Tube Drawing Research Articles

Change in Surface Roughness on the Inner and Outer Surfaces of the Microtube during Hollow Sinking.

Hollow sinking experiments and tensile tests were conducted to clarify the evolution of surface roughness during hollow sinking. Stainless steel tubes (outer diameter: 1.5 mm; wall thickness: 0.045 mm) featuring a single grain spanning the wall thickness achieved via annealing as the starting material. The tube was drawn without an internal tool using a draw bench by controlling the tube drawing speed ratio of the die entrance and exit sides. The surface roughnesses of the inner and outer surfaces at the die entrance and exit sides of the drawn tube were compared with the surface roughnesses of the inner and outer surfaces under the uniaxial tensile deformation of the starting material. As a result, two major findings were revealed; the surface roughness formation behavior during the hollow sinking; the uniaxial tensile deformation exhibits a tube on both sides of the entrance and the exit of a die. Former uniaxial tensile deformation forms surface roughness of the tube at the die-entrance-side. However, hollow sinking reduces the roughness. The tube keeps its small roughness even though it is applied the later uniaxial tensile deformation behind the die exit. Furthermore, the conventional formula to predict the surface roughness of a metal sheet caused by the uniaxial tensile deformation can predict the surface roughness of a tube in the hollow sinking. At both die entrance and exit sides, the roughness of the inner surface was larger than that of the outer surface at the die entrance and exit side. The outer surface of the tube contacts the inside of a die when the tube passes through the die. The height of the convex parts decreased at that moment. Hollow sinking suppressed the increase in surface roughness of the inner surface as the outer surface was smoothed in the die. However, due to the formation of surface roughness after leaving the die, there is an overall increasing trend in inner surface roughness.

Clinical Application of ISO and CEN/TS Standards for Liquid Biopsies-Information Everybody Wants but Nobody Wants to Pay For.

Liquid biopsies are emerging as valuable clinical biomarkers for cancer monitoring. Although International Organization for Standards (ISO) and Technical Specifications from the European Committee for Standardization (CEN/TS) standardized workflows exist, their implementation in clinical practice is underdeveloped. We aimed to assess the applicability of ISO and CEN/TS standards in a real-world clinical setting, with a particular focus on evaluating the impact of preanalytical parameters and hemolysis on liquid biopsy analysis. We evaluated 659 peripheral blood samples from advanced prostate cancer patients against ISO and CEN/TS standards and documented all essential criteria, including tube draw order, filling level, temperature, and time tracking from blood draw to storage. We assessed hemolysis and its effect on circulating tumor DNA (ctDNA) and circulating tumor cell (CTC) analysis. Our results demonstrated a high compliance rate, with 96.2% (634/659) of samples meeting essential ISO and CEN/TS criteria. We did not observe a significant impact on ctDNA or CTC detection rates between hemolytic and nonhemolytic samples. Hemolysis was identified in 12.9% (40/311) of plasma samples from our advanced prostate cancer cohort, and within the draw order of 5 blood collection tubes, hemolysis did not significantly increase from tube 1 to 5. In total, 83.8% (552/659) of blood collection tubes had high fill levels above 80% of nominal filling level. Our study demonstrates the feasibility and benefits of adhering to ISO and CEN/TS standards in a clinical liquid biopsy study. The standards revealed that hemolysis occurred frequently but did not impair downstream ctDNA and CTC analysis in our cohort of advanced prostate cancer patients.

Evaluation of the outcomes of biliary-enteric reconstruction in robotic radical resection of hilar cholangiocarcinoma: a single-center propensity score matching analysis

Although robotic radical resection for hilar cholangiocarcinoma (HCCA) has been reported in some large hepatobiliary centers, biliary-enteric reconstruction (BER) remains a critical step that hampers the operation’s success. This study aimed to evaluate the feasibility and quality of BER in robotic radical resection of HCCA and propose technical recommendations. A retrospective study was conducted on patients with HCCA who underwent minimally invasive radical resection at Zhejiang Provincial People’s Hospital between January 2016 and July 2023. A 1:2 propensity score matching (PSM), widely used to reduce selection bias, was performed to evaluate the outcomes, especially BER-related data, between the robotic and laparoscopic surgery. Forty-six patients with HCCA were enrolled; ten underwent robotic-assisted resection, while the others underwent laparoscopic surgery. After PSM at a ratio of 1:2, 10 and 20 patients were assigned to the robot-assisted and laparoscopic groups, respectively. The baseline characteristics of both groups were generally well-balanced. The average liver resection time was longer in the robotic group than in the laparoscopic group (139.5 ± 38.8 vs 108.1 ± 35.8 min, P = 0.036). However, the former had less intraoperative blood loss [200 (50–500) vs 310 (100–850) ml], despite no statistical difference (P = 0.109). The number of residual bile ducts was 2.6 ± 1.3 and 2.7 ± 1.2 (P = 0.795), and anastomoses were both 1.6 ± 0.7 in the two groups (P = 0.965). The time of BER was 38.4 ± 13.6 and 59.1 ± 25.5 min (P = 0.024), accounting for 9.9 ± 2.8% and 15.4 ± 4.8% of the total operation time (P = 0.001). Although postoperative bile leakage incidence in laparoscopic group (40%) was higher than that in robotic group (10%), there was no significant difference between the two groups (P = 0.204); 6.7 ± 4.4 and 12.1 ± 11.7 days were observed for tube drawing (P = 0.019); anastomosis stenosis and calculus rate was 10% and 30% (P = 0.372), 0% and 15% (P = 0.532), respectively. Neither group had hemorrhage- or bile leakage-related deaths. Robotic radical resection for HCCA may offer perioperative outcomes comparable to conventional laparoscopic procedures and tends to be advantageous in terms of anastomosis time and quality. We are optimistic about its wide application in the future with the improvement of surgical techniques and experience.

Solid-Phase Orientation (Die Drawing) of Polymer Tubes to Enhance Mechanical Properties of Bioresorbable Vascular Scaffolds

Die-drawing, also known as solid phase orientation, is a technique used to enhance the mechanical properties of polymers for non-medical applications [1]. Arterius has adapted and optimised this technology to manufacture state-of-the-art bioresorbable polymeric scaffolds (stents) based on polylactic acid (PLA) for vascular and non-vascular applications. The mechanical properties of the polymer are improved by orientating the polymer chains and introducing crystallinity to the polymer. As the PLA polymer is drawn over a mandrel and through a die, close to the glass transition temperature (Tg > 55 °C), the polymer chains align, gradually increasing orientation with the bi-axial draw, thus promoting significantly improved mechanical properties. In-house testing of the die-drawn tubing compared to the extruded tubing showed an increase in tensile modulus up to 79.7%, yield strength increases of up to 121.5%, ultimate tensile strength increases of up to 267.9% and elongation at break increase of up to 1,022.8%. The die-drawing process also introduces crystallinity into the PLLA tubing, initially the amorphous extruded tube has a crystallinity of around 1.3% which increased to around 40% crystallinity after the die-drawn process. Another attribute of the orientated polymer tubing is the radial strength it provides to the scaffold once it has been laser cut into an innovative closed-cell design, which is comparable to market-leading metallic stents.

Precise glucose measurement in sodium fluoride-citrate plasma affects estimates of prevalence in diabetes and prediabetes.

Estimates of glucose concentrations vary among types of blood samples, which impact on the assessment of diabetes prevalence. Guidelines recommend a conversion factor to calculate plasma glucose from measurements of glucose in whole blood. The American Diabetes Association recommends the use of blood drawing tubes containing sodium fluoride (NaF) and citrate, which have not yet been evaluated regarding possible differences in glucose concentration and conversion factors. Thus, we compared glucose measurements in NaF-citrate plasma and venous whole blood and estimated the impact of differences on diabetes and prediabetes prevalence. Glucose differences were calculated by Bland-Altman analysis with pairwise comparison of glucose measurements from whole blood and NaF-citrate plasma (n=578) in clinical studies of the German Diabetes Center. Subsequently, we computed the impact of the glucose difference on diabetes and prediabetes prevalence in the population-based National Health and Nutrition Examination Survey (NHANES). Even upon conversion of whole blood to plasma glucose concentrations using the recommended conversion factor, mean glucose concentration difference remained 4.72 % higher in NaF-citrate plasma. Applying the higher glucose estimates, increases the population-based diabetes and prediabetes prevalence by 13.67 and 33.97 % or more than 7.2 and 13 million people in NHANES, respectively. Additional economic burden could be about 20 $ billion per year due to undiagnosed diabetes. The recommended conversion factor is not valid for NaF-citrate plasma. Systematic bias of glucose measurements due to sampling type leads to clinically relevant higher estimates of diabetes and prediabetes prevalence.

Cold Drawing of AISI 321 Stainless Steel Thin-Walled Seamless Tubes on a Floating Plug.

The paper presents the results of an analysis of the process of drawing AISI 321 stainless steel thin-walled seamless tubes on a floating plug. The influence of the geometry of dies and plugs, drawing velocity, and lubricants on the possibility of carrying out the pipe drawing process without a loss of strength of the lubricating film and, consequently, disturbance of the forming process and tube cracking, and also on the temperature in the drawing process, the mechanical properties of the tubes drawn, and the microhardness and roughness of the inner and outer surface of the tubes was investigated. The parameters of the drawing tools used were as follows: angle of drawing dies α = 16° and floating plugs with angles of inclination of the conical part of the plug β = 11.5°, 13°, and 14°. The drawing dies and floating plugs were made of G10 sintered carbide. Drawing speed was varied over the range 1 to 10 m/min. The study used several lubricants. Tubes with dimensions (outer diameter D0, wall thickness g0 before drawing process) D0 = 19 mm, g0 = 1.2 mm and D0 = 18 mm, g0 = 1.2 mm were drawn to produce tubes with dimensions (outer diameter Dk, wall thickness gk after drawing process) Dk = 16 mm, gk = 1.06 mm on a drawbench with the same total elongation, while the diameter and wall thickness were changed. During the process, continuous measurements were made of the drawing force and temperature in the deformation zone and on the tube surface. It was found that the drawing process causes a decrease in the roughness parameters Ra and Rz of the inner surface of the tubes. Moreover, after drawing, an increase of 30-70% was observed in the microhardness of the tube material in relation to the microhardness of the charge material. Based on the test results, it can be concluded that the work of frictional forces is the main direction of optimization of tube drawing on a floating plug process of hard-deforming materials.

GENERALIZED UPPER BOUND FORMULATION OF SOME RIGID-TRIANGLE VELOCITY FIELDS FOR PLANE-STRAIN EXTRUSION AND TUBE DRAWING

In this paper, upper bound solutions for plane-strain extrusion and plug drawing are presented using rigid-triangle velocity fields, assuming both the shear friction ([Formula: see text]) and the Coulomb friction ([Formula: see text]) conditions at the interfaces. For shear friction condition, the solutions are obtained following the classical approach. For this case, the energy dissipation rates of individual triangles are shown to be equal. For Coulomb friction condition, the analysis is carried out by the generalized upper bound formulation proposed by Collins. The energy dissipation rates of the individual triangles, in the deformation zone, for this friction condition, are found to be in geometric progression. Formulae are provided for the calculation of the lengths of contact and the contact pressures at the die/metal and plug/metal interfaces. Results are presented for mean extrusion/drawing stresses, as a function of reduction, for specified friction conditions and die/plug geometry. Values of optimum die/plug angles are determined graphically for given reductions and friction conditions. Finally, results for an alternative velocity field are presented for which the contact pressures on the die and the plug are nearly equal. The theoretical values are compared with some numerical and experimental results available in the literature.

Friction-related size effect during IN718 tube drawing: Realization of ultra-low friction

Drawing process, with the advantages of high accuracy and efficiency, is a common process for tube production. The high friction in tube drawing leads to high drawing forces, easy breakage of tube and high production costs, etc. It is urgent to reduce friction coefficient during the tube drawing. However, the effect of contact area on friction (friction-related size effect) along with the coupling effects of surface roughness, lubricants, and coatings is still unclear or even contradictory, which causes the reduction of the friction coefficient in tube drawing to become a challenge. In this study, taking IN718 tube drawing as the research object, the influence mechanism of contact area (1.25–12.06 mm2) as well as the coupling effects of surface roughness (0.513–0.622 µm), lubrication status, and coatings on friction was explored to reduce the friction coefficient as much as possible. Firstly, a new multi-sensor drawing device is designed to obtain contact pressure and drawing force, combined with finite element model, to characterize friction coefficient during the tube drawing. Secondly, the finite element model considering pits and lubricant is designed to reveal the friction mechanism in tube drawing. The results indicate that as the nominal contact area increases, the proportion of actual contact area decreases, leading to a decrease in friction coefficient, from 0.1102 to 0.0502, a decrease of 54.36%. The reduction of roughness leads to the weakening of plough effect, the coating leads to a transformation of the friction pair, and the lubricant bears some pressure, all of which can lead to a decrease in the friction coefficient, from 0.1203 to 0.0351, a decrease of 70.79%. By designing appropriate contact area (12.06 mm2), surface roughness (0.513 µm), lubrication status (graphite), and coating (sodium fluoride), the friction coefficient is sharply reduced from 0.1203 to 0.0014, a decrease of 98.79%. This in turn leads to a significant increase in the deformation amount, viz., the single pass drawing deformation amount is greatly improved from 14.22% to 49.65%. The research results have significantly reduced production costs.

Analysis of high velocity forming of metallic tubes

Metal forming is vital in many manufacturing industries for resizing and reshaping of raw metallic tubes and sheets. Conventional forming processes like forging, rolling, tube drawing and extrusion are associated with high-cost complex tools which are applicable for specific shape and size. High velocity deformation process utilizes impact energy for forming and deformation takes place at high velocity. This paper analyses the high velocity forming of 6061 aluminium tubes, formed under electromagnetic force. Numerical simulation is used to understand dynamic conditions of electromagnetic compressive forming.

Vplyv technologických parametrov pri prievlačnom ťahaní rúr na ich výsledné vlastnosti a presnosť

The article is focused on the implementation of experimental tests in order to monitor the impact of technological parameters during the drawing of tubes on their resulting properties and accuracy. In experimental tests, samples of seamless tubes with dimensions of Ø14, Ø16 and Ø18 were used, which were pulled by pressing to the final outer diameter of Ø12. Measurements of internal and external diameter as well as tensile tests to determine mechanical properties were carried out before and after drawing on the tubes. Experimental tests were carried out in order to optimize the drawing process to reduce the number of operations and reduce production costs.

3D scanning and 3D printing to develop internally helically ribbed tubes

We developed 3D scanning and rapid prototyping-based approach for an easier design of high precision, single pass tube drawing technology dedicated to the manufacturing of high-quality internally helically ribbed tubes. The major difficulty in the currently used process design is the identification of floating plug stability criterion allowing manufacturing of high precision helical ribs. The novelty of the proposed approach is therefore to use a combination of 3D scanning and rapid prototyping processes to design a complex floating plug geometry based on minimizing membrane energy. It was combined with computer-aided design of drawing die geometry and process parameters of the optimal tube drawing.

Relative Position of Plug and Die on Forming Accuracy of Shaped Tube by Cold Drawing

In the actual industrial production and manufacturing, tube drawing plays an extremely important role. In this study, a device with adjustable relative plug position is designed, the influence of relative plug position on the dimensional accuracy and the drawing force of drawn tube was investigated. The results show that different relative plug positions affect the inner and outer surface dimensions of the tube respectively. Therefore, the relative plug position can be distinguished according to the following rules in industrial production. When the position of the plug relative to the die is backward, the outer surface dimension of the drawn tube is qualified but the inner surface dimension is unqualified. When the position of the plug relative to the die is forward, the inner surface dimension of the drawn tube is qualified but the outer surface dimension is unqualified. The relative position of the plug is mainly due to the different radial force given to the tube by the plug and the die, resulting in the unqualified size of the drawn tube. When the plug is positioned backward relative to the die, the tube is subjected to the radial force of the plug first and then the radial force of the die. When the plug is positioned forward relative to the die, the tube is subjected to the radial force of the die first and then the radial force of the plug.

A statistical approach in the FEM simulation analysis of geometrical product specification during the cold tube drawing process

The cold drawing process produces high-quality tubes with precise dimensions, good surface quality, and higher strength due to cold forming. The tube drawing is used to reduce the cross section of the produced tubes. Depending on the reduction size, the outer diameter and wall thickness of the final tube changes. Due to the fact that cold drawing of tubes is mostly the last operation of production, it is necessary to pay attention to the process parameters and geometry of the forming tools. This paper presents a statistical evaluation of the influence of the wall thickness of the pre-tube, die diameter, and pre-tube diameter on the measured responses, which were the outer diameter and wall thickness of final tube, after the FEM simulations of the drawing process. For these purposes, a factorial design with three input factors was implemented. The goal of using the simulations was also to investigate whether the single-pass type of tube drawing would guarantee useful statistical results that could lead to significant time and cost reductions. The FEM simulations were executed using DEFORM software of Scientific Forming Technologies Corporation with Design of Experiment application module of this software. A factorial design of experiment has been processed in Minitab v. 17 software. The results show that most of the factors significantly influenced the response variables.

Special Cases of the Application of Forces in the Deformation Zone during Tube Drawing and Sheet Forming

Special Cases of the Application of Forces in the Deformation Zone during Tube Drawing and Sheet Forming

ANALYSIS AND COMPARISON OF GEOMETRIC DIMENSIONS OF COLD DRAWN TUBES USING FEM SIMULATION

The paper focuses on the analysis and comparison of tube wall thickness after cold drawing. The tube wall thickness obtained by the experiment was compared with the wall thickness obtained using finite element method (FEM) simulation in the simulation software DEFORM-3D. For the experiment the tube sinking technology was performed and all tubes were made of steel E235. Tubes were the outer diameter of Ø14, Ø16, Ø18 mm and the tube wall thickness was 1 and 2 mm. All tubes were drawn by single-pass tube sinking technology to the final diameter of Ø12 mm. Tube sinking process is a tube drawing technology through a drawing die without the use of a mandrel. Tube sinking is used as a final drawing operation, especially in the production of precision tubes of smaller diameter. The resulting comparison showed that the tube wall thickness obtained by the simulation in the DEFORM software very well matches with tube wall thickness obtained in the experiments. Based on the results, it can be stated that in the future it will be possible to replace some of the real experiments with FEM simulation in the DEFORM software.

THE RESEARCH OF INFLUENCE SIZE STRAIN AND NUMBER OF DRAWS ON DIMENSIONAL ACCURACY OF SEAMLESS TUBES MADE OF STEEL E235 AND E355

The die drawing process is used as a final drawing operation, especially in the production of precise tubes of smaller diameter, while the advantage of the mentioned technology is a reduction of the drawing force and thereby also the decrease of the risk of possible tube rupture during the drawing process. The paper is focused on the research of the influence of the strain size and the method drawing process on the final thickness of the wall and the outer diameter of the tube during die drawing. The sinking drawing experiment was performed by single-pass and two-pass drawing technology to the final tube diameter Ø12 mm without inter-operational annealing. The output of the paper are bar graphs that allows to compare the influence of the strain size and the method of tube drawing technology (single-pass and two-pass) on the dimensional accuracy of the final Ø12 mm tubes made of E235 and E355 steel. The advantage of the single-pass drawing technology when achieving the required wall thickness within the prescribed tolerance (±10 %) would be a reduction of the number of draws.It was found that only in one case of the two-pass drawing technology of E355 steel tube production, the permitted positive tolerance of the tube wall thickness was slightly exceeded, in the case of increasing the reduction (size strain R) from 24 % to 32 %.

The effect of ultrasonic vibrations on residual stresses and material properties of steel tubes during the cold tube drawing process

ABSTRACT In this study, the ultrasonically assisted plug vibrating tube drawing system was developed for an industrial draw bench and investigated using experimental and finite element (FE) modelling. The effect of ultrasonic vibrations on the induced residual stresses on the drawn steel tubes is evaluated using the mechanical and X-ray diffraction (×RD) method. The results indicate that the distribution of induced residual stresses mostly shows compressive stresses under ultrasonic vibrations. In contrast, the residual stresses are tensile in nature for conventionally drawn tubes, which are not very desirable. The experimental results show 11% reduction in draw load, while the FE analysis shows a 13% reduction in draw load, which indicates that the experimental and FE results are in good agreement. In addition, the effect of ultrasonic vibrations on the tensile strength, yield strength and percentage elongation is investigated and compared with samples from conventionally drawn tubes. The ultrasonic-assisted tube drawing has resulted in favourable tensile properties, which helps in improving the formability limit of the tubes. The Von Miss stress distribution obtained indicates that the ultrasonically assisted drawing results in a more uniform and lower Von Mises stress when compared to conventionally drawn tubes.

Extraordinary ductility enhancement of Mg-Nd-Zn-Zr alloy achieved by electropulsing treatment

Mg-Nd-Zn-Zr (JDBM) alloy was studied as a candidate for biodegradable implant material because of its moderate mechanical properties, good biocompatibility, and favorable uniform degradation behavior. To verify whether JDBM alloy exhibits electroplasticity effect and then study the mechanism of electropulsing treatment on JDBM alloy, in this study, homogenized and pre-tensile deformed samples were treated by electropulsing. After the electropulsing treatment, the average grain size was refined due to recrystallization, micron-scale Mg12Nd secondary phases precipitated slightly, while the morphology of nanoscale Zr particles changed from rodlike to ellipsoidal shape. The elongation to failure (EL) increased obviously for the homogenized and pre-tensile deformed JDBM alloy samples after electropulsing treatment, accompanying with no obvious sacrifice of the yield strength (YS) for the former and an evident decrease of YS for the latter, mainly due to the reduction of the dislocation density. The YS decrement and EL increment (77.57%) for the latter are more apparent attributed to the higher density of dislocations introduced by pre-tensile deformation. Therefore, the electropulsing treatment can obviously improve the mechanical properties of JDBM alloy, especially for the plasticity. The present work opens a new window for the fabrication of JDBM alloy profiles with high mechanical properties, especially for the plasticity, such as the cold drawing wires and tubes for biomedical applications. It also could provide theoretical references for other magnesium alloy processing.

Fabrication and characterization of biodegradable Zn-Cu-Mn alloy micro-tubes and vascular stents: Microstructure, texture, mechanical properties and corrosion behavior

Zinc (Zn) alloys are a promising biodegradable material for vascular stent applications. This study aimed to fabricate biodegradable Zn-2.0Cu-0.5Mn alloy micro-tubes and vascular stents with high dimensional accuracy and suitable mechanical properties, and to investigate their microstructure, texture, mechanical properties and corrosion behavior. The micro-tubes and vascular stents were successfully fabricated by a combined process of extrusion, drawing, laser cutting and electrochemical polishing. The microstructures of as-extruded and as-drawn micro-tubes consisted of Zn matrix with near-equiaxed grains (average grain size: ∼2 µm) and second phases of ε (CuZn4) and MnZn13 with different sizes. The texture evolved from basal planes approximately paralleling to deformation direction for as-extruded micro-tube to approximately perpendicular to deformation direction for as-drawn micro-tube, because predominant deformation mechanisms changed from basal <a> dislocation slip during tube extrusion to prismatic <a> dislocation, pyramidal <c+a> dislocations, and {101¯2} twins during tube drawing. As-drawn micro-tube exhibited suitable mechanical properties with an ultimate tensile strength of about 298 MPa and elongation of about 26% as a stent material. Moreover, the processed stent with a thickness of about 125 µm possessed sufficient radial strength of about 150 kPa and good balloon expandability. In addition, as-drawn tube exhibited an in vitro corrosion rate of about 158 µm/year with a basically uniform corrosion morphology. These results indicated that biodegradable Zn-2.0Cu-0.5Mn alloy is a promising vascular stent material candidate, and the procedure for processing the micro-tube and stent is practical and effective. Statement of significanceFabrication of micro-tubes followed by laser cutting and polishing is a common way to prepare metallic vascular stents. However, it is quite challenging to fabricate Zn-based stents using this standard method, and there is a lack of studies reporting processing details in the past. Biodegradable Zn-2.0Cu-0.5Mn alloy micro-tubes and vascular stents with high dimensional accuracy and suitable mechanical properties were successfully fabricated by a combined process in this study. As-drawn micro-tube exhibited an ultimate tensile strength of about 298 MPa and elongation of about 26%. The stent possessed sufficient radial strength of about 150 kPa and good balloon expandability. We demonstrated a practical method to fabricate biodegradable Zn-based micro-tubes and stents with high dimensional accuracy and mechanical properties.

On implementation of a semi-analytic strategy to develop an analytical solution of a steady-state isothermal tube drawing model

In this paper, we consider an isothermal glass tube drawing model consisting of three coupled nonlinear partial differential equations. The steady-state solution of this model is required in order to investigate its stability. With the given initial and boundary conditions, it is not possible to determine an analytical solution of this model. The difficulty lies in determining the constants of integrations while solving the second order ordinary differential equation analytically appearing in the steady-state model. To overcome this difficulty, we present a numerical based approach for the first time to develop an analytical solution of the steady-state isothermal tube drawing model. We use a numerical technique called shooting method to convert the boundary value problem into a set of initial value problems. Once the model has been converted into a system of differential equations with initial values, an integrating technique is implemented to develop the analytical solution. The computed analytical solution is then compared with the numerical solution to better understand the accuracy of obtained solution with necessary discussions.