In recent years, micro-mechanical systems, particularly micro-electromechanical systems (MEMS), have seen significant advancements, with micro-internal gears playing a critical role in components like planetary gear reducers. As an internal gear manufacturer, we recognize the importance of precision in producing internal gears for such applications. Bulk metallic glasses (BMGs), specifically Zr-based alloys like Zr55Al10Ni5Cu30, offer exceptional properties such as high strength, hardness, wear resistance, and corrosion resistance at room temperature. In the supercooled liquid region, they exhibit superplasticity and excellent formability, allowing for accurate replication of mold geometries and surface topographies. This makes them ideal for micro-forming processes, where dimensional accuracy and minimal post-processing are crucial for internal gears. The demand for high-quality internal gears from internal gear manufacturers drives the need for optimized forming techniques.
This article explores the backward extrusion process for manufacturing micro-internal gears using Zr55Al10Ni5Cu30 BMG. We focus on determining optimal superplastic deformation parameters, designing an effective die structure, and validating the process through finite element analysis. The goal is to achieve flat end surfaces and precise shapes for micro-internal gears, reducing the need for subsequent machining. As internal gear manufacturers seek efficient production methods, this research provides insights into enhancing the fabrication of internal gears with complex micro-features.
The micro-internal gear considered here has key parameters typical of those produced by internal gear manufacturers: a module of m = 0.08 mm, tooth count Z = 39, pressure angle α = 20°, axial height h = 3.0 mm, and outer wall diameter D = 4.4 mm. Such small dimensions necessitate precise control over the forming process to avoid defects and ensure the functionality of internal gears in micro-mechanical assemblies. Internal gear manufacturers often face challenges in maintaining end-face flatness and avoiding eccentricity in micro-internal gears, which can be addressed through advanced die designs and parameter optimization.
Determination of Superplastic Deformation Parameters
To establish the optimal forming conditions for Zr55Al10Ni5Cu30 BMG in the supercooled liquid region, we conducted thermal analysis and constant-temperature, variable-strain-rate micro-compression tests. The supercooled liquid state is characterized by a temperature range between the glass transition onset temperature (Tg onset) and the crystallization temperature (Tx), where the material exhibits Newtonian viscous flow and superplasticity. For internal gear manufacturers, understanding these parameters is essential to produce high-quality internal gears with minimal defects.
Differential scanning calorimetry (DSC) at a heating rate of 1 K/s revealed the thermal properties of the BMG. The glass transition onset temperature was measured at Tg onset = 673 K, the glass transition end temperature at Tg end = 688 K, and the crystallization temperature at Tx = 774 K, resulting in a supercooled liquid region of 86 K. Isothermal DSC tests were performed to assess the time-temperature-transformation (T-T-T) behavior, ensuring that deformation occurs without crystallization. We determined that at a temperature of 708 K, the BMG remains amorphous for over 1800 seconds, providing a sufficient window for forming processes. This is critical for internal gear manufacturers aiming to achieve precise internal gears without structural changes.
Micro-compression tests on a Gleeble 3500 thermal simulation machine provided stress-strain curves at T = 708 K and varying strain rates. The results indicate that the flow stress of the BMG is highly sensitive to strain rate, with higher strain rates leading to increased deformation resistance and reduced fillability. The stress-strain relationships are summarized in the following table, which internal gear manufacturers can use to select appropriate strain rates for producing internal gears:
| Strain Rate (s-1) | Flow Stress (MPa) | Remarks |
|---|---|---|
| 1.0 × 10-4 | ~20 | Newtonian flow dominant |
| 5.0 × 10-4 | ~35 | Ideal for micro-forming |
| 1.0 × 10-3 | ~50 | Moderate stress |
| 2.5 × 10-3 | ~70 | Upper limit for superplasticity |
Based on these experiments, we established that the optimal strain rate for superplastic deformation is ε ≤ 2.5 × 10-3 s-1, where the flow stress remains below 70 MPa, and the material behaves in a Newtonian viscous manner. The constitutive model for the BMG in the supercooled liquid state was derived as:
$$ \sigma = 16308 \dot{\epsilon}^{0.96} $$
where σ is the flow stress in Pa, and ε̇ is the strain rate in s-1. This model aids internal gear manufacturers in predicting material behavior during the forming of internal gears. For the backward extrusion process, we selected a punch speed of v = 0.001 mm/s, resulting in an average strain rate range of 5.56 × 10-4 s-1 to 5 × 10-3 s-1 and a forming time of approximately 1600 seconds, ensuring complete filling of micro-internal gear teeth without crystallization.
Die Design for Backward Extrusion of Micro-Internal Gears
The design of the extrusion die is crucial for achieving flat end surfaces and precise dimensions in micro-internal gears. Internal gear manufacturers often encounter issues such as eccentricity, uneven material flow, and end-face irregularities in conventional backward extrusion processes. To address these, we developed a floating die structure with a sleeve mechanism for enhanced guidance and end-face flattening.
The die assembly consists of a punch, die, punch sleeve, support spring, and sleeve spring. The punch sleeve provides lateral guidance to the punch, preventing offset and ensuring uniform clearance between the punch and die. This is vital for maintaining the symmetry of internal gears during formation. The floating die mechanism allows the die to move downward under the support spring during forming, facilitating automatic ejection of the formed part. The sleeve spring applies a compressive force to the workpiece end-face, promoting triaxial stress states that improve material flow and fillability into the micro-features of internal gears.
The working process of the die can be divided into two stages: initial forming and ejection. During forming, the punch moves downward, and the punch sleeve, under sleeve spring tension, compresses the workpiece end-face. As material flows upward into the gap between the punch and die, the punch sleeve moves upward, increasing the spring force and ensuring a flat end surface. After forming, the die continues downward, ejecting the workpiece, while the sleeve spring assists in detaching the workpiece from the punch during retraction. This design minimizes post-processing for internal gear manufacturers by producing internal gears with ready-to-use end faces.
Key parameters of the die design are summarized in the table below, which internal gear manufacturers can reference for similar applications:
| Component | Parameter | Value | Function |
|---|---|---|---|
| Punch | Speed | 0.001 mm/s | Controls forming rate |
| Punch Sleeve | Spring preload | 79 N | Applies end-face pressure |
| Sleeve Spring | Elastic modulus | 79 N/mm | Maintains compressive force |
| Support Spring | Stiffness | Designed for ejection | Facilitates floating die motion |
This die structure not only enhances the precision of internal gears but also reduces wear on tooling, benefiting internal gear manufacturers in terms of longevity and cost-efficiency. By incorporating these elements, we can produce micro-internal gears with dimensions matching the requirements of micro-planetary gear reducers, such as those with m = 0.08 mm and Z = 39.
Finite Element Analysis of Backward Extrusion Process
To validate the proposed die design and forming parameters, we performed finite element analysis (FEA) using Deform 3D software. The simulation models the backward extrusion of Zr55Al10Ni5Cu30 BMG at T = 708 K, comparing cases with and without the punch sleeve. This analysis helps internal gear manufacturers visualize material flow, stress distribution, and potential defects in internal gears.
The FEA model incorporated the constitutive equation derived earlier:
$$ \sigma = 16308 \dot{\epsilon}^{0.96} $$
where σ is in Pa and ε̇ in s-1. The punch speed was set to v = 0.001 mm/s, with a sleeve spring preload of 79 N and an elastic modulus of 79 N/mm. The simulation tracked the forming load, stress distribution, and material fill into the micro-internal gear teeth.
The load-stroke curves from the simulation are shown in the table below, highlighting the differences between the two die configurations:
| Punch Stroke (mm) | Load without Sleeve (kN) | Load with Sleeve (kN) | Remarks |
|---|---|---|---|
| 0.5 | ~0.5 | ~0.6 | Initial forming phase |
| 1.0 | ~1.2 | ~1.4 | Steady increase |
| 1.6 | ~1.8 | ~2.0 | Maximum load, full fill |
The results indicate that the die with the punch sleeve requires a slightly higher load (up to 2.0 kN) compared to the sleeve-less design (1.8 kN), but both are well below the typical equipment limit of 20 kN. This confirms the feasibility of the sleeve design for internal gear manufacturers, as it does not impose excessive demands on machinery.
Stress distribution analysis at a punch stroke of 1.6 mm reveals significant improvements with the punch sleeve. In the sleeve-less case, the equivalent stress on the workpiece ranges from 0 to 10 MPa, with incomplete filling at the end-face corners. In contrast, with the sleeve, the stress distribution is more uniform, ranging from 30 to 40 MPa in the internal gear teeth region, ensuring complete fill and a flat end surface. The triaxial compressive stress state induced by the sleeve enhances material flow into the micro-features, which is critical for achieving the precise tooth profiles required by internal gear manufacturers for internal gears in high-precision applications.
The von Mises stress distribution can be described by the following equation, which internal gear manufacturers can use for similar simulations:
$$ \sigma_{v} = \sqrt{\frac{(\sigma_{1} – \sigma_{2})^2 + (\sigma_{2} – \sigma_{3})^2 + (\sigma_{3} – \sigma_{1})^2}{2}} $$
where σ1, σ2, and σ3 are the principal stresses. In the sleeve-assisted case, the stresses are more balanced, reducing the risk of defects in internal gears.
Conclusion
In this study, we have established a comprehensive backward extrusion process for manufacturing micro-internal gears from Zr55Al10Ni5Cu30 bulk metallic glass. The optimal forming parameters include a temperature of 708 K, a strain rate ε ≤ 2.5 × 10-3 s-1, and a punch speed of 0.001 mm/s, with a sleeve spring preload of 79 N and elastic modulus of 79 N/mm. These parameters ensure superplastic deformation without crystallization, producing internal gears with high dimensional accuracy and flat end surfaces.
The designed floating die with a punch sleeve addresses common challenges faced by internal gear manufacturers, such as eccentricity and end-face irregularities. Finite element analysis validates that this die structure promotes uniform stress distribution and complete filling of micro-internal gear teeth, reducing the need for post-processing. The constitutive model σ = 16308 ε̇0.96 provides a reliable basis for simulating material behavior.
For internal gear manufacturers, this research offers a practical approach to enhancing the production of internal gears for micro-mechanical systems. Future work could explore other BMG compositions or scale-up processes for larger internal gears. By adopting these techniques, internal gear manufacturers can improve the quality and efficiency of internal gear production, meeting the growing demands of advanced micro-devices.