ccitonline.com

A. Project Title
FORCE CALCULATION AND APPROXIMATION FOR FORGING AND UPSETTING

B. Author Complete Name
Radifan Wirahadyanto

C. Affiliation

Department of Mechanical Engineering, Faculty of Engineering, Universitas Indonesia

D. Abstract

Accurate prediction of forming force is a critical requirement in the design and analysis of upsetting (forging) processes. Conventional analytical approaches based on the Upper Bound Method (UBM) provide physically consistent force estimations but are limited by static geometry assumptions and the need for repeated manual recalculation as deformation progresses. In real forging operations, workpiece geometry evolves continuously, making single-step analytical solutions insufficient for reliable force prediction.
This work presents a Python-based iterative calculator that integrates the Upper Bound Method with incremental geometry updating to efficiently approximate the continuous forging process. The upsetting deformation is discretized into small height reductions, and at each increment, workpiece width is updated using volume constancy while the forming force is recalculated from the analytical upper bound expression. The adopted numerical approach is incremental, explicit, and computationally inexpensive, allowing rapid evaluation without the complexity of full finite element simulations.
The results demonstrate that the iterative method captures the nonlinear increase in forming force caused by geometry evolution and frictional effects, which are underestimated by single-step analytical evaluations. The proposed tool significantly reduces approximation time while maintaining consistency with upper bound theory. This approach is suitable for preliminary process design, parametric studies, and educational applications in metal forming analysis.

E. Author Declaration

1. Deep Awareness (of) I
   • In undertaking this project, the author consciously acknowledges that all knowledge, reasoning ability, and technical capability originate solely from The One and Only, The Creator of the universe and all that exists within it. This awareness establishes humility and responsibility in the engineering process, recognizing that human intellect is limited and that true understanding arises through remembrance of God.
   • This state of awareness corresponds to the concept of nafs, the fundamental human reality embedded within the heart (qalb), which governs intention, perception, and ethical conduct. By maintaining this awareness throughout the project, the author seeks to ensure that the development of artificial intelligence serves not merely technical efficiency, but also truth, responsibility, and benefit to humanity.
2. Intention of the Project Activity
   • The intention (niyyah) of this project is to develop an AI-based engineering tool that aids decision-making in manufacturing processes while remaining aligned with ethical principles, honesty, and usefulness. The project is intended as an act of learning and contribution, not self-glorification, and is pursued for the sake of God, with the aim of advancing engineering understanding, educational clarity, and responsible use of artificial intelligence.

F. Introduction

In metal forming analysis, especially upsetting (forging) processes, determining the required forming force is a critical design task. Traditional analytical solutions rely on the Upper Bound Method (UBM).

The Upper Bound Method calculates forming force by assuming a kinematically admissible velocity field and computing the rate of internal power dissipation and frictional power, which are then equated to external power. While analytically elegant, this approach requires:

• Assumptions about geometry,
• Simplifications regarding friction and deformation uniformity,
• Repeated recalculation when geometry changes during deformation.

In real forging processes, geometry evolves continuously (height decreases, width increases), which makes single-step analytical calculations insufficient for accurate force prediction.

3. Initial Thinking (About the Problem)

From an engineering and computational perspective, the key difficulties are:

1. Force depends on geometry, but geometry changes during deformation.
2. Manual recalculation for each deformation step is time-consuming.
3. Analytical solutions provide only snapshots, not continuous evolution.
4. Engineers need fast, iterative feedback to evaluate:
   • Force trends
   • Machine capacity limits
   • Influence of friction and strain

Thus, the problem becomes:

How can we compute forging force efficiently while continuously updating geometry, without resorting to time-consuming full numerical simulations (e.g., FEM)?

G. Methods & Procedures
4. Idealization

The following idealizations are adopted:

1. Plane strain condition
   Length of workpiece ≫ width and height.
2. Rigid–perfectly plastic material
   Material characterized by a constant flow stress .
3. Volume constancy
   Plastic deformation is incompressible:
   A0 = w0 · h0 = wi · hi

4. Flat dies
   No die deformation.
5. Upper Bound velocity field
   As used in the lecture notes for Pwz and .
6. Friction modeled using friction factor
   According to:
   τ=m⋅k

5. Instruction Set

The iterative calculator follows this instruction set:

1. Input initial parameters
   • Initial width
   • Initial height
   • Flow stress
   • Friction factor
   • Number of iterations
2. Initialize geometry
   • Compute initial area
3. Iteration loop (i = 1 … N)
   • Reduce height by a small increment
   • Update width using volume constancy
   • Compute half-width and half-thickness
   • Calculate forming force
   • Store results

4. Output
   • Force vs iteration
   • Geometry evolution
   • Final forming force

This replaces repeated analytical recalculations with automatic, fast updates.

H. Results & Discussion

1. Iterative Force Evolution

The iterative approach reveals that:

• As height decreases, width increases due to volume constancy
• The term increases rapidly
• Forming force grows nonlinearly
• Early iterations underestimate final force if geometry change is ignored

This explains why single-step analytical solutions often fail in practice.

2. Reduction of Approximation Time

Compared to manual or spreadsheet-based calculations:

Once implemented, the calculator:

• Updates geometry automatically
• Evaluates force in milliseconds
• Enables parametric studies (vary , , iterations)

3. Physical Interpretation

The calculator directly reflects the theory:

• Pwz → internal power increases with strain
• → implicit in geometric change rate
• Increasing force reflects:
  • Higher frictional dissipation
  • Larger contact width
  • Barreling tendency (even if not explicitly modeled)

Thus, the calculator is not a black box, but a computational extension of the lecture theory.

I. Conclusion, Closing Remarks, and Recommendations

This project successfully demonstrates the integration of spiritual awareness, engineering computation, and artificial intelligence through the DAI5 framework. The resulting AI agent is not merely a computational tool, but a reflective system that aligns technical decision-making with ethical intention.

J. Acknowledgments

The author expresses gratitude to Prof. Ir. Ahmad Indra Siswantara, Ph.D, from the Mechanical Engineering Department, Universitas Indonesia who introduced the DAI5 framework, enabling a holistic approach to engineering problem-solving.

K. (References) Literature Cited

1. Hosford, W. F., & Caddell, R. M. (2011). Metal forming: Mechanics and metallurgy (4th ed.). Cambridge University Press.
2. Avitzur, B. (1983). Metal forming: Processes and analysis. McGraw-Hill.
3. Dieter, G. E. (1986). Mechanical metallurgy (3rd ed.). McGraw-Hill.
4. Johnson, W., & Mellor, P. B. (1983). Engineering plasticity. Ellis Horwood.
5. Brosius, A. (2023). Umformtechnik – Lecture notes. Universität Dresden.

L. Appendices

https://drive.google.com/drive/folders/15tzXoMJooylcILaxh3WQyTOVsQWkTSzp