Generalized cutting force model for peripheral milling of wood, based on the effect of density, uncut chip cross section, grain orientation and tool helix angle

The influence of the grain angle on the cutting force when milling wood is not yet detailed, apart from particular cases (end-grain, parallel to the grain, or in some rare cases 45°-cut). Thus, setting-up wood machining operations with complex paths still relies mainly on the experience of the operators because of the lack of scientific knowledge easily transferable to the industry. The aim of the present work is to propose an empirical model based on specific cutting coefficients for the assessment of cutting force when peripheral milling of wood based on the following input: uncut chip thickness and width, grain angle (angle between the tool velocity vector and the grain direction of the wood), density and tool helix angle. The specific cutting coefficients were determined by peripheral milling with different depths of cut wood disks issued from different wood species on a dynamometric platform to record the forces. Milling a sample into a round shape (a disk) allows to measure the cutting forces toward every grain angle into a sole basic diameter reduction operation. Force signals are then post-processed to carefully clean the natural vibrations of the system without impacting their magnitudes. The experiment is repeated on five species with a large range of densities, machining two disks per species for five depths of cut in up- and down milling conditions for three different tool helix angles. Finally, a simple cutting force model, based on the previously cited parameters, is proposed, and its robustness analysed.

Stochastic Cutting Force Modeling and Prediction in Machining

As the cutting force plays an important role in machining, the modeling of cutting force has drawn considerable interests in recent years. However, most of current methods were focused on the deterministic modeling of cutting force, while the inherent stochasticity of cutting force is rarely considered for general metal cutting machining. Thus, a stochastic model is proposed in this paper to predict the stochastic cutting force by considering realistic cutting conditions, including the inhomogeneity of cutting material and the multi-mode machining system. Specifically, we transform the constant cutting coefficient in previous models into a stationary Gaussian process in the proposed stochastic model. As for the tool vibration, the uncut chip thickness is also modeled in a stochastic manner. Moreover, it is found that the random cutting coefficients can be estimated conveniently through experiments and effectively simulated by stochastic differential equations at any timescale. Then, the stochastic cutting force can be predicted numerically by combining the stochastic model and the multi-mode dynamic equations. For verification, a three-mode machining system was set up, and workpieces with different metal alloys were tested. It is found that the random cutting coefficients estimated are insensitive to cutting parameters, and the prediction results show satisfactory agreement with experimental results in both time and statistical domains. The proposed method can provide rich statistical information of cutting forces, which can facilitate related applications like tool condition monitoring when the on-line measurement of cutting force is not preferred or even impossible.

Identification of Polynomial Cutting Coefficients for a Dual-Mechanism Ball-end Milling Force Model

Background: Calibration of cutting coefficients is the key content in modeling a mechanistic cutting force model. Generally, in modeling cutting force for ball end milling, the tangent, radial and binormal cutting force coefficients are each considered as a polynomial, respectively. This fact is due to the dependency between the cutting force coefficients and the cutting edge inclination angle which is variable in ball-end mills. Objective: This paper presents an approach to determine the polynomial cutting force coefficients. Methods: In this approach, the cutting force coefficients are expressed as explicit linear equations about the average slotting forces. After analysis of the least square regression method which is utilized in the cutting coefficients evaluation, the principle of cutting parameters choice in calibration experiment and the relationship between the order of polynomial and the number of experiments are presented. Besides, a lot of patents on identification of polynomial cutting coefficients for milling force model were studied. Results: Finally, a series of semi-slotting verification cutting tests were arranged, the measured force agrees well with the predicted force, which demonstrates the effectiveness of this approach. Conclusion: Based on the calibration method proposed in this paper, the cutting coefficients can be determined through (m+2) slotting experiments for m-degree shearing coefficients polynomial theoretically.

Specific Cutting Forces of Isotropic and Orthotropic Engineered Wood Products by Round Shape Machining

The set-up of machining parameters for non-ferric materials such as wood and wood-based materials is not yet defined on a scientific basis. In this paper, a new rapid experimental method to assess the specific cutting coefficients when routing isotropic and orthotropic wood-based materials is presented. The method consists of routing, with different depths of cut, a given material previously machined to a round shape after having it fixed on a dynamometric platform able to measure the cutting forces. The execution of subsequent cuts using different depths of cut allows the calculation of the specific cutting coefficients. With the measurement being done during real routing operations, a method to remove machine vibrations was also developed. The specific cutting coefficients were computed for the whole set of grain orientations for orthotropic materials and as an average for isotropic ones. The aim of this paper is to present and validate the whole method by machining selected materials such as Polytetrafluoroethylene—PTFE (isotropic), Medium Density Fiberboard—MDF (isotropic), beech Laminate Veneer Lumber—LVL (orthotropic) and poplar LVL (orthotropic). The method and the proposed analysis have been shown to work very effectively and could be used for optimization and comparison between materials and processes.