Manuel Paredes

An optimization process for extension spring design

This paper presents a calculation process to optimize the design of helical extension springs whatever the nature of the specifications. This process can be used even in the early design stages as data are set with interval values. It includes a large set of constraints, which can express the designers requirements, but also the standards and the technical capability limits of spring manufacturers. The problem is resolved using the Excel solver. The required starting point is automatically calculated by a dedicated algorithm, which uses interval arithmetic. Two examples are presented.

Optimal design of conical springs

Mechanical systems often use springs to store energy though their axial length must sometimes be significantly reduced. This leads to the use of conical springs as they are able to telescope. Designers of mechanical systems can call on a large number of tools to assist them though most of these are merely validation tools requiring concomitant trial and error strategies. Optimization strategies can be applied to provide synthesis assistance tools for which the designer simply specifies his requirement. Thus the tool directly indicates the spring best suited to standards and requirements. Recent advances in the study of constant pitch conical springs have provided analytical expressions of their behavior even in the non-linear phase. Considering this, we have used optimization strategies to provide a synthesis tool for conical spring design. An example of application is presented. The tool introduced here is thus a synthesis assistance tool that can be of considerable interest for designers who require a conical spring in their design.

Advanced assistance tool for optimal compression spring design

The main industrial programs for spring design do not make most of the powerful capabilities for optimization currently available. Usually, such software simply provides comprehensive validation tools. This paper introduces an advanced sizing tool for compression spring design. This tool can be used at any design stage and involves a specification sheet to provide data including interval values. Interval analysis and optimization processes are then run to provide the best design as output. High-level assistance functionalities are also presented and illustrated through a case study.

Analytical Behavior Law for a Constant Pitch Conical Compression Spring

Cylindrical compression spring behavior has been described in the literature using an efficient analytical model. Conical compression spring behavior has a linear phase but can also have a nonlinear phase. The rate of the linear phase can easily be calculated but no analytical model exists to describe the nonlinear phase precisely. This nonlinear phase can only be determined by a discretizing algorithm. The present paper presents analytical continuous expressions of length as a function of load and load as a function of length for a constant pitch conical compression spring in the nonlinear phase. Whals basic cylindrical compression assumptions are adopted for these new models (Wahl, A. M., 1963, Mechanical Springs, Mc Craw-Hill, New York). The method leading to the analytical expression involves separating free and solid/ ground coils, and integrating elementary deflections along the whole spring. The inverse process to obtain the spring load from its length is assimilated to solve a fourth order polynomial. Two analytical models are obtained. One to determine the length versus load curve and the other for the load versus length curve. Validation of the new conical spring models in comparison with experimental data is performed. The behavior law of a conical compression spring can now be analytically determined. This kind of formula is useful for designers who seek to avoid using tedious algorithms. Analytical models can mainly be useful in developing interactive assistance tools for conical spring design, especially where optimization methods are used.

An Assistance Tool for Spline Coupling Design

This research was motivated by the absence of a means to design a straight spline coupling in a reliable way. It is shown that the strain and pressure distribution in a spline coupling are not uniform. To predic t t these phenomena, an assistance tool would be of key interest. In this paper, a simplified finite element model has been made of a spline coupling to build a dimensioning tool for such couplings. This tool can give information about strain on the outside diameter of the sleeve and axial torque distribution. This study is based on an experimentally validated three-dimensional finite element model of the coupling under torsional load. Different sleeve sizes and loading methods are tested to highlight their effects on the axial torque distribution

Obtaining an optimal compression spring design directly from a user specification

Abstract Common mechanical components can be designed manually but this involves problem simplifications. A computer can help to develop a suitable approach for optimizing design. Industrial software for spring design is comprehensive tools for validation only. To improve design assistance to the designer, this paper presents software which not only is comprehensive but also can serve as a dimensional synthesis tool for compression spring design. It exploits an optimization process for use even in the early design steps as specifications are set with interval values. It includes a large set of constraints which can express not only the designer specifications but also the standards and the technical capability limits of spring manufacturers. This process has been successfully tested by a spring manufacturer, who has used it to solve real industrial problems for 2 years. One case study is presented.

Tuned nonlinear energy sink with conical spring: design theory and sensitivity analysis

This paper is devoted to the study of a Nonlinear Energy Sink (NES) intended to attenuate vibration induced in a harmonically forced linear oscillator (LO) and working under the principle of Targeted Energy Transfer (TET). The purpose motivated by practical considerations is to establish a design criterion that first ensures that the NES absorber is activated and second provides the optimally tuned nonlinear stiffness for efficient TET under a given primary system specification. Then a novel NES design yielding cubic stiffness without a linear part is exploited. To this end, two conical springs are specially sized to provide the nonlinearity. To eliminate the linear stiffness, the concept of a negative stiffness mechanism is implemented by two cylindrical compression springs. A small-sized NES system is then developed. To validate the concept, a sensitivity analysis is performed with respect to the adjustment differences of the springs and an experiment on the whole system embedded on an electrodynamic shaker is studied. The results show that this type of NES can not only output the expected nonlinear characteristics, but can also be tuned to work robustly over a range of excitation, thus making it practical for the application of passive vibration control.

Tolerance optimization by modification of Taguchi’s robust design approach and considering performance levels: Application to the design of a cold-expanded bushing

This paper defines a method for the optimization of design parameter tolerances. The general architecture of the proposed method is identical to that of the robust design reference method proposed by Taguchi but its content is different as the tolerances are considered as functions to be maximized here, while Taguchi’s method rather considers these tolerances as fixed data. Instead of looking for design parameters that minimize the sensitivity of some performance criteria, the design parameters are calculated so as to obtain maximal tolerance intervals, thus minimizing manufacturing costs. Performance criteria are then considered in terms of optimization constraints: each criterion gives rise to an inequality constraint that specifies the minimum level of performance that the designer wants to achieve. The possibilities offered by this method are illustrated through its use in the preliminary design of a cold-expanded bushing. In this case, tolerance optimization enables the allowable tolerances on the design diameters to be increased and performance levels are defined on the residual radial stress at the bushing/part contact radius and on the residual orthoradial (hoop) stress at the part inner radius.

Analytical and Experimental Study of Conical Telescoping Springs With Nonconstant Pitch

Most research papers that exploit conical springs focus only on conical springs with a constant pitch. In order to increase the range of possibilities for designers, this paper proposes a study of conical springs with other types of spirals projected on the conical shape. This study is related to three other types of conical springs: with a constant helix angle, with a constant stress at solid and with a fully linear load-length relation. For each spring, we give the equation of the spiral, the formula of the initial stiffness, and formulae to calculate the nonlinear part of the load-length relation for fully telescoping springs. We also report an experimental study performed to analyze the accuracy of the proposed study based on springs made by fused deposition modeling.

Enhanced Formulae for Determining Both Free Length and Rate of Cylindrical Compression Springs

Cylindrical compression springs have been commonly exploited in mechanical systems for years and their behavior is considered as well identified. Nevertheless, it appears that, even though old research studies suggest correcting the rate formula, the main industrial software dedicated to spring design exploits the uncorrected one. In order to evaluate the accuracy of the analytical formulae for spring behavior, an experimental study was performed, which tried to cover the common design space. This study was done using the two common coil ends: closed and ground ends, and closed and not ground ends. Moreover, the accuracy of the load–length relation was investigated whereas older studies focused only on the spring rate. It appears that the common uncorrected formulae give satisfactory results only when large numbers of coils are involved. We also highlight, for the first time, that it is interesting to correct not only the spring rate but also the free length of the spring.