Barth Dynamic Factor (Gear)
Calculate a gear's dynamic (velocity) factor by Barth's equation, K_v = (6.1 + v) ÷ 6.1, from the pitch-line velocity v (m/s). The dynamic factor amplifies the transmitted static load to account for the DYNAMIC EFFECTS of high-speed meshing: as teeth engage and disengage rapidly, profile imperfections, pitch errors, tooth deflections under load and inertia generate VIBRATIONS and impacts that raise the real tooth load above the nominal load from torque. The higher the pitch-line velocity, the greater these effects — so K_v grows with v. Barth's equation (with constant 6.1, in m/s) is one of several empirical dynamic-factor formulas, suited to reasonably accurate cut teeth; variants with different constants exist for cast (coarser) or ground (more precise) teeth. The dynamic design load is the nominal tangential load times K_v. In high-speed gears, controlling vibration (manufacturing accuracy, modified profiles, balancing) is essential to limit K_v and noise. It is a key factor in AGMA design. Enter the pitch-line velocity.
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Fator dinâmico de Barth (engrenagem)
O fator dinâmico (de velocidade) de uma engrenagem, pela equação de Barth, é K_v = (6,1 + v) ÷ 6,1, a partir da velocidade na linha primitiva v (m/s). Ele majora a carga estática transmitida para levar em conta os efeitos dinâmicos do engrenamento em alta velocidade: à medida que os dentes engrenam e desengrenam rapidamente, imperfeições no perfil, erros de passo, deflexões dos dentes sob carga e a inércia geram vibrações e impactos que aumentam a carga real sobre os dentes acima da nominal (calculada pelo torque). Quanto maior a velocidade periférica, maiores esses efeitos — por isso K_v cresce com v. A equação de Barth (constante 6,1, em m/s) é uma das várias fórmulas empíricas para o fator dinâmico, adequada para dentes cortados com precisão razoável; há variantes com constantes diferentes para dentes fundidos (mais grosseiros) ou retificados (mais precisos, K_v menor). A carga dinâmica de projeto é a carga tangencial nominal multiplicada por K_v. Em engrenagens de alta velocidade, o controle das vibrações (precisão de fabricação, perfis modificados, balanceamento) é essencial para limitar K_v e o ruído. É um fator-chave no dimensionamento pela AGMA. Informe a velocidade na linha primitiva.
Related Tools
Gear Dynamic Load
Calculate the effective dynamic load on gear teeth, F_d = F_t·K_v, from the nominal tangential force F_t (N) and the dynamic factor K_v. The dynamic load is the REAL tangential force the teeth bear in operation, larger than the nominal force (simply torque over radius) because of the dynamic effects of meshing at speed. These effects — vibrations, contact impacts, tooth deflections under load and manufacturing errors — make the instantaneous tooth load fluctuate and peak above the average, especially at high pitch-line velocities. The dynamic factor K_v (from Barth or other formulas) quantifies this amplification. The dynamic load is then used in strength checks: in Lewis bending stress (risk of tooth breakage at the root) and Hertzian contact stress (risk of surface fatigue and pitting). Using the nominal load without amplifying by the dynamic factor would underestimate the demands and lead to undersized gears that fail prematurely by fatigue. It is an essential, classic step in gear design. Enter the nominal tangential force and the dynamic factor.
Gear Tooth Bending Stress (Lewis)
Calculate the bending stress at a gear tooth root by the Lewis equation, σ = F_t ÷ (b·m·Y), from the tangential force F_t (N), the tooth face width b (mm), the module m (mm) and the Lewis form factor Y (dimensionless, a function of tooth count). Lewis's 1892 equation was the first rational treatment of gear-tooth strength and is still the basis of BENDING design. It models the tooth as a cantilever beam fixed at the root: the tangential force transmitted between teeth (from the torque) creates a bending moment that tends to break the tooth at the root — the catastrophic failure where a tooth cracks and snaps. The form factor Y accounts for tooth geometry (gears with more teeth are 'fatter' at the root and stronger, higher Y). The computed stress is compared with the material's bending fatigue strength (with safety factors), since gears endure millions of cycles. The basic Lewis formula is then refined by the AGMA standard with stress-concentration, dynamic, load-distribution and surface-condition factors. It is one of the two fundamental gear design criteria (the other is contact stress). Enter the tangential force, face width, module and Lewis form factor.
Half-Wave Dipole Length
Calculate the physical length of a half-wave dipole, L = (150 ÷ f)·VF, from the frequency f (MHz) and the velocity factor VF (typically ~0.95 for wires, correcting the end effect). The result, in metres, is the total length of the dipole antenna resonant at the desired frequency — each arm is half this value. The half-wave dipole is the most used reference antenna, with 2.15 dBi gain. The velocity factor makes the antenna slightly shorter than a half wavelength in vacuum. Enter the frequency and the velocity factor.
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.