling segment. The latter can be left to vibrate freely or muted with a continuous distribution of dampers. Although the simplest soundboard representation is not dissimilar from the other more complex models, the dynamics of the soundboard affect the decay time of the note, the force transmitted to it, and the vibration of the radiating surface of the soundboard.

Topology optimisation of multiple robot links considering screw connections

AbstractThis paper presents a method for the lightweight design of robotic links subject to dynamic loads and requirements on the overall system stiffness. It includes (1) a decomposition scheme to enable separate component optimization and (2) an approach based on topology optimization for optimal load path design of screw connections. The approach reduces computing cost and mass of designs with screw connections.

Graphics processing unit/artificial neural network-accelerated large-eddy simulation of swirling premixed flames

Within the scope of reacting flow simulations, the real-time direct integration (DI) of stiff ordinary differential equations for the computation of chemical kinetics stands as the primary demand on computational resources. Meanwhile, as the number of transport equations that need to be solved increases, the computational cost grows more substantially, particularly for those combustion models involving direct coupling of chemistry and flow such as the transported probability density function model. In the current study, an integrated graphics processing unit-artificial neural network (GPU-ANN) framework is introduced to comply with heavy computational costs while maintaining high fidelity. Within this framework, a GPU-based solver is employed to solve partial differential equations and compute thermal and transport properties, and an ANN is utilized to replace the calculation of reaction rates. Large eddy simulations of two swirling flames provide a robust validation, affirming and extending the GPU-ANN approach's applicability to challenging scenarios. The simulation results demonstrate a strong correlation in the macro flame structure and statistical characteristics between the GPU-ANN approach and the traditional central processing unit (CPU)-based solver with DI. This comparison indicates that the GPU-ANN approach is capable of attaining the same degree of precision as the conventional CPU-DI solver, even in more complex scenarios. In addition, the overall speed-up factor for the GPU-ANN approach is over two orders of magnitude. This study establishes the potential groundwork for widespread application of the proposed GPU-ANN approach in combustion simulations, addressing various and complex scenarios based on detailed chemistry, while significantly reducing computational costs.

Design and application of composite lanchester damper for milling thin-walled part

Thin-walled parts often produce chatter during mechanical processing due to their poor stiffness. Increasing damping can effectively improve the equivalent stiffness of thin-walled parts and weaken the vibration generated during the machining process. Based on the principles of fluid viscous damping and eddy current damping, this article proposes a design scheme for a composite viscous damper. It optimizes the structural parameters of the composite Lanchester damper according to the optimal damping coefficient. Finally, a composite viscous damper was manufactured, and modal tests showed that the amplitude of the first three vibration modes decreased by 83%, 90%, and 85% after installing the damper. In the milling test, the vibration amplitude of the thin-walled part decreased by the highest of 77%.

Analyzing the effects of polymeric dielectric materials on micro capacitive pressure sensors: A model incorporating displacement-dependent porosity

Recently, the extensive utilization of porous polymeric materials to amplify the sensitivity of capacitive devices is noticeable. The absence of an effective mathematical model for studying these devices has spurred the development of a comprehensive mathematical model in the current work. This model is formulated to analyze the static and dynamic behavior of systems incorporating a porous polymer dielectric material within the gap between flexible and fixed microplates. The derived nonlinear governing equations encompass the effects of electrostatic force, von-Karman nonlinear strains, and displacement-dependent porosity. Employing spatial decomposition, the resulting nonlinear algebraic equations and ordinary differential equations are leveraged to study the static and transient dynamic behavior, as well as the frequency response of the sensor using a learning approach. Two scenarios are investigated to assess the impact of various geometrical and physical parameters on sensor sensitivity one with a polymeric material and another without, each with distinct parameter values. The results reveal that the inclusion of a polymeric dielectric material increases electrostatic force but concurrently elevates the equivalent stiffness of the structure. The effectiveness of using a polymeric dielectric material is contingent upon the specific geometrical and physical properties of the sensor. Moreover, the obtained results in simplified cases are compared to existing numerical and experimental data, demonstrating a high degree of agreement. This work significantly contributes to advancing the understanding of sensors incorporating porous polymer dielectric materials and underscores their potential for enhanced sensitivity across diverse applications.

POSTURAL CONTROL IMPAIRED IN MYOARTHROKINETIC AND NEURO-SENSORY DISORDERS

Interdependent subsystems involved in dynamic posture and locomotion are represented by osteoarticular, neuromuscular, sensory systems. Postural control is maintained by somato-sensory, visual vestibular feedback, integrated at the level of the locomotor system and the central nervous system. Postural stability is disturbed in mio-arthro-kinetic disorders. In proprioceptive loss, the automatic postural responses are diminished in amplitude and delayed in time; stretch reflexes in soleus and medial gastrocnemius are severely diminished; balance-correcting responses in tibialis anterior are diminished and delayed; backward motion of the trunk is reduced; movement strategies and synergies are disturbed. In peripheral vestibular loss, there are increased trunk responses to disruptive stimuli, with hypermetric trunk muscle responses and hypometric knee responses, but unchanged synergies; pathological changes to the modulation depth are produced; the amplitude of balance correcting responses in ankle muscles is severely reduced. Visual input serves to decrease the stiffness of the musculoskeletal system; it can be accomplished by decreasing the level of muscular activity across the joints of the lower limbs (in eyes-open subjects) or by reducing the gains of the other postural feedback mechanisms, the proprioceptive or vestibular systems (in eyes-closed subjects). Keywords: postural control, proprioceptive insufficiency, vestibular impairment.

A rapid prediction model for the radiation efficiency of baffled constrained layer damping plate

It’s well-known that constrained layer damping (CLD) can effectively reduce the vibration and radiation noise from the (plate-like or shell-like) thin-walled structures under various of dynamic excitations. As one of the key properties deciding the CLD’s performance, the CLD’s acoustic radiation characteristics has always been a focus of researchers. In this study, an analytical model based on equivalent principle is proposed to predict the acoustic radiation efficiency of the CLD plate. In this model, a laminated CLD plate is equivalent to a single-layer plate and the equivalent stiffness and loss factor are obtained using the strain energy method. The vibration velocity of the plate is calculated using mode-superposition method and the sound pressure on the plate surface is calculated using Rayleigh integral formula. Variable mesh sizes and frequency steps are employed to improve the calculation efficiency. The difference between the base and CLD plates in sound radiation characteristics is investigated using this model. The results indicate that CLD involving a damping layer with a low Young’s modulus can mitigate more vibration at low frequencies. A higher Young’s modulus of the damping layer results in a higher radiation efficiency of the CLD plate between the fundamental and critical frequencies. By increasing the loss factor, the spatially averaged mean square velocity would decrease, more modes would contribute to the response, and the CLD plate can consequently achieve a higher radiation efficiency below the critical frequency. Moreover, the simplified formulae for the average radiation efficiency of the CLD plate is developed to achieve the rapid calculation. Its accuracy is then validated by comparing the results to the more comprehensive model.

A Review of Cross-Scale Theoretical Contact Models for Bolted Joints Interfaces

Bolted joints structures are critical fastening components widely used in mechanical equipment. Under long-term loading conditions, the bolted joints interface generates strong nonlinearities within the system. The nonlinear stiffness inside the bolt leads to changes in the stiffness of the whole system. This affects the dynamic characteristics of the whole system. It brings challenges and difficulties to the performance prediction and reliability assessment of the equipment. A cross-scale theoretical model study based on the microscopic contact mechanism can provide a more comprehensive understanding and cognition of the degradation behavior of bolted joints interfaces. The current development status and deformation process of asperity models are summarized. The research progress of statistical summation model and contact fractal model based on microscopic contact mechanism is analyzed. The experimental methods for parameter identification of connection interfaces are reviewed. The study of numerical modelling of bolted joints structures from the surface contact mechanism is briefly described. Future research directions for cross-scale modelling of bolted joints structures are outlined.

TSDT vs CPT and FSDT for Free Vibration Analysis of Functionally Graded Incompressible Plates

This article studies vibrational behavior of incompressible functionally graded plates through utilizing classical, first-order shear, and third-order shear deformation plate theories. Plate material properties are presumed to differ continuously in the thickness direction concurringto a power law function. The motion and continuity equations are produced using three different plate theories, and then they are analytically solved for rectangular plates with simple supports utilizingNavier's method. The results are verified by obtaining the plate natural frequency for the power law index value equals zero and comparing them to those reported in previous works. It is shown that transverse vibrational analysis of the classical and first-order shear deformationplate theories for incompressible plates are not as precise as thecompressible ones. It is shown that this issue is due to the fact that according to those theories, unlike the higher order theories, the hydrostatic pressure cannot participate in carrying the bending loads. Consequently, the equivalent flexural stiffness and as a result flexural frequencies decrease. So, to analyze the vibrational behavior of functionally graded incompressibleplates, whether the plate is either thin or thick, higher order theories should be adopted. Also, it is demonstrated that TSDT is the simplest shear deformation plate theory for which the hydrostatic pressure can contribute to withstandig the bending moments. So, it can be a practical theory for free vibration analysis of functionally graded incompressible plates. Finally, this theory has been taken into consideration to analyze the vibrational behavior of rectangular plates made of functionally graded incompressible materials Also detailed parametric studies have been carried out.

Experimental Research on the Floating Amount of Shield Tunnel Based on the Innovative Cumulative Floating Amount Calculation Method

The study of shield tunnel segment flotation is crucial for controlling the precision of underground excavation projects. Based on Winkler’s beam foundation theory, the load structure method, and the equivalent continuous beam model, and by considering the mechanical and spatial conditions that cause segment flotation, a novel theoretical calculation method for cumulative flotation is proposed using a simplified equivalent stiffness model of the tunnel. Additionally, a new concept of “equivalent flotation force” is introduced. The rationality and applicability of this theoretical calculation method are verified by comparing it with on-site construction data from the Yuanjiang River Crossing Tunnel Project in Changde, Hunan Province, China. The experimental results demonstrate that the theoretical calculation closely approximates the surface deformation monitoring data of the tunnel alignment in the eastern section of the project, and their deformation patterns are similar. Near the starting shaft, there is significant settlement influenced by stratum loss due to smaller tunnel flotation, with greater settlement occurring in the upper part. However, at approximately 45 m into both sections, they enter a deformation stability zone showing significant correlation in longitudinal deformation. Through comparison and verification of on-site experiments and theoretical model analysis, we preliminarily elucidate the feasibility of this innovative cumulative flotation theoretical calculation method which provides an important theoretical basis for assessing segment flotation issues in subsequent tunnel shield construction evaluations.

Equivalent single-layer model for hierarchical diamond honeycomb sandwich panels using variational asymptotic method

Sandwich panels with a hierarchical core facilitate the optimal utilization of limited materials to enhance bearing capacity in strategic locations. Nevertheless, the complex sub-structural cells have hindered extensive investigation into their static and modal characteristics. The objective of this study is to obtain the effective plate properties by homogenizing the representative unit cell and subsequently applying them to a two-dimensional equivalent single layer model (2D-ESL) based on the variational asymptotic method (VAM). Furthermore, three-point bending test of 3D-printed specimen and 3D detailed finite element results are employed to confirm the predictions of 2D-ESL under various load and boundary conditions. The effects of material factors (such as fiber volume fraction and layup configuration) and structural parameters (including aspect ratio, hierarchy ratio, and slenderness ratios of ribs and ligaments) on the equivalent stiffness and modal characteristics are also examined. Moreover, sandwich panels with different hierarchical configurations (including 2, 3 and infinite segments within the inclined ribs) are investigated to provide valuable insights for selecting appropriate hierarchies based on specific conditions. Notably, the transition from polyline to arc-shaped segments has been proven to effectively mitigate local stress concentration, leading to a more uniform distribution of local displacement.

Stability prediction for robotic milling based on tool tip frequency response prediction by considering the interface stiffness of spindle-tool system

The change of tool tip frequency response caused by the posture dependence of robot dynamic is one of the key problems that make it difficult to accurately predict the milling stability of robot. In this paper, a tool tip frequency response prediction method considering the interface stiffness characteristics of spindle-tool system is proposed for stability prediction of robotic milling under the condition of posture variation. Firstly, the interface stiffness models of spindle-toolholder, toolholder-spring clip and spring clip-tool are established based on Yoshimura's unit area method. Then, The dynamics model for the robot body and the interface stiffness models for spindle-tool system are imported into the finite element analysis model of the spindle system, so that the prediction of the tool tip frequency response is realized by harmonic response analysis. Compared with the experimental results, the maximum error of the natural frequency was not more than 2 %, and the maximum error of the amplitude was not more than 12 %. Finally, the 2 DOF robot milling stability prediction model is established. Then the robot milling chatter is predicted considering redundant degrees of freedom from the perspective of regenerative chatter prediction theory, and the accuracy of prediction results is verified by milling experiment.

Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology

Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.

The effects of ply clustering positions and orientations on multi‐directional composite laminates' low velocity impact resistance

AbstractIn this paper, nine different carbon fiber laminates containing clusters are designed using the ant colony ACO algorithm, which have similar equivalent bending stiffnesses and B‐matrices, with the differences being the fiber orientation of the clusters and the position of the clusters in the laminates. The dynamic mechanical characterization of laminates for low velocity impact (LVI) at three different energies was carried out by means of a falling weight impact experiment. The experimental results show that the main form of failure of the laminate is delamination failure at low energy impacts, and shear fracture becomes more and more obvious with the elevation of the impact energy, which was observed in detail by the stereo microscope and electron microscope. The damage area of the laminate and the force and displacement curves after 30 J energy impact were compared by x‐ray scanning to derive the effects of the angle of the ply cluster fibers and the different positions of the ply clusters in the laminate on the impact resistance of the laminate. In conclusion, when designing the laminate, consideration should be given to designing 45° clusters on the impacted side and 90° clusters in the middle layer of the laminate to obtain the best impact resistance.Highlights Designed 9 types of laminates with different laminate structures based on ACO algorithm. Different laminates have similar equivalent bending stiffnesses and the B matrix as close to 0 as possible. LVI tests at three energies were performed on 9 types of laminates. The effects of different orientations of the clusters and the position of the clusters in the laminate on the impact resistance of the laminate were investigated.

Stiffly Stable Diagonally Implicit Block Backward Differentiation Formula with Adaptive Step Size Strategy for Stiff Ordinary Differential Equations

Stiffly Stable Diagonally Implicit Block Backward Differentiation Formula with Adaptive Step Size Strategy for Stiff Ordinary Differential Equations

Real-time multibody simulation of vehicle wheel suspensions of different topologies with elastokinematic properties

AbstractDriving simulators are becoming increasingly important in vehicle development, as they allow test drivers to evaluate the driving characteristics of a vehicle at an early stage of the development process. Vehicle dynamics models used for such real-time applications are usually simplified to achieve sufficiently low computation times, especially with respect to the elastokinematic properties of the wheel suspension. This contribution introduces a real-time capable multibody simulation model for wheel suspensions taking into account their elastokinematics. The underlying data model allows the parametrization of different suspension topologies. Linear-implicit integration methods enable real-time capable integration of the underlying numerically stiff equation of motion without major model simplifications. It is shown how the computational effort of linear-implicit integration can be reduced by explicitly taking the suspension topology into account. A versatile process for the analytical online-linearization of the equation of motion of arbitrary suspension topologies is presented. Both a double wishbone and a multilink suspension are simulated with very high accuracy in real-time on a standard PC.

Strength prediction of the notched composite laminates from equivalent un-notched laminates

In this paper, a theoretical failure model is proposed to predict ultimate strength of fiber-reinforced composite laminate with a circular hole. In the failure model, the laminate with a circular hole is modeled by an equivalent intact laminate which contains laminae with the same stacking sequence but with equivalent stiffness and strength derived by micromechanics and point stress formulation, respectively. The ultimate strength of this equivalent intact laminate is calculated by the improved Puck’s failure theory combined with stiffness degradation model. The failure model so formulated is applied to notched laminates with arbitrary stacking sequences. The capability is demonstrated by strength predictions of several multidirectional notched laminates, including [45∘/0∘/−45∘/90∘]2s AS4/3501-6 notched laminates, [45∘/90∘/−45∘/0∘]4s IM7/8552 notched laminates and [0∘/902∘/0∘]4s AS4/3502 cross-ply notched laminates, which are in good agreement with experimental results.

A study of controlling the transverse vibration of a beam-plate system by utilizing a nonlinear coupling oscillator

In the engineering field, prolonged exposure of complex structures to high-strength vibration environments can lead to various engineering challenges. This underscores the importance of effectively managing the vibration of complex structures. Given the extensive utilization of beams and plates in the construction of intricate structures, this study incorporates a nonlinear coupling oscillator into the beam-plate system and formulates a vibration analysis model for this system. The governing equations of the system are derived theoretically and solved numerically using the Galerkin truncation method. This study focuses on the operational modes of the nonlinear coupling oscillator based on accurate numerical results. Meanwhile, the influence of parameters belonging to the nonlinear coupling oscillator on the transverse vibration responses of the beam-plate system is systemically studied. Upon meticulous examination of the numerical results, the operational states of the nonlinear coupling oscillator encompass the normal vibration suppression mode and the quasi-periodic vibration suppression mode. The alteration in the linear elastic coupling stiffness of the beam-plate system impacts the effectiveness of vibration suppression in the nonlinear coupling oscillator. This influence stems from the fact that changes in the linear elastic coupling stiffness directly affect the nonlinear forces exerted on the beam-plate system within a nonlinear coupling oscillator. Within a feasible range, the nonlinear stiffness and viscous damping can be chosen as the adjustable parameters for the nonlinear coupling oscillator to regulate the vibration of the beam-plate system by adjusting the motion mass of the nonlinear coupling oscillator, which presents a challenge. The appropriate utilization of the nonlinear coupling oscillator demonstrates favorable control effectiveness in managing the transverse vibration of the beam-plate system. The study presented in this work offers a method to simultaneously control the vibration of each component within beam-plate coupling systems.