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Keywords = variable stiffness transmission mechanism

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19 pages, 3316 KiB  
Article
Optimization Design of Dynamic Cable Configuration Considering Thermo-Mechanical Coupling Effects
by Ying Li, Guanggen Zou, Suchun Yang, Dongsheng Qiao and Bin Wang
J. Mar. Sci. Eng. 2025, 13(7), 1336; https://doi.org/10.3390/jmse13071336 - 13 Jul 2025
Viewed by 297
Abstract
During operation, dynamic cables endure coupled thermo-mechanical loads (mechanical: tension/bending; thermal: power transmission) that degrade stiffness, amplifying extreme responses and impairing configuration optimization. To address this, this study pioneers a multi-objective optimization framework integrating stiffness characteristics from mechanical/thermo-mechanical analyses, with objectives to minimize [...] Read more.
During operation, dynamic cables endure coupled thermo-mechanical loads (mechanical: tension/bending; thermal: power transmission) that degrade stiffness, amplifying extreme responses and impairing configuration optimization. To address this, this study pioneers a multi-objective optimization framework integrating stiffness characteristics from mechanical/thermo-mechanical analyses, with objectives to minimize dynamic extreme tension and curvature under constraints of global configuration variables and safety thresholds. The framework employs a Radial Basis Function (RBF) surrogate model coupled with NSGA-II algorithm, yielding validated Pareto solutions (≤6.15% max error vs. simulations). Results demonstrate universal reduction in extreme responses across optimized configurations, with the thermo-mechanically optimized solution achieving 20.24% fatigue life enhancement. This work establishes the first methodology quantifying thermo-mechanical coupling effects on offshore cable safety and fatigue performance. This configuration design scheme exhibits better safety during actual service conditions. Full article
(This article belongs to the Special Issue Advanced Studies in Marine Structures)
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25 pages, 7687 KiB  
Article
A Piezoelectric-Actuated Variable Stiffness Miniature Rotary Joint
by Yifan Lu, Yifei Yang, Xiangyu Ma, Ce Chen, Tong Qin, Honghao Yue and Siqi Ma
Materials 2025, 18(14), 3289; https://doi.org/10.3390/ma18143289 - 11 Jul 2025
Viewed by 418
Abstract
With the acceleration of industrialization, deformable mechanisms that can adapt to complex environments have gained widespread applications. Joints serve as carriers for transmitting forces and motions between components, and their stiffness significantly influences the static and dynamic characteristics of deformable mechanisms. A variable [...] Read more.
With the acceleration of industrialization, deformable mechanisms that can adapt to complex environments have gained widespread applications. Joints serve as carriers for transmitting forces and motions between components, and their stiffness significantly influences the static and dynamic characteristics of deformable mechanisms. A variable stiffness joint is crucial for ensuring the safety and reliability of the system, as well as for enhancing environmental adaptability. However, existing variable stiffness joints fail to meet the requirements for miniaturization, lightweight construction, and fast response. This paper proposes a piezoelectric-actuated variable stiffness miniature rotary joint featuring a compact structure, monitorable loading state, and rapid response. Given that the piezoelectric stack expands and contracts when energized, this paper proposes a transmission principle for stiffness adjustment by varying the pressure and friction between active and passive components. This joint utilizes a flexible hinge mechanism for displacement amplification and incorporates a torque sensor based on strain monitoring. A static model is developed based on piezoelectric equations and displacement amplification characteristics, and simulations confirm the feasibility of the stiffness adjustment scheme. The mechanical characteristics of various flexible hinge structures are analyzed, and the effects of piezoelectric actuation capability and external load on stiffness adjustment are examined. The experimental results demonstrate that the joint can adjust stiffness, and the sensor is calibrated using the least squares algorithm to monitor the stress state of the joint in real time. Full article
(This article belongs to the Special Issue Advanced Design and Synthesis in Piezoelectric Smart Materials)
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30 pages, 4288 KiB  
Article
Adaptive Control of the Aerodynamic Flaps of the Savonius Rotor Under Variable Wind Loads
by Alina Fazylova, Kuanysh Alipbayev, Teodor Iliev and Nazgul Kaliyeva
Appl. Sci. 2025, 15(11), 6096; https://doi.org/10.3390/app15116096 - 28 May 2025
Viewed by 416
Abstract
This study presents the development of an adaptive control system for aerodynamic flaps of a two-tier vertical-axis Savonius wind rotor to improve performance under variable wind loads. The approach includes detailed kinematic and dynamic modeling of the flap actuation mechanism, accounting for real-world [...] Read more.
This study presents the development of an adaptive control system for aerodynamic flaps of a two-tier vertical-axis Savonius wind rotor to improve performance under variable wind loads. The approach includes detailed kinematic and dynamic modeling of the flap actuation mechanism, accounting for real-world nonlinearities such as backlash, friction, and impact loads. The mechanical transmission system is analyzed to evaluate the influence of design parameters on system dynamics and control accuracy. A mathematical model of an adaptive PID controller is proposed, capable of real-time adjustment of gain parameters based on external wind torque. Numerical simulations under various wind conditions demonstrate that adaptive tuning significantly enhances system stability, reduces overshoot, and ensures faster response compared to fixed-parameter controllers. Sensitivity analysis confirms the importance of mass distribution, mechanical stiffness, and damping in minimizing vibrations and ensuring durability. The developed system provides a reliable solution for efficient wind energy conversion in dynamic environments, including urban and coastal applications. Full article
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19 pages, 2497 KiB  
Article
Dynamic Motion-Based Optimization of Support and Transmission Mechanisms for Legged Robots
by Kun Zhang, Zhaoyang Cai and Lei Zhang
Biomimetics 2025, 10(3), 173; https://doi.org/10.3390/biomimetics10030173 - 11 Mar 2025
Viewed by 886
Abstract
In order to improve the dynamic performance of legged robots, this paper proposes a method for optimizing the parameters of the leg mechanism based on dynamic motion. The proposed method consists of two key parts as follows: support mechanism optimization and transmission mechanism [...] Read more.
In order to improve the dynamic performance of legged robots, this paper proposes a method for optimizing the parameters of the leg mechanism based on dynamic motion. The proposed method consists of two key parts as follows: support mechanism optimization and transmission mechanism optimization. For the support mechanism, a mechanism analysis index based on robot motion energy is introduced to evaluate the robot dynamic motion performance. Under the structure stiffness constraint, this index can quantitatively analyze the influence of the range of motion and structure mass on the robot motion performance, thereby guiding the design of parameters such as the range of motion, structure thickness, and U-flange position of the mechanism. For the transmission mechanism, this paper optimizes the linkage length and knee joint angle for transmission ratio. Considering the variable transmission ratio and robot motion characteristics, the parameters are optimized to reduce the torque and speed requirements of the leg joint. This method determines the optimal mechanism parameters for dynamic performance based on the specified motion energy requirements, and it also optimizes the linkage length. The results show that the peak torque of the knee joint motor is reduced by 18.5%, and the peak speed is reduced by 24.8%. Full article
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12 pages, 6442 KiB  
Article
Design and Validation of an Improved Rotational Variable Stiffness Mechanism
by Carl Nelson, Kasey Moomau and Yucheng Li
Machines 2025, 13(1), 6; https://doi.org/10.3390/machines13010006 - 25 Dec 2024
Cited by 1 | Viewed by 974
Abstract
In various aspects of robotics, including human–robot interaction, the ability to dynamically adjust the apparent stiffness of an interaction (e.g., between the robot and its environment or between the robot and its payload) has become an important capability. Various means have been developed [...] Read more.
In various aspects of robotics, including human–robot interaction, the ability to dynamically adjust the apparent stiffness of an interaction (e.g., between the robot and its environment or between the robot and its payload) has become an important capability. Various means have been developed in recent years to achieve this, notable among them the so-called variable lever devices. In this paper, we present a new variable lever mechanism based on a gear–rack pair. This unique design combines the functionality of the lever itself with that of the stiffness-adjustment transmission. We show through simulations and hardware experiments the relatively large resulting range of achievable stiffness adjustment and efficient operation. Full article
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16 pages, 6732 KiB  
Article
Study on Structural Parameter Sensitivity and the Force Transmission Mechanism of Steel–Concrete Joints in Hybrid Beam Bridges
by Lijun Jia, Shanshan Yuan, Jiawei Li, Tingying Wu, Gangyi Zhan and Huiteng Pei
Buildings 2024, 14(3), 708; https://doi.org/10.3390/buildings14030708 - 6 Mar 2024
Cited by 1 | Viewed by 1239
Abstract
In this study, a refined model of the Shanghai Damaogang Bridge’s (hybrid beam type) box deck joints is established. The correctness of the model is verified by construction monitoring. For the front and back bearing plates, the force performance of the joint members [...] Read more.
In this study, a refined model of the Shanghai Damaogang Bridge’s (hybrid beam type) box deck joints is established. The correctness of the model is verified by construction monitoring. For the front and back bearing plates, the force performance of the joint members under the most unfavorable loads is investigated, and the force transmission mechanism is analyzed. The influence of the bearing plate thickness and the joints’ stiffness on the stress distribution of the joint members, the internal force of the joints, and the force-transfer efficiency is investigated by the method of controlling variables, and the optimal structural parameters of the nodes are also studied. The results show that, within the proximity of the back bearing plate, the thickness of the back bearing plate affects stress distribution in the joint. The increased stiffness of the welding studs makes the range of shear force along the bridge direction of the top and bottom welding studs larger, and the longitudinal distribution of welding stud shear force is more uneven. The concrete structure bears a higher proportion of the internal force in the joint compared to the steel structure. Full article
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24 pages, 65934 KiB  
Article
A Novel 3D-Printed Negative-Stiffness Lattice Structure with Internal Resonance Characteristics and Tunable Bandgap Properties
by Jiayang Liu and Shu Li
Materials 2023, 16(24), 7669; https://doi.org/10.3390/ma16247669 - 15 Dec 2023
Cited by 4 | Viewed by 2009
Abstract
The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a [...] Read more.
The bandgap tuning potential offered by negative-stiffness lattice structures, characterized by their unique mechanical properties, represents a promising and burgeoning field. The potential of large deformations in lattice structures to transition between stable configurations is explored in this study. This transformation offers a novel method for modifying the frequency range of elastic wave attenuation, simultaneously absorbing energy and effectively generating diverse bandgap ranges. In this paper, an enhanced lattice structure is introduced, building upon the foundation of the normal negative-stiffness lattice structures. The research examined the behavior of the suggested negative-stiffness lattice structures when subjected to uniaxial compression. This included analyzing the dispersion spectra and bandgaps across different states of deformation. It also delved into the effects of geometric parameter changes on bandgap properties. Furthermore, the findings highlight that the normal negative-stiffness lattice structure demonstrates restricted capabilities in attenuating vibrations. In contrast, notable performance improvements are displayed by the improved negative-stiffness lattice structure, featuring distinct energy band structures and variable bandgap ranges in response to differing deformation states. This highlights the feasibility of bandgap tuning through the deformation of negatively stiffened structures. Finally, the overall metamaterial structure is simulated using a unit cell finite element dynamic model, and its vibration transmission properties and frequency response patterns are analyzed. A fresh perspective on the research and design of negative-stiffness lattice structures, particularly focusing on their bandgap tuning capabilities, is offered in this study. Full article
(This article belongs to the Special Issue 3D Printed Functional Lattice Structures)
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20 pages, 37838 KiB  
Article
Research on Self-Stiffness Adjustment of Growth-Controllable Continuum Robot (GCCR) Based on Elastic Force Transmission
by Mingyuan Wang, Jianjun Yuan, Sheng Bao, Liang Du and Shugen Ma
Biomimetics 2023, 8(5), 433; https://doi.org/10.3390/biomimetics8050433 - 18 Sep 2023
Cited by 6 | Viewed by 1959
Abstract
Continuum robots have good adaptability in unstructured and complex environments. However, affected by their inherent nature of flexibility and slender structure, there are challenges in high-precision motion and load. Thus, stiffness adjustment for continuum robots has consistently attracted the attention of researchers. In [...] Read more.
Continuum robots have good adaptability in unstructured and complex environments. However, affected by their inherent nature of flexibility and slender structure, there are challenges in high-precision motion and load. Thus, stiffness adjustment for continuum robots has consistently attracted the attention of researchers. In this paper, a stiffness adjustment mechanism (SAM) is proposed and built in a growth-controllable continuum robot (GCCR) to improve the motion accuracy in variable scale motion. The self-stiffness adjustment is realized by antagonism through cable force transmission during the length change of the continuum robot. With a simple structure, the mechanism has a scarce impact on the weight and mass distribution of the robot and required no independent actuators for stiffness adjustment. Following this, a static model considering gravity and end load is established. The presented theoretical static model is applicable to predict the shape deformations of robots under different loads. The experimental validations showed that the maximum error ratio is within 5.65%. The stiffness of the robot can be enhanced by nearly 79.6%. Full article
(This article belongs to the Special Issue Design and Control of a Bio-Inspired Robot)
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28 pages, 7670 KiB  
Article
Vibration Performance Analysis and Multi-Objective Optimization Design of a Tractor Scissor Seat Suspension System
by Shuai Zhang, Weizhen Wei, Xiaoliang Chen, Liyou Xu and Yuntao Cao
Agriculture 2023, 13(1), 48; https://doi.org/10.3390/agriculture13010048 - 23 Dec 2022
Cited by 12 | Viewed by 3158
Abstract
The combination of characteristic parameters is the key and difficult point to improving the vibration attenuation of scissor seat suspension. This paper proposes a multi-objective optimization method based on entropy weight gray correlation to optimize the combination of characteristic parameters with better vibration [...] Read more.
The combination of characteristic parameters is the key and difficult point to improving the vibration attenuation of scissor seat suspension. This paper proposes a multi-objective optimization method based on entropy weight gray correlation to optimize the combination of characteristic parameters with better vibration attenuation. The differential equation of seat suspension motion is derived through mechanical analysis, and a simplified driver seat suspension single degree of freedom model is constructed. The range of spring stiffness and damper damping is calculated theoretically. Through main effect analysis and analysis of contribution, the main influencing factors of seat suspension vibration attenuation are studied, and the influence correlation of the main factors is analyzed. On this basis, the spring stiffness and damper damping are taken as control variables, and the upper plane acceleration, displacement, and transfer rate of the seat suspension are taken as optimization objectives. The Optimal Latin Hypercube Sampling (OLHS) was used to sample the Design of Experiments (DoE), fit the RBF surrogate model, and screen the optimal solution based on the MNSGA-II algorithm and entropy weight gray relation ranking method. The comparative analysis of the performance before and after optimization shows that the vibration reduction performance response indexes of the acceleration, displacement, and transmissibility of the optimized seats are increased by 66.41%, 2.31%, and 8.19%, respectively. The design and optimization method proposed in this study has a significant effect on the vibration reduction of seats, which provides a reference for the optimization of the vibration reduction performance of seat suspension. Full article
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21 pages, 4540 KiB  
Article
Fatigue Reliability Design Method for Large Aviation Planetary System Considering the Flexibility of the Ring Gear
by Ming Li, Yuan Luo and Liyang Xie
Appl. Sci. 2022, 12(20), 10361; https://doi.org/10.3390/app122010361 - 14 Oct 2022
Cited by 7 | Viewed by 2233
Abstract
As the foundation and core of various heavy aircraft transmission systems, the reliability level of large-scale aviation planetary mechanism restricts the economic affordability and service safety for the aircraft to a great extent. This paper takes the heavy helicopter planetary mechanism as the [...] Read more.
As the foundation and core of various heavy aircraft transmission systems, the reliability level of large-scale aviation planetary mechanism restricts the economic affordability and service safety for the aircraft to a great extent. This paper takes the heavy helicopter planetary mechanism as the research object, and aims to improve the fatigue reliability level of the system. The fatigue load history of the gear teeth under the coupling of global elastic behavior of the system is calculated using a hierarchical finite element method, and the fatigue strength distribution of gear teeth is fitted based on the gear low circumference fatigue test with the minimum order statistics transformation method to provide cost-effective load and strength input variables for the system reliability prediction model. Based on this, a mapping path from the key structural elements of large-scale aviation planetary mechanism to the system reliability indexes is established, and then a new method of reliability-driven multi-objective optimization design for planetary mechanism structural dimensions is proposed. Finally, the influence law of ring gear rim thickness on the fatigue reliability of the planetary gear train is analyzed and the NSGA-Ⅱ genetic algorithm is used to determine the optimal stiffness matching result of the rim size of the designated type of large aviation planetary system. The stiffness potential of the core structural elements is maximized as a way to balance the contradiction between reliability and lightweight requirements of a large aviation planetary system. Full article
(This article belongs to the Special Issue Fracture & Failure Prevent: Reliability, Proactivity and Practice)
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14 pages, 3721 KiB  
Article
Analysis of Vibration Characteristics of Podded Propulsor Shafting Based on Analytical Method
by Yaqi Tian, Cong Zhang, Lei Yang, Wu Ouyang and Xincong Zhou
J. Mar. Sci. Eng. 2022, 10(2), 169; https://doi.org/10.3390/jmse10020169 - 27 Jan 2022
Cited by 8 | Viewed by 3297
Abstract
Podded propulsors are widely used in warships and cruise ships, which have a higher requirement of vibrational and acoustic design. Therefore, studying vibration characteristics and the transmission mechanism of podded propulsor shafting is significant for reducing vibration and ensuring the safe operation of [...] Read more.
Podded propulsors are widely used in warships and cruise ships, which have a higher requirement of vibrational and acoustic design. Therefore, studying vibration characteristics and the transmission mechanism of podded propulsor shafting is significant for reducing vibration and ensuring the safe operation of ships. This paper establishes a model of podded propulsor shafting by analytical method. The shafting is simplified to a heterogeneous variable cross-section beam, while bearings are seen as springs. The podded propulsor shafting has one radial-thrust hybrid bearing and one radial bearing. The excitations from the propeller and cabin are considered. The influences of bearing stiffness, bearing location, and excitation on vibration characteristics of shafting are analyzed. The main conclusions are as follows: Based on the analysis of the area that resonance frequency is sensitive to the change of bearing stiffness, the resonance frequencies of the shafting can be adjusted to the proper range. The large span between hybrid bearing and radial bearing leads to low stiffness of shafting and low resonances frequencies. Under radial excitations, the low vibration always occurs at the hybrid bearing, motor shafting, or propeller end of shafting. This research provides theoretical support for the design and optimization of vibration reduction of podded propulsor shafting. Full article
(This article belongs to the Special Issue Developments in Marine Propulsors)
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14 pages, 6857 KiB  
Article
A 3D-Printed Continuously Variable Transmission for an Electric Vehicle Prototype
by Marcos R. C. Coimbra, Társis P. Barbosa and César M. A. Vasques
Machines 2022, 10(2), 84; https://doi.org/10.3390/machines10020084 - 24 Jan 2022
Cited by 9 | Viewed by 4823
Abstract
This paper aims to present the design of a new 3D-printed continuously variable transmission (CVT) developed for an electric vehicle prototype competing in Shell Eco-marathon electric battery category, a world-wide energy efficiency competition sponsored by Shell. The proposed system is composed of a [...] Read more.
This paper aims to present the design of a new 3D-printed continuously variable transmission (CVT) developed for an electric vehicle prototype competing in Shell Eco-marathon electric battery category, a world-wide energy efficiency competition sponsored by Shell. The proposed system is composed of a polymeric conic geared friction wheel assembled in the motor axle and directly coupled to the rear tire of the vehicle. The conical shape allows to implement a continuous variation of the geared friction wheel diameter in contact with the tire. The motor with the geared friction wheel was mounted over a board with linear bearings, allowing the speed ratio to change by moving the board laterally. A computational simulation model of a prototype electric vehicle with the proposed 3D-printed CVT was created in Matlab/Simulink environment to obtain the traction force in the geared friction wheel and also to analyze the vehicle performance. The simulation results demonstrated possibilities of increasing vehicle speed range output and available torque in the rear traction wheel. Also, it is shown with the simulated model that the designed CVT consumes 10.46% less energy than a fixed transmission ratio, demonstrating the CVT concept’s potential for battery consumption reduction. Lastly, a 3D-printing slicing software with an optimization algorithm plug-in was used to determine the best printing parameters for the conic geared friction wheel based on the tangential force, maximum displacement and safety factor. When compared to the original part with a 100% infill density, the optimized solution reduced the component mass by about 12% while maintaining safe mechanical resistance and stiffness. Full article
(This article belongs to the Special Issue 3D-Printed Machine Elements and Mechanical Devices)
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13 pages, 2711 KiB  
Article
The Effects of Altering the Center of Pressure in Standing Subjects Exposed to Foot-Transmitted Vibration on an Optimized Lumped-Parameter Model of the Foot
by Stefano Marelli, Delphine Chadefaux, Katie Goggins, Tammy Eger, Diego Scaccabarozzi and Marco Tarabini
Vibration 2021, 4(4), 893-905; https://doi.org/10.3390/vibration4040050 - 30 Nov 2021
Cited by 2 | Viewed by 3010
Abstract
Many workers are exposed to foot-transmitted vibration, which can lead to the development of vibration-induced white foot: a debilitating condition with neurological, vascular and osteoarticular symptoms. To design effective prevention mechanisms (i.e., boots and insoles) for isolating workers from vibration exposure, continued model [...] Read more.
Many workers are exposed to foot-transmitted vibration, which can lead to the development of vibration-induced white foot: a debilitating condition with neurological, vascular and osteoarticular symptoms. To design effective prevention mechanisms (i.e., boots and insoles) for isolating workers from vibration exposure, continued model development of the foot’s biodynamic response in different positions is necessary. This study uses a previously developed model of the foot–ankle system (FAS) to investigates how altering the center of pressure (COP) location can change the biodynamic response of the FAS to standing vibration exposure. Formerly published experimental responses for apparent mass and transmissibility at five anatomical locations in three COP positions were used to optimize the model. Differences occurred with the Kelvin–Voigt elements used to represent the soft tissues of the foot sole: at the heel, the distal head of the metatarsals and distal phalanges. The stiffness increased wherever the COP was concentrated (i.e., forward over the toes or backward over the heel). The variability of the model parameters was always greatest when the COP was concentrated in the heel. This suggests future FAS models need to more clearly address how the soft tissue of the plantar fat pad is modelled. Full article
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7 pages, 2733 KiB  
Proceeding Paper
Preliminary Design and Validation of a 3D-Printed Continuously Variable Transmission for an Electric Vehicle Prototype
by Marcos R. C. Coimbra, Társis P. Barbosa and César M. A. Vasques
Eng. Proc. 2021, 11(1), 11; https://doi.org/10.3390/ASEC2021-11178 - 15 Oct 2021
Cited by 2 | Viewed by 1572
Abstract
This article discusses the progress made in developing a new 3D-printed continuously variable transmission (CVT) for an electric vehicle (EV) prototype competing in the Shell Eco-marathon electric battery category, a global energy efficiency competition sponsored by Shell. The proposed system is composed of [...] Read more.
This article discusses the progress made in developing a new 3D-printed continuously variable transmission (CVT) for an electric vehicle (EV) prototype competing in the Shell Eco-marathon electric battery category, a global energy efficiency competition sponsored by Shell. The proposed system is composed of a polymeric conic gear assembled in the motor axle and directly coupled to the rear tire of the vehicle. The conical shape allows to implement a continuous variation of the gear diameter in contact with the tire. The motor with the gear was mounted over a board with linear bearings, allowing the speed ratio to change by moving the board laterally. A 3D-printing slicing software with an optimization algorithm plug-in was used to determine the best printing parameters for the conic gear based on the tangential force, maximum displacement and safety factor. When compared to the original part with a 100% infill density, the optimized solution reduced the component mass by about 12% while maintaining safe mechanical resistance and stiffness. Full article
(This article belongs to the Proceedings of The 2nd International Electronic Conference on Applied Sciences)
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20 pages, 32409 KiB  
Article
Enhancing Vibration Isolation Performance by Exploiting Novel Spring-Bar Mechanism
by Baiyang Shi, Jian Yang and Tianyun Li
Appl. Sci. 2021, 11(19), 8852; https://doi.org/10.3390/app11198852 - 23 Sep 2021
Cited by 8 | Viewed by 3000
Abstract
This study investigates the use of a spring-bar mechanism (SBM) in a vibration suppression system to improve its performance. The SBM, comprising bars and springs, is configured with a conventional linear spring-damper isolator unit. The dynamic response, force transmissibility, and vibration energy flow [...] Read more.
This study investigates the use of a spring-bar mechanism (SBM) in a vibration suppression system to improve its performance. The SBM, comprising bars and springs, is configured with a conventional linear spring-damper isolator unit. The dynamic response, force transmissibility, and vibration energy flow behaviour are studied to evaluate the vibration suppression performance of the integrated system. It is found that the SBM can introduce hardening, softening stiffness, or double-well potential characteristics to the system. By tuning the SBM parameters, constant negative stiffness is achieved so that the natural frequency of the overall system is reduced for enhanced low-frequency vibration isolation. It is also found that the proposed design yields a wider effective isolation range compared to the conventional spring-damper isolator and a previously proposed isolator with a negative stiffness mechanism. The frequency response relation of the force-excited system is derived using the averaging method and elliptical functions. It is also found that the system can exhibit chaotic motions, for which the associated time-averaged power is found to tend to an asymptotic value as the averaging time increases. It is shown that the time-averaged power flow variables can be used as uniform performance indices of nonlinear vibration isolators exhibiting periodic or chaotic motions. It is shown that the SBM can assist in reducing force transmission and input power, thereby expanding the frequency range of vibration attenuations. Full article
(This article belongs to the Special Issue Vibration Problems in Engineering Science—the New Paradigm)
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