The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Y Hao - One of the best experts on this subject based on the ideXlab platform.
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effect of warping on natural frequencies of symmetrical cross ply laminated composite non cylindrical Helical Springs
International Journal of Mechanical Sciences, 2013Co-Authors: Y HaoAbstract:Abstract Free vibration problem of symmetrical cross-ply laminated composite non-cylindrical Helical Springs with rectangular cross-section is investigated. The effect of the warping deformation of wire cross-section on natural frequencies is first considered in the formulation. The differential equations of motion for the Springs, which consist of 14 first-order partial differential equations with variable coefficients, are derived using naturally curved and twisted anisotropic beam theory. The natural frequencies of the Springs are found from improved Riccati transfer matrix by iteration. The element transfer matrix is calculated by the use of the Scaling and Squaring method and Pad´e approximations. Three examples are presented for different types of Springs with rectangular cross-section under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FE-results using three-dimensional solid layered element (Solid 46) in ANSYS code. Numerical results reveal that the warping deformation has a significant influence on the natural frequencies, which should be considered in the free vibration analysis of the Springs. Finally, the effects of various parameters and different stacking sequences on the natural frequencies for symmetrically laminated barrel Springs with rectangular cross-section have also been studied.
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warping effect in free vibration analysis of unidirectional composite non cylindrical Helical Springs
Meccanica, 2013Co-Authors: Y HaoAbstract:The differential equations of motion for unidirectional composite non-cylindrical Helical Springs including warping, which consist of 14 first-order partial differential equations with variable coefficients, are first derived based on arbitrary spatially curved anisotropic beam theory. An analytical formula for the warping function of Saint-Venant’s torsion of unidirectional composite beams with rectangular cross-section is also obtained. The natural frequencies are determined using improved Riccati transfer matrix method. The element transfer matrix is calculated by the use of the Scaling and Squaring method and Pad’e approximations. Comparisons are made with the EF-results on the natural frequencies of the Springs, made from rectangular wire, with inclusion of the warping effect. Information is given on the effect on the natural frequencies of the ratio of radii of the minimum cylinder to the maximum cylinder, the helix pitch angle and the number of active turns. Numerical results reveal that the warping deformation has a significant influence on the natural frequencies, which should be considered in the free vibration analysis of such Springs.
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improved riccati transfer matrix method for free vibration of non cylindrical Helical Springs including warping
Shock and Vibration, 2012Co-Authors: Y HaoAbstract:Free vibration equations for non-cylindrical (conical, barrel, and hyperboloidal types) Helical Springs with noncircular cross-sections, which consist of 14 first-order ordinary differential equations with variable coefficients, are theoretically derived using spatially curved beam theory. In the formulation, the warping effect upon natural frequencies and vibrating mode shapes is first studied in addition to including the rotary inertia, the shear and axial deformation influences. The natural frequencies of the Springs are determined by the use of improved Riccati transfer matrix method. The element transfer matrix used in the solution is calculated using the Scaling and Squaring method and Pad'e approximations. Three examples are presented for three types of Springs with different cross-sectional shapes under clamped-clamped boundary condition. The accuracy of the proposed method has been compared with the FEM results using three-dimensional solid elements (Solid 45) in ANSYS code. Numerical results reveal that the warping effect is more pronounced in the case of non-cylindrical Helical Springs than that of cylindrical Helical Springs, which should be taken into consideration in the free vibration analysis of such Springs.
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free vibration analysis of cylindrical Helical Springs with noncircular cross sections
Journal of Sound and Vibration, 2011Co-Authors: Y HaoAbstract:Abstract The free vibration analysis of cylindrical Helical Springs with noncircular cross-sections is carried out by means of an analytical study. In the governing equations of motion of a spring, all displacement functions and a generalized warping coordinate are defined at the centroidal principal axis. The effects of the rotational inertia, axial and shear deformations, including torsion-related warping deformations, are also considered in the formulations. Explicit analytical expressions that give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA, and the Muller root search method is used to determine the natural frequencies. Numerical examples are provided for Springs with elliptic, rectangular and equilateral triangular cross-sections, and subjected to clamped–clamped and clamped–free boundary conditions. The natural frequencies are presented for a range of geometric parameters. In the case of elliptical wires, results are presented for the aspect ratio λ=a/b ranging from 3/5 to 5/3, the helix pitch angle α ¯ from 5 to 12.5, the number of active turns n from 6 to 12, and the ratio of cylinder radius to minor axis R/2a ranging from 20/3 to 50/3. Validation of the proposed model has been achieved through comparison with a finite element model using three-dimensional solid elements and the results available in published literature, which in these cases indicates a good correlation.
Shilong Wang - One of the best experts on this subject based on the ideXlab platform.
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improved pi neural network based tension control for stranded wire Helical Springs manufacturing
Control Engineering Practice, 2017Co-Authors: Qi Zhang, Shilong Wang, Jie Zhou, Anrui Zhang, Qing LiuAbstract:Abstract During the winding process of stranded wire Helical Springs (SWHSs), uneven wire tension always results in high rejection rate and non-compliance service life of SWHSs. Combining the proportion integral neural network (PINN) with a simplified actuator model, this paper presents a new control scheme for the SWHS CNC machine to keep the wire tension uniform. The PINN is improved by introducing an error variance ratio, accounting for the interaction between wires, as a modifying factor in the second hidden layer. The actuator model is simplified based on the analysis of the dynamic characteristics of the actuator. The output value of the improved PINN is transferred into control voltage value by the simplified model. The tension of each wire is controlled by an improved PINN. In order to enhance the control performance, the network parameters are updated using the gradient-based back-propagation method. The validity and consistency of the improved PINN are verified by experiments. The results indicate that (1) the computation load is slight; (2) the rising time of the step response is within 1 s; (3) 89%-96% of tension deviation values of the wire 1 and wire 3 under different process parameters are within 10% of the reference tension value; (4) the standard deviation of the wire 2 with large disturbance is 8.24 N. Compared with other algorithms (incremental PI, multiple PIDNN, PI based particle swarm optimization), the control scheme based on the improved PINN has less computation load, faster response speed and better performance in the time-varying and nonlinear system with larger disturbance.
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static response of stranded wire Helical Springs to axial loads a two state model
Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2013Co-Authors: Shilong Wang, Yu Zhao, Jie ZhouAbstract:Stranded wire Helical Springs are fundamental mechanical components used in high-end vibration absorption systems. The static axial response model is an important tool for the design and manufacturing of the spring. The wires within the spring have been assumed to be in contact with each other when the spring is unloaded by commonly used models for modelling the static axial response; hence, significant error has been introduced. To improve the estimation accuracy of the static axial response, this article proposes a two-state model by assuming that the spring possesses two states during the loading process. Moreover, in this model, the friction between adjacent wires is neglected and the spring is unwound to be a straight strand in the initial step of the analysis. The model is almost piecewise linear and is able to model the nonlinearity of the load–strain relationship of the spring. Adopting the proposed model, the dependence of the stiffness of the spring on the spring geometries is analysed. To evalu...
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Modeling and identification of the dynamic behavior of stranded wire Helical Springs
Journal of Vibroengineering, 2013Co-Authors: Yu Zhao, Shilong Wang, Jie Zhou, Cheng ChengAbstract:A stranded wire Helical spring is a cylindrical Helical spring wound by a wire strand. Owing to its unique structure, the spring features special dynamic behavior such as nonlinear stiffness, hysteresis and hardening overlap. The dynamic response model, which gives an accurate description of the dynamic behavior, of the spring is a very important tool for designing systems using the spring as well as evaluating the responses of such systems. However, no accurate model has been reported. In the present study, a modified normalized Bouc-Wen model is proposed to model the dynamic behavior of the spring. A simple yet effective identification method is developed for identifying the model parameters using experimental data. Numerical simulations and periodic loading experiments were carried out to validate the proposed model and identification method. The results verify that the proposed model and method are effective for modeling and identifying the dynamic behavior of stranded wire Helical Springs.
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Motion Model of Helical Springs under Vibrational Condition
Journal of Mechanical Engineering, 2012Co-Authors: Shilong WangAbstract:When Helical Springs,especially stranded-wire Helical Springs are impacted,the movement of every spring coil will be very complicated owing to various factors,such as the mass,inertia,resonance of Springs,the elastic deformation of steel material and the internal friction induced by the relative slipping among different steel wires of stranded-wire Helical Springs.Based on that,a set of motion models of various Helical Springs under vibrational condition are proposed and they can be used to measure the relationships between displacement and time,velocity and time,acceleration and time for every spring coil.The experimental results show that the motion models of Helical Springs,combining a non-contact and multi-channel testing unit developed by correlative project team,are successfully in revealing the rules about how the motion of spring coils changes with the time going,which can offer experimental basis for the dynamic design theory of Helical Springs.
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Experimental Research of Dynamic Parameters of Stranded-Wire Helical Springs under Impact Load
International Conference on Mechanical Engineering and Technology (ICMET-London 2011), 2011Co-Authors: Shilong Wang, Yu Zhao, Jie Zhou, Mingming Zhang, Zhiqiang WangAbstract:When stranded-wire Helical Springs are impacted, the movement of every spring coil will become very complicated owing to various factors, such as the mass, inertia and resonance of spring, the internal friction of steel wires, also the relative slipping during different steel wires of stranded-wire Helical Springs. Base on that, a non-contact and multi-channel detection device of dynamic parameters of stranded-wire Helical Springs is proposed, which involves the design of mechanical structure, the lectotype and installation of sensors, the hardware and software module of signal acquisition and analysis. This device, combining a novel algorithmic of data processing special for Springs, can be used to measure the relationships between displacement and time, velocity and time, acceleration and time for every spring coil. The results show that when stranded-wire Helical Springs are impacted, all spring coils will vibrate, also this movement will transmit to the fixed end in the form of longitudinal wave and reflect there; the relationship between displacement and axial length of spring coils point is non-linear, the same situation for the relation between velocity and spring coils’ position; additionally, in the beginning of impact there is a large deformation in the active end, whereas on the contrary, little deformation in the fixed end while on the other hand there is a large deformation in the fixed end when the wave reaches there and reflects. Therefore, in practical design work of stranded-wire Helical Springs, it is necessary to analyze the impact response of Springs in order to avoid the phenomenon of excessive deformation of some spring coils by selecting reasonable parameters.
Zhou Jie - One of the best experts on this subject based on the ideXlab platform.
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Study on Modelling Method of Stranded Wire Helical Springs
Computer Simulation, 2010Co-Authors: Zhou JieAbstract:In order to make up the deficiency of existing modelling methods for stranded wire Helical Springs,two new modelling methods were proposed based on the forming principle of the single wire in the stranded wire Helical Springs.In the first method,the differential geometry equation of the central curve for single wire was derived,and this equation could be used to finish rapid modelling of different structure for stranded wire Helical Springs in most modelling codes.Then the stranded wire Helical Springs model with closed ends was built by changing the pitches of the central line of stranded wire Helical Springs in the second method.Finally,modelling cases were given based on the two methods.The results indicate the effectiveness and rightness of the new methods,which can meet the different requirements for the simulation and FE analysis of the stranded wire Helical Springs.
Vebil Yildirim - One of the best experts on this subject based on the ideXlab platform.
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A Closed-Form Buckling Formula for Open-Coiled and Properly Supported Circular-Bar Helical Springs
Sciendo, 2018Co-Authors: Vebil YildirimAbstract:As a continuation of the author’s previous studies on the buckling analysis of Helical Springs, a closed-form formula having been obtained with the help of the artificial neural network (ANN) is proposed and discussed in detail for the first time for a cylindrical close/open-coiled Helical spring with fixed ends and having a solid circular section. As far as the author knows there is no such a formula in the open-literature to consider the effects of all stress resultants (torsional and bending moments, axial and shearing forces), large helix pitch angles together with the axial and shear deformations on the buckled state. The present formula may be used in a wide range of the total number of active turns, the ratio of the free axial length to the mean helix diameter, and the spring index. It is yet again revealed that it is not appropriate to use the elementary theory to determine the critical buckling loads for open-coiled Springs. The present formula may allow the deeper understanding of spring buckling mechanism and to be used directly and safely in the design processes of such closely/open-coiled Springs
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numerical buckling analysis of cylindrical Helical coil Springs in a dynamic manner
2009Co-Authors: Vebil YildirimAbstract:The free vibration equations of cylindrical isotropic Helical Springs loaded axially, developed by the author are solved numerically based on the transfer matrix method to perform buckling analysis in a dynamic manner. The axial and shear deformation effects together with the rotatory inertia effects are all considered based on the first order shear deformation theory. For the determination of the vertical tip deflection of Helical Springs with large pitch angles, closed-form equation obtained by the author based on Castigliano’s first theorem is used to take into account for the whole effect of the stress resultants such as axial and shearing forces, bending and torsional moments on the tip deflection. A good agreement is observed with related benchmark studies.
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expressions for predicting fundamental natural frequencies of non cylindrical Helical Springs
Journal of Sound and Vibration, 2002Co-Authors: Vebil YildirimAbstract:Abstract Numerical and analytical studies are performed for the free vibration analysis of non-cylindrical (conical, barrel and hyperboloidal types) Helical Springs. The stiffness matrix method is used in the numerical analysis. A total of 12 degrees of freedom (six displacements and six rotations) is described for an element. The exact element stiffness matrix and the exact concentrated element inertia matrix are used in the formulation. The rotary inertia, the shear and extensional deformation effects are considered in the analysis. Comparison of the numerical results with the reported results obtained numerically and experimentally gives satisfactory values. After verification of the numerical frequencies, the non-dimensional fundamental frequencies of fixed–fixed non-cylindrical Helical Springs with circular section are expressed in a simple formula with a maximum absolute relative error of 5% using those numerical values for the constant helix pitch angles (5°, 10°, and 15°). These expressions restricted to the fundamental frequencies are also verified with ANSYS results.
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free vibration of uniaxial composite cylindrical Helical Springs with circular section
Journal of Sound and Vibration, 2001Co-Authors: Vebil YildirimAbstract:Abstract The free vibration problem of unidirectional composite cylindrical Helical Springs is modelled theoretically as a continuous system considering the rotary inertia, shear and axial deformation effects. The first order shear deformation theory is employed in the mathematical model. The 12 scalar ordinary differential equations governing the free vibration behavior of cylindrical Helical Springs made of an anisotropic material are solved simultaneously by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy by using the effective numerical algorithm available in the literature. The theoretical results are verified with the reported values, which were obtained theoretically and experimentally for straight beams and Helical Springs. A parametric study is performed to investigate the effects of the number of active coils, the helix pitch angle and material types on the first six natural frequencies of Helical Springs with circular section and fixed–fixed ends.
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Linear free vibration analysis of cross-ply laminated cylindrical Helical Springs
International Journal of Mechanical Sciences, 2000Co-Authors: Vebil Yildirim, Erol SancaktarAbstract:A linear free vibration analysis of symmetric cross-ply laminated cylindrical Helical Springs is performed based on the first-order shear deformation theory. Considering the rotary inertia, the shear and axial deformation effects, governing equations of symmetric laminated Helical Springs made of a linear, homogeneous, and orthotropic material are presented in a straightforward manner based on the classical beam theory. The free vibration equations consisting of 12 scalar ordinary differential equations are solved by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy. The soundness of the present results are verified with the reported values which were obtained theoretically and experimentally. After presenting the non-dimensional graphical forms of the free vibrational characteristics of (0°/90°/90°/0°) laminated Helical spring made of graphite-epoxy material (AS4/3501-6) with fixed–fixed ends, a non-dimensional parametric study is worked out to examine the effects of the number of active turns, the shear modulus in the 1–2 plane (G12), the ratio of the cylinder diameter to the thickness (D/d), and Young's moduli ratio in 1 and 2 directions (E1/E2) on the first six natural frequencies of a uniaxial composite Helical spring with clamped-free, clamped-simple, and clamped–clamped ends.
Jie Zhou - One of the best experts on this subject based on the ideXlab platform.
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improved pi neural network based tension control for stranded wire Helical Springs manufacturing
Control Engineering Practice, 2017Co-Authors: Qi Zhang, Shilong Wang, Jie Zhou, Anrui Zhang, Qing LiuAbstract:Abstract During the winding process of stranded wire Helical Springs (SWHSs), uneven wire tension always results in high rejection rate and non-compliance service life of SWHSs. Combining the proportion integral neural network (PINN) with a simplified actuator model, this paper presents a new control scheme for the SWHS CNC machine to keep the wire tension uniform. The PINN is improved by introducing an error variance ratio, accounting for the interaction between wires, as a modifying factor in the second hidden layer. The actuator model is simplified based on the analysis of the dynamic characteristics of the actuator. The output value of the improved PINN is transferred into control voltage value by the simplified model. The tension of each wire is controlled by an improved PINN. In order to enhance the control performance, the network parameters are updated using the gradient-based back-propagation method. The validity and consistency of the improved PINN are verified by experiments. The results indicate that (1) the computation load is slight; (2) the rising time of the step response is within 1 s; (3) 89%-96% of tension deviation values of the wire 1 and wire 3 under different process parameters are within 10% of the reference tension value; (4) the standard deviation of the wire 2 with large disturbance is 8.24 N. Compared with other algorithms (incremental PI, multiple PIDNN, PI based particle swarm optimization), the control scheme based on the improved PINN has less computation load, faster response speed and better performance in the time-varying and nonlinear system with larger disturbance.
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static response of stranded wire Helical Springs to axial loads a two state model
Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2013Co-Authors: Shilong Wang, Yu Zhao, Jie ZhouAbstract:Stranded wire Helical Springs are fundamental mechanical components used in high-end vibration absorption systems. The static axial response model is an important tool for the design and manufacturing of the spring. The wires within the spring have been assumed to be in contact with each other when the spring is unloaded by commonly used models for modelling the static axial response; hence, significant error has been introduced. To improve the estimation accuracy of the static axial response, this article proposes a two-state model by assuming that the spring possesses two states during the loading process. Moreover, in this model, the friction between adjacent wires is neglected and the spring is unwound to be a straight strand in the initial step of the analysis. The model is almost piecewise linear and is able to model the nonlinearity of the load–strain relationship of the spring. Adopting the proposed model, the dependence of the stiffness of the spring on the spring geometries is analysed. To evalu...
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Modeling and identification of the dynamic behavior of stranded wire Helical Springs
Journal of Vibroengineering, 2013Co-Authors: Yu Zhao, Shilong Wang, Jie Zhou, Cheng ChengAbstract:A stranded wire Helical spring is a cylindrical Helical spring wound by a wire strand. Owing to its unique structure, the spring features special dynamic behavior such as nonlinear stiffness, hysteresis and hardening overlap. The dynamic response model, which gives an accurate description of the dynamic behavior, of the spring is a very important tool for designing systems using the spring as well as evaluating the responses of such systems. However, no accurate model has been reported. In the present study, a modified normalized Bouc-Wen model is proposed to model the dynamic behavior of the spring. A simple yet effective identification method is developed for identifying the model parameters using experimental data. Numerical simulations and periodic loading experiments were carried out to validate the proposed model and identification method. The results verify that the proposed model and method are effective for modeling and identifying the dynamic behavior of stranded wire Helical Springs.
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Experimental Research of Dynamic Parameters of Stranded-Wire Helical Springs under Impact Load
International Conference on Mechanical Engineering and Technology (ICMET-London 2011), 2011Co-Authors: Shilong Wang, Yu Zhao, Jie Zhou, Mingming Zhang, Zhiqiang WangAbstract:When stranded-wire Helical Springs are impacted, the movement of every spring coil will become very complicated owing to various factors, such as the mass, inertia and resonance of spring, the internal friction of steel wires, also the relative slipping during different steel wires of stranded-wire Helical Springs. Base on that, a non-contact and multi-channel detection device of dynamic parameters of stranded-wire Helical Springs is proposed, which involves the design of mechanical structure, the lectotype and installation of sensors, the hardware and software module of signal acquisition and analysis. This device, combining a novel algorithmic of data processing special for Springs, can be used to measure the relationships between displacement and time, velocity and time, acceleration and time for every spring coil. The results show that when stranded-wire Helical Springs are impacted, all spring coils will vibrate, also this movement will transmit to the fixed end in the form of longitudinal wave and reflect there; the relationship between displacement and axial length of spring coils point is non-linear, the same situation for the relation between velocity and spring coils’ position; additionally, in the beginning of impact there is a large deformation in the active end, whereas on the contrary, little deformation in the fixed end while on the other hand there is a large deformation in the fixed end when the wave reaches there and reflects. Therefore, in practical design work of stranded-wire Helical Springs, it is necessary to analyze the impact response of Springs in order to avoid the phenomenon of excessive deformation of some spring coils by selecting reasonable parameters.
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Mathematical model for determination of strand twist angle and diameter in stranded-wire Helical Springs
Journal of Mechanical Science and Technology, 2010Co-Authors: Shilong Wang, Jie Zhou, Song Lei, Hong XiaoAbstract:The twist angle of strands has a significant effect on the performance of stranded-wire Helical Springs. This paper proposes two models (a precise mathematical model and an approximate mathematical model) for calculation of the twist angle and the diameter of strands formed of an arbitrary number of wires. These two parameters can be derived from the screw pitch of strands and the diameter and number of their wires, regardless of the model used. In comparative and analytical studies, it was determined that for strands with the same number of wires, the larger the ratio of the screw pitch to the diameter of the wires is, the smaller the relative errors of the two models are. Only when the foresaid ratio is two times larger than the number of wires, the results of the approximate mathematical model can be acceptable. In other cases, the approximate mathematical model cannot be used. Finally, application software was developed for direct precise-mathematical-model calculation of the twist angle and diameter of strands formed of arbitrary wires.