Compliant Sheet Research Articles

Buckled elastic sheet as a vortex generator in dual channels

This study presents a dual-channel vortex generator (VG) that leverages the snap-through behaviour of flexible sheets. The VG outperforms a similar-sized rigid VG in generating vortices within dual-channel flows while minimizing pressure loss. Numerical simulations using the immersed boundary-lattice Boltzmann method analyse the dynamics and vortex generation performance of the sheet under various system parameters. Two distinct modes are identified for the elastic sheet: a sustained snap-through mode (SSTM) and a dormant mode (DM). The sheet's mode is predominantly influenced by its length ratio (L*), bending stiffness $(K_b^\ast )$ and flow strength, with the mass ratio having a minimal impact. The sheet exhibiting regular SSTM can effectively generate vortices in both channels and the vortex generation performance can be conveniently tuned by altering the sheet's initial buckling (i.e. L*). An increase in $K_b^\ast $ results in a higher critical Reynolds number (Rec) required for mode transition. An increase in L*, however, initially raises Rec and then lowers it, suggesting an optimal length ratio (approximately 0.7 for our considered system) for minimizing the Rec necessary to trigger SSTM. Furthermore, a disparity in the flow strength between channels is found to suppress the snap-through of the sheet; a greater disparity, however, is permissible to induce the SSTM of more compliant sheets. These findings underscore the potential of snap-through behaviour for enhanced flow manipulation in dual-channel systems.

Pristine and Coated Carbon Nanotube Sheets—Characterization and Potential Applications

A carbon nanotube (CNT) sheet is a nonwoven fabric that is being evaluated for use in different textile applications. Several properties of pristine CNT sheets and CNT sheets coated with a polysilazane sealant and coating were measured and compared in the paper. The polysilazane coating is used to reduce the shedding of CNT fibers from the sheet when the sheet is in contact with surfaces. Most fabrics show some shedding of fibers during the washing or abrasion of the fabric. This study showed that the coating reduces the shedding of fibers from CNT fabric. The coating also increased the flame resistance of the fabric. The pristine and coated sheets both have low strength but high strain to failure. The pristine and coated CNT sheet densities are 0.48 g/cc and 0.65 g/cc, respectively. The pristine CNT sheet is approximately 27 μ thick. The coated sheet is approximately 24 μ thick. The coating may have densified the sheet, making it thinner. The thickness of the compliant sheets was difficult to measure and is a source of error in the properties. Characterization results are given in this paper. The results are for comparison purposes and not to establish material properties data. Possible applications for CNT sheets are briefly discussed.

Adjustable, radii-controlled embedded lamina (RadiCEL) hinges for folding of thick origami-adapted systems

This work presents a method for creating hinge-like motion for origami-adapted mechanisms using internal membranes attached between rigid panels. The goal is to remove adhesive requirements, preserve panel volume for use as hard stops, and reduce parasitic motion experienced by other membrane joint types, while keeping the stress in the membrane below the stress limits. Two configurations are presented. The first is the general case called the radii-controlled embedded lamina (RadiCEL) hinge. The second is a special case and is referred to as the Radii-Controlled Regionally Sandwiched Compliant Sheets (RC-ReCS). These two configurations are described for a planar, single-folding mechanism with a description of ways in which the adjustability can be utilized to benefit various design requirements. A comparison between methods is presented, focusing on the axial parasitic motion of each configuration. Each configuration is applied to a degree-4 origami vertex, with a discussion of the benefits of each and a multi-vertex pattern is also presented. Finally, the RadiCEL hinge is presented as the hinge used in a foldable metasurface antenna.

Multi-objective trajectory optimization of the manipulator transferring compliant sheet metal parts

The deformation of the compliant part is the key factor that affects the production efficiency of the automobile press line. Considering multi-manipulator trajectories and part contours, this paper quantitatively analyzes the deformation of compliant parts when the manipulator transfers sheet metal parts. A multi-objective co-optimization method is proposed to generate smooth motion curves with smaller velocity, acceleration, and jerk. Based on the built-in module of rigid to flex in ADAMS software, some rigid parts such as the end effector and sheet metal part are transformed into compliant ones. And the redundant manipulator in the press line is taken as the representative case to check whether the trajectory performance is conducive to deformation suppression. Simulation result shows that the jerk curve without cusp points is more conducive to suppressing the part deformation than that with cusp points.

Stacked electrostatic angle sensor implemented in micro robot leg joints

Recently, micro walking robots have attracted considerable research interest, as they can move robustly in various terrains and are especially useful in swarm applications. To realize angle control for the robots, external sensors such as rotary encoders were attached to joints. When assembling external sensors and joint components, careful handling and positioning are needed. However, robots requiring intricate assembly of multiple components are not optimal for the above-mentioned applications. We proposed the integration of robot frames and capacitive angle sensors to one compliant sheet. Moreover, a stacked electrostatic angle sensor was developed by alternately folding two ribbon electrodes. The angle was estimated from the capacitance based on the distance between the electrodes. The sensor was designed and fabricated. Furthermore, we constructed the angle feedback control system using the proposed sensor. Feedback control within the range of 0° to 30° could be realized.

Integrated Tolerance and Fixture Layout Design for Compliant Sheet Metal Assemblies

Part tolerances and fixture layouts are two pivotal factors in the geometrical quality of a compliant assembly. The independent design and optimization of these factors for compliant assemblies have been thoroughly studied. However, this paper presents the dependency of these factors and, consequently, the demand for an integrated design of them. A method is developed in order to address this issue by utilizing compliant variation simulation tools and evolutionary optimization algorithms. Thereby, integrated and non-integrated optimization of the tolerances and fixture layouts are conducted for an industrial sample case. The objective of this optimization is defined as minimizing the production cost while fulfilling the geometrical requirements. The results evidence the superiority of the integrated approach to the non-integrated in terms of the production cost and geometrical quality of the assemblies.

Optimal design of fixture layouts for compliant sheet metal assemblies

A preeminent factor in the geometrical quality of a compliant sheet metal assembly is the fixture layout that is utilized to perform the assembly procedure. Despite the presence of a great number of studies about the optimization of assembly fixture layouts, there is not a comprehensive algorithm to optimize all design parameters of fixture layouts for compliant sheet metal assemblies. These parameters are the location and type of hole and slot in each part, the slot orientation, and the number and location of additional clamps. This paper presents a novel optimization method that optimizes all these parameters simultaneously to maximize the geometrical quality of the assemblies. To attain this goal, compliant variation simulations of the assemblies are utilized along with evolutionary optimization algorithms. The assembly springback and contacts between parts are considered in the simulations. After determining the optimal design parameters, the optimal positions of locators are fine-tuned in another stage of optimization. Besides, a top-down design procedure is proposed for applying this method to multi-station compliant assemblies. The presented method is applied to two industrial sample cases from the automotive industry. The results evidence a significant improvement of geometrical quality by utilizing the determined fixture layout from the presented method compared with the original fixture layouts of the sample cases.

MEMS fabrication of compliant sheet for micro hexapod robots

Micro hexapod robots are desirable tools for exploring hazardous environments such as areas affected by natural disasters. Our objective is to reduce the cost of fabricating micro hexapod robots and contribute to their mass production. Conventionally, when the micro robot is assembled, it is necessary to handle, align, and assemble the micro parts, and these processes increase the fabrication cost. We propose a fabrication system in which the robot is assembled from one compliant sheet fabricated using MEMS processes. This method can streamline the processes of handling and aligning the micro parts. The joint element of the robot is composed of a compliant hinge, and the joints are driven by shape memory alloy (SMA) actuators. In this study, we assembled a hexapod robot from one compliant sheet fabricated by the MEMS processes. Furthermore, SMA actuators were attached to the robot, and testing of the joints was performed.

Folding of Thick Origami Through Regionally Sandwiched Compliant Sheets

Abstract The regional sandwiching of compliant sheets (ReCS) technique presented in this work creates flat-foldable, rigid-foldable, and self-deploying thick origami-based mechanisms. Regional sandwiching of the compliant sheet is used to create mountain-valley assignments for each fold about a vertex, constraining motion to a single branch of folding. Strain energy in deflected flexible members is used to enable self-deployment. This work presents the methods to design origami-based mechanisms using the ReCS technique, including volume trimming at the vertex of the compliant sheet and of the panels used in the sandwich. Three physical models, a simple single fold mechanism, a degree-four vertex mechanism, and a full tessellation, are presented to demonstrate the ReCS technique using acrylic panels with spring and low-carbon steels. Consideration is given to the risk of yielding of the compliant sheet due to parasitic motion with possible mitigation of yielding by decreasing the thickness of the sheet.

Nonlinear Material Model in Part Variation Simulations of Sheet Metals

Current methodologies for variation simulation of compliant sheet metal assemblies and parts are simplified by assuming linear relationships. From the observed physical experiments, it is evident that plastic strains are a source of error that is not captured in the conventional variational simulation methods. This paper presents an adaptation toward an elastoplastic material model with isotropic hardening in the method of influence coefficients (MIC) methodology for variation simulations. The results are presented in two case studies using a benchmark case involving a two-dimensional (2D) quarter symmetric plate with a centered hole, subjected to both uniaxial and biaxial displacement. The adaptation shows a great reduction in central processing unit time with limited effect on the accuracy of the results compared to direct Monte Carlo simulations.

Robust fixture design of compliant assembly process based on a support vector regression model

Fixtures are used to locate and clamp parts and subassemblies during the compliant assembly process of automotive body parts. As a result, the assembly quality of compliant sheet metal parts is mainly determined by fixture locating layouts and variation sources, such as manufacturing variation of parts and fixture locating variation. This paper proposes a robust fixture design method of the compliant assembly process based on a support vector regression model. Firstly, an assembly variation modeling method of compliant sheet metal parts is discussed during the assembly subprocesses of fixture locating, welding gun clamping, weld finishing, and welding gun releasing. The combined assembly variation model describes a numeric relationship between the assembly variation of key measurement points and all variation sources under a certain fixture locating layout. Further, to solve the difficulty of directly obtaining the parameter model between the assembly variation and fixture design layouts under a certain variation source level, a response surface modeling method based on a support vector regression model is presented. And a whole assembly robust objective function is presented to realize the combining consideration of the whole assembly quality control with different assembly quality controls of different areas. Finally, a taillight bracket assembly is used to demonstrate the robust fixture design method. Results show that the proposed method is feasible and the assembly quality under the robust fixture locating layout has been greatly increased.

Quality and productivity driven trajectory optimisation for robotic handling of compliant sheet metal parts in multi-press stamping lines

Abstract This paper investigates trajectory generation for multi-robot systems that handle compliant parts in order to minimise deformations during handling, which is important to reduce the risk of affecting the part’s dimensional quality. An optimisation methodology is proposed to generate deformation-minimal multi-robot coordinated trajectories for predefined robot paths and cycle-time. The novelty of the proposed optimisation methodology is that it efficiently estimates part deformations using a precomputed Response Surface Model (RSM), which is based on data samples generated by Finite Element Analysis (FEA) of the handled part and end-effector. The end-effector holding forces, plastic part deformations, collision-avoidance and multi-robot coordination are also considered as constraints in the optimisation model. The optimised trajectories are experimentally validated and the results show that the proposed optimisation methodology is able to significantly reduce the deformations of the part during handling, i.e. up to 12% with the same cycle-time in the case study that involves handling compliant sheet metal parts. This investigation provides insights into generating specialised trajectories for material handling of compliant parts that can systematically minimise part deformations to ensure final dimensional quality.

Tolerance analysis of compliant, feature-based sheet metal structures for fixtureless assembly

Products made of compliant sheet metals are widely used in automotive, aerospace, appliance and electronics industries. One of the most important challenges for the assembly process with compliant parts is dimensional quality, which affects product functionality and cost. Joining fixtures serve to position and secure the parts in the assembly process and thus significantly contribute to product quality. However, these fixtures are costly and inflexible. Feature-based fixturing is an approach to reduce fixtures in the assembly process. The approach relies on part-inherent fastening features that ensure the fixture functions. This paper presents an approach to calculate assembly variations for feature-based fixturing in the automotive body shop. The mathematical fundamentals are described and the approach was implemented using a numerical model. The model was validated and applied to car body structures. The validation shows a high quality of the model and the suitability to predict assembly variations. Finally, an assembly that is built with conventional fixtures is compared to an assembly that is set up with feature-based fixturing. This comparison shows that the approach of feature-based fixturing has a high potential to meet the requirements and thus being applied in the future.

Assembly force modelling method on fixtures of automotive body compliant sheet metal parts

Some assembly forces will be generated on fixtures because of some existing variation sources during the welding process of automotive body compliant metal parts. This article proposes an assembly force modelling method on fixtures during the welding process of compliant sheet metal parts to decrease the assembly forces. The assembly force models on fixtures are established to show the influence relationship between assembly forces and all variation sources, and the finite element method is used to obtain all influence coefficients of assembly forces. The obtained assembly force models on fixtures describe the propagating principle of assembly forces in all welding subprocesses. Cases of different fixture layouts show that the fixture layout can greatly influence assembly forces on fixtures. So assembly forces on fixtures can be decreased through the optimization of variation sources and the fixture layout. This method can also be referred for other assembly processes, such as adhesive connection and fastener connection of compliant sheet metal parts.

Multi-objective optimization based on improved non-dominated sorting genetic algorithm II for tolerance allocation of auto-body parts

The auto-body is usually composed of compliant sheet metals. The assembly variation is inevitable in the process of auto-body assembly. A reasonable tolerance allocation method for compliant sheet ...

Quantifying the Frictional Forces between Skin and Nonwoven Fabrics.

When a compliant sheet of material is dragged over a curved surface of a body, the frictional forces generated can be many times greater than they would be for a planar interface. This phenomenon is known to contribute to the abrasion damage to skin often suffered by wearers of incontinence pads and bed/chairbound people susceptible to pressure sores. Experiments that attempt to quantify these forces often use a simple capstan-type equation to obtain a characteristic coefficient of friction. In general, the capstan approach assumes the ratio of applied tensions depends only on the arc of contact and the coefficient of friction, and ignores other geometric and physical considerations; this approach makes it straightforward to obtain explicitly a coefficient of friction from the tensions measured. In this paper, two mathematical models are presented that compute the material displacements and surface forces generated by, firstly, a membrane under tension in moving contact with a rigid obstacle and, secondly, a shell-membrane under tension in contact with a deformable substrate. The results show that, while the use of a capstan equation remains fairly robust in some cases, effects such as the curvature and flaccidness of the underlying body, and the mass density of the fabric can lead to significant variations in stresses generated in the contact region. Thus, the coefficient of friction determined by a capstan model may not be an accurate reflection of the true frictional behavior of the contact region.

Soft Origami: Classification, Constraint, and Actuation of Highly Compliant Origami Structures

Herein, we discuss the folding of highly compliant origami structures—“Soft Origami.” There are benefits to be had in folding compliant sheets (which cannot self-guide their motion) rather than conventional rigid origami. Example applications include scaffolds for artificial tissue generation and foldable substrates for flexible electronic assemblies. Highly compliant origami has not been contemplated by existing theory, which treats origami structures largely as rigid or semirigid mechanisms with compliant hinges—“mechanism-reliant origami.” We present a quantitative metric—the origami compliance metric (OCM)—that aids in identifying proper modeling of a homogeneous origami structure based upon the compliance regime it falls into (soft, hybrid, or mechanism-reliant). We discuss the unique properties, applications, and design drivers for practical implementation of Soft Origami. We detail a theory of proper constraint by which an ideal soft structure's number of degrees-of-freedom may be approximated as 3n, where n is the number of vertices of the fold pattern. Buckling and sagging behaviors in very compliant structures can be counteracted with the application of tension; we present a method for calculating the tension force required to reduce sagging error below a user-prescribed value. Finally, we introduce a concept for a scalable process in which a few actuators and stretching membranes may be used to simultaneously fold many origami substructures that share common degrees-of-freedom.

Physics-driven Shape Variation Modelling at Early Design Stage

Modern markets are becoming increasingly competitive emphasizing the importance of achieving Right First Time (RFT) during the early design stage as a key enabler facilitating cost and time-to-launch (or time-to-market) reduction. One of the leading challenges to deliver RFT is the lack of effective methods to model product errors at early design stage. Usually, the assembly process is designed under the assumption of ideal (nominal) products. On the contrary, it has been demonstrated that product errors (both geometrical and dimensional) affect the performance of the final assembly. To facilitate easy decision making at early design stage, new methods and models are required to support design engineers. In this study, a framework has been proposed for early design support to generate product variation.International standard provides guidelines for product control and inspection (ISO-GPS or ASME-GD&T); however, the integration of tolerance standard into nominal sized CAD models is not yet achieved. Current, Computer Aided Tolerancing (CAT) tools mainly capable to model orientation and position tolerance specifications, whereas part shape errors are omitted. This paper presents an innovative physics-driven simulation framework to model shape errors of compliant sheet metal parts at early design stage.The modelling framework consists of three important stages: (i) initial shape error prediction using physic-based simulation, such as, stamping process simulation; (ii) individual orthogonal shape error modes/patterns identification based on decomposition techniques, such as, Geometric Modal Analysis (GMA); and, (iii) simulation of shape error variation classes by assigning distribution to each orthogonal shape error modes. The proposed approach enables to generate shape errors at early design stage of assembly process which can be utilized to optimize the assembly process, including fixture design and joining process parameters. An industrial automotive component illustrates the proposed methodology.

Assembly variation modeling method research of compliant automobile body sheet metal parts using the finite element method

This paper presents a new assembly variation model of compliant automobile body sheet metal parts through building the variation propagation models of different assembly processes. The Method of Influence Coefficients is adopted to deduce the assembly variation model and the Finite Element Method is used to solve the assembly variation model parameters. A case of two cantilever beam assembly is supplied to validate the proposed assembly variation modeling method. The result shows that the proposed assembly variation modeling method can effectively predict the assembly quality of the automobile body parts.

An improved sensitivity-free probability analysis in variation assessment of sheet metal assemblies

Propagation of part tolerances through the assembly process affects the quality and overall performance of the products. Therefore, it is crucial to have a comprehensive model in order to analyse the relationship between part tolerances and final assembly errors. Assembly processes are often complex and nonlinear in nature. In sheet metal assemblies, the most important factor that makes the process nonlinear is contact interaction between mating parts during the assembly process. Another important feature in sheet metal variation analysis is the effect of geometric covariance. In sheet metal components, covariance always occurs since the surface continuity conditions force the deformation of the neighbouring points to be correlated. This paper aims to develop a new methodology for variation analysis of compliant sheet metal assemblies focusing on nonlinear contact analysis and including the effect of geometric covariance. The proposed methodology integrates a nonlinear finite element analysis with an improved sensitivity-free probability analysis in order to predict the final assembly variation. The efficiency of the developed approach is evaluated by an experimental case study as well as Monte Carlo simulation.