Academic literature on the topic 'Force-Position Transducer'

The objective of this study was to investigate the validity of power measurement techniques utilizing various kinematic and kinetic devices during the jump squat (JS), squat (S) and power clean (PC). Ten Division I male athletes were assessed for power output across various intensities: 0, 12, 27, 42, 56, 71, and 85% of one repetition maximum strength (1RM) in the JS and S and 30, 40, 50, 60, 70, 80, and 90% of 1RM in the PC. During the execution of each lift, six different data collection systems were utilized; (1) one linear position transducer (1-LPT); (2) one linear position transducer with the system mass representing the force (1-LPT+MASS); (3) two linear position transducers (2-LPT); (4) the force plate (FP); (5) one linear position transducer and a force plate (1-LPT+FP); (6) two linear position transducers and a force place (2-LPT+FP). Kinetic and kinematic variables calculated using the six methodologies were compared. Vertical power, force, and velocity differed significantly between 2-LPT+FP and 1-LPT, 1-LPT+MASS, 2-LPT, and FP methodologies across various intensities throughout the JS, S, and PC. These differences affected the load–power relationship and resulted in the transfer of the optimal load to a number of different intensities. This examination clearly indicates that data collection and analysis procedures influence the power output calculated as well as the load–power relationship of dynamic lower body movements.

In this paper, the study for the bonding tool position of ultrasonic transducers for thermosonic Flip-Chip LED bonding is presented. Improving the efficiency of ultrasonic transducers plays an important role in the bonding process. To obtain the actual movement of ultrasonic transducer, finite element method ATILA was employed to get more detailed information. To verify the reliability of simulation results, the impedance characteristic and resonance frequency of the transducer mechanical system have been measured using a LCR meter. Moreover, different mounting position of bonding tool on the transducer was studied. Use ATILA to find the best tool position, and vibration amplitude of the tool was measured by Laser Doppeler Vibrometer. Experimental bonding results are verified by in-house shear force test bed.

A sensing device is described which measures the magnitude, direction, and position of force in the plane of the sensor. The basic sensing method is by strain gauge bridges, the outputs of which are amplified and fed via Analogue to Digital (A/D) converters to a microcomputer for calculation of the force characteristics. The transducer system is shown to be capable of measuring quasi static forces; experimental measurements confirming the feasibility of the device. Further research work is planned to improve the accuracy of the system and to ascertain and improve its capability of measuring dynamic forces.

Background: Lower extremity muscle power is critical for daily activities and athletic performance in clinical populations. Objective: The purpose of this study was to determine the reliability and validity of 3 clinically feasible methods to measure lower extremity muscle power during a leg press. Methods: Ten of 26 subjects performed 2 sessions of 5 submaximal leg presses separated by 3-7 days in this repeated-measures cross-sectional design; the remaining performed 1 test session. Power was calculated independently for each method [simple video, linear position transducer, and accelerometer] and compared to the reference force plate. Test-retest reliability was evaluated using intraclass correlation coefficients (ICC). Pearson’s correlation coefficient (r), Bland-Altman plots with 95% limits of agreement (LOA), and mean bias percentages (%) were used to determine relative and absolute validity. Results: Power measures were reliable for all methods (ICC=.97-.99). All were highly correlated with the force plate (r=.96-.98). Mean bias was -0.8% (LOA: -16.57% to 14.98%) (video), -13.21% (LOA: -23.81% to -2.61%) (position transducer) compared to the force plate. Proportional bias was observed for accelerometry. Conclusion: All methods were reliable and highly correlated with the force plate. Only the video and position transducer demonstrated absolute validity. The position transducer was the most feasible method because of its simplicity and accuracy in measuring power.

Force measurement is a science discipline that experiences significant progress with the introduction of new materials and evaluation methods. Many different sensor types, working on different principles, have been developed and reviewed and have found use in medicine as well as many other industries. New trends and demands require a size reduction and simple applicability, with the use of, for example, micro electromechanical systems (MEMS). For purposes of this study, the initial MEMS body is supplemented by its scaled version. Force measurement in this study works on the force to time-delay conversion principle. A compact compliant mechanical body (CCMB) with an embedded parallel resonant circuit (PRC) acting as a transducer realizes the conversion. Depending on the resonant frequency of the transducer (CCMB or MEMS), we have measured the applied force based on the reverse influence of the transducer on the surrounding EM field. The analysis shows that the transducer’s resonant frequency has a detectable reverse influence on the voltage-controlled oscillator (VCO) DC supply current. The force influencing the transducer is determined by the DC supply current ripple position during the VCO frequency sweep. The study presents the method proposal and mathematical analysis, as well as its function verification by simulation and prototype measurements. The proposed principle was validated on a CCMB prototype capable of measuring forces up to ∼2.5 N at a sampling frequency of ∼23 kHz, while the measured time-delay ranges from 14.5 µs to 27.4 µs.

Ultrasonic particle manipulation is a noncontact method for controlling microscale objects, such as cells or microparticles, using an acoustic field. In this study, a 2D array of capacitive micromachined ultrasonic transducers (CMUTs), placed horizontally in immersion, generated ultrasonic waves in the vertical direction, and the oil’s surface increased due to the radiation force of the ultrasonic waves. In addition, the radiation force directly exerted a force on a floating particle. By measuring the movement of the reflected laser light by the moving oil surface, the height of the oil’s surface deformed by the acoustic radiation force (ARF) was measured. The ARF made a floating particle, as well as the oil’s surface, move. The particle moved radially away from the surface position above the transducer, and its velocity was determined by its position on the fluid’s surface. When a single channel was operated, it moved 0.4 mm at an average speed of 90 μm/s, and when two adjacent channels were operated, it moved 1.2 mm at a speed of 272 μm/s. The particles moved in any direction on the surface of the oil by controlling the actuation channel using an electrical switch.

A system is described for collection and processing of data from a cycle ergometer. Cycle pedals, specially made to withstand the extremely high forces exerted during maximal power cycling, contain transducers to measure pedal angle relative to the crank and foot forces both perpendicular and parallel to the pedal surface. An additional transducer monitors crank position. Output signals are conditioned, amplified, digitized by a 12-bit analog-to-digital converter, fed into a computer at 100 Hz/channel, and mathematically smoothed to attenuate noise. For each sample interval, foot force components perpendicular and parallel to the crank arm are calculated. Power generated on each crank revolution is determined from transducer information. Computer graphics display pedaling parameters vs. crank angle in both rectangular and circular format. Data files containing variables descriptive of pedaling force curves are produced to enable computerized statistical analysis of cycling performance.

A novel design concept of multi-degree-of-freedom (multi-DOF) piezoelectric actuator is introduced in the paper. The main idea is to connect two identical piezoelectric transducers by hyperelastic material in order to increase the total number of degrees-of-freedom of the system. Such design principle also allows to separate vibrations of two piezoelectric transducers and to control them independently. The ring- and cylinder-type piezoelectric transducers were used to design two multi-DOF ultrasonic actuators for precise laser beam positioning. Reflecting mirror is mounted on the top of the actuator and is preloaded by magnetic force. Both disc- and cylinder-type actuators can realize up to six degrees-of-freedom, i.e., to rotate the mirror about three axes employing one transducer and to position mirror in the plane by using another transducer. Bidirectional rotation and translation motion of the mirror are obtained by switching excitation signals between different electrodes of the transducers. Both the numerical simulation and physical prototype were used to verify operating principle of the actuators. Numerical investigation of the piezoelectric actuator was performed to investigate modal-frequency and harmonic response analysis while experimental study was performed to measure electrical and mechanical output characteristics of the piezoelectric actuator. A mathematical model of contacting force control was proposed, and numerical verification was performed when the mirror need to be rotated according to the specific motion trajectory.

Eight muscles invest the human tongue: four extrinsic muscles have external origins and insert into the tongue body and four intrinsic muscles originate and terminate within the tongue. Previously, we noted minimal activation of the genioglossus tongue muscle during impeded protrusion tasks (i.e., having subjects push the tongue against a force transducer), suggesting that other muscles play a role in the production of tongue force. Accordingly, we sought to characterize genioglossus tongue muscle activities during impeded and unimpeded protrusion tasks (i.e., having subjects slowly and smoothly move the tongue out of their mouth). Electromyographic (EMG) and single motor-unit potentials of the extrinsic genioglossus muscle were recorded with tungsten microelectrodes and EMG activities of intrinsic tongue muscles were recorded with hook-wire electrodes inserted into the anterior tongue body. Tongue position was detected by an isotonic transducer coupled to the tongue tip. Protrusive force was detected by a force transducer attached to a rigid bar. Genioglossus and intrinsic tongue muscles were simultaneously active in both impeded and unimpeded protrusion tasks. Genioglossus whole muscle EMG and single motor-unit activities changed faithfully as a function of tongue position, with increased discharge associated with protrusion and decreased discharge associated with retraction back to the rest position. In contrast, during the impeded protrusion task drive the genioglossus muscle remained constant as protrusion force increased. Conversely, intrinsic tongue muscle activities appropriately followed changes in both tongue position and force. Importantly, we observed significantly higher levels of intrinsic muscle activity in the impeded protrusion task. These observations suggest that protrusion of the human tongue requires activation of the genioglossus and intrinsic protrudor muscles, with the former more important for establishing anterior–posterior tongue location and the latter playing a greater role in the generation of protrusive force. A biomechanical model of these actions is provided and discussed.

Background: The intensity or load of a strength training exercise is commonly considered to be the most important factor contributing to muscular strength and power. Traditionally in strength training, intensity is defined as the percentage of the maximum weight that can be lifted once i.e. 1 repetition maximum. For power development exercises, the velocity can be used to measure the intensity. A linear position transducer is able to measure kinetic and kinematic variables. Velocity-based training refers to the usage of a linear position transducer to track movement velocity of an exercise and thus, using velocity, rather than load, as a measurement of intensity. Purpose: The purpose of this systematic review was to provide an analysis of the existing velocity-based training research utilizing a linear position transducer. The study also aimed to investigate the validity and reliability of different commercial linear position transducers for kinetic and kinematic measurements.   Method: A systematic review was conducted from 19 studies on velocity-based training that met the selection criteria and underwent a quality assessment. Results: It was possible to predict the 1 repetition maximum using velocity and the minimal velocity threshold was stable across different relative intensities. Performing squats at either maximal velocity, or stopping at a velocity loss of <40% could significantly improve 1 repetition maximum, increase mean velocity during a set of squats as well as vertical jump performance. Two linear position transducer were found to have excellent validity and reliability for both kinetic and kinematic measurements. Conclusion: Velocity-based training was beneficial for enhancing neuromuscular adaptions and could be used to predict the 1 repetition maximum. When using of a linear position transducer for power development, it is suggested that it is valid and reliable for both kinetic and kinematic measurements.

Specificity is a key programming principle for optimal transfer of physiological adaptation of training to improved athletic performance. In resistance training, it has long been identified that the closer the mechanical specificity between the training exercise and outcome performance, the greater the transfer of improved capacity. Bilateral resistance exercises are predominately prescribed for the development of maximum strength and are well demonstrated to enhance athletic performance. However, unilateral exercises appear to demonstrate greater specificity to movements such as running and change of direction as these movements are predominantly single leg actions. Nonetheless, the unstable nature and comparatively lower magnitude of external resistance could be theorised to relegate unilateral exercises to be inferior to bilateral exercises and thus of less benefit for enhancing performance. To investigate the differences in transfer between bilateral and unilateral resistance training to athletic performance of sprint acceleration and change of direction, a series of biomechanical and training intervention studies were implemented. The first study established the reliability of the one repetition maximum (1RM) step-up test (Chapter Three). Ten moderately trained participants completed four familiarisation sessions before two repeated strength testing sessions on separate days. Reliability was estimated as the typical error ±90% confidence limits (CL), expressed as a coefficient of variation (CV%) and the intraclass correlation (ICC). The CV% for all comparisons ranged between 2.0% and 5.3% with average of left and right leg CV% less than the smallest worthwhile change. Importantly, the test was deemed reliable to monitor improvements in lower body unilateral strength. Second, the validity and reliability of barbell displacement in heavy back squats was established (Chapter Four). Twelve well-trained rugby players (1RM 90° squat = 196.3 ± 29.2kg) completed two sets of two repetitions at 70%, 80% and 90% of 1RM squats. Barbell displacement was derived from three methods across four load categories (120-129kg, 140-149kg, 160-169kg and 180-189kg) including: 1) Linear Position Transducer attached 65cm left of barbell centre, 2) 3D motion analysis tracking of markers attached to either end of the barbell, and 3) cervical marker (C7) (criterion measurement). Validity was calculated using typical error of the estimate as CV% ±90% CL, mean bias as a percentage and Pearson product moment correlation (r). Intraday reliability was calculated using ICC and the typical error expressed as CV% ±90% CL. Laterality of marker position increased bias between the criterion measure (C7) and predicted measures (LPT bias = 0.9-1.5%; r = 0.96-0.98; barbell ends bias = 4.9-11.2%; r = 0.71-0.97). Moderate reliability was obtained for most measures of barbell displacement (All loads: LPT: CV% = 6.6%, ICC = 0.67; barbell ends: CV% = 5.9- 7.2%, ICC = 0.55-0.67; C7: CV% = 6.6%, ICC = 0.62). Due to a combination of heavy external barbell load and the pliant nature of the barbell, overestimation can occur with increasing external load and as the position tracking location moves laterally (barbell ends). The linear position transducer demonstrated high validity to the criterion and high trial-to-trial reliability. Completing methodological rigour, within-session reliability of kinetic and kinematic variables of the squat and step-up were investigated (Chapters Five to Eight). Fifteen welltrained rugby players completed two testing sessions. Session one involved squat and step-up 1RM strength testing. Session two involved four maximal repetitions of squat and step-up at 70%, 80% and 90% 1RM assessed by three-dimensional motion analysis and in-ground triaxial force plates. Reliability was calculated for each load range using CV% ±90% CL and ICC. Across all load ranges squat and step-up peak and average ground reaction force (GRF) and total concentric impulse were found to have acceptable measures of reliability below 10% and ICC above 0.85. The majority of loads for squat and step-up displacement, concentric duration, and maximum knee flexion angle were reliable (CV% < 10%, ICC > 0.75). For the squat, measures of peak and average velocity were reliable (CV < 10%) whilst step-up velocity measures were less reliable (CV%0.60). Reliability findings permitted confident interpretation of key variables of squat and step-up performance and application to training. A comparison of kinetics and kinematics between squat and step-up were conducted to provide insight for potential training application. In-ground tri-axial force plates and threedimensional motion analysis were used to capture force output and movement patterns of four maximal efforts of squats and step-ups at 70%, 80% and 90% of 1RM. The concentric phase kinetics and kinematics of each exercise were analysed using effect sizes (ES ± 90% confidence limits). Large to very large differences in peak and average GRF per leg were found for the step-up compared to the squat at all loads (Peak GRF ES: 2.56 ± 0.19 to 2.70 ± 0.37; Average GRF ES: 1.45 ± 0.27 to 1.48 ± 0.29). Additionally, per leg, the squat was inferior to the stepup for impulse at 70% (0.71 ± 0.40) and 80% (0.30 ± 0.41). The difference at 90% 1RM was unclear. Peak velocity was greater for the squat compared to the step-up across all loads squat produced large differences in peak velocity at all loads (ES = -1.74 ± 0.48 to -1.33 ± 0.48). The comparable GRF per leg between step-up and squat suggests overload sufficient for strength development in the step-up, despite a lower absolute magnitude of external resistance. Although appearing to provide sufficient overload for strength development, a training study was designed to determine the practical application of resisted step-ups on strength development and measures of speed and change of direction performance. The final study recruited academy level rugby players (age = 23.1 ± 4.3 years, mean training age = 5.4 ± 2.9 years; 1RM 90° squat = 178 ± 27 kg) assigned to one of two groups – a bilateral (BIL) training group or a unilateral (UNI) training group. Subjects completed a comprehensive 18-week program involving a familiarisation, training and maintenance phases. Back squat and step-up strength testing was analysed for within- and between-group differences using ES ± 90% CL. Both intervention groups showed practically important within group improvements in their primary exercise during the training phase (ES ± 90% CL: BIL = 0.79 ± 0.40; UNI = 0.63 ± 0.17) with transfer to their non-trained resistance exercise (BIL stepup = 0.22 ± 0.37: UNI squat = 0.44 ± 0.39). Between groups, the improvement in squat 1RM was unclear (ES = -0.34 ± 0.55), however unilateral resistance training showed an advantage to step-up 1RM (ES = 0.41 ± 0.36). The bilateral and unilateral training groups improved 20m sprint (ES: BIL = -0.38 ± 0.49; UNI = -0.31 ± 0.31), however the difference between the groups was unclear (ES = 0.07 ± 0.58). Whilst both groups had meaningful improvements in COD (BIL COD average = -0.97 ± 0.32: UNI squat = -0.50 ± 0.54), bilateral resistance training had a greater transfer to COD performance than unilateral (between groups ES = 0.72 ± 0.55). As such, practically important increases in lower body strength can be achieved with bilateral or unilateral resistance training. Whilst increases in strength positively improved sprint acceleration, the BIL group demonstrated superior improvements in COD perhaps due to the limited eccentric training stimulus of the step-up exercise. This demonstrates the importance of targeting the underlying physiological stimulus for adaptation and not purely likeness of movement specificity of the target performance. The research sought to address specificity and transfer of training as it pertains to bilateral and unilateral lower body resistance training. The results demonstrate that high GRF is produced per leg, comparable between the squat and step-up suggesting sufficient strength development stimulus of the step-up. Differences in total concentric impulse and velocity may provide variable training applications of either exercise. When incorporated into a resistance training program, unilateral and bilateral exercises can develop maximum strength. Importantly, strength development was demonstrated in the performance of the non-trained bilateral or unilateral exercise, demonstrating a level of transfer. Further, the training study revealed that sprint acceleration over 20m can be developed using either squat or step-up. However, whilst both groups improved COD performance, squat training had a superior transfer to COD than step-up training. This suggests that step-up training may sufficiently improve lower body strength and acceleration, however, the application to COD performance may require additional training stimulus to enhance adaptation potentially due to the lack of eccentric overload in the step-up.

STUDY 1: RELIABILITY OF PERFORMANCE MEASUREMENTS DERIVED FROM GROUND REACTION FORCE DATA DURING COUNTERMOVEMENT JUMP AND INFLUENCE OF SAMPLING FREQUENCY. STUDY 2: COMPARISON OF FOUR DIFFERENT METHODS TO MEASURE POWER OUTPUT DURING THE HANG POWER CLEAN AND THE WEIGHTED JUMP SQUAT. STUDY 3: DOES PERFORMANCE OF HANG POWER CLEAN DIFFERENTIATE PERFORMANCE OF JUMPING, SPRINTING, AND CHANGING OF DIRECTION? STUDY 4: COMPARISON OF WEIGHTED JUMP SQUAT TRAINING WITH AND WITHOUT ECCENTRIC BRAKING.

With improvements in actuation technology and sensory systems, it is becoming increasingly feasible to create powered exoskeletal garments that can assist with the movement of human limbs. This class of robotics referred to as human-machine interfaces will one day be used for the rehabilitation of paralysed, damaged or weak upper and lower extremities. The focus of this project was the development of an exoskeletal interface for the rehabilitation of the hands. A novel sensor was designed for use in such a device. The sensor uses simple optical mechanisms centred on a spring to measure force and position simultaneously. In addition, the sensor introduces an elastic element between the actuator and its corresponding hand joint. This will allow series elastic actuation (SEA) to improve control and safely of the system. The Hand Rehabilitation Device requires multiple actuators. To stay within volume and weight constraints, it is therefore imperative to reduce the size, mass and efficiency of each actuator without losing power. A method was devised that allows small efficient actuating subunits to work together and produce a combined collective output. This work summation method was successfully implemented with Shape Memory Alloy (SMA) based actuators. The actuation, sensory, control system and human-machine interface concepts proposed were evaluated together using a single-joint electromechanical harness. This experimental setup was used with volunteer subjects to assess the potentials of a full-hand device to be used for therapy, assessment and function of the hand. The Rehabilitation Glove aims to bring significant new benefits for improving hand function, an important aspect of human independence. Furthermore, the developments in this project may one day be used for other parts of the body helping bring human-machine interface technology into the fields of rehabilitation and therapy.

Doctor of Philosophy (PhD)
With improvements in actuation technology and sensory systems, it is becoming increasingly feasible to create powered exoskeletal garments that can assist with the movement of human limbs. This class of robotics referred to as human-machine interfaces will one day be used for the rehabilitation of paralysed, damaged or weak upper and lower extremities. The focus of this project was the development of an exoskeletal interface for the rehabilitation of the hands. A novel sensor was designed for use in such a device. The sensor uses simple optical mechanisms centred on a spring to measure force and position simultaneously. In addition, the sensor introduces an elastic element between the actuator and its corresponding hand joint. This will allow series elastic actuation (SEA) to improve control and safely of the system. The Hand Rehabilitation Device requires multiple actuators. To stay within volume and weight constraints, it is therefore imperative to reduce the size, mass and efficiency of each actuator without losing power. A method was devised that allows small efficient actuating subunits to work together and produce a combined collective output. This work summation method was successfully implemented with Shape Memory Alloy (SMA) based actuators. The actuation, sensory, control system and human-machine interface concepts proposed were evaluated together using a single-joint electromechanical harness. This experimental setup was used with volunteer subjects to assess the potentials of a full-hand device to be used for therapy, assessment and function of the hand. The Rehabilitation Glove aims to bring significant new benefits for improving hand function, an important aspect of human independence. Furthermore, the developments in this project may one day be used for other parts of the body helping bring human-machine interface technology into the fields of rehabilitation and therapy.

Transducers based on dielectric electroactive polymers (DEAP) offer an attractive balance of work density and electromechanical efficiency. For example in automation and haptic applications, especially multilayer transducers are used to scale up their absolute deformation and force. Depending on the application different transducer controls have to be realized to match the specifications of the particular application. However, analogous to conventional electromechanical drive systems an inner sensor-less force control can be realized for DEAP transducers, too. For this force control the nonlinear relations between voltage and electrostatic pressure as well as the electromechanical coupling have to be considered. The resulting open-loop force control can be used for superimposed motion controls, such as position, vibration and impedance controls. Therefore, within this contribution the authors propose a model-based feedforward force control based on an overall model of the transducer that does not require any force measurement. Finally, the derived open-loop force control interface is experimentally validated using in-house developed DEAP stack-transducers and driving power electronics.

The thin faceplate adaptive secondary mirrors are controlled by means of electromagnetic force actuators, which seem to be a suitable choice in terms of stroke, accuracy and cost [Del Vecchio, Gallieni et al.; Biasi, Gallieni et al. in this Conference]. Those actuators need a local control loop to achieve a linear position response. The position sensor is definitely a crucial component of this control loop: both high sensitivity and high speed have to be achieved at same time.

The article deals with the architecture, performance, and experimental tests of a test bench for servo-actuators used in flight controls. After the state of the art on the subject, the innovative architecture of the built bench is described, in which flight control actuator under test and load actuator are not in line but mounted perpendicularly. The model of the bench actuating systems is then presented, consisting of the servo-controlled hydraulic actuator, load cell, speed transducer, angular position transducer of the coupling and pressure transducers. For each of these components the nonlinear multi-physics mechatronic model is described, according to the adopted solutions. The adopted force control algorithm is discussed, showing the integrative compensation on the action line and proportional-derivative on the feedback, with speed feedforward. The experimental tests carried out on the bench under stalled conditions are also presented, whose results concerning time and frequency responses are compared with those obtained through the linearized and non-linear numerical model. Finally, the non-linear models of the flight control actuator under test, controlled in position, and of the loading servo-actuator of the bench are joined together, and the results of various simulations are described.

In this paper a novel electrostatic MEMS combined shock sensor and normally-closed switch is presented. The switch uses combined attractive and repulsive forcing to toggle a cantilever beam to and from the pulled-in position. The attractive force is generated through a parallel plate electrode configuration and induces pull-in. The repulsive force is generated through electrostatic levitation from a third electrode and serves to pull the beam out of its pulled-in position. A triboelectric transducer converts impact energy to electrical energy to provide voltage for the third electrode, which temporarily opens the switch if enough impact energy is supplied. Triboelectricity addresses the high voltage requirement for electrostatic levitation. The multi-electrode sensor also addresses the low current output from the generator because it acts as an open circuit between the parallel plate and levitation electrodes. A theoretical model of the switch is derived to analyze stability and the dynamic response of the cantilever. Threshold voltages to pull-in and release the beam through repulsive forcing is calculated. Output voltage plots from a prototype generator under a single impact are applied to the sensor-switch model to demonstrate the working principle of the sensor-switch is feasible.

The majority of oil and refined-product pipelines in Brazil have their protection system designs based on spring-type pressure relief valves. Thus, the proper design and operation of these valves is essential to ensure the safety of transport pipelines and loading/unloading terminals during any abnormal operation conditions that generate a surge pressure. In simple terms, these valves have a disk which is pressed by a spring against the inlet nozzle of the valve. When the pressure rises, the force generated on the surface of the disc increases and, depending on the pressure relief valve set point, the force due to pressure overcomes the force exerted by the spring, causing the disk to rise and discharge the fluid through the outlet nozzle to the relief line, reducing the pressure level within the pipeline. Despite its importance, most commercial applications do not present a specific model to simulate the transient behavior of pressure relief valves. This paper presents an experimental study aimed at determining the dynamic behavior of a commercial spring-type relief valve. The valve was installed in a pipe loop instrumented with pressure and flow transducers. The transient motion of the valve disc was measured with a fast-response displacement transducer. The transient in the flow loop was generated by the controlled closing of a block valve positioned downstream of the relief valve. The recorded transient data for disc position, upstream and downstream pressures, and discharge flow rates were used to compute the discharge coefficient as a function of opening fraction and the opening fraction as a function of time. Simulation models based on a spring-mass damped system were developed and implemented in a PID-actuator-control valve system. The systems were implemented in a commercial pipeline simulation program modeling the experimental loop employed in the tests. The numerical and experimental data of the block valve closure transient were compared displaying good agreement. Simulations results employing a generic relief valve model frequently used in simulations were also obtained revealing problems associated with this approach.

Converted energy from ambient loading in civil and mechanical structures is typically used as a viable alternative. Although, piezoelectric vibration harvesters have been widely used given their energy conversion ability, these elements exhibit a narrow natural frequency response range, thus considerably limiting the levels of harvestable power. Recently our group has introduced the concept of using mechanically-equivalent frequency modulators that can transform the low-amplitude and low-rate service and ambient deformations into an amplified input to the piezoelectric transducer. The introduced methods allow energy generation and conversion within the unexplored quasi-static frequency range (≪ 1 Hz). The post-buckling behavior of bilaterally constrained columns was used for frequency up-conversion, and piezoelectric cantilever beams, attached to the columns, were used for energy conversion. The introduced concept was experimentally validated and finite element simulations were developed to evaluate the effect of system parameters (stiffness, thickness, and walls gap) on the position of the snap-through transition events and the levels of force-displacement at the multiple-equilibrium configurations. It was shown that the considered system parameters can determine the absolute levels of force and displacement, but they offer limited control on the number and the relative spacing between the energy-drop events. This paper shows that the combination of multiple slender elastic columns modulators, in parallel configurations, allows for the tailoring of the number and magnitude of the mode branch switching during the postbuckling response of the complete system. Experimental and numerical results are presented to validate the proposed concept.