Calculation method and experimental study of coulomb friction coefficient in sheet metal forming

Abstract

Friction is one of the important factors influencing the formability of sheet metal and improving the forming quality. According to the relationship between the drawing force and the stroke, the linear fitting algorithm of the friction coefficient is given based on the least squares method. Based on the drawing die of the cylindrical parts, a friction coefficient measuring apparatus is developed, which has fixed calculation program. Through a series of deep drawing tests, the friction coefficients and force-stroke curves are measured for different combinations of sheet metal and lubricant. What’s more,the drawing process of the cylindrical part with different specifications is carried out to examine the application of the measured friction coefficient. The results show that the friction coefficient calculated by the linear fitting algorithm can accurately reflect the friction state of the whole drawing process; the measurement of the friction coefficient is not limited by the size of the mould; the established test system, can be used for the measurement of friction coefficient in sheet metal forming.

Introduction

Compared to the castings or forgings, the metal stamping parts have the smaller quality, less materials, better organization and lower cost, so they are widely used in automotive, aircraft, electronic information, instrumentation and other fields. As an important technical parameter of sheet metal, the friction coefficient influenced by many factors, such as blank material, die geometry parameters, lubrication condition, forming process parameters, directly affects the quality of the forming parts. Therefore, it is important to determine the friction condition of different forming processes, which is of great significance to determine the formability of sheet metal and improve the forming quality.

From a numerical point of view, the virtual try-out of sheet metal forming(SMF) based on the finite element method has enormous economical advantage, where, the contact friction problem is a very interesting topic [1]. Furthermore, tribological properties and frictional processes play a decisive role in determining the quality of forming parts [2]. Coulomb friction model was frequently used in simulations to model the frictional behaviour of contacting solids, which used a constant coefficient characterizing the friction condition in the entire contact area during the whole forming process [3]. In addition, some numerical simulations showed a difference in metal flow owing to the differences in the friction coefficient [4]. Therefore, the selection of the constant value directly affects the accuracy of the model and the simulation results. In fact, the friction coefficient is generally estimated by experience at present, which leads to the error between the friction model and the actual forming process.

In the process of SMF, the research of friction condition is mainly focused on two aspects: theoretical research and experimental study. The purpose of theoretical research is to establish a mechanical friction model to predict the friction in the forming process. Based on the classical coulomb friction model, many improved friction models are proposed. For instance, a new friction model in terms of lubricant viscosity and surface roughness was suggested using the finite element analysis of SMF processes [5]; a new friction model under dry contact conditions of metal forming processes was developed, which is a function of contact area ratio and strain hardening exponent [6]; considering the change of the surface texture and its influence on the friction behavior on the macro-scale, a advanced friction model was developed for large-scale forming simulations [7]; based on local contact conditions, a new friction model was presented and used in the finite element simulations of the deep drawing process [8]. While, the complexity of the models increase there difficulty of the practical application.

Friction test is the most effective and direct way to study the friction state in SMF process, which roughly divided into three categories: drawbead simulator [9], strip-tension friction tests [10], bending-under-tension (BUT) tests [11]. Later researchers [12], [13], [14], [15], [16] improved these classical friction test devices, to investigate the effect of blank material, surface roughness and lubricant viscosity on friction coefficient. However, fundamentally speaking, these devices are only simulators to study the friction, which is can not fully reflect the complex friction condition in the actual forming process. For example, drawbead simulator mainly tests the friction condition between the die and blank holder, which is failed to reflect the change of friction coefficient in each region caused by different stress modes. While, for BUT tests, the device is so simple that it is easy to measure the lubricant quality, but not be applied in the process with a changed bending angle. As a result, the measured friction coefficient has great limitations.

SMF is a complex process of elastic-plastic deformation, accompanied by nonlinear stress-strain relations, complex boundary conditions, and large deformation. At present, it is difficult to build a mathematical or mechanical friction model that can reflect the entire plastic deformation process, but also for all the SMF forming. Therefore, we have selected the drawing process of cylindrical parts, which has a more typical friction conditions.Furthermore, Zhao et al. had investigated the stress and strain distribution and the friction state between sheet-blank holder and sheet-die radius, and established the accurate mechanical model of deep drawing process [17]. Further more, they developed an intellectualized control system for deep drawing processing of axi-symmetric shell part, which could monitor and output the blank holder force, drawing force, stroke and friction coefficient [18]. However, the measured friction coefficient can not reflect the entire drawing process, which will be discussed in Section 2.2, and the identification system obtains too many parameters to ensure a higher accuracy, so Zhao is more inclined to use neural network for online identification in his latter research [19], [20], [21].

Based on the punch force-stroke curve in deep drawing established by Zhao, the nonlinear problem is transformed into a linearized calculation according to the least squares method, and the linear fitting algorithm of friction coefficient is obtained. Then, a friction coefficient test system is built, which has fixed calculation program. A series of deep drawing tests for different combinations of sheet metal and lubricant is carried out and the accuracy of the calculation method is verified by comparing the theoretical and measured force-stroke curves.