Transition Fillet Treatment in Equal-Diameter Tee Extrusion Die Design

Literature Overview

This paper by Xu Jisheng, Su Shenggui, and Tang Jinglin from Yanshan University, published in New Technology New Process (Issue 1, 1995, p. 22), addresses a specific but critical aspect of die design for extruding equal-diameter tee fittings. The paper focuses on the transition fillet treatment at the intersection of two cylindrical cavities in the extrusion die, and discusses both the geometric design of the fillet and the CNC machining programming approach.

Core Technical Challenge

In the extrusion of tee fittings, the die cavity must reproduce the complex geometry of the tee, including the intersection region where the branch pipe meets the main pipe. The intersection of two cylinders of equal diameter creates a hyperboloid surface, which presents significant challenges for both die design and machining. Without proper fillet treatment, the sharp intersection edges would cause severe stress concentrations in the die material, leading to premature die failure, and would also impede material flow during extrusion, resulting in defects such as wall thickness variation, surface tearing, and die wear at the intersection.

Fillet Design Principles

Design Parameter	Recommended Value	Rationale
Fillet radius (R)	2–5 mm (for standard tees)	Balances stress relief and geometric fidelity
Fillet depth	0.5–1.0 mm	Prevents material stagnation while maintaining wall thickness
Transition angle	30°–45° from vertical	Optimizes material flow convergence
Surface finish of fillet	Ra ≤ 0.8 μm	Reduces friction and material adhesion

The fillet serves three primary functions: first, it reduces stress concentration in the die at the geometric discontinuity, extending die life; second, it provides a smooth material flow path during extrusion, preventing material stagnation and ensuring uniform wall thickness; and third, it facilitates die machining and grinding, as sharp internal corners are extremely difficult to machine with conventional tools.

CNC Machining Programming Methodology

The paper introduces a CNC machining programming approach for the fillet geometry. The intersection of two equal-diameter cylinders can be mathematically described using parametric equations, and the fillet can be modeled as a toroidal surface that smoothly transitions between the two cylindrical surfaces. The CNC programming involves:

Defining the base geometry of the two intersecting cylinders using parametric surface equations.
Computing the fillet surface as an offset from the intersection curve, with the fillet radius as a design variable.
Generating toolpath coordinates using three-axis or four-axis CNC milling strategies.
Applying adaptive feed and speed control to maintain surface quality at the fillet region, where tool engagement changes rapidly.

A key programming consideration is the avoidance of toolpath discontinuities at the fillet boundary, which can cause surface marks and dimensional inaccuracies. The use of continuous G02/G03 arc interpolation or high-resolution linear interpolation is essential for achieving the required surface finish.

Engineering Practice Considerations

In production environments, the die fillet treatment directly impacts the quality of the extruded tee fitting. Insufficient fillet radius leads to wall thickness variation at the branch intersection, which can result in failure during pressure testing or service. Excessive fillet radius, on the other hand, can lead to material overfill and flashing, requiring additional trimming operations. The optimal fillet radius must be determined through a combination of theoretical analysis and trial extrusion, considering the material being extruded (carbon steel, alloy steel, or stainless steel), the extrusion temperature, and the extrusion speed.

The die material selection is also critical. For high-volume production, die materials such as H13 hot work tool steel or tungsten carbide are commonly used. The fillet region is particularly susceptible to wear due to high material flow velocity and localized stress, so surface hardening treatments (such as nitriding or carbonitriding) are often applied to extend die life.

Study Insights and Reflections

This paper, though brief, addresses a fundamental aspect of die design that is often overlooked in favor of more visible features. The intersection fillet in a tee extrusion die is a small but critical detail that significantly impacts both die durability and product quality. The emphasis on CNC programming methodology reflects the transition from traditional manual die-making to computer-aided manufacturing, which was a significant development in the mid-1990s. For modern engineers, the principles described here remain relevant, even as die design has evolved to incorporate finite element analysis and computational fluid dynamics for material flow simulation. The key takeaway is that geometric continuity at intersection regions is essential for both manufacturing feasibility and product quality, and that the fillet design must be treated as a primary design parameter rather than a secondary detail.