Numerical optimisation of process parameters for combined quasi‐static and impulse forming

Rozgic̀, Marco; Taebi, F.; Stiemer, Marcus

doi:10.1002/pamm.201210301

Cited by 2 publications

(4 citation statements)

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“…On the other hand the formulation introduced in [2] can be applied to a broad number of applications. The method works as a black box because it only needs the solution of the PDE and works with numerical approximations to the derivatives, which have been proven to be stable [3]. In particular the method is robust against model changes.…”

Section: Resultsmentioning

confidence: 99%

“…Optimization problem (1) is a quadratic problem in the vector of displacements u, with linear equality constraints in u. The vector b (p) on the right hand side of the equality constraint is the only quantity depending on the parameter vector p. The numerical comparison will be made with the following problem, which is discussed in full detail in [2,3]:…”

Section: Linear Elastic Modelmentioning

confidence: 99%

“…Mathematical optimization and simulation offers to be a tool to achieve these enhancements, due to its versatility and its lower cost compared to experiments. To find optimal parameter sets various black-box methods have been exploited and applied [2,3]. The major drawbacks of these methods are that they strongly rely on the finite element method (FEM) solver in use, and that no exact derivative information can be utilized.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Comparison of Optimization Methods for Process Parameters Identification in Forming Technology

Stiemer

2014

Proc Appl Math and Mech

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Section: Resultsmentioning

confidence: 99%

Section: Linear Elastic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Comparison of Optimization Methods for Process Parameters Identification in Forming Technology

Stiemer

2014

Proc Appl Math and Mech

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“…In earlier works [4] the effects of function linearisation in the scope of linear elasticity have been studied. Following this approach the current work investigates the influence of the finite-element discretisation on the identification of ideal force parameters in the case of viscoplasticity.…”

Section: Model Problemmentioning

confidence: 99%

Enhanced Identification of Process Parameters in Technological Forming

Rozgic̀

Appel

Stiemer

2013

Proc Appl Math and Mech

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Mathematical optimisation of real technological forming processes requires expensive simulations to evaluate objective function and constraint values as well as their derivative and Hessian information. The costs of these evaluations are directly correlated to the refinement depth of the finite-element discretisation. This work investigates the effect of the refinement level on the result and convergence behaviour of algorithmic process parameter identification with an elastoviscoplastic material model. Numerical optimisation in forming technologyIn 1998 Vohnout [1] pointed out, that an extension of classical forming limits is possible by combining quasi-static deep drawing with an impulse forming method as, e.g., electromagnetic forming. In the second process strain rates of several 1000 s −1 are achieved by Lorentz forces triggered in a work piece by the magnetic field of an adjacent tool coil, which is excited by a pulsed current of several 10000 Ampère within approximately 10 µs (see [2] for details). However, it has become obvious, that process parameters (e.g., frequency, amplitude, damping of the input current, drawing radii, tribological parameters, etc.) that really lead to an extension of classical forming limits are experimentally difficult to find. To this end, Taebi et al. [3] proposed a method to determine suitable parameters by mathematical optimisation. A finite-element-simulation of the whole process chain has been developed in [3] and employed to compute the deviation of a work piece deformed by deep drawing and subsequent electromagnetic forming from an ideal shaped one. This has been used in the context of the SQP method to determine optimum process parameters. The optimisation problem reads as follows:Here s(λ, x) denotes a parametrisation of the computed surface of the work piece depending on a list of parameters λ ∈ Ê n and s opt (x) a prescribed ideal form, further S is a referential configuration with area meas S. The function c measures the distance of a minor and major strain pair (ǫ 1 , ǫ 2 ) to the forming limit surface, i.e., to the locus of material failure (necking) in a forming limit diagram extended by an axis for the strain rate (see [3] for details). The constraints ensure that forming limits are never violated. This type of forming limits for dynamical processes extend the classical forming limit diagram. Model ProblemIn earlier works [4] the effects of function linearisation in the scope of linear elasticity have been studied. Following this approach the current work investigates the influence of the finite-element discretisation on the identification of ideal force parameters in the case of viscoplasticity. Although the mechanical model accounts for strain rate effects the constraints in this scope result from a quasi-static failure analysis, since the main concern here is the convergence behaviour of the proposed algorithm, for the time being. The elastoviscoplastic model for small deformations studied in this scope is based on [5] and is given bywith the deformation field...

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Numerical optimisation of process parameters for combined quasi‐static and impulse forming

Cited by 2 publications

References 3 publications

Numerical Comparison of Optimization Methods for Process Parameters Identification in Forming Technology

Numerical Comparison of Optimization Methods for Process Parameters Identification in Forming Technology

Enhanced Identification of Process Parameters in Technological Forming

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