# Influencing Factors of Pine Wood Milling Force Based on Principal Component Analysis and Multiple Linear Regression

## TL;DR

This study uses PCA and MLR to identify key factors affecting milling forces in pine wood processing, offering a strategy to optimize cutting parameters for efficiency and reduced damage.

## Contribution

A novel hybrid modeling approach combining PCA and MLR is introduced to optimize wood milling parameters and reduce forces.

## Key findings

- PCA extracted four principal components explaining 92.78% of variance in milling forces.
- Cutting depth significantly increased triaxial milling forces via PC1.
- Optimized parameters reduced triaxial milling forces by 62.3% compared to maximum values.

## Abstract

Milling force is a parameter affecting wood processing quality, tool life, and energy consumption, and its variation is influenced by the multi-factor coupling of cutting parameters and tool geometric factors. This study systematically investigates milling forces during the processing of pine wood (Pinus sylvestris var. mongholica Litv.) using a hybrid modeling approach combining principal component analysis (PCA) and multiple linear regression (MLR). Firstly, PCA was employed to reduce the dimensionality of the tool rake angle (γ), helix angle (λ), cutting depth (h), feed per tooth (Uz), and triaxial milling forces (Fx, Fy, Fz); this eliminated the multicollinearity among variables and extracted the integrated features. Subsequently, an MLR model was constructed using the principal components as independent variables to quantitatively evaluate the contribution of each factor to milling forces. The results support the conclusion that PCA successfully extracted the first four principal components (cumulative variance contribution rate: 92.78%), with PC1 (49.16%) characterizing the comprehensive milling force effect and PC2 (15.03%) primarily reflecting the characteristics of the tool geometric parameters. The established MLR model demonstrated a high significance (R2: Fx = 0.915, Fy = 0.907, Fz = 0.852). The cutting depth exerted a significant positive driving effect on the triaxial milling forces via PC1 (each 1 mm increase in depth increased the PC1 score by 0.64 units, resulting in increases of 27.2%, 26.6%, and 21.8% for Fx, Fy, and Fz, respectively). The helix angle significantly suppressed Fy through PC2 (β = −0.090, p < 0.001), whereas the rake angle exhibited a weak negative effect on Fx via PC3 (β = −0.015). Parameter optimization identified the combination γ = 25°, λ = 30°, h = 0.5 mm, and Uz = 0.1 mm∙z−1 as optimal, which reduced the triaxial milling forces by 62.3% compared to the experimental maximum. This study provides a theoretical foundation and novel parameter optimization strategy for the efficient, low-damage processing of wood materials.