In many gear mesh stiffness models, the single tooth pair mesh stiffness is commonly approximated as having a parabolic-like symmetric shape along the path of contact with a fixed or contact ratio ...dependent amplitude. Even though this is a valid approximation under certain conditions, there is an asymmetry being disregarded and an amplitude being roughly approximated. In this work, a new straightforward analytical expression for the single tooth pair slice mesh stiffness is defined resorting to a parabolic approximation of the tooth pair structural stiffness that requires the definition of the asymmetry, relative amplitude and maximum value as a function of the gear parameters. In order to validate the developed work in terms of applicability and accuracy, a random sample of gears have their tooth pair structural stiffness approximation tested. The established asymmetry, relative amplitude and maximum value allow, in a fast and simple fashion, to obtain an accurate approximation. Different formulations of the single tooth pair slice mesh stiffness are compared, highlighting the importance of including the asymmetry and showing the improvements due to the new parameters.
•Modeling of single tooth pair slice mesh stiffness with straightforward expressions.•Definition of the stiffness asymmetry, relative amplitude and maximum value.•Fast and accurate expressions for gear mesh stiffness modeling.
•The NCM is comprehensively studied to design QZS for vibration isolation.•Hardening stiffness is preferred for better compensating the negative stiffness.•A confirmatory system is established to ...verify the effectiveness of the NCM and the isolation performance.
Various quasi-zero stiffness (QZS) vibration isolators have been emerged in recent years and applied successfully in low-frequency vibration isolation. However, in most cases, the general approach to achieving QZS is still limited to compensating the negative stiffness of the bistable structure by linear springs. Here, a nonlinear compensation method (NCM) for realizing QZS is developed and the corresponding methodology is systematically investigated. Specifically, for a certain negative stiffness structure (not limited to bistable structure), QZS can be obtained by utilizing hardening stiffness to compensate. A confirmatory QZS vibration isolation system is established to fully verify the effectiveness of the NCM. The confirmatory system exploits rhombus structure to generate nonlinear negative stiffness, which can be compensated by nonlinear positive stiffness (provided by repulsive magnets). The static analysis is completed to reveal the inherent stiffness compensation mechanism. The dynamic and experimental results demonstrate that the proposed QZS system has low resonant frequency and wide effective vibration isolation frequency band. The NCM has reference significance in realizing QZS and is beneficial to develop diversified low-frequency vibration isolators.
Quasi‐zero‐stiffness (QZS) isolators of high‐static‐low‐dynamic stiffness play an important role in ultra‐low frequency vibration mitigation. While the current designs of QZS mainly exploit the ...combination of negative‐stiffness corrector and positive‐stiffness element, and only have a single QZS working range, here a class of tailored mechanical metamaterials with programmable QZS features is proposed. These programmed structures contain curved beams with geometries that are specifically designed to enable the prescribed QZS characteristics. When these metamaterials are compressed, the curved beams reach the prescribed QZS working range in sequence, thus enabling tailored stair‐stepping force‐displacement curves with multiple QZS working ranges. Compression tests demonstrate that a vast design space is achieved to program the QZS features of the metamaterials. Further vibration tests confirm the ultra‐low frequency vibration isolation capability of the proposed mechanical metamaterials. The mechanism of QZS stems solely from the structural geometry of the curved beams and is therefore materials‐independent. This design strategy opens a new avenue for innovating compact and scalable QZS isolators with multiple working ranges.
A class of tailored mechanical metamaterials, containing many optimally designed curved beams, is proposed. By digitally assembling the basic building blocks that contain two curved beams, programmable quasi‐zero‐stiffness (QZS) features including both the QZS displacement range and QZS payload can be achieved. The obtained QZS can be employed for ultra‐low frequency vibration isolation without sacrificing the loading capacity.
Soft robots have the appealing advantages of being highly flexible and adaptive to complex environments. However, the low‐stiffness nature of the constituent materials makes soft robotic systems ...incompetent in tasks requiring relatively high load capacity. Despite recent attempts to develop stiffness‐tunable soft actuators by employing variable stiffness materials and structures, the reported stiffness‐tunable actuators generally suffer from limitations including slow responses, small deformations, and difficulties in fabrication with microfeatures. This work presents a paradigm to design and manufacture fast‐response, stiffness‐tunable (FRST) soft actuators via hybrid multimaterial 3D printing. The integration of a shape memory polymer layer into the fully printed actuator body enhances its stiffness by up to 120 times without sacrificing flexibility and adaptivity. The printed Joule‐heating circuit and fluidic cooling microchannel enable fast heating and cooling rates and allow the FRST actuator to complete a softening–stiffening cycle within 32 s. Numerical simulations are used to optimize the load capacity and thermal rates. The high load capacity and shape adaptivity of the FRST actuator are finally demonstrated by a robotic gripper with three FRST actuators that can grasp and lift objects with arbitrary shapes and various weights spanning from less than 10 g to up to 1.5 kg.
A fast‐response, stiffness‐tunable (FRST) soft actuator is fabricated by hybrid multimaterial 3D printing. Owing to the thermomechanical properties of an embedded shape memory polymer layer, the actuator exhibits flexibility when heated and high stiffness (120 times stiffer than its purely elastomeric counterpart) when cooled. Assisted by Joule‐heating and fluidic cooling, the heating–cooling cycle is completed within 32 s.
Arterial stiffness, a leading marker of risk in hypertension, can be measured at material or structural levels, with the latter combining effects of the geometry and composition of the wall, ...including intramural organization. Numerous studies have shown that structural stiffness predicts outcomes in models that adjust for conventional risk factors. Elastic arteries, nearer to the heart, are most sensitive to effects of blood pressure and age, major determinants of stiffness. Stiffness is usually considered as an index of vascular aging, wherein individuals excessively affected by risk factor exposure represent early vascular aging, whereas those resistant to risk factors represent supernormal vascular aging. Stiffness affects the function of the brain and kidneys by increasing pulsatile loads within their microvascular beds, and the heart by increasing left ventricular systolic load; excessive pressure pulsatility also decreases diastolic pressure, necessary for coronary perfusion. Stiffness promotes inward remodeling of small arteries, which increases resistance, blood pressure, and in turn, central artery stiffness, thus creating an insidious feedback loop. Chronic antihypertensive treatments can reduce stiffness beyond passive reductions due to decreased blood pressure. Preventive drugs, such as lipid-lowering drugs and antidiabetic drugs, have additional effects on stiffness, independent of pressure. Newer anti-inflammatory drugs also have blood pressure independent effects. Reduction of stiffness is expected to confer benefit beyond the lowering of pressure, although this hypothesis is not yet proven. We summarize different steps for making arterial stiffness measurement a keystone in hypertension management and cardiovascular prevention as a whole.
•Deformation generated by dominant load is resisted by key structural stiffness.•Relieve pretension but maintain key structural stiffness constant.•Key structural stiffness is described in the ...eigen-space of tangent stiffness matrix.•Reduced geometrical stiffness is compensated by enhancing elastic stiffness.•Rehabilitate key structural stiffness by adjusting cross-sectional areas of cables.
Cable net structures are generally highly tensioned to resist the deformation induced by external loads, while the peripheral structural members are heavily burdened to balance the pretension. A numerical strategy is proposed to relieve the pretension without changing the structural geometry and deformation by exchanging the stiffness components, i.e., the structural elastic stiffness and geometrical stiffness. Based on the eigen-decomposition of the tangent stiffness matrix, the stiffness resistance to the deformation generated by a dominant load is quantified for any direction of eigenvector. The key structural stiffness is therefore defined and characterized by those eigenvalues and their corresponding eigenvectors with significant stiffness resistances. The contributions to the key structural stiffness are evaluated for the structural elastic stiffness and geometrical stiffness, respectively, and whether the decrease in key structural stiffness due to the pretension reduction can be compensated with the elastic stiffness by changing the cross-sectional areas of cables is analyzed. Then, the variations in isolated or closely spaced eigenvalues and their corresponding eigenvectors are estimated based on the first-order perturbation analysis of the tangent stiffness matrix. The underdetermined system of linear equations between the adjustments of the cross-sectional areas of cables and the expected variation in the key structural stiffness is established, and its least squares solution is employed to minimize the rehabilitation cost of the key structural stiffness. The proposed numerical strategy is applied to rehabilitate the key structural stiffness of an illustrative saddle-shaped cable net structure, whose pretension is proportionally decreased to different levels, by adjusting the cross-sectional areas of cables, and its accuracy and validity are verified. The applicability of the numerical strategy is also discussed in terms of the contribution coefficient of elastic stiffness to the key structural stiffness and the magnitude of pretension reduction.
In this paper, a novel thin-wall milling strategy named “L-stock method” is proposed. The demand of thin walls has continued its increase due to the strict goal setting of reducing carbon emission. ...However, its practical machining method has not changed for a long time even though many measures were proposed in the literature. In the proposed method, the directional relationships between the cutting process and the compliant direction are focused, and plunge milling is applied aggressively, which leaves an “L”-shaped stock material, to increase the workpiece stiffness. The synergetic advantages of the proposed method are verified mainly by experiments.
Human–robot interaction of human augmentation robots presents a considerable challenge in achieving accurate and robust interaction force control. This paper proposes a novel softening nonlinear ...elastic mechanism with continuous adjustability (SNEMA) to address this challenge. The SNEMA achieves softening stiffness behavior through a nonlinear mapping relationship between the lengths of the diamond diagonals. This unique stiffness profile, featuring high stiffness for low output and low stiffness for high output, strikes a balance between the output force range and force resolution. Moreover, the continuous and convenient adjustment of the stiffness profile is realized by utilizing two antagonistic linear springs, enabling optimal stiffness matching for different output force ranges. Bench tests were conducted to validate the stiffness modeling and evaluate the force tracking and interaction performance of the developed SNEMA. Experimental results demonstrate the capability of the SNEMA to achieve precise force control and good collision safety in human–robot interaction. The proposed SNEMA is finally deployed on the Centaur robot to demonstrate its advantages in practical application.
•A softening nonlinear elastic mechanism with continuous adjustability is proposed.•The analytical stiffness model is derived to guide the mechanical design.•Adjustable profiles facilitate stiffness matching across various output force ranges.•Experiments validate the stiffness model, ensuring accurate and robust force control.
A high-static-low-dynamic stiffness (HSLDS) vibration isolator based on a tunable nesting-type electromagnetic negative stiffness (NS) mechanism is presented. The stiffness characteristics of the ...HSLDS system can be tuned by regulating the current in the coil. When the current is zero, the HSLDS system may degenerate into a passive isolator. The distinctive features of this proposed isolation system are demonstrated from two aspects: 1) In contrast to passive isolators, the proposed isolator can further widen the bandwidth of vibration isolation and improve the isolation performance near the natural frequency of the passive system; and 2) compared with certain other electromagnetic isolation systems, the proposed system has a more compact structure, heavier load capacity, and higher NS-generating efficiency. The proposed electromagnetic NS mechanism consists of four permanent magnets and four coil windings. Analytical models of the electromagnetic force and the displacement transmissibility are established. To select an appropriate structural parameter for the prototype, the effects of geometric parameters on transmissibility are discussed from a theoretical viewpoint. The vibration isolation performance of the proposed isolator system is verified, and a tuning strategy is investigated through experiments.
•An improved time-varying mesh stiffness model for a helical gear pair considering axial mesh force component is proposed.•The axial tooth bending stiffness, axial tooth torsional shear stiffness and ...axial gear foundation stiffness models are proposed.•A rapid time-varying mesh stiffness calculation method is established, in which each stiffness components can be obtained by the integration along the gear width.
An improved time-varying mesh stiffness (TVMS) model of a helical gear pair is proposed, in which the total mesh stiffness contains not only the common transverse tooth bending stiffness, transverse tooth shear stiffness, transverse tooth radial compressive stiffness, transverse gear foundation stiffness and Hertzian contact stiffness, but also the axial tooth bending stiffness, axial tooth torsional stiffness and axial gear foundation stiffness proposed in this paper. In addition, a rapid TVMS calculation method is proposed. Considering each stiffness component, the TVMS can be calculated by the integration along the tooth width direction. Then, three cases are applied to validate the developed model. The results demonstrate that the proposed analytical method is accurate, effective and efficient for helical gear pairs and the axial mesh stiffness should be taken into consideration in the TVMS of a helical gear pair. Finally, influences of the helix angle on TVMS are studied. The results show that the improved TVMS model is effective for any helix angle and the traditional TVMS model is only effective under a small helix angle.
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