Numerical Studies on the Stiffness of Arc Elliptical Cross-section Helical Spring Subjected to Circumference Force

Due to its excellent properties, elliptical cross-section helical spring has been widely used in automobile industry, such as valve spring, arc spring used in Dual Mass Flywheel and so on. Existing stiffness formulae of helical spring remain to be tested, and stiffness property of elliptical cross-section arc spring has been little studied. Hence, study on the stiffness of elliptical cross-section helical spring is significant in the development of elliptical cross-section helical spring. This paper proposes a method to study the stiffness property of elliptical cross-section helical spring that the experiment design method is adopted with finite element analysis. Firstly, the finite element analysis method was used to verify the cylindrical (circular cross-section and elliptical cross-section) springs. Then, the regression formula was designed and derived compared with the reference springs’ stiffness formulae by experimental design. Last, regression formula was verified with existing experiment data. The novelty in this paper is that simulation technology of arc spring was investigated and a stiffness regression equation of arc elliptical cross-section spring was obtained using orthogonal regression design, with significance in wide use of the arc elliptical cross-section helical spring promotion.

An innovative X-shaped vibration isolation mount with tunable quasi-zero-stiffness property

Passive vibration isolation is always preferable in many engineering practices. To this aim, an innovative, compact, and passive vibration isolation mount is studied in this paper. The novel mount is adjustable to different payloads due to a special oblique and tunable stiffness mechanism, and of high vibration isolation performance with a wider quasi-zero-stiffness range due to the deliberate employment of negative stiffness of the X-shaped structure. The X-shaped structure has been well studied recently due to its excellent nonlinear stiffness and damping properties. In this study, by using of the negative stiffness property within the X-shaped structure, the X-shaped mount (X-mount) can have an obviously larger vibration displacement range which maintains the quasi-zero-stiffness property. A special oblique spring is thus introduced such that the overall equivalent stiffness can be much easily adjusted. Systematic parametric study is conducted to reveal the critical design parameters and their relationship with vibration isolation performance. A prototype and experimental validations are implemented to validate the theoretical results. It is believed that the X-mount would provide an innovative technical upgrade to many existing vibration isolation mounts in various engineering practices and it could also be the first prototyped mount which can offer adjustable quasi-zero stiffness conveniently.

Numerical Study Of The Targeted Energy Transfer Between The Euler-Bernoulli Beam And A Nonlinear Energy Sink

Targeted energy transfer (TET) refers to the spatial transfer of energy between a primary structure of interest and isolated oscillators called the energy sink (ES). In this work, the primary structure of interest is a slender beam modeled by the Euler-Bernoulli theory, and the ES is a single-degree-of-freedom oscillator with either linear or cubic nonlinear stiffness property. The objective of this study is to characterize the TET and the effectiveness of ES under impact and periodic excitations. By using the scientific computation package, MATLAB, numerical simulations are carried out based on excitations of various strength and locations. Both time and frequency domain characterizations are used. For the impact excitation, the ES with the cubic nonlinear stiffness property is more superior to the linear oscillator in that larger percentage of the impact energy can be dissipated there. The main energy transfer was found to be due to a 3- to-1 frequency coupling between the first bending mode and the ES. For the periodic excitation, however, both linear and nonlinear ES exhibit generally poorer performance than the case with the impact excitation. Future works should focus on the frequency-energy relationship of the periodic solution of the underlying Hamiltonian, as well as using finite element model to verify the simulation results.

Numerical Study Of The Targeted Energy Transfer Between The Euler-Bernoulli Beam And A Nonlinear Energy Sink

Targeted energy transfer (TET) refers to the spatial transfer of energy between a primary structure of interest and isolated oscillators called the energy sink (ES). In this work, the primary structure of interest is a slender beam modeled by the Euler-Bernoulli theory, and the ES is a single-degree-of-freedom oscillator with either linear or cubic nonlinear stiffness property. The objective of this study is to characterize the TET and the effectiveness of ES under impact and periodic excitations. By using the scientific computation package, MATLAB, numerical simulations are carried out based on excitations of various strength and locations. Both time and frequency domain characterizations are used. For the impact excitation, the ES with the cubic nonlinear stiffness property is more superior to the linear oscillator in that larger percentage of the impact energy can be dissipated there. The main energy transfer was found to be due to a 3- to-1 frequency coupling between the first bending mode and the ES. For the periodic excitation, however, both linear and nonlinear ES exhibit generally poorer performance than the case with the impact excitation. Future works should focus on the frequency-energy relationship of the periodic solution of the underlying Hamiltonian, as well as using finite element model to verify the simulation results.

Design and Fabrication a Lightweight Spring Made of Natural Rubber for a Motorcycle’s Shock Absorber

This research aims to design and fabricate a spring made of natural rubber for a lightweight motorcycle’s shock absorber. This study is carried out in four main steps. First, a stiffness property of a steel coil spring and a damping property of a commercial shock absorber were tested using an Instron® material testing machine and a test rig. Second, six different types of rubber compounds (A-1, A-2, A-3, B-1, B-2, and B-3) were formulated and the best compound was selected to use for a rubber spring. Third, the rubber spring was designed and analyzed using the finite element method to investigate the best model. Finally, a prototype of the rubber spring was fabricated and tested. The steel coil spring was replaced by the rubber spring and tested for its damping property within a real shock absorber. The results of the prototype testing showed that the weight of the rubber spring was lower than the steel coil spring about 48%. The stiffness property of the rubber spring was higher than the steel coil spring around 43% and the damping property of the shock absorber using rubber spring was higher than the damping property of the shock absorber using steel coil spring about 6%. The rubber spring provided more advantages than the steel coil spring for its good corrosion resistance, lightweight, and ease of maintenance. However, the implementation of the rubber spring in the real motorcycle and its fatigue life should be studied in the next future.