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.
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Gear dynamic load
The effective dynamic load on gear teeth is F_d = F_t·K_v, from the nominal tangential force F_t and the dynamic factor K_v. It is the real tangential force the teeth carry in operation, larger than the nominal value (simply the torque divided by the radius) because of the dynamic effects of meshing at speed. Those effects — vibration, impact at the tooth contact, tooth deflection under load and manufacturing errors — make the instantaneous tooth load fluctuate and reach peaks above the average, especially at high pitch line velocities. The dynamic factor K_v (from the Barth equation or other formulas) quantifies that magnification. The dynamic load then feeds the strength checks: the Lewis bending stress (risk of the tooth breaking at the root) and the Hertzian contact stress (risk of surface fatigue and pitting). Using the nominal load without the dynamic factor would underestimate the demand and lead to undersized gears that fail early by fatigue. It is an essential and classic step in gear sizing. Enter the nominal tangential force and the dynamic factor.
Related Tools
Gear Tooth Bending Safety Factor
Calculate the bending safety factor of a gear tooth, FS = σ_perm ÷ σ, from the material's allowable (permissible) bending stress σ_perm (MPa, the bending fatigue strength with its factors) and the acting bending stress σ (MPa, from Lewis/AGMA from the load). It is the final bending-design check: the material strength must exceed the demand with adequate margin. Gears run for millions to billions of cycles, so the allowable stress is the material's bending FATIGUE strength (at the design-life cycle count), adjusted by reliability, temperature and life factors. Required safety factors depend on criticality and uncertainty (typically 1.5-3 for bending). If FS is insufficient, the module is increased (bigger, stronger teeth), the face width, or a better material/heat treatment used. A tooth breaking by bending fatigue is a CATASTROPHIC, sudden failure (unlike pitting, which gives progressive signs), since the broken tooth comes loose and can damage the whole drive — so bending is designed with generous margins. With the pitting (contact) safety factor, it defines the gear's robustness. Enter the allowable stress and the acting stress.
Gear Torque
Calculate the torque transmitted by a gear, T = (F_t·d) ÷ 2000, from the tangential force F_t (N) and the pitch diameter d (mm); the result is in N·m (the 2000 converts d/2 from mm to m). Torque is the moment the gear transmits about its axis, and the tangential force F_t acts at the pitch radius (d/2), creating that moment. This relation is the bridge between the POWER/torque side (what the shaft transmits) and the TOOTH-FORCE side (what sizes the strength): from shaft torque, the tooth tangential force (F_t = 2T/d) is obtained, which then feeds the bending (Lewis) and contact (Hertz) calculations. Conversely, given the tangential force, the torque is obtained. In a gear train, torque CHANGES at each stage by the gear ratio (a reduction that multiplies speed by 1/i multiplies torque by i, conserving power minus losses), while power stays roughly constant. So a reducer's last stage (low speed) transmits the HIGHEST torque and needs the most robust gears. Knowing the torque at each gear is essential to size teeth, shafts, keys and bearings. Enter the tangential force and the pitch diameter.
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.
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.
Cubic Mean Load (Bearing)
Calculate the equivalent mean load of a bearing under a cycle with two different loads, P_m = ∛(P₁³·U₁ + P₂³·U₂), from the loads P₁ and P₂ (N) and the time (or revolution) fractions during which they act U₁ and U₂ (with U₁ + U₂ = 1). Many bearings do not work under CONSTANT load: the load varies over the operating cycle (a press loading and unloading, a motor accelerating and decelerating, a machine with different work phases). To compute life in this case, the variable cycle is replaced by an equivalent CONSTANT load causing the same fatigue damage — the mean load. But the mean is NOT arithmetic: since fatigue damage is proportional to load CUBED (the life exponent p=3), the mean load is a time-fraction-weighted mean, but with the loads cubed (then cube-rooted) — the so-called cubic mean or 'fatigue-weighted mean'. This makes HIGH loads weigh disproportionately more (a double load causes 8× more damage), so even a small fraction of time at high load dominates the result. This formula (here for two load levels; it generalizes to several) is essential to size bearings in variable-load machines, avoiding underestimating the damage. Enter the two loads and their time fractions.
Residual Member Clamping Force
Calculate the residual clamping force on the members (clamped parts) of a bolted joint under external load, F_m = F_i − (1 − C)·P, from the preload F_i (N), the joint stiffness constant C and the external tensile load P (N). When an external load P tries to separate the parts, it does not go entirely to the bolt — most, (1−C)·P, acts to RELIEVE the compression between the members. The residual force F_m is how much clamping STILL holds the parts together after the external load is applied. This value is crucial for several reasons: while F_m stays POSITIVE (compression), the joint is closed and tight, and the bolt is protected (feels only C·P); if F_m reaches ZERO, the joint SEPARATES (and the bolt takes the whole load). In SEALED joints (gaskets, engine joints, pressurized pipe flanges), the residual member force is what keeps the seal compressed and prevents leaks — so it must stay above a minimum value, even under maximum service load (internal pressure, for example). Computing F_m is essential to ensure the joint stays tight and sealed in operation, and it is the criterion that sets the minimum required preload. Enter the preload, the stiffness constant and the external load.
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