INFLUENCE OF CUTTING FORCES ON THE STABILITY AND PERFORMANCE OF DISK BLADES IN PROCESSING SEMI-FINISHED FOOD PRODUCTS

ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-12 111 UDK 665.3351 INFLUENCE OF CUTTING FORCES ON THE STABILITY AND PERFORMANCE OF DISK BLADES IN PROCESSING SEMI-FINISHED FOOD PRODUCTS Sohibov Ibodullo Adizmurodovich Assistant Lecturer at the Department of Vehicle Engineering, Bukhara State Technical University [email protected] Annotation. This study investigates the impact of cutting forces on the stability and rigidity of disk blades used in the processing of semi-finished food products. We analyze static and dynamic stability under various loads, derive mathematical expressions for force components, and propose a physical model for sliding cutting. The model incorporates elastic and elastoplastic stress fields, considering microstructural interactions. Results demonstrate that critical forces leading to blade instability can be predicted using derived formulas, enhancing machine design for improved precision and efficiency. This work provides theoretical foundations for optimizing cutting processes in food engineering. Keywords: Cutting forces, blade stability, food processing, sliding cutting, stress analysis. Introduction. In food processing industries, the precision of cutting semi-finished products is crucial for maintaining product quality and operational efficiency. The accuracy of dimensions obtained during cutting is determined by the cutting tool's ability to resist loads encountered during operation, which is evaluated through its rigidity and stability. Rigidity is characterized by the blade's deflection under lateral forces, while stability refers to the blade's capacity to maintain a straight deflection shape under cutting and feed forces. Static stability is assessed by the critical force value at which the blade loses its flat shape and deflects sideways. Dynamic stability is defined by conditions where parametric resonant vibrations occur in the blade under variable loads during cutting, leading to loss of resistance to cutting forces and inability to maintain cutting flatness. This paper examines the technological forces arising during the cutting of semi-finished food products using a disk-shaped blade positioned at an angle γ to the vertical, moving at velocity V. The material being processed moves horizontally at velocity Vf. We derive force components and critical stability thresholds, and present a physical model for sliding cutting based on isotropic material assumptions and classical solutions for stress and deformation. Materials and Methods. The analysis is based on mechanical engineering principles applied to food processing machinery. We consider a disk blade under combined cutting and feed forces, as illustrated in a schematic diagram of technological forces (Figure 1, equivalent to original 1). ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-12 112 Figure 1. Technological forces diagram. The total cutting force R = R1 + R2 is inclined at the cutting friction angle from the normal to the blade. The feed force vector is decomposed into components Px and Py. From the diagram: tan 𝛽 = 𝑃𝑦 𝑃𝑥 Equating expressions yields: 𝑃 𝑥= 𝑅𝑐𝑜𝑠(𝛽 + 𝛾) 𝑃 𝑦= 𝑅𝑠𝑖𝑛(𝛽 + 𝛾) Using the sine theorem in the triangle: 𝑃 𝑥 sin(𝛼) =𝑃 𝑦 sin(𝛽) =𝑅 sin(𝛼 + 𝛽) The projection of the full cutting force is: 𝑁 = 𝑅𝑐𝑜𝑠𝛾 An opposing vector acts in the opposite direction: 𝑇 = 𝑅sin 𝛾 For vertical blade positioning, γ = 0, simplifying to: 𝑁 = 𝑅, 𝑇 = 𝑂 Blade Loading Scheme Thin blades operate under tensile forces N applied to the strip, providing necessary stability to the cutting edge (Figure 2, equivalent to original 2). Experiments show that the tangential force component Pt has minimal impact on the blade's stressed state since Pt << N. Potential loss of stability and deviation of the cutting edge from the cutting plane occur due to Px and Py forces. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-12 113 Figure 2. Diagram of applying forces to a thin plate-like knife/blade. The normal component of the total cutting force acts in the plane of the blade’s greatest rigidity, causing deflection. The blade remains stable until this force reaches a critical value, at which it loses its flat deflection shape and bulges sideways. Upon loss of stability, the blade's rigidity becomes zero. If Py ≠ 0, the blade's strip rotates in the plane of least rigidity, manifesting as oscillatory motion. The critical force Pcr for pre-stressed strip stability loss is given by: 𝑃 𝑐𝑟 =𝜋^2 𝐸𝐼 𝑙2+ 𝑁 Where E is the elastic modulus of the blade material during torsion, It is the moment of inertia, l is the span length, and N is the tensile force. Assumptions include: uniform distributed load approximated as concentrated at the center of span l; no stabilizing effect from lateral surfaces of the cut material; hinged supports allowing free rotation about y and z axes but restricted about x, matching actual machine conditions. Lateral force Py arises from cutting edge inclination due to grinding irregularities, folds, and other defects. Additional factors include assembly inaccuracies in machine components and heterogeneity in the material's structural, mechanical, and strength properties. These result in low Py values, significantly below Px, but the direction aligns with the blade's least rigidity plane, heightening sensitivity. Beyond static loads from cutting and tension, blades experience inertial loads from reciprocating motions of working organs, depending on mechanism parameters and cutting regimes. These induce vibrations in the machine body, reducing longevity and processing accuracy. Physical Model for Sliding Cutting. Modeling sliding cutting assumes classical solutions for isotropic materials and macro-objects describe deformations and stresses under the blade. Due to potential deviations in actual micro-relief shapes, both deterministic and stochastic approaches are necessary. Limited accuracy in initial microgeometry data necessitates accepting approximate solutions. The physical basis of sliding cutting is complex and cannot be fully explained by material destruction via crushing by the blade edge. It is envisioned as simultaneous penetration of the cutting wedge and interaction of blade micro-reliefs with the material. The process is examined at macro-scale (sample or blank size) and micro-scale (surface contact layer). Upon introducing the cutting wedge in direction V, a complex stress-deformation state arises in the material volume. The stress field in the elastic medium created by the cutting wedge corresponds to ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-12 114 the Boussinesq field [81; 10-13-b], with principal stress trajectories shown in Figure 3a (equivalent to original 3. a). Principal stresses σ1 and σ3 act in the symmetry plane through the load axis, being tensile and compressive, respectively. In plane consideration, the circumferential stress is zero. Maximum for σ1 is at θ = 0. Principal normal stresses can be represented via contour lines (isostatics), with excess contact pressure as the unit. As the wedge penetrates, local plastic deformation occurs at the contact point despite overall elastic interaction (Figure 3b, equivalent to original 3. b), associated with micro-destruction initiation as cracks. The term "crack" is justified by studies showing elastomer destruction mechanisms akin to brittle bodies, involving direct bond breakage during crack growth. Experiments also indicate that even low-viscosity fluids can fracture via cracks at sufficiently high loading speeds. Figure 3. Elastic and elastoplastic force field in the material to be cut. Results and Discussion. The derived force components reveal that blade stability is critically dependent on the normal force N and lateral components. The critical force formula accounts for tensile pre-stress, enhancing stability. In practice, defects and material heterogeneities amplify sensitivity to low lateral forces, leading to deviations. The physical model highlights the transition from elastic to elastoplastic regimes, with micro-cracks initiating destruction. This dual-scale approach explains the complexity of sliding cutting, differing from simple crushing models. Inertial loads, tied to cutting regimes, exacerbate vibrations, underscoring the need for optimized parameters to minimize machine wear and improve cut precision. ISSN: 2582-4686 SJIF 2021-3.261,SJIF 20222.889, 2024-6.875 ResearchBib IF: 9.948 / 2024 VOLUME-5, ISSUE-12 115 Conclusion. This analysis elucidates the role of cutting forces in blade stability and proposes a comprehensive physical model for sliding cutting in food processing. By quantifying critical thresholds and stress fields, the study aids in designing more robust machinery. Future work should incorporate experimental validation and stochastic elements for micro-relief variations. REFERENCES 1. Мустафаев Х.С. Повышение эффективности работы машин дискового типа для резания пищевых материалов: Автореф.дис...канд. техн. Наук, - М.: 1991.-24 с; 2. Мачихин Ю.А. Реометрия пищевого сырья и продуктов: Справочник // - М.: Агропромиздат, 1990. -271 с; 3. M.I. Amonov. 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