Spherical Hinge Research Articles

Fine analysis and size optimization of spherical hinge in swivel construction

Contact stress and friction torque are the two primary mechanical responses of a spherical hinge. In general engineering practice, the calculation methods for contact stress and friction in spherical hinges often involve simplifying the spherical hinge into a planar hinge. To accurately analyze the stress state of the spherical hinge, it is essential to establish a detailed model. In this study, 17 groups of spherical hinge models were developed. The support radius, curvature radius, and thickness of the spherical hinge are considered influencing factors, while the maximum contact stress, friction torque, and amount of steel used are treated as responses. A three-factor, three-level, and three-response design is implemented. Using the response surface method, optimization design is conducted, resulting in two proposed optimization schemes. The maximum contact stress is reduced by 40.10% and 10.91%, respectively, while the friction torque is decreased by 0.82% and 26.50%, respectively. The maximum error between the predicted and calculated values is 7.04%. This indicates that the model presented in this study possesses sufficient predictive accuracy and can effectively guide the selection of spherical hinge dimensions.

Investigation on load - transfer characteristics of spherical hinge structure of swivel bridge based on scale distortion model

The mechanical properties of the swivel spherical hinge, a critical component in swivel bridge structures, remain inadequately understood. This study precisely examines the load-transfer characteristics of the swivel spherical hinge using a combination of finite element simulation and scaled model loading tests. An optimized hinge model, accounting for distortion effects and strategic placement of measurement points, was constructed and tested in the laboratory. Results indicate that the scaled model exhibited consistent elastic deformation, ensuring structural integrity and stability. The results indicate that under a 122 kN load, the average discrepancy between the experimental data and numerical predictions was only 1.53 %, highlighting the numerical model's accuracy and reliability. Additionally, the center of the slider experienced a compressive stress of approximately 2.7 MPa, while the edge endured 5.3 MPa, reflecting a non-uniform load distribution. Stress concentrations at the slider's projection were 2–5 times greater than at other measurement points on the steel-concrete interface of the hinges. The lower spherical hinge surface displayed a complex stress pattern combining tensile and compressive stresses, resulting from slider compression and hinge surface expansion. This research provides valuable insights into the load-transfer mechanisms of swivel spherical hinges, offering guidance for the design and construction of swivel bridges.

Design and tension distribution optimization of a 9-DOF cable-driven parallel spray-painting robot with 3 degrees of redundancy

This paper presents a 9-DOF cable-driven parallel spray-painting robot (CDPSR) with 3 ° of redundancy (DORs) for automated spraying on large, curved surfaces and proposes a feasible cable tension region (FCTR) calculation algorithm for multi-redundant robots. The end effector of the CDPSR consists of two moving platforms connected by a spherical hinge and driven by 12 cables, enabling 9 DOFs of motion (3 for translation and 6 for rotation). Given that the CDPSR has three DORs, a multi-dimensional FCTR vertex calculation algorithm is introduced. The FCTR is an adjacent, continuous, and closed convex hull in every dimension; therefore, the vertices of the FCTR can be determined sequentially and dimensionally. For DOR=3, the vertices on one face of the convex polyhedron are first determined and then extended to adjacent faces until the polyhedron is closed. An experimental prototype of the proposed robot was constructed and experiments on spray trajectory planning and FCTR calculation validation were conducted. The results of the simulations and experiments verified the motion performance of the CDPSR and the accuracy and efficiency of the FCTR calculation algorithm.

Про стійкість обертання вільної системи двох пружно зв’язаних гіроскопів Лагранжа, один з яких має ідеальну рідину

On the basis of the known equations of motion of the system of coupled gyrostats by P. V. Kharlamov and the state function by S. L. Sobolev, the equations of rotation of a free system of two elastically coupled Lagrange gyroscopes were derived, one of which has an arbitrary axisymmetric cavity completely filled with an ideal incompressible fluid. The rigid bodies are connected by an elastic restoring spherical hinge. A transcendental characteristic equation of the perturbed uniform rotation of the mechanical system under consideration is derived. Taking into account the fundamental tone of the fluid oscillation, a characteristic equation of the fifth order is obtained. On the basis of the Liénard – Chipart criterion written in the inor form, the necessary conditions for the stability of the uniform rotation of the Lagrange gyroscopes and the fluid are written out as a system of four inequalities. With respect to the elasticity coefficient, these inequalities have degrees 1, 3, 6 and 8, respectively. Analytical studies of the leading coefficients of these stability conditions are carried out. It is shown that when the center of mass of the first solid body with liquid or the second does not coincide with the common point of these bodies, then at sufficiently large values of the elasticity coefficient the necessary stability conditions will always be satisfied. In the absence of elasticity in the hinge, the characteristic equation has a double zero root and in this case the stability conditions require additional studies. The obtained stability conditions are exact for an ellipsoidal cavity and approximate for other axisymmetric cavities. To clarify the obtained glass conditions for these voids, it is necessary to take into account additional tones of oscillation of an ideal liquid.

Numerical and experimental investigations on influence of spherical hinge mandrel on deformation characteristics of large diameter tube in small-radius NC rotary bending

Numerical and experimental investigations on influence of spherical hinge mandrel on deformation characteristics of large diameter tube in small-radius NC rotary bending

Origin and tuning of bandgap in chiral phononic crystals

The wave equation revealing the wave propagation in chiral phononic crystals, established through force equilibrium law, conceals the underlying physical information, such as the essence of the motion coupling and the inertial amplification effect. This has led to a controversy over the bandgap mechanism. In this article, we theoretically unveil the reason for this controversy, and put forward an alternative approach from wave behavior to formulate the wave equation, offering an alternative pathway to articulate the bandgap physics directly. Based on the physics revealed by our theory method, we identify the obstacles in coupled acoustic and optic branches to widen and lower the bandgap. Then we introduce an approach based on spherical hinges to decrease the barriers, for customizing the bandgap frequency and width. Finally, we validate our proposal through numerical simulation and experimental demonstration.

Design, modeling, and control of a long stroke compliant tip-tilt-piston micropositioning stage driven by voice coil motors.

In this paper, a long-stroke parallel compliant tip-tilt-piston micropositioning stage driven by voice coil motors (VCMs) is proposed. The stage is equipped with three sets of driving arms, which include a spherical hinge, VCM, and parallelogram guide mechanism, evenly spaced at 120° intervals. The spherical hinge is composed of orthogonal leaf-spring beams, and the VCM is embedded into the parallelogram mechanism to form a compact design. The compliance matrix method and the geometric method facilitated the determination of compliance in all six degree-of-freedom directions of the spherical hinge and the derivation of kinematic equations for decoupling the motion of the stage. In addition, finite element analysis was utilized to determine the maximum stroke and stress of the stage. To validate the proposed design, a stage prototype was constructed and subjected to experimental testing. Furthermore, a feedback controller was designed, integrating proportional integral controller, notch filter, and sliding mode controller feedforward. The experimental results indicate that the stage can achieve a long stroke of ±50.75 mrad × ±44.2 mrad × ±4.425mm, with the natural frequencies in the three-axis direction of 22.3 × 25.5 × 25.5Hz3. In addition, the maximum relative tracking error was maintained below 5.25%, highlighting the effectiveness of the control technique in achieving a high tracking performance.

Friction Characteristics and Lubrication Properties of Spherical Hinge Structure of Swivel Bridge

A spherical hinge structure is a key swivel bridge element that must be considered when evaluating friction characteristics and lubrication properties to meet the rotation requirement. Polytetrafluoroethylene (PTFE)-based spherical hinge sliders and lubrication coating have been employed for over 20 years, but with the growing tonnage of swivel bridge construction, their capacity to accommodate the required lubrication properties can be exceeded. In this manuscript, the optimal friction coefficient of the spherical hinge is obtained through the finite element analysis method. Four lubrication coatings and four spherical hinge sliders are prepared and tested through a self-developed rotation friction coefficient test, four-ball machine test, dynamic shear rheological test, and compression and shear performance test to evaluate the lubrication and friction properties of the spherical hinge structure. The results of the finite element analysis show that the optimum rotation friction coefficient of the spherical hinge structure is 0.031–1.131. The test results illustrate that the friction coefficient, wear scar diameter, maximum non-seize load, phase transition point, and thixotropic ring area of graphene lubrication coating are 0.065, 0.79 mm, 426 N, 14.6%, and 64,878 Pa/s. The graphene lubrication coating has different degrees of improvement compared with conventional polytetrafluoroethylene lubrication coating, showing more excellent lubrication properties, bearing capacity, thixotropy, and structural strength. Compressive and shear tests demonstrate that polyether ether ketone (PEEK) has good compressive and shear mechanical properties. The maximum compressive stress of PEEK is 87.7% higher than conventional PTFE, and the shear strength of PEEK is 6.07 times higher than that of PTFE. The research results can provide significantly greater wear resistance and a lower friction coefficient of the spherical hinge structure, leading to lower traction energy consumption and ensuring smooth and precise bridge rotation.

Compliance and Kinetostatics of a Novel 2PRS-2PSS Compliant Parallel Micromanipulator: Modeling and Analysis.

A novel 2PRS-2PSS (P represents the prismatic pair, R represents the revolute hinge, S represents the spherical hinge) compliant parallel micromanipulator with two translational DOFs and two rotational DOFs is presented, and its compliance model and kinetostatic model are sequentially developed and analyzed. Initially, an analytical model used to describe the compliance of this micromanipulator was developed using the compliance matrix method (CMM). Through a comparison with finite element analysis, the accuracy of this analytical model is confirmed, and the influence of various dimensional and structural parameters on the compliance behavior is investigated. Subsequently, the micromanipulator is treated as an equivalent spring system, allowing for the derivation of its governing equation based on the established compliance model. From this equation, a kinetostatic model relating input forces to output displacements is derived. Validation of this model is performed by comparing analytical results with finite element simulations under specific motion trajectories, revealing a maximum relative error of 6.18%. This close agreement verifies the accuracy of the kinetostatic model. Finally, the impact of the parameters of the flexure hinge on the mapping matrix is examined to offer insights into minimizing undesired displacements, providing valuable guidance for optimizing the micromanipulator's performance.

Design and testing of a high precision parallel manipulator with hyperbolic–elliptic flexure hinges

A novel six-degree-of-freedom (6-DOF) parallel manipulator (PM) with a 6-PSS configuration is designed as a piston error compensation mechanism in an optical system. To meet the high-precision adjustment requirement, the prismatic hinges are driven by nanometer resolution piezoelectric motors, and hyperbolic–elliptic (H-E) flexure hinges are used as spherical hinges because of their zero clearance and greater precision transmission capability than traditional rigid hinges. The analysis of the closed-loop vector relationship of the kinematic chain of the leg results in the construction of the kinematic equation, which can satisfy the inverse kinematic solution within a certain precision. The Newton–Raphson method is used for the iteration to solve the forward kinematics. A kinematic simulation was performed to verify the accuracy and effectiveness of the kinematic model using the rigid–flexible coupling finite element method. The workspace of the PM was analyzed using inverse kinematics and kinematics simulation. Two test systems were constructed to test the working performance of the PM. The experimental tests demonstrated that the resolution reached the nanometer level and the travel reached the millimeter level.

Free and Forced Bending-Torsional Oscillations of an Anisotropic Elongated Plate Fixed on a Spherical Hinge

Free and Forced Bending-Torsional Oscillations of an Anisotropic Elongated Plate Fixed on a Spherical Hinge

An innovative experimental device for characterizing the responses of monopiles subjected to complex lateral loading

Offshore wind turbines are usually founded on monopiles. During the operation period, the structure is subjected to complex lateral loading from wind, wave and current. The soils surrounding those monopiles may deform with increasing the number of loading cycles, leading to tilting of the whole structure; hence, it is vital to carry out physical model tests to examine the long-term performance of monopiles. This study proposes an innovative experimental setup for centrifuge modelling of the response of monopiles under complex lateral loading. Hydraulic actuators are adopted to apply lateral loads on model pile, and electrohydraulic servo-valves and associated controllers are used to achieve a closed loop position or load control. A carefully designed spherical hinge and load bars are used to connect the model pile and actuator shafts. This enables that the pile can rotate freely and can move vertically freely. A centrifuge test on a winged monopole subjected to perpendicular lateral loading was carried out at 100g. The experimental results shed light on pile responses in the cyclic loading and constant loading directions.

RESEARCH ON UNBALANCED WEIGHING EXPERIMENT OF MULTI-POINT BRACED SWIVEL CABLE-STAYED BRIDGE

To guarantee the safety of the swivel process, the weighing experiment before the swivel is especially important. Based on this, this paper takes a twin-tower, double-cable prestressed concrete swivel cable-stayed bridge as the background and suggests a multi-point braced swivel weighing experiment involving the joint force of the arm-brace and the spherical hinge to solve problems such as a particular obstacle in the relying project's swivelling process. Firstly, the relevant weighing experiment formulas for various circumstances were theoretically derived. The field test results were then used to calculate the jacking force at the limit state during the jacking process, which was then substituted into the relevant formulae, and the relevant parameters of the weighing experiment were calculated. Finally, the counterweight is adjusted based on the weighing results to carry out the structural rotation. The angular velocity was stable during the swivelling process, and the structure was successfully swivelled. The successful practice of a multi-point braced swivel weighing experiment involving the joint force of the arm-brace, and the spherical hinge can provide a reference for the design and construction of similar bridges.

Design of a Novel Flexible Spherical Hinge and Its Application in Continuum Robot

Abstract Compliant mechanisms, which can be integrally machined and without assembly, are well suited as joints for continuum robots (CRs), but how to incorporate the advantages of the compliant mechanism into the arm design is a key issue in this work. In this paper, a novel type of flexible spherical-hinged (FSH) joint composed of tetrahedron elements with a fixed virtual remote center of motion (RCM) at the bottom is proposed, and then extended to the CR and end-effector. In the arm design, the error compensation principle is used to offset the parasitic motion of the CR under external load (pressure and torque) and improve the bending and torsional isotropy of the arm through different series combinations, and then the stiffness model of the FSH joint and the statics model of the CR are developed using the 3D chain pseudo-rigid body model (3D-CPRBM) and tested. The results show that the 3D-CPRBM can effectively predict the deformation of the FSH joint and the CR. Moreover, the maximum standard deviation of the bending angle of the FSH joint in each direction is only 0.26 deg, the repeatable positioning accuracy of the CR can reach 0.5 deg, and the end-effector has good gripping ability and self-adaptive capability.

Experimental study on the axial tensile properties of polypropylene fiber reinforced concrete

In order to study the axial tensile properties of polypropylene fiber reinforced concrete, an axial tensile test device for concrete is developed in this paper. The device is composed of three parts: rigid frame, spherical hinge and puller, and specimen fabrication part. The test device can accurately measure the tensile strength and peak tensile strain of concrete, and perfectly solves the eccentricity problem of concrete specimens under tension. It can measure the post peak segment tensile strain, such that the whole process tensile stress–strain curve can be obtained. The axial tensile test of polypropylene fiber concrete was carried out using the above test device, and the results show that the tensile strength of concrete can be clearly improved by adding polypropylene fiber, which makes the tensile failure of concrete show certain plastic characteristics. The test results show that with the increase in fiber content, the tensile strength of concrete increases first and then decreases. The effects of polypropylene fiber content and curing age on the tensile properties of concrete were studied and the optimum polypropylene fiber content was determined. When the fiber content is 0.9 kg/m3, the tensile strength of concrete reaches the maximum value. The splitting tensile test of concrete under the same condition was carried out simultaneously. The damage phenomenon and test results of the axial tensile test and splitting tensile test of concrete were compared and analyzed, and the applicability of the new developed device in the concrete axial tensile test was verified.

Issues of Developing Equal-Strength Two-Layer Spherical Rubber-Metal Hinges

Development of equal-strength two-layer spherical rubber­metal hinges (RMH), described in the paper, is associated with the problem that with an equal thickness of the layers of rubber bushings and an equal opening angle, there is a significant difference in their radial stiffness and relative deformation of the rubber. With hinge dimensions corresponding to those of the hinges used in the undercarriage of locomotives, there is a difference in relative deformation of inner and outer bushings by about 1,5 times. As a result, it is proposed to determine the load capacity of spherical two-layer RMH by the value of relative deformation of the rubber of the most loaded bushing. Also, studies have been carried out on the possibilities of creating a uniformly deformable design of a spherical two-layer RMH.To determine the characteristics of a spherical rubber-metal hinge, applied digital computer modelling based on the finite element method. A proposed parametrised geometric model of a spherical two-layer RMH and a finite element model of an elastic bushing offer the ratio of radial stiffnesses of outer and inner bushings, which is close to the preliminarily determined one, based on the equations of the theory of elasticity in displacements in a spherical coordinate system.It has been established that to achieve uniform elasticity by changing the opening angle, the opening angle of the outer reinforcement of RMH should be approximately 1,5 times less than the opening angle of the inner one. This makes it possible to reduce the width of outer reinforcement of RMH by 25 % but raises the problem of strength and rigidity of outer edges of intermediate reinforcement. Also, equal elasticity of hinge bushings can be achieved due to their different thicknesses, while to achieve non-uniform stiffness of bushings within ± 5 %, it is required to ensure that deviation of the intermediate cage diameter during hinge manufacture is less than ± 0,1 %.The obtained research results prove the practical possibility of creating an equally strong (with equal bushing rigidity) spherical two-layer RMH. The issue of searching for a compromise design of RMS, acceptable from the point of view of loading of the intermediate cage and of the requirements for manufacturing accuracy, requires further study.

Voice coil motor-driven multi-DOF compliant parallel micropositioning stage based on a large range beam-based spherical hinge and fully symmetrical layout

With the recent rapid developments in the field of precision engineering, demand for the large range multi-degrees-of-freedom (DOF) micropositioning stage has increased significantly. In this paper, to solve the problems of small motion range, local stress concentration, and low motion accuracy caused by the parasitic motion of the traditional flexure hinge in the multi-DOF micropositioning stage, we first propose a type of large-range beam-based flexure spherical hinge (BFSH). Subsequently, based on the proposed BFSH, a large range 3-DOF θxθyz spatial micropositioning stage driven by the voice coil motor is designed employing parallel branch chains and a fully symmetrical layout. This arrangement realizes theoretical motion decoupling in structural design. Furthermore, we use the geometric method to derive kinematic equations of the moving platform, which are used as the decoupling matrix of the control loop. Based on the compliance matrix method and Lagrange’s method, the compliance matrix model of the BFSH, the 3-DOF micropositioning stage, and the stage dynamic model are determined respectively. Additionally, finite element analysis and experimental tests are conducted to verify the accuracy of the analytical model and assess the static and dynamic performance of the designed 3-DOF stage. Moreover, a fractional order phase advanced proportional integral controller is designed for closed-loop control to track the sinusoidal trajectory and spherical trajectory. The results reveal that the stage can achieve the desired large workspace of ± 21.5 mrad × ± 20.3 mrad × ± 3.23 mm, as well as excellent decoupling and trajectory tracking performance.

Optimization of Swivel Spherical Hinge Structure Design Based on the Response Surface Method

The accurate analysis of key components of a spherical hinge structure directly affects bridge quality and safety during construction. Considering the key components of a spherical joint structure as the research object, a refined calculation model for the spherical joint is established to examine its stress using finite element analysis. The influence of design parameters on the mechanical characteristics of the spherical hinge structure is systematically analyzed. The response surface method (RSM), devised using a Box–Behnken design, is used to optimize the design of the spherical hinge structure parameters. A response surface model is established to derive the scheme of the optimized spherical hinge structure design. Moreover, by comparing the structural contact stress and rotational traction force before and after optimization, the effectiveness and necessity of the spherical hinge structure optimization are verified. The result comparison shows that the maximum contact stress and rotational traction force in the spherical hinge structure after optimization are reduced by 13.86% and 8.42%, respectively, compared with those before optimization. The relative error between the calculated and predicted values is approximately 3%, indicating that the RSM is feasible for optimizing key components of the spherical hinge structure. Its optimization effect is evident. Based on the identified optimal parameters of the spherical hinge structure, a range of recommended design parameters for the key structure of the rotating spherical hinge at different load carrying capacities is established using the interpolation method, which provides a valuable reference for engineering practice.

A new quasi-static friction model for the spherical hinge bearing in structural engineering

For most frictional issues in structural engineering, the classical friction law named after Coulomb is a reliable and convenient tool, but it cannot be used to predict a slippage-related quasi-static process due to the lack of relevant items. In this paper, based on some commonly used dynamic friction models, a new rate-independent friction model is proposed to describe a quasi-static frictional process in structural field, e.g., the motion of a spherical hinge bearing in a pedestrian bridge under reciprocal pedestrian and temperature loads. Most quasi-static processes happen at the pre-sliding regime when a friction contact tends to slide slightly before the Coulomb friction is reached. The well-known Dahl model, LuGre model, and other test-based dynamic models are surveyed, and their shortcomings in engineering use are summarized subsequently. The new model, the same as the Dahl model, is rate-independent, but adopts a more engineering-oriented form. On the basis, it can be easily applied on a finite element analysis by adjusting a built-in ideal elastoplastic model. Meanwhile, the accuracy has no obvious decrease according to a test-based comparison between the Dahl model and the new. The coefficient of stiffness deviation, defined as the deviation of the pre-sliding friction stiffness from the initial friction stiffness, is introduced into the new model, which makes the model possible to predict the energy dissipation at the pre-sliding regime and can be well explained by the asperity-based theory at microscopic level. The impacts from the curvature and the coverage of a contact on the coefficient of static friction are assessed by the finite element method. It is shown that the curvature has very few impacts while the coverage is highly positively related to the observed coefficient of friction. A friction test of a spherical hinge is then carried out to verify the new model. By data regression, the coefficient of stiffness deviation for the proposed model and the exponent for the Dahl model are identified as 0.492 and 2.272, respectively. A comparison of friction torque-slippage hysteresis loops shows both the Dahl model and the proposed model have good predication as the normal force is large enough and the proposed one is even better in some load cases. Finally, a brief application on a pedestrian bridge of the new model is introduced. It indicates that there will be some mechanical residuals when a spherical hinge is applied with a reciprocating load, but the residuals tend to be limited.

Parameter sensitivity analysis under failure condition of lifting device mechanism

The sensitivity of each influencing parameter in the selected range of the complex multi-hinge space flap mechanism under typical fault conditions is studied, and the influence degree of each parameter and its dispersion on the driving torque of the mechanism is determined. Firstly, the rigid-flexible coupling dynamic model of the mechanism is established considering the flap deformation, and then the influence of four parameters that may cause mechanism failures, such as hinge friction, aerodynamic load, driving speed and assembly error, on the driving torque of the mechanism is explored. Then, the drive torque of the mechanism under each parameter value is given, finally, the sensitivity of each selected parameter is obtained by the direct de rivation method. The results show that the parameters are positively correlated with the driving torque, the aerodynamic load coefficient and hinge friction parameters are the most sensitive to the driving performance of the mechanism, while the driving speed is the smallest. After the aerodynamic load increased by 30%, the maximum driving torque of the inner mechanism increased by 28.8%; when the hinge friction parameter was in the range of 0~0.05, the maximum torque of the inner and outer mechanisms increased by 8.6% and 8.4% respectively. In engineering applications, the lubrication of each spherical hinge should be increased, the driving speed should be reduced, and the manufacturing and assembly accuracy should be improved.To a certain extent, it can prevent failures and improve the reliability of the flap mechanism.