Stiffness Model Research Articles

Modelling of stiffness of ‘Irene’ apple during storage and shelf-life

Modelling of stiffness of ‘Irene’ apple during storage and shelf-life

Research on Bowden Cable–Fabric Force Transfer System Based on Force/Displacement Compensation and Impedance Control

Bowden cable–fabric is a key force transfer device for flexible exoskeletons, and its precise control of force/displacement is a significant factor in the human–machine interaction of flexible exoskeletons. In this paper, a force/displacement control method based on friction compensation and impedance control was proposed based on a flexible Bowden cable–fabric force transfer testbed system. First, a set of in vitro experimental platforms simulating Bowden cable–fabric force transfer was built according to a typical flexible exoskeleton force transfer system, and following the walking gait of lower limbs, the expected force and knee joint motion were set. Secondly, the Bowden cable–fabric force transfer friction model was constructed as the basis of the system’s force transfer compensation. In addition, the stiffness model of Bowden cable–fabric and the lower leg movement model were established and combined with impedance control to realize the precise control of system displacement. Finally, the damping and stiffness parameters suitable for the system were obtained through the impedance control simulation. In terms of the experiment, an in vitro Bowden cable–fabric force transfer experimental platform was built, and the expected force with the input peak value of 40 N, 50 N, and 60 N was set. Through the friction and position compensation model of Bowden cable–fabric force transfer and impedance control, the relative root-mean-square errors of the output force and expected force were obtained as 2.53%, 2.16%, and 2.07%, respectively. Therefore, the effectiveness of the proposed method is verified, which provides a foundation for the engineering application of flexible exoskeletons.

A Modified Model for Identifying the Characteristic Parameters of Machine Joint Interfaces

The contact parameters of joint interfaces have a great influence on the dynamic performance of the machine tool, and the dynamic performance determines the machining precision of the machine tool. Therefore, it is important to accurately identify the contact parameters of joint interfaces to improve the machining precision of the machine tool. In this paper, a method of identifying the joint interface stiffness parameters based on a joint simulation in Matlab and Ansys is first proposed, and then stiffness parameters of joint interfaces between the bed and column of the precision grinding machine are identified by applying the method. Finally, the feasibility and high efficiency of the proposed method are proved by comparing the natural frequencies of the simulation and the experiment. In order to further analyze the influence of joint contact parameters on the performance of the joint interfaces, the theoretical model of the normal stiffness of the joint interfaces based on fractal geometry is amended and verified by taking into account the asperity interaction and elastic–plastic deformation. Then, the modified model is extended to a three-dimensional model, which is more in line with the actual situation. Finally, the influencing factors of the joint interface stiffness are analyzed. The conclusions of this paper are of great significance in the dynamic performance analysis and structural design of machine tools.

Design and analysis of a novel flexible variable stiffness damping mechanism for grinding electric spindle

The purpose of this research is to design a flexible variable stiffness damping mechanism to solve the load impact problem in the grinding process of permanent magnet electric spindle. Firstly, combined with the structure and usage scene of the grinding permanent magnet electric spindle, according to the design principles and technical indicators, a novel flexible variable stiffness vibration damping joint is proposed. Then the stiffness and energy storage model of the flexible variable stiffness damping mechanism is established, and the stiffness and energy storage characteristics of the mechanism are analyzed. The strength and dynamic characteristics of the flexible variable stiffness mechanism are analyzed by Ansys and Adams, respectively. Finally, an experimental platform for the comprehensive performance verification of the flexible variable stiffness damping mechanism is built to verify the dynamic characteristics and damping effect of the mechanism. The research results show that the designed flexible variable stiffness structure has better vibration damping effect and can improve the grinding performance of the permanent magnet electric spindle.

Stiffness analysis and optimization of an asymmetric 3T1R parallel mechanism

In this paper, an asymmetric 3T1R parallel mechanism is proposed that has higher stiffness in specific directions. The stiffness model is established by using virtual spring theory, and the Cartesian stiffness matrix is obtained. The stiffness performance evaluation indices are deduced by the dimensionless parameterization method. Under the condition of satisfying the high-speed performance and dexterity, the optimal size parameters of the mechanism are got by using the DE (differential evolution) algorithm with stiffness performance as the index. By comparing the stiffness performance atlases before and after the optimization, it is showed that the stiffness performance has been improved and the reachable workspace has been increased. The results verify the feasibility of the proposed performance indices and optimization algorithm.

Experimental statistical modeling of tensile properties and flexural stiffness of recycled high-density polyethylene (rHDPE) thermoplastic using response surface methodology (RSM)

The widespread use of thermoplastic polymer products, particularly high-density polyethylene (HDPE), in daily consumer goods has led to the generation and accumulation of large amounts of plastic waste. This waste poses a significant threat to the environment due to the challenges and limitations in managing plastic waste effectively. Establishing new large volume applications of recycled HDPE (rHDPE) would incentivize recycling by creating new revenue streams. Before rHDPE (specifically rHDPE-talc blends) can be used more heavily in lieu of or in addition to virgin HDPE (vHDPE), its material properties in relation to application temperatures must be better understood. This study focused on characterizing tensile and flexural properties of rHDPE-talc blends across broad talc filler content and temperature ranges. Experimentally, tensile strength, elastic modulus, storage modulus, and nominal yield strain data were collected. Tensile strength and elastic modulus were observed to increase with an increase in talc content and decrease with an increase in temperature. Conversely, yield strain was observed to decrease with an increase in talc content and increase with an increase in temperature. Response Surface Methodology (RSM) was applied using the Central Composite Design (CCD) statistical experimental design approach to study the stiffness and strength of rHDPE and the effects that temperature and talc filler content have on these mechanical properties. The surfaces generated in this analysis fit the data well, with coefficients of determination greater than 0.94 for all but one property, storage modulus, which was 0.80. The evaluation of model performance revealed that the surfaces yielded good correlation and statistical significance. The results provide useful relationships that can be considered for use in practical applications involving rHDPE-talc blends, including engineering applications.

Dynamic coupling of multi-degrees of freedom constrained-layer vibration neutralizers: A new methodology

Dynamic neutralizers, also known as dynamic absorbers, are efficient means of mitigating vibrations in structures. They have been particularly effective in addressing broad-band passive vibration control in structures with high modal density through the use of multi-degrees of freedom (MDoF) and viscoelastic materials (VEMs). Therefore, sandwich-type or constrained-layer beams can offer great potential when used as MDoF control devices. However, there is limited literature exploring these structures as auxiliary systems, with coupling typically assumed to be single-point and limited to only translational degrees of freedom (DoFs). In this context, this article presents a methodology to determine the dynamic behavior of a compound system, coupling the displacement and rotation DoFs between a metal structure–referred to as the primary system–and a MDoF auxiliary system. The coupling is achieved by utilizing an equivalent dynamic stiffness obtained at the base of the auxiliary system through ANSYS finite-element software, providing a robust and comprehensive approach. A Matlab code transfers the auxiliary system's geometry and properties to ANSYS, where the dynamic stiffness at the base is determined and subsequently coupled to the primary system. A MDoF auxiliary system of the constrained-layer type with VEM was studied, and both single-point and distributed coupling were analyzed. The auxiliary system was attached to a cantilever metal beam for numerical and experimental validation. The proposed generalized equivalent dynamic stiffness model accurately estimates the response of the compound system, offering a 25% reduction in response computation time compared to the finite-element model of the complete compound system. This methodology enables the accurate representation of compound system dynamics while minimizing computational time, making it valuable for the optimal design of a set of MDoF viscoelastic dynamic neutralizers.

Research on the modification of the tool influence function for robotic bonnet polishing with stiffness modeling

Robotic bonnet polishing (RBP) technology is widely used in the polishing process of optical components, but industrial robots have the characteristics of a wide processing range and low body stiffness. Therefore, in the actual polishing process, there are different polishing forces due to different stiffnesses, which leads to different tool influence functions (TIF) affecting the surface quality of optical components. To achieve a uniform surface quality of the components polished by the RBP, we modeled the stiffness of the robot and modified the TIF in conjunction with the Preston equation, finally verifying the accuracy of the modified model through experiments. The results of the fixed-point polishing experiments show that the maximum relative error before the TIF correction is 12.5% and the maximum relative error after the correction is 2.8% within the robot's 600mm*600mm machining range. The results of the plane polishing experiments show that the maximum relative error before the TIF correction is 13% and the maximum relative error after the correction is 1.7%. Therefore, a method for TIF corrections from RBP based on stiffness modeling has important engineering implications.

Kinetostatics-based stiffness analysis of continuum manipulators considering non-constant cross sections

Continuum manipulators are widely used for their compliant and dexterous nature, but their design and modeling are simplified by keeping the cross-section constant. Inspired by biological structures like elephant trunks and octopus tentacles, previous studies have proposed continuum manipulators featuring non-constant cross sections, but few of them study how the cross sections affect the manipulator’s properties, such as stiffness. In this paper, a general kinetostatic model and a stiffness model are presented for continuum manipulators with non-constant cross sections and experimental validations are conducted under various actuating and loading conditions. Moreover, comparative stiffness analysis is performed among manipulator designs with different non-constant cross sections. The results indicate a significant impact of cross-section-varying rates on the system stiffness along different directions. This approach and analysis are significant for the structure design and stiffness optimization of continuum manipulators, particularly in applications where stiffness is a primary objective.

Stiffness analysis and parameter optimization of six-dimensional force sensor with the novel circular flexible spherical joint

As robot haptic provider, six-dimensional force sensors are an indispensable component of industrial intelligence. To address the disadvantages of the existing six-dimensional force sensor, a novel circular flexible spherical joint is proposed, its stiffness model is derived by numerical analysis method and microelement, and the stiffness model of the circular flexible spherical joint is verified by finite element simulation. A parallel six-dimensional force sensor is designed based on a circular flexible spherical joint, and a mathematical model of the sensor was established. Based on the genetic algorithm, the structural optimization design of the circular flexible spherical joint was performed, and the structural parameters of the circular flexible spherical joints are obtained by analyzing isotropy. Finally, according to the optimization results, a sensor was developed and calibration experiments were carried out. The experimental results show that the maximum error of the sensor is 1.85%, which verifies the effectiveness of the mathematical model of the sensor, which has high measurement accuracy and can accurately measure the six-dimensional external force and moment applied to the sensor.

Matrix stiffness induces Drp1-mediated mitochondrial fission through Piezo1 mechanotransduction in human intervertebral disc degeneration

BackgroundExtracellular matrix stiffness is emerging as a crucial mechanical cue that drives the progression of various diseases, such as cancer, fibrosis, and inflammation. The matrix stiffness of the nucleus pulposus (NP) tissues increase gradually during intervertebral disc degeneration (IDD), while the mechanism through which NP cells sense and react to matrix stiffness remains unclear. In addition, mitochondrial dynamics play a key role in various cellular functions. An in-depth investigation of the pathogenesis of IDD can provide new insights for the development of effective therapies. In this study, we aim to investigate the effects of matrix stiffness on mitochondrial dynamics in IDD.MethodsTo build the gradient stiffness model, NP cells were cultured on polystyrene plates with different stiffness. Western blot analysis, and immunofluorescence staining were used to detect the expression of mitochondrial dynamics-related proteins. Flow cytometry was used to detect the mitochondrial membrane potential and intracellular Ca2+ levels. Apoptosis related proteins, ROS level, and TUNEL staining were performed to assess the effect of substrate stiffness on NP cells.ResultsStiff substrate increased phosphorylation of dynamin-related protein 1 (Drp1) at Ser616 by activating extracellular signal-regulated kinase 1/2 (ERK1/2) pathway, which promoted mitochondrial fission and apoptosis in NP cells. Furthermore, Piezo1 activation was involved in the regulation of the post-translational modifications of Drp1 and mitochondrial fission caused by matrix stiffness. Inhibition of Piezo1 and ERK1/2 can effectively reduce stiffness-induced ROS elevation and apoptosis in NP cells.ConclusionsOur results revealed that stiff substrate causes Piezo1 activation and Ca2+ influx, results in ERK1/2 activation and phosphorylation of Drp1 at S616, and finally leads to mitochondrial fission and apoptosis in NP cells. These findings reveal a new mechanism of mechanotransduction in NP cells, providing novel insights into the development of therapies for treating IDD.

Motion Performance Study of 2UPR-1RPS/2R Hybrid Robot Based on Kinematics, Dynamics, and Stiffness Modeling

Abstract The unique structural characteristics of hybrid robots, such as few degrees-of-freedom (DOF) and redundant constraints, lead to a series of challenges in the establishment of theoretical models. However, these theoretical models are indispensable parts of motion control. Therefore, this paper focuses on establishing the kinematics, dynamics, and stiffness models for an Exechon-like hybrid robot, which are then used for error compensation and velocity planning to improve the robot’s motion performance. First, the kinematic model is derived through intermediate parameters and the kinematics equivalent chains. By analyzing the parasitic motion due to few DOF, the redundant equations in the model are eliminated to obtain the solution of inverse kinematics. Second, based on the beam element, the optimal equivalent configuration of the moving platform which connects the parallel part and serial part is determined, and then an entire equivalent structure of the robot is formed. It helps establish the stiffness model by using the matrix structure analysis method. Next, the dynamic model is established by combining the Newton–Euler method with co-deformation theory to solve the underdetermined dynamic equations caused by redundant constraints. Finally, the compensation method is designed based on the stiffness model and kinematic model to improve the end positioning accuracy of the robot; the velocity planning algorithm is designed based on the dynamic model and kinematic model to enhance the smoothness of the robot motion. The methods proposed in this paper are also of referential significance to other Exechon-like hybrid robots.

Design of a Novel Flexible Spherical Hinge and Its Application in Continuum Robot

Abstract Compliant mechanisms, which can be integrally machined and without assembly, are well suited as joints for continuum robots (CRs), but how to incorporate the advantages of the compliant mechanism into the arm design is a key issue in this work. In this paper, a novel type of flexible spherical-hinged (FSH) joint composed of tetrahedron elements with a fixed virtual remote center of motion (RCM) at the bottom is proposed, and then extended to the CR and end-effector. In the arm design, the error compensation principle is used to offset the parasitic motion of the CR under external load (pressure and torque) and improve the bending and torsional isotropy of the arm through different series combinations, and then the stiffness model of the FSH joint and the statics model of the CR are developed using the 3D chain pseudo-rigid body model (3D-CPRBM) and tested. The results show that the 3D-CPRBM can effectively predict the deformation of the FSH joint and the CR. Moreover, the maximum standard deviation of the bending angle of the FSH joint in each direction is only 0.26 deg, the repeatable positioning accuracy of the CR can reach 0.5 deg, and the end-effector has good gripping ability and self-adaptive capability.

Kinematic and stiffness modelling and performance evaluation of a new PRS-PRU-PUR overconstrained parallel mechanism

Kinematic and stiffness modelling and performance evaluation of a new PRS-PRU-PUR overconstrained parallel mechanism

Modeling and simulation of the equivalent vertical stiffness of leaf spring suspensions

In vehicle multi-body dynamics (MBD) modeling, the stiffness parameterization of leaf spring (LS) is an unavoidable challenge regardless of the selection of modeling methods. On the contrary, the parameterization of Coil Spring (CS) stiffness is easy to achieve by adjusting the scale factor. Therefore, a novel LS stiffness parameterization method by treating the suspension stiffness as an intermediate variable through a CS stiffness is proposed based on the virtual displacement theory. The proposed method is then implemented in the vehicle-level modeling of a commercial Van with front transverse leaf spring suspensions and rear longitudinal parabolic leaf spring suspensions. The MBD model is validated by natural frequency tests and suspension stiffness simulations. Furthermore, the vertical acceleration of the car body is also verified. Results show that the root mean square (RMS) values of body vertical acceleration in the equivalent CS model are just slightly lower than that in the LS suspensions. The applicability and capability of the proposed method are proven to address the limitation of LS stiffness parameterization in MBD modeling. It lays the groundwork for efficiently simulating the LS suspension in vehicle ride and handling design and optimization.

Fusing the Wireless Technique Optical Fiber Force Sensor for Remote Monitoring of Sleeping Posture

This article presents a novel three-dimensional-printable optical fiber force sensor used to guide the rehabilitation of patients with heart failure (HF), and builds the corresponding sleeping posture monitoring system. The designed sensing probe is mainly composed of a lamina emergent spring (LES), a prismatic-tip optical fiber, and a wireless-based signal collection module including WiFi and Bluetooth. A data and theoretical model-driven method has been proposed to derive the stiffness model of the LES with a small error of less than 10% compared with the experimental stiffness. To better obtain the sleeping posture characteristics, a herringbone sensing probe layout scheme with eight sensors has been proposed with consideration of the fiber bending-induced light loss. The calibration and performance experiments have been implemented to validate the reliability of the sensing probe including the wireless transmission function. A Sparrow Search Algorithm optimized back propagation neural network has been designed to distinguish the typical six sleeping postures with a high recognition accuracy of 98.1%. Several experiments have been carried out to verify the real-time performance, the feasibility of mutibed remote monitoring, and the long-term monitoring capability of the sleeping posture monitoring system. The monitoring results can be shared with the user's family member mobile phone or monitoring center to check their sleeping postures. Such merits indicate that fusing the wireless technique optical fiber force sensor has huge potential to guide the rehabilitation of HF patients

Thermal effect modeling of axial static stiffness of motorized spindle unit

Thermal effect modeling of axial static stiffness of motorized spindle unit

Interpolation time-optimized aortic pulse wave velocity estimation by 4D flow MRI

Four-dimensional flow magnetic resonance imaging-based pulse wave velocity (4D flow PWV) estimation is a promising tool for measuring regional aortic stiffness for non-invasive cardiovascular disease screening. However, the effect of variations in the shape of flow waveforms on 4D flow PWV measurements remains unclear. In this study, 4D flow PWV values were compared using cross-correlation algorithm with different interpolation times (iTs) based on flow rate and beat frequency. A critical iT (iTCrit) was proposed from in vitro study using flexible and stiff phantom models to simultaneously achieve a low difference and a low computation time. In vivo 4D flow PWV values from six healthy volunteers were also compared between iTCrit and the conventionally used interpolation time of 1 ms (iT1 ms). The results indicated that iTCrit reduced the mean difference of in vitro 4D flow PWV values by 19%, compared to iT1 ms. In addition, iTCrit measured in vivo 4D flow PWV, showing differences similar to those obtained with iT1 ms. A difference estimation model was proposed to retrospectively estimate potential differences of 4D flow PWV using known values of PWV and the used iT. This study would be helpful for understanding the differences of PWV generated by physiological changes and time step of obtained flow waveforms.

Design and analysis of ultra-low moment noise flexure pivot in space gravitational wave detectors

To control the pointing accuracy of the telescope in the space gravitational wave detector at the nano-radian level, it is essential to design a flexure pivot with extremely low rotational moment nonlinearity during rotation. This study derives the theoretical equation of the nonlinear rotational moment of flexure pivot based on the beam bending strain energy equation and completes the design of ultra-low moment noise flexure pivot by integrating the structural form of conventional cross-spring flexure pivot. The nonlinear moment noise distribution in the frequency domain of three kinds of flexure pivots is then compared regarding TianQin’s circular high orbits. Then the relevant finite element simulation analysis will be performed for the flexure pivot structures, respectively, to ensure the accuracy of its rotational stiffness model and verify the correctness of nonlinear moment theory optimization through physical experiments. The results show that the optimized flexure pivot can effectively reduce the nonlinearity, and basically meet the nonlinear moment requirements in space gravitational wave detection.

Effective Stiffness and Seismic Response Modification Models Recommended for Cantilever Circular Columns of RC Bridges, First Part: Serviceability Limit State

This paper’s main aim was to explain the process of characterising the structural over-strength factor (R), seismic behaviour factor (Q), and the effective elastic stiffness, Keff, of cantilever-reinforced concrete (RC) urban bridge columns with solid circular cross-sections for use in seismic design under the Serviceability Limit State (SLS). Similarly, mathematical models have been proposed to determine the average values of effective stiffness and seismic response modification factors suggested for cantilever-reinforced concrete bridge columns at SLS. This is because multiple design codes stipulate that cantilever RC bridge columns must meet the SLS requirements. Therefore, to comply, the lateral displacement ductility demand must not exceed unity after a moderate or small earthquake. While the behaviour of the materials remains in the elastic range, this performance criterion can be conservative. If the materials undergo small deformations, the slight damage can be quickly repaired to meet the SLS.