Fixed-Diamond Abrasive Wire-Saw Cutting Force Modeling Based on Changes in Contact Arc Lengths

At a Glance

Metadata	Details
Publication Date	2023-06-20
Journal	Micromachines
Authors	Liang Lie, Shujuan Li, Kehao Lan, Jiabin Wang, Ruijiang Yu
Institutions	Xi’an University of Technology
Citations	10
Analysis	Full AI Review Included

Executive Summary

This research presents a validated, iterative mathematical model for predicting cutting forces and surface morphology during the fixed-abrasive diamond wire (FAW) sawing of monocrystalline silicon.

Core Achievement: Established a dynamic model that accurately predicts the trend of cutting force changes and resulting saw marks throughout the entire slicing process, achieving high correlation with experimental results.
Model Innovation: The model incorporates a random distribution of abrasive particles and dynamically calculates the contact arc length (S) and wire bow angle (γ), challenging previous assumptions that these parameters remain static.
Process Dynamics: The cutting process is confirmed to have two distinct stages: an initial rising stage (characterized by material accumulation and increasing bow angle/force) and a stable stage (where material removal matches feed rate).
Validation Accuracy: Comparison between simulation and experiment showed the error in stable-stage cutting force was consistently less than 6%. Errors in predicting saw mark central angle and curvature were also kept below 5%.
Parameter Sensitivity: Simulation results indicate that the total slicing time is significantly more sensitive to changes in the part feed rate (V_x) than to changes in the wire velocity (V_s).
Mechanism Insight: Increased wire velocity reduces the bow angle and cutting force by increasing the material removal rate, while increased feed rate increases the bow angle and cutting force due to higher accumulated unremoved material.

Technical Specifications

Parameter	Value	Unit	Context
Wire Saw Radius (R_w)	0.1	mm	Fixed-diamond wire saw specification
Abrasive Particle Density (C)	34	particles/mm²	Measured on wire surface
Silicon Hardness (H)	13.5	GPa	Monocrystalline Si ingot
Abrasive Cone Half Angle (θ)	65	°	Used in single abrasive force calculation
Wire Tension (T)	15	N	Set experimental parameter
Part Dimensions (Ingot)	36 x 23 x 200	mm	Silicon ingot size
Cutting Surface Thickness (L_c)	23	mm	Used for contact arc length calculation
Wire Velocity (V_s) Range	1.0 to 1.5	m/s	Tested cutting parameters
Part Feed Rate (V_x) Range	0.5 to 0.75	mm/min	Tested cutting parameters
Cutting Force Simulation Error	< 6	%	Maximum error in stable stage comparison
Saw Mark Curvature Error	< 5	%	Maximum error in wafer surface prediction
Dynamometer Resolution (X, Y)	1/160	N	ATI FT19500 sensor
Dynamometer Range (Z-axis)	100	N	ATI FT19500 sensor

Key Methodologies

The study combined experimental cutting using a WXD170 machine with an iterative mathematical model implemented via MATLAB, focusing on dynamic process variables.

Experimental Setup: Monocrystalline silicon ingots were cut using a single-line reciprocating FAW saw. Cutting forces were measured in real-time using an ATI FT19500 dynamometer.
Abrasive Particle Modeling: The distribution of JR2-type diamond abrasives on the nickel-plated wire was modeled as random in the x-y plane. The height (d) of the active particles was assumed to follow a normal distribution, with only particles within one standard deviation (k = 68%) considered active in cutting.
Geometric Relationship Establishment: A geometric model was established relating the contact arc length (S) to the wire bow angle (γ) and the wire bending distance (h). The bending distance (h) is the key dynamic variable, representing the accumulation of unremoved material.
Iterative Force Calculation: An iterative algorithm was developed to calculate the cutting force (F_n) at each time step. This calculation relies on balancing the volume of material removed by the wire (U_w) against the volume required by the part feed (U_p).
- If U_w < U_p (Initial Stage), unremoved material accumulates, increasing h, γ, and F_n.
- If U_w = U_p (Stable Stage), the system reaches equilibrium, and F_n stabilizes.
Single Particle Force Calculation: The force on a single abrasive particle (F_a) was calculated based on the depth of penetration (g), the abrasive tip angle (65°), and the material hardness (H = 13.5 GPa). The total cutting force (F_n) is the sum of the horizontal components of the tension (T) and the forces exerted by all active abrasive particles.
Surface Morphology Analysis: After cutting, the wafer surface was analyzed using a Keyence VHX-5000 3D microscope. The radius and central angle of the resulting saw marks were measured geometrically and compared directly against the model’s predictions for contact arc length and bow angle.

Commercial Applications

This research provides critical modeling and validation tools for optimizing precision slicing processes, primarily impacting the following sectors:

Photovoltaic Wafer Production: Directly applicable to optimizing the slicing of silicon ingots for solar cells, minimizing kerf loss, and improving wafer yield by controlling cutting force and reducing sub-surface damage.
Semiconductor Substrate Manufacturing: Essential for the high-precision slicing of hard and brittle materials like SiC and monocrystalline Si, ensuring high surface quality and dimensional accuracy required for advanced electronic devices.
Advanced Materials Processing: The modeling approach can be adapted for the precision cutting of other difficult-to-machine materials used in optics (e.g., sapphire, quartz) or specialized electronics.
Machine Tool Design and Control: Provides a theoretical basis for developing advanced control systems for FAW saws, allowing for dynamic adjustment of wire tension and feed rate to maintain the process within the desired stable cutting stage.
Process Optimization Consulting: The validated model allows engineers to simulate the effects of changing V_x and V_s parameters without extensive physical testing, leading to faster process optimization and reduced operational costs.

View Original Abstract

Monocrystalline silicon is widely used in the semiconductor market, but its hard and brittle physical properties make processing difficult. Fixed-diamond abrasive wire-saw (FAW) cutting is currently the most commonly used cutting method for hard and brittle materials due to advantages such as narrow cutting seams, low pollution, low cutting force and simple cutting process. During the process of cutting a wafer, the contact between the part and the wire is curved, and the arc length changes during the cutting process. This paper establishes a model of contact arc length by analyzing the cutting system. At the same time, a model of the random distribution of abrasive particles is established to solve the cutting force during the cutting process, using iterative algorithms to calculate cutting forces and chip surface saw marks. The error between the experiment and simulation of the average cutting force in the stable stage is less than 6%, and the errors with respect to the central angle and curvature of the saw arc on the wafer surface are less than 5% between the experiment and simulation. The relationship between the bow angle, contact arc length and cutting parameters is studied using simulations. The results show that the variation trend of the bow angle and contact arc length is consistent, increasing with an increase in the part feed rate and decreasing with an increase in the wire velocity.

Tech Support

Original Source

DOI: https://doi.org/10.3390/mi14061275

References

2020 - Experiment and theoretical prediction for surface roughness of PV polycrystalline silicon wafer in electroplated diamond wire sawing [Crossref]
2017 - Analytical Force Modeling of Fixed Abrasive Diamond Wire Saw Machining With Application to SiC Monocrystal Wafer Processing [Crossref]
2023 - Study on nanometer cutting mechanism of single crystal silicon at different temperatures [Crossref]
2023 - Molecular dynamics simulation on crystal defects of single-crystal silicon during elliptical vibration cutting [Crossref]
2022 - Theoretical study on sawing force of ultrasonic vibration assisted diamond wire sawing (UAWS) based on abrasives wear [Crossref]
2020 - Characterization of electroplated diamond wires and the resulting workpiece quality in silicon sawing [Crossref]
2018 - Experimental investigation of tool wear in electroplated diamond wire sawing of silicon [Crossref]
2012 - Silicon Crystal Growth and Wafer Technologies [Crossref]
2016 - Wire sawing technology: A state-of-the-art review [Crossref]
2011 - Investigation of long waviness induced by the wire saw process [Crossref]