Parametrical optimization of compression helical springs against instability

Krużelecki, Jacek

doi:10.1007/bf01199245

Cited by 2 publications

(4 citation statements)

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“…To date, all the authors such as the researchers of [2]- [11] have selected the wire diameter d, the mean coil diameter D and the number of active coils n as design variables of helical springs in the examples of the monographs on optimization.…”

Section: B Analysis Of Error In Optimum Design Of Helical Springmentioning

confidence: 99%

“…The optimal design of helical springs is over 100 years old (Henderson 1884-1885) [11], but a serious mistake in optimization design of helical springs has been widely used by researchers and designers for a long time. So far, in almost all of the literature, such as in [2]- [11], wire diameter d, mean coil diameter D and number of active coils n are design variables in the optimization design model of helical springs.…”

Section: Introductionmentioning

confidence: 99%

“…So far, in almost all of the literature, such as in [2]- [11], wire diameter d, mean coil diameter D and number of active coils n are design variables in the optimization design model of helical springs. In fact, only one variable (d or D) is independent variable in the three design variables (d, D and n).…”

Section: Introductionmentioning

confidence: 99%

“…Krużelecki [11] presented the parametrical optimization problem of helical springs against instability. Such an initial distribution of a helix angle and radius of a spring is sought in the assumed class of functions which ensure maximal value of the critical axial compressive force under equality and inequality constraints.…”

Section: Introductionmentioning

confidence: 99%

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Correction of a Popular Error in the Optimization Design of Helical Springs

Li¹,

Wang²,

Liu³

2017

IJMO

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Abstract-In the optimized design of helical springs, wire diameter d, mean coil diameter D and number of active coils n as design variables are a prevalent mistake. This paper analyzes and demonstrates this error. When loads F 1 , F 2 and deflections λ 1 , λ 2 are known, the number of active coils n is the dependent variable of wire diameter d and mean coil diameter D in the formula of n. It is known that if some design variables are dependent variables, there must be some equality constraints between them. Almost none of monographs has constrained the number of active coils n by equality constraint as yet. Therefore, in most optimization results of helical springs the number of active coils n is wrong, where value of n is not calculated by the formula of n. The formula of shear stress in spring shows that the wire diameter d and the mean diameter D are independent variables. The wire diameter d and the mean diameter D as design variables are more reasonable in the actual optimization process of helical springs design. Reducing the three design variables to two design variables not only can meet the requirements of the design objective of helical springs but also can significantly improve the efficiency of the helical springs optimization.Index Terms-Helical springs, optimization design, number of active coils n, design variable, dependent variable.

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Section: B Analysis Of Error In Optimum Design Of Helical Springmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations