A finite element analysis of orthogonal rubber cutting

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Abstract

An explicit plane strain FE model using ABAQUS/Explicit was developed to analyze rubber cutting using high-speed steel (HSS) tools. The initial and deformed meshes, as the cutting reaches steady state condition, are first described. The neo-Hookean constitutive model for the hyperelastic material considering the effective stress failure criterion is then introduced. The advantages of applying explicit method on the simulation of rubber cutting process over its implicit counterpart are discussed. The model was used to predict cutting forces, chip shape, stress and strain fields, and strain energy distribution in the chip and workpiece. Orthogonal cutting experiments were conducted for several rake angles and feeds to validate the FE model. Good agreement was found between the predicted and measured cutting forces. Favorable cutting conditions for formation of a smooth machined surface were identified by both simulations and experiments. The finite element model provides new insight into the chip formation process of rubber cutting.

Introduction

Rubber is designated as loosely cross-linked macromolecular polymers (frequently also called elastomers). Rubber can be stretched by at least double their original length by the effect of a weak force at room temperature (or higher temperatures) and return quickly to their original shape (rubber-like elastic behavior) on removal of the force [1]. Rubber is widely used in various military equipments and industries in a wide range of applications including liner layers of armored vehicles, tires, springs, shock isolators, noise and vibration absorbers, seals, corrosion and abrasion protection, and electrical and thermal insulators. Most rubber components are typically manufactured by a molding process in which a composition of raw material and addition additives are subjected to a controlled temperature-pressure cycle to produce the desired shapes and properties. The disadvantages of this method include the high cost and labor-intensive process of manufacturing the mold and the inflexibility of the mold to various designs [2]. As an alternative, rubber machining is proposed to reduce production costs by eliminating the molding process, which would be especially useful for manufacturing low volume prototype parts and other applications requiring a complex shape and frequently modified designs. Potential applications of machining rubber include prototype tire and footwear tread patterns, custom seals for biomedical applications, tire recycling industries and specialty vibration dampers. Rubber possesses many unique material properties, compared to other engineering materials. Under ambient temperature, rubber has a very low elastic modulus and high percentage of elongation before fracture. Rubber could deteriorate even melt in the machining process as the excessive heat is generated and accumulated during the machining process due to rubber's low thermal conductivity, hysteresis and low softening temperature. Improper usage of organic coolants and lubricants during the machining process can also deteriorate rubber's mechanical properties [1], [2]. All of above make the machining of rubber a really challenging task.

Very little experimental research on rubber machining has been reported because of the material complexity of rubber and the machining process itself. High speed rubber milling experiment was conducted by Jin and Murakawa [3]. They used several carbide end mill tools of various sizes and helix angles to cut grooves on three types of soft rubber, H-NBR, Norbornone rubber and silicone rubber, at various speeds. Better surface quality in terms of roughness and flatness was observed for machining at high speeds with high helix angle cutters. Lewis [4] conducted a series of milling tests on ambient and solid carbon dioxide cooled rubber plates with woodworking tools of different geometries. Fixture design and tool shape was found crucial in producing a clean groove surface. Strenkowski et al. [5] and Rodkwan [6] performed several elastomer turning experiments with HSS tools of various geometries and cutting parameters. Large rake angles, cutting speeds and feed rates were found helpful to form a good surface finish. Even less numerical analysis has been performed on simulating rubber machining processes. Strenkowski et al. [5] and Rodkwan [6] studied the indentation of elastomers and preliminary elastomer cutting simulation by using ABAQUS/Standard.

Finite element method has been widely used as an appropriate numerical method to simulate machining processes for many years. Orthogonal cutting process is the most simplified process without losing the nature of cutting. Finite element analysis of orthogonal cutting process, particularly for metal, has been studied extensively [7], [8], [9]. It has been proved to be a very efficient way to study the metal cutting process. Based on that, finite element analysis of more complex work and tool geometries and their configurations has been carried out [10].

Orthogonal rubber cutting is a complex nonlinear, large deformation process bundled with material failure criterion. It has all three sources of nonlinearities, i.e., material nonliearity (hyperelastic material), boundary nonlinearity (contact behavior) and geometric nonlinearity (finite deformation). To address these problems, the explicit dynamic FEA code, ABAQUS/Explicit, was used in this study. Several advantages by using ABAQUS/Explicit for modelling orthogonal rubber cutting processes are summarized as follows [10]. (1) It is a well known nonlinear FEA code and widely used by academic research units as well as industries. Its effectiveness to nonlinear problems has been proved by many practical examples. (2) It has an extensive material library including almost all material models currently known, if not, the users can define their own material subroutines once the constitutive laws have been derived. (3) Crack propagation is much more easy and flexible to implement using the element deletion option compared to its implicit counterpart. (4) Algorithm is conditional stable as long as the time increment is less than the critical stability limit. Iteration, assembly and inverse of stiffness matrix can be avoided by using explicit integral formulation and lumped mass matrix. Therefore, computational cost for each time increment is reduced significantly.

In this paper, the finite element analysis procedure of orthogonal rubber cutting, including the design of finite element meshes, and determination of hyperelastic material model coefficient, is first described. Detailed finite element analysis results, such as cutting forces, chip shape, and stress, strain and strain energy density fields, are then presented to gain better understanding of orthogonal rubber cutting process. Cutting forces measured from orthogonal cutting experiments were used to validate the FE model. Good agreement was found between the computed and measured forces.

Section snippets

Finite element analysis procedure

A finite element analysis of orthogonal rubber cutting was conducted using experimentally determined material properties to predict the cutting forces, chip shape and machined surface profile. Three rake angles (10°, 30°, and 50°) were simulated for three feeds of 0.064, 0.127, and 0.254 mm, respectively.

Numerical results

The predicted von Mises stress contours are shown in Fig. 2(a–c) for rake angles of 10°, 30°, and 50°, respectively. These figures also show photographs of the actural chips and machined surfaces that were obtained in the cutting experiments. As can be seen in Fig. 2(a), the simulation predicted a discountinuous chip that agrees with the chips obtained in the experiments. Similarly, Fig. 2(c) shows that the simulation predicted a continuous chip with small curvature that matches the

Cutting experiments

A series of rubber turning tests were conducted, as shown in Fig. 6, using a conventional Republic Lagun CMZ lathe to validate the finite element model and to better understand the chip formation process and cutting conditions for which a smooth machined surface finish can be achieved. The workpiece consisted of a rubber tube with a large diameter of 95.25 mm and a small wall thickness of 11.61 mm. Table 1 lists some properties for the selected test rubber material. To achieve orthogonal

Conclusions

A plane strain finite element model was developed for simulating the orthogonal rubber cutting process. Neo-Hookean hyperelastic material model was implemented as user material subroutine to simulate the nonlinear mechanical behaviors of rubber-like material. The model was used to predict the cutting forces, chip shape, stress and strain contours, and the strain energy density field in the chip and workpiece. Orthogonal cutting experiments were conducted for several rake angles and feeds. Good

Acknowledgments

The authors gratefully acknowledge the support of National Science Foundation (Dr. K.P. Rajurkar, Program Director) under grant DMI-0099829. The Lord Corporation is acknowledged for supplying test samples and providing material response data.

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