1001Ferramentas
📐 Calculators

Chip Shear Angle

Calculate the shear-plane angle in chip formation, φ = arctan[(r_c·cos α) ÷ (1 − r_c·sin α)], from the cutting ratio r_c (undeformed chip thickness ÷ deformed chip thickness, always < 1) and the tool rake angle α (degrees). In the orthogonal cutting model (the basis of machining theory), material is not 'scraped': it undergoes intense SHEAR deformation along an inclined plane — the shear plane — where it turns from part to chip almost instantly. That plane's angle, φ, is a central measure of cutting mechanics: LARGER shear angles mean thinner chips, less deformation, lower cutting force and energy and less heat — all desirable. The angle depends on the cutting ratio (measured by comparing chip thickness to feed) and the tool rake angle: tools with more positive rake give larger shear angles and cut with less effort (but have a more fragile edge). Merchant's theory relates φ to chip-tool friction and rake angle, and predicts the angle that minimizes energy. From chip measurements, this calculation lets you analyze cutting efficiency and the influence of tool geometry and lubrication. Enter the cutting ratio and the rake angle.

Result

Ângulo de cisalhamento do cavaco

O ângulo do plano de cisalhamento na formação do cavaco é φ = arctan[(r_c·cos α) ÷ (1 − r_c·sen α)], a partir da razão de corte r_c (espessura do cavaco indeformado ÷ espessura do cavaco deformado, sempre menor que 1) e do ângulo de saída α da ferramenta. No modelo de corte ortogonal — a base da teoria da usinagem —, o material não é simplesmente 'raspado': ele sofre uma intensa deformação por cisalhamento ao longo de um plano inclinado, o plano de cisalhamento, onde passa de peça a cavaco quase instantaneamente. O ângulo desse plano, φ, é uma medida central da mecânica do corte: ângulos de cisalhamento maiores significam cavacos mais finos, menor deformação, menores força e energia de corte e menos calor gerado — tudo desejável. O ângulo depende da razão de corte (medida comparando a espessura do cavaco com o avanço) e do ângulo de saída da ferramenta: ferramentas com ângulo de saída mais positivo geram ângulos de cisalhamento maiores e cortam com menos esforço (mas têm aresta mais frágil, sujeita a lascamento). A teoria de Merchant relaciona φ ao atrito cavaco-ferramenta e ao ângulo de saída, e prevê o ângulo que minimiza a energia de corte. Este cálculo, a partir de medições do cavaco coletado, permite analisar a eficiência do corte e a influência da geometria da ferramenta e da lubrificação (que, reduzindo o atrito, aumenta φ). Informe a razão de corte e o ângulo de saída.

Related Tools

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Machining Cutting Power

Calculate the cutting power in machining, P_c = (F_c·Vc) ÷ 60000, from the main cutting force F_c (N) and the cutting speed Vc (m/min); the result is in kW (60000 converts N·m/min to kW). Cutting power is the mechanical power the operation consumes to remove material, decisive for machine selection: the spindle motor must supply this power (plus losses, dividing by drive efficiency, typically 0.7-0.9) without stalling in the cut. If the required power exceeds the available, the machine loses speed, the cut jams or the tool breaks — so heavy roughing needs robust machines. Cutting power also relates to MRR by the specific cutting energy (P_c = u·Q, where u is energy per unit volume removed) — a practical alternative to estimate it directly from removed volume. Computing power is essential for planning (choosing the right machine), optimizing parameters (extracting the most from available power) and estimating energy use and heating. Enter the cutting force and the cutting speed.

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Tool Life (Taylor's Equation)

Calculate a cutting tool's life by Taylor's equation, T = (C ÷ Vc)^(1/n), from the constant C (the cutting speed giving 1 minute of life, characteristic of the tool-material pair), the cutting speed Vc (m/min) and the exponent n (depending on tool material). Formulated by F. W. Taylor in 1907 from thousands of tests, this is machining's most famous relation and describes a fundamental trade-off: the HIGHER the cutting speed, the SHORTER the tool life — and steeply, since it is a power law. The exponent n quantifies the sensitivity: for HSS n ≈ 0.1 (life drops very fast with speed), for carbide n ≈ 0.2-0.3, for ceramic n ≈ 0.4-0.6 (less sensitive, allowing much higher speeds). Taylor's equation is the basis of economic OPTIMIZATION of machining: there is an optimal cutting speed minimizing total cost per part, balancing cutting time (falling with speed) against tool and change-downtime cost (rising with speed). Speeds above optimum 'burn' costly tools too fast; below, waste machine time. Enter the constant C, the cutting speed and the exponent n.

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Bolt Shear Stress

Calculate the shear stress in transversely loaded bolts, τ = F ÷ (n·A), from the total shear force F (N), the number of bolts (or shear planes) n and each bolt's area A (mm²). Unlike tensioned joints (where the bolt is tightened and the load is axial), in SHEAR joints the bolts resist a transverse force tending to slide one part over another (as in steel structural connections, splice plates, flanges under lateral load). The force is distributed among the bolts and each works in shear — hence the stress is force divided by the number of bolts times the area. There can be SINGLE shear (one shear plane) or DOUBLE shear (two planes, when the bolt passes through three plates), doubling capacity. The area used depends on whether the shear plane passes through the threaded part (use the tensile area) or the smooth shank (nominal-diameter area). Shear stress is compared with the bolt material's shear strength (typically ~0.6 of tensile strength). In structures, bearing-type (bolt in shear/bearing) and slip-critical (preload friction transmits load without bolt shear) connections are distinguished — this formula covers shear resistance. Enter the shear force, the number of bolts and the area.

The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.