Existence of a weak solution to a nonlinear induction hardening problem with Leblond-Devaux model for a steel workpiece

2021 ◽  
pp. 106156
Author(s):  
Van Chien Le ◽  
Marián Slodička ◽  
Karel Van Bockstal
Keyword(s):  
Weak Solution ◽  
Induction Hardening

On a Nonlinear System of Reaction-Diffusion Equations

2006 ◽  
Vol 11 (2) ◽  
pp. 115-121 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Weak Solution ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic System ◽  
Positive Parameter ◽  
Nonlinear Elliptic ◽  
Positive Weak Solution

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system.

Electrotechnical Problems during Induction Hardening of Large Products

2019 ◽  
Vol 90 (12) ◽  
pp. 781-785 ◽  
Author(s):  
V. B. Demidovich ◽  
Yu. Yu. Perevalov
Keyword(s):  
Induction Hardening

Effect of Inductor Design on the Hardness after Induction Hardening using Line Inductors

2018 ◽  
Vol 73 (4) ◽  
pp. 202-210
Author(s):  
D. Schlesselmann ◽  
C. Krause ◽  
M. Schaudig
Keyword(s):  
Induction Hardening

Bearing Steels for Induction Hardening – Part II

2016 ◽  
Vol 71 (5) ◽  
pp. 218-229 ◽  
Author(s):  
M. Wendel ◽  
F. Hoffmann ◽  
W. Datchary
Keyword(s):  
Induction Hardening ◽  
Bearing Steels

SAE 1053

Alloy Digest ◽  
1977 ◽  
Vol 26 (11) ◽  
Keyword(s):  
Corrosion Resistance ◽  
Carbon Steel ◽  
Physical Properties ◽  
Tensile Properties ◽  
Induction Hardening ◽  
High Strength ◽  
Heat Treating ◽  
Agricultural Machinery ◽  
Hand Tools ◽  
Steel Mills

Abstract SAE 10053 is an oil or water-hardening machinery and tool steel for applications where a shallow-hardening steel of high strength with moderate toughness meets the requirements. It is commonly used for parts where induction hardening or austempering are employed. SAE 1053 is recommended for agricultural machinery and tools, hand tools, shafts, springs and heavy-machinery parts. This datasheet provides information on composition, physical properties, hardness, elasticity, and tensile properties. It also includes information on corrosion resistance as well as forming, heat treating, machining, and joining. Filing Code: CS-70. Producer or source: Carbon steel mills.

scholarly journals Initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Liming Xiao ◽  
Mingkun Li
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Higher Order ◽  
Evolution Problem ◽  
Positive Energy ◽  
Initial Boundary Value

AbstractIn this paper, we study the initial boundary value problem for a class of higher-order n-dimensional nonlinear pseudo-parabolic equations which do not have positive energy and come from the soil mechanics, the heat conduction, and the nonlinear optics. By the mountain pass theorem we first prove the existence of nonzero weak solution to the static problem, which is the important basis of evolution problem, then based on the method of potential well we prove the existence of global weak solution to the evolution problem.

scholarly journals Influence of Deep Rolling and Induction Hardening on Microstructure Evolution of Crankshaft Sections made from 38MnSiVS5 and 42CrMo4

2021 ◽  
Vol 76 (3) ◽  
pp. 175-194
Author(s):  
A. Fischer ◽  
B. Scholtes ◽  
T. Niendorf
Keyword(s):  
Process Parameters ◽  
Microstructure Evolution ◽  
Surface Hardening ◽  
Qualitative Evaluation ◽  
Induction Hardening ◽  
Deep Rolling ◽  
Automotive Components ◽  
Hardening Treatment ◽  
Steel Grades ◽  
Definition Of

Abstract In order to improve properties of complex automotive components, such as crankshafts, in an application-oriented way, several surface hardening treatments can be applied. Concerning the material performance the definition of adequate process parameters influences the resulting surface properties and, thus, the effectiveness of surface hardening treatments. To analyze most relevant process-microstructure-property relationships, the present paper reports results obtained by two different well-established surface hardening procedures, i. e. deep rolling as a mechanical treatment and induction hardening as a thermal treatment. For each hardening process widely used crankshaft steel grades, i. e. a medium carbon 38MnSiVS5 microalloyed steel and a quenched and tempered 42CrMo4 were selected and thoroughly characterized upon processing, using equal parameter settings. The results reveal that deep rolling in contrast to induction hardening proves to be a less sensitive surface layer treatment with regard to small differences in the initial microstructure, the chemical composition and the applied process parameters. Differences in microstructure evolution with respect to the applied surface hardening treatment are studied and discussed for the highly stressed fillet region of automotive crankshaft sections for all conditions. In this context, high-resolution SEM-based techniques such as EBSD and ECCI are proven to be very effective for fast qualitative evaluation of induced microstructural changes.

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