Parallel Leaf Springs Research Articles

A Novel Piezo Inertia Actuator Utilizing the Transverse Motion of Two Parallel Leaf-Springs.

A novel linear piezo inertia actuator based on the transverse motion principle is proposed. Under the action of the transverse motion of two parallel leaf-springs, the designed piezo inertia actuator can achieve great stroke movements at a fairly high speed. The presented actuator includes a rectangle flexure hinge mechanism (RFHM) with two parallel leaf-springs, a piezo-stack, a base, and a stage. The mechanism construction and operating principle of the piezo inertia actuator are discussed, respectively. To obtain the proper geometry of the RFHM, we have used a commercial finite element program COMSOL. To investigate the output characteristics of the actuator, the relevant experiment tests including loading capacity, voltage characteristic, and frequency characteristic are adopted. The maximum movement speed and the minimum step size are 27.077 mm/s and 32.5 nm, respectively, confirming that the RFHM with two parallel leaf-springs can be used to design a piezo inertia actuator with a high speed and accuracy. Therefore, this actuator can be used in applications with fast positioning and high accuracy.

Design, Modeling, and Evaluation of a Class-A Triaxial Force-Balance Accelerometer of Linear Based Geometry

Abstract A new class-A force-balance accelerometer (FBA) is designed, simulated, and evaluated. The focus of this work was to design a low-cost but high-performance instrument. The FBA has output voltage proportional to ground acceleration, flat response from direct current to 200 Hz, output range ± 10 V differential (40Vpp, peak-to-peak) and sensitivity 2.5 V/g, which provides a ± 4g range. Unlike other well-established designs with rotational pendulum systems and single-coil actuators that present partially nonlinear performance, the proposed design is based on a linear motion spring-mass mechanism with two parallel leaf springs and a double symmetrical magnet-coil force actuator. This architecture ensures that the displacement transducer’s response is linear and that an acting force on the seismic mass is not disturbed by any cross-axial motion. This force depends on displacement only, as imposed by the electronic control circuit, which is implemented on a small high-density printed circuit board (PCB) mounted on top of the mechanical construction. The plates of the variable capacitance displacement transducer consist of ordinary PCBs for cost efficiency. The coils of the force actuator are placed on each side of the moving plate of the capacitive transducer and the magnets are placed on the aluminum rigid frame of the device. The central moving plate of the variable capacitor and the attached force actuator coils, along with some extra aluminum mass, consist the accelerometer’s seismic mass. The performance of the accelerometer is evaluated in terms of earthquake data records and in comparison of its response with that of a commercial FBA with corresponding specifications. The instrument’s self-noise was also measured over a long period of operation and proved to comply with typical FBA application requirements and commercial product standards.

Nonlinear dynamics of new magneto-mechanical oscillator

This study presents modelling and analysis of a new magneto-mechanical (MM) oscillator (Wiercigroch et al., 2020), which pays a special attention to mechanical and magnetic nonlinearities for large amplitude responses. The oscillator is comprised of a box structure made of two parallel leaf springs with one end fixed and the other clamped with a proof mass, and an electromagnetic actuator. A solenoid and a permanent magnet are the main parts of the actuator, which acts directly on the proof mass providing an accurate and versatile excitation by varying intensity and frequency of the input current. The new model for a beam of large deflection is based up the constitutive relation of nonlinear beam theory. A new design of the electromagnetic actuator with a pair of identical solenoids and a new concept of quasi-constant force (QCF) are proposed, which aims to generate a nearly constant amplitude force for a constant input current. The mathematical model of the MM oscillator is systematically developed and discussed for different types of excitations depending on designs and parameters of the electromagnetic actuator. The undertaken nonlinear dynamics analysis demonstrates versatility of the electromagnetic actuator to generate a wide spectrum of excitations. The prediction from the modelling were validated by the previous work (Costa et al., 2020). The study exemplify that the electromagnetic actuator provides a wide range of excitation patterns and can be used to study experimentally subtle nonlinear phenomena.

Examination of Tool Shank Structure for the Purpose of Restraint of Chatter Vibration

In turning by engine lathe, it is empirically known that chatter vibration may be suppressed when the cutting tool is mounted upside down on the tool post (hereinafter, this method called ‘upside-down tool mounting method’). This study discusses the suppression mechanism of chatter vibration of this tool mounting in terms of the tool vibration trajectory such as vibration direction and amplitude. Because the translational motion in the height direction of the tool is dominant in upside-down tool mounting, the vibration in the tool axis direction is reduced compared to that of usual tool mounting. The effect suppresses chatter vibration in upside-down tool mounting method. Then, tool shank structures for the normal cutting operations were designed to demonstrate the similar tool vibration trajectory to the cutting opetation with the upside-down tool mounting. A parallel leaf spring structure promotes the translational component in the tool height direction to reduce the chatter vibration. The chatter vibration largely depends on the tool vibration trajectory as well as modal paramters of tool clamping.

Development of precision blank carriage for manufacturing large gratings and echelles

A long-travel positioning device, which combines a ball-screw-driven coarse stage with a fine one, driven by piezoelectric translator, to achieve the long-distance traveling, up to 500 mm, as well as high-precision positioning, is crucial in the field of diffraction grating fabrication at nanometer scale. In this article, we present the design of the fine-feed drive stage with resolution as high as 20 nm and propose a single neuron-based proportional–integral–derivative controller to realize ultra-precision positioning. A high-performance piezoelectric translator is used to drive the mechanism, and the parallel leaf springs are used to guide the moving platform with preload force. A dynamic model of the precision positioning mechanism has been established by considering the Hertzian contact. In addition, the static and dynamic properties are investigated with the laser interferometry tracking methodology. The experimental results indicate that the positioning accuracy of less than 10 nm is obtained with the single neuron-based proportional–integral–derivative controller and also demonstrate the excellent performance of the proposed mechanism and control strategy.

Development of an energy harvesting device with a contactless plucking mechanism driven by a skeletal muscle

We propose an energy harvesting device driven by the contraction of an electrically-stimulated skeletal muscle that can be used as an alternative to batteries for implantable medical devices. In order to realize a durable generator, this device has a contactless plucking mechanism comprising parallel leaf springs and magnets, with which the generator can be driven without friction. By utilizing this mechanism, the generator can be driven not only in the contraction phase of the muscle, but also during relaxation. For the design we optimized the stiffness of the springs, the gap between the magnets, and the magnetic circuit in order to maximize the power generated. The power generated by a prototype in a benchtop experiment was 35.8 μW, which is sufficient to drive an implantable medical device. Furthermore, we evaluated the power generated in an ex-vivo experiment in which the gastrocnemius muscle of a toad weighing 193.4 g was electrically stimulated to drive the mechanism. In this experiment, 18.1 μW of power was generated from a skeletal muscle weighing only 3.5 g. It was also confirmed that the power generated exceeded the power required to electrically stimulate the skeletal muscle. The results showed the feasibility of an energy harvesting system utilizing the proposed mechanism.

A Subnano-g Electrostatic Force-Rebalanced Flexure Accelerometer for Gravity Gradient Instruments.

A subnano-g electrostatic force-rebalanced flexure accelerometer is designed for the rotating accelerometer gravity gradient instrument. This accelerometer has a large proof mass, which is supported inversely by two pairs of parallel leaf springs and is centered between two fixed capacitor plates. This novel design enables the proof mass to move exactly along the sensitive direction and exhibits a high rejection ratio at its cross-axis directions. Benefiting from large proof mass, high vacuum packaging, and air-tight sealing, the thermal Brownian noise of the accelerometer is lowered down to less than 0.2 with a quality factor of 15 and a natural resonant frequency of about . The accelerometer’s designed measurement range is about ±1 mg. Based on the correlation analysis between a commercial triaxial seismometer and our accelerometer, the demonstrated self-noise of our accelerometers is reduced to lower than 0.3 over the frequency ranging from 0.2 to 2 Hz, which meets the requirement of the rotating accelerometer gravity gradiometer.

電気刺激による筋収縮を駆動源とした体内発電機構の研究

We proposed an active in vivo power generation system using electrical muscle stimulation as an alternative to an implanted battery and a-transcutaneous drive line. In this system, skeletal muscle contraction generated by applying electrical stimulation was used to drive a power generator. In this paper, an electromagnetic induction type one was designed to be compact, durable and efficient. The muscle contraction is transmitted to an oscillator supported by parallel leaf springs through a non-contact clutch mechanism using magnetic force. The experimental electric power generation was 20.9 μW, and the energy efficiency was 24.7%.

Isotropic springs based on parallel flexure stages

We define isotropic springs to be central springs having the same restoring force in all directions. In previous work, we showed that isotropic springs can be advantageously applied to horological time bases since they can be used to eliminate the escapement mechanism [7]. This paper presents our designs based on planar serial 2-DOF linear isotropic springs. We propose two architectures, both based on parallel leaf springs, then evaluate their isotropy defect using firstly an analytic model, secondly finite element analysis and thirdly experimental data measured from physical prototypes. Using these results, we analyze the isotropy defect in terms of displacement, radial distance, angular separation, stiffness and linearity. Based on this analysis, we propose improved architectures stacking in parallel or in series duplicate copies of the original mechanisms rotated at specific angles to cancel isotropy defect. We show that using the mechanisms in pairs reduces isotropy defect by one to two orders of magnitude.

Effect of yaw angle misalignment on brake noise and brake time in a pad-on-disc-type apparatus with unidirectional compliance for pad support

A pad-on-disc-type brake apparatus was constructed based on a theoretical principle for suppressing frictional vibration. The pad for this apparatus was supported by parallel leaf springs with a unidirectional compliance. Braking tests were conducted using the apparatus under a constant normal load. It has been found that a yaw angle misalignment between the directions of the pad and disc motions provides a positive damping to suppress the frictional vibration and brake noise. In addition, it has been also found that when an appropriate misalignment angle is selected, a low-noise performance and a good braking performance can be achieved simultaneously.

STIFFNESS ANALYSIS OF TWO COMPLIANT PIVOTS USED IN SERIES ELASTIC ACTUATORS

A compliant pivot used in series elastic actuators (SEAs) can be of great practical use for saving structure space. The analysis of load-deflection behavior for such pivots can provide an analytical mechanical design method. In this paper, two pivots are proposed for the corresponding implementation. Based on the Awtar accurate approximations, the two annulus compliant pivots are further simplified to linear stiffness behavior for the SEAs applications. Specifically, an annulus compliant pivot based on parallel leaf-springs is firstly analyzed. After that, we focus on a special kind of annulus compliant pivot whose degree of constraint (DOC) was released. Finally, the accuracy characteristics of the models are identified by comparing with the results obtained by nonlinear finite element analysis.

Structure Design of 2D Convert Probe by Single-Sensor

A 2-D convert micrometer probe by single-sensor for gear measurement. One group of parallel leaf springs was used as the micro-movement guide rail. A precise transducer was used as the detector and a special slope is used as conversion device. The gear’s tangential measurement and radial measurement can be achieved by only one sensor. In this paper, the overall structure of the probe was studied. Using geometry method, probe’s radial displacement caused by tangential measurement in the structure of parallel leaf springs was analyzed and the probe’s two-dimensional convert structure was discussed.

Holding and Preloading Mechanism Using a Buckling Parallel Leaf Spring for Ultrasonic Linear Motor

To increase the applicability of ultrasonic linear motors, we have developed a holding mechanism for the transducer using parallel leaf springs. The present mechanism is compact since the parallel leaf spring structure has functions for both holding and preloading at the same time. Also, a special design for the spring characteristics provides a non-linear load-displacement region with buckling phenomena. These results in a constant preload for some range of the displacement, then the motor performance does not alter even after abrasion of contact surfaces. In this report, the relationship between the dimension of the leaf spring and the force-displacement curves was investigated in order to obtain the design appropriate for constant preloading. Moreover, the effect of the vibration reduction by the holding mechanism was investigated theoretically and experimentally. The vibration reduction was as small as less than 10 % since the stiffness in terms of the vibration direction was relatively small. Finally, the dynamic responses of the motor with the holding mechanism were measured for a sinusoidal control signal. No prominent peak was observed in the motor's responses, however, the motor velocity change was distorted near the natural frequency of the holding mechanism.

Analytical and experimental investigation of a parallel leaf spring guidance

The consequences for the static and dynamic system behaviour of misalignment in an overconstrained direction are analysed. Therefore, a relatively simple parallel leaf spring guidance, which is overdetermined only once, serves as a case to gain insight. A multibody program using flexible beam theory is used to determine the change in vibration mode frequencies and stiffnesses due to misalignment. A previously developed beam element for modelling the leaf springs is shown to be able to describe these phenomena with a limited number of elements. Buckling loads and associated buckling modes are also determined analytically. An instrument has been fabricated to measure the change of vibration mode frequencies due to a rotational misalignment in the overconstrained direction. Experiments using wire spark eroded leaf springs are in good agreement with the calculations. Differences between the experimental and calculated results are attributed to the imperfections in the hardware model, in particular residual stresses, and the assumptions used for the beam element in the numerical model. A small misalignment, in this case 0.8–5.8 mrad, causes strong change of static and dynamic system behaviour. The decreased stiffnesses perpendicular to the compliant direction are disturbing, because these are designed to be large to enhance precision manipulation. The negative effects of overconstrained design are largest if relatively thin and wide leaf springs are used. If the misalignment is kept below 50% of the angle of which a bifurcation occurs, the overconstrained design of the parallel leaf spring mechanism does not significantly influence the system natural frequencies and stiffness.

Thick Film Accelerometers in LTCC Technology—Design Optimization, Fabrication, and Characterization

Diaphragms and beams for force and pressure sensors, e.g., are state of the art in mechanical elements of MEMS in LTCC technology. These elements sustain small strains and small deformations under load. A number of sensor and actuator applications, however, require movable elements that allow higher deformations while the local strains are still low. Springs, accelerometers, actuators, positioners, and valves are examples of such applications. For an accelerometer we developed an approach fabricate leaf springs, integrated into the LTCC technology. The working principle of the accelerometer is based on a seismic mass disposed on two parallel leaf springs that carry piezoresistors connected such that they form a measuring bridge. In the first design optimization step, we used an FEA model for finding an optimized design meeting our sensitivity requirements, inclusiding resonance frequency. In the second step, we made a tolerance analysis that calculates the probability distributions of functional variables from the probability distributions of the design parameters. This enables the probability of a system failure to be deduced. In a final design step, a design of the ceramic thick film accelerometer was calculated that minimizes the system failure probability. As a result we obtained a design optimized with respect to a set of functional requirements and design tolerances. The results of the computations using the FEA models were compared to results of measurement data acquired from prototypes of the accelerometer.

Novel shear tools for viscoelastic characterization of packaging polymers

In order to calculate cure induced stresses, reliable material data is needed over a large modulus range. This paper concerns the derivation of correction equations needed for the interpretation of dynamic mechanical experiments on two different shear tools. For the first shear tool, consisting of an excitator plate sliding between two fixed parallel plates, the effect of the finite clamp stiffness on both the elastic and the viscoelastic modulus components are discussed. It turns out that this shear tool produces reliable results for modulus values in the range from 200 MPa and lower. The second shear tool consists of two parallel leaf springs between which the initially fluid sample is introduced. Clamping of the leaf spring ends and vertical displacement of the center then causes the sample to shear. Exact as well as approximate analytical solutions for the force–displacement relation are derived and are shown to compare well with finite element results. This second shear tool has a typical measuring range for modulus values of 20 MPa and higher.

Structural Analysis of Directional Deflection Beams

Parallel leaf springs are often used for precise linear motion because of their simplicity and freedom from static friction in cases where elasticity and high deformation are required. Using a parallel beam in force sensing requires minimum deflection and limited stress concentration. We previously proposed a unidirectional force sensor based on the H-slit parallel beam structure – an extension of conventional parallel beam. In this paper, we use finite element analysis (FEA) to investigate parallel beam structures that deflect easily in one direction, and evaluate the optimum profile for the notch in the H-slit beam and applications of the parallel beam structure.

Relation Between Friction and Plastic Deformation Examined by Using Periodic Asperity Arrays Fabricated on an AFM Multipurpose Cantilever

The relation between friction force and plastic deformation was determined by using FIB (focused ion beam)-processed multipurpose cantilevers for an AFM (atomic force microscope). First, a multipurpose cantilever consisting of a sliding block, parallel leaf spring, and hinge was made by using an FIB. Then, copper pyramids were rubbed against an unmodified area or periodic asperity arrays fabricated on the cantilever under loads of 23 to 960 nN. Under higher loads (∼900 nN), the friction coefficient measured for an asperity array was lower than that for an unmodified area and decreased with decreasing curvature radius of the asperity peak, and the specific volume change rate increased with decreasing curvature radius of the asperity peak.

Quantitative measurement of sliding friction dynamics at mesoscopic scales: The lateral force apparatus

We describe an apparatus designed to quantitatively measure friction dynamics at the mesoscopic scale. This lateral force apparatus, LFA, uses double parallel leaf springs in leaf-spring units as force transducers and two focus error detection optical heads, optical heads, to measure deflections. The design of the leaf-spring units is new. Normal spring constants are in the range of 20–4000 N/m, and lateral spring constants are 7–1000 N/m. The optical heads combine a 10 nm sensitivity with a useful range of about 100 μm. The proven range of normal forces is 400 nN–150 mN. The leaf-spring units transduce friction and normal forces independently. Absolute values of normal and friction forces are calibrated. Typical errors are less than 10%. The calibration is partly in situ, for the sensitivity of the optical heads, and partly ex situ for the normal and lateral spring constants of the leaf-spring units. There is minimal coupling between the deflection measurements in the lateral and normal directions. This coupling is also calibrated in situ. It is typically 1% and can be as low as 0.25%. This means that the displacements of the tip can be measured accurately in the sliding direction and normal to the surface. Together, these characteristics make the LFA, well suited for quantitative study of friction dynamics at mesoscopic scales. Furthermore the design of the leaf-spring unit allows exchange of tips which may be fabricated (e.g., etched) from wire material (d≈0.4 mm) and can have customized shapes, e.g., polished flat squares. The ability of the LFA to study friction dynamics is briefly illustrated by results of stick-slip measurements on soft polymer surfaces.

Using FIB-processed AFM cantilevers to determine microtribology characteristics

Microtribology characteristics were determined by using a combination of single asperities and three types of FIB (focused ion beam)-processed cantilevers for AFM (atomic force microscope). First, single gold asperities were rubbed with single and parallel leaf springs. For the parallel leaf spring, the pull-off force was proportional to the worn area of the gold asperity peak. The total volume of the gold asperity only slightly changed with rubbing. Second, the friction force on a worn asperity was measured by using a double parallel leaf spring, and the results showed that the friction force was proportional to the sum of the normal load and the pull-off force.