Multi-scale friction modeling for manufacturing processes: The boundary layer regime

This paper presents a multi-scale friction model for largescale forming simulations. A friction framework has been developed including the effect of surface changes due to normal loading and straining the underlying bulk material. A fast and efficient translation from micro to macro modeling, based on stochastic methods, is incorporated to reduce the computational effort. Adhesion and ploughing effects have been accounted for to characterize friction conditions on the micro scale. A discrete model has been adopted which accounts for the formation of contact patches ploughing through the contacting material. To simulate metal forming processes a coupling has been made with an implicit Finite Element code. Simulations on a typical metal formed product shows a distribution of friction values. The modest increase in simulation time, compared to a standard Coulomb-based FE simulation, proves the numerical feasibility of the proposed method

자동차용 판재성형 해석 적용을 위한 다중 스케일 마찰 모델 개발 및 평가

학위논문(박사) -- 서울대학교대학원 : 공과대학 재료공학부, 2022.2. 이명규.Sheet metal forming of advanced high strength steels (AHSS) has drawn significant attentions in automotive industry for their improved fuel efficiency by lightweightness and passenger safety by higher strength. However, the manufacturing of automotive parts with the AHSS accompanies inferior springback and formability compared to the conventional lower strength steels, which results in more time consuming trial and error in the tool design stage. To overcome this challenges in applying the AHSS to the automotive parts, finite element simulations have been commonly used as a numerical tool for predicting springback and formability of sheet metal parts prior to real try-out. Accurate modeling of finite element simulation in sheet metal forming process requires reliable numerical techniques, constitutive models, realistic boundary conditions, etc. Among these, the friction is one of important factors to determine the accuracy of the simulation, but it has been overlooked in most simulations. The frictional behavior in sheet metal forming is known to be very complex and depend on various parameters such as surface roughness, contact pressure, sliding velocity, lubrication condition, etc. However, it is a common practice to use the simplest Coulomb friction law in the finite element modeling. In the present study, a microscale asperity based friction model is further modified by imposing new model parameters for satisfying force equilibrium between contact surfaces. In addition, a geometrical shape model of the tool surface is newly proposed to determine the plowing effect of the friction. The tool geometry is modeled based on primary summits in tool height distribution determined by the measured wavelength, rather than the summits dependent on the resolution of surface measurement instrument. The friction models are required not only in the preceding boundary lubrication condition, but also in the mixed-boundary lubrication condition where sufficient lubrication exists in non-contacting surface valleys. The hydrodynamic friction model uses a load-sharing concept that considers the lubrication area and metal-to-metal contact separately. In this study, the hydrodynamic friction model is combined with the boundary lubrication friction model to account for the friction in the mixed lubrication domain. The lubricant film thickness, calculated as the volume of non-contacting surface valleys, is used to realize the coupling. The film lubrication behavior is implemented by the finite element coding of the Reynolds equation, which enables the calculation of the hydrodynamic pressure. To validate the boundary lubrication friction model, the calculated friction coefficient and the measured friction coefficient are compared according to the contact pressure under boundary lubrication conditions. Also, the boundary lubrication friction model is verified by the finite element simulation that is applied to the U-draw/bending process. Finally, the boundary lubrication friction model and the mixed boundary lubrication friction model are applied to the finite element simulation of the newly developed press-forming process, which represents the influence of various variables such as contact pressure, sliding speed and lubrication. The results of the validations show that the developed multi-scale friction models and their implementation can be efficiently used to the sheet metal forming simulations where the frictional behavior is critical for the quality of the automotive parts.AHSS(고장력강판)의 판금 성형은 경량화에 의한 연비 향상과 고강도화에 의한 승객 안전으로 자동차 산업에서 큰 주목을 받고 있습니다. 그러나 AHSS를 이용한 자동차 부품 제조는 기존의 저강도 강재에 비해 스프링백 및 성형성이 좋지않기에 툴 설계 단계에서 시행착오가 더 많이 발생하게 됩니다. 자동차 부품에 AHSS를 적용할 때 이러한 문제를 극복하기 위해 유한 요소 시뮬레이션은 실제 시험 전에 판재 성형 부품의 스프링백 및 성형성을 예측하기 위한 수치해석적 도구로 일반적으로 사용되었습니다. 판재 성형 공정에서 유한 요소 시뮬레이션의 정확한 모델링은 신뢰할 수 있는 수치해석적 기술, 구성 방정식, 정확한 경계 조건 등이 필요합니다. 이 중 마찰은 시뮬레이션의 정확도를 결정하는 중요한 요소 중 하나이지만 대부분의 시뮬레이션에서 간과되어 왔습니다. 판재 성형에서 마찰 거동은 매우 복잡하고 표면 거칠기, 접촉 압력, 미끄럼 속도, 윤활 조건 등과 같은 다양한 매개변수에 따라 달라지는 것으로 알려져 있습니다. 그러나, 대부분의 유한 요소 해석에서 가장 간단한 쿨롱 마찰 법칙을 사용하는 것이 일반적입니다. 본 연구에서는 접촉면 사이의 힘 평형을 만족시키기 위해 새로운 모델 매개변수를 부과하여 마이크로 스케일 돌기 기반 마찰 모델을 추가로 수정했습니다. 또한 마찰의 쟁기질 효과를 결정하기 위해 툴 표면의 기하학적 형상 모델이 새로 제안되었습니다. 툴 형상은 표면 측정 장비의 분해능에 의존하는 정점이 아니라 측정된 파장에 의해 결정되는 툴표면 높이 조도의 서밋을 기반으로 모델링됩니다. 마찰모델은 경계윤활조건뿐만 아니라 충분한 윤활이 존재하는 혼합경계윤활조건에서도 필요하다. 유체역학적 마찰 모델은 윤활 영역과 금속 대 금속 접촉을 별도로 고려하는 하중 공유 개념을 사용합니다. 본 연구에서는 유체역학적 마찰 모델을 경계 윤활 마찰 모델과 결합하여 혼합 윤활 영역의 마찰을 설명합니다. 비접촉 표면 밸리의 부피로 계산된 윤활유 필름 두께는 커플링을 구현하는 데 사용됩니다. 필름 윤활 거동은 유체역학적 압력의 계산을 가능하게 하는 Reynolds 방정식의 유한 요소 방법을 사용해 구현됩니다. 경계 윤활 마찰 모델을 검증하기 위해 경계 윤활 조건에서 접촉 압력에 따라 계산된 마찰 계수와 측정된 마찰 계수를 비교합니다. 또한 경계 윤활 마찰 모델은 U-draw/bending 과정에 적용된 유한 요소 시뮬레이션을 통해 검증되었습니다. 마지막으로 경계 윤활 마찰 모델과 혼합 경계 윤활 마찰 모델을 새로 개발된 프레스 성형 공정의 유한 요소 시뮬레이션에 적용했는데, 이는 접촉 압력, 미끄럼 속도 및 윤활과 같은 다양한 변수의 영향을 나타냅니다. 검증 결과는 개발된 다중 스케일 마찰 모델과 그 구현이 마찰 거동이 자동차 부품 품질에 중요한 판재 성형 시뮬레이션에 효율적으로 사용될 수 있음을 보여줍니다.1. Introduction 1 1.1. Sheet metal forming and deep drawing process 1 1.2. Motivation and objective 2 1.3. Literature review 5 1.3.1. Friction modeling on the boundary lubrication condition 6 1.3.2. Friction modeling on the mixed-boundary lubrication condition 22 2. Friction model in boundary lubrication 35 2.1. Framework of friction model in boundary lubrication 35 2.2. Statistical contact model for describing surface deformation 38 2.2.1. Assumptions for modeling 39 2.2.2. Flattening of workpiece asperity due to normal load 41 2.2.3. Flattening of workpiece asperity due to normal load and sliding 48 2.2.4. Flattening of workpiece asperity due to normal load and bulk strain 50 2.3. Friction model through a new approach 53 2.3.1. An elliptical paraboloid asperity model 53 2.3.2. A tool geometry model 56 3. Friction model in mixed-boundary lubrication 65 3.1. Overview of the mixed-boundary friction model (Hol [106]) 67 3.2. Finite element modeling for film fluid behavior 71 3.3. Verification of the developed finite element modeling 75 4. Application of boundary lubrication and mixed-boundary lubrication friction model to sheet metal forming process 82 4.1. Friction model parameters 82 4.1.1. Material properties 82 4.1.2. Surface data 83 4.1.3. Friction experiments 86 4.2. Application to sheet metal forming processes under non-lubrication conditions 91 4.2.1. Application to U-draw/bending simulation 94 4.2.2. Application to prototype press-forming process without lubricant 105 4.3. Application to sheet metal forming processes under lubrication conditions 116 5. Conclusions 129 Reference 134박

Numerical Simulation in Microforming for Very Small Metal Elements

Microforming is a technology of very small metal elements production, which are required as a parts for many industrial products resulting from microtechnology. This chapter gives a review of the state-of-the-art microforming of metals and its numerical simulations. Phenomena occurring in the miniaturization of microbulk-forming technologies are described. The main problems in microforming are size effects, which have physical and structural sources and directly affect the material flow mechanics in microscale. Size effects must be taken into account in all areas of the forming process chain, demanding new solutions, especially in workpiece structure and die surface numerical modeling

Advanced friction modeling in sheet metal forming

The Coulomb friction model is frequently used for sheet metal forming simulations. This model incorporates a constant coefficient of friction and does not take the influence of important parameters such as contact pressure or deformation of the sheet material into account. This article presents a more advanced friction model for large-scale forming simulations based on the surface changes on the micro-scale. When two surfaces are in contact, the surface texture of a material changes due to the combination of normal loading and stretching. Consequently, shear stresses between contacting surfaces, caused by the adhesion and ploughing effect between contacting asperities, will change when the surface texture changes. A friction model has been developed which accounts for these microscopic dependencies and its influence on the friction behavior on the macro-scale. The friction model has been validated by means of finite element simulations on the micro-scale and has been implemented in a finite element code to run large scale sheet metal forming simulations. Results showed a realistic distribution of the coefficient of friction depending on the local process conditions