#mechanical-engineering

O-Ring-Dichtungs-Design-Mathematik als API, lokal und deterministisch berechnet – die Squeeze-, Gland- und Stretch-Werte, die ein Ingenieur oder Hersteller für eine Dichtung entwirft. Der Squeeze-Endpunkt liefert die Kompression, die die Dichtung bewirkt: Squeeze = (Querschnitt − Nuttiefe) ÷ Querschnitt, also wird eine 0,139-Zoll-Schnur in einer 0,113-Zoll-tiefen Nut um 18,7 % gequetscht, und bewertet das Ergebnis – etwa 10–16 % eignet sich für dynamische (hin- und hergehende) Dichtungen und 15–30 % für statische – und, bei gegebener Nutbreite, den Nutfüllgrad, der unter etwa 85 % bleiben sollte, damit der Gummi Platz zum Ausdehnen durch Hitze oder Flüssigkeitsquellung hat. Der Gland-Endpunkt arbeitet umgekehrt: Aus dem Querschnitt und ob die Dichtung statisch oder dynamisch ist (oder einem Ziel-Squeeze) gibt er die Nuttiefe und eine Breite zurück, die für etwa 70 % Füllung ausgelegt ist – typischerweise das 1,3- bis 1,5-fache des Querschnitts – plus einen Eckradius. Der Stretch-Endpunkt prüft die Installation: Stretch = (Paarungsdurchmesser − O-Ring-ID) ÷ ID, der unter etwa 5 % auf einer Stange bleiben sollte, da Dehnung den Querschnitt verringert und Squeeze stiehlt. Alles wird lokal und deterministisch berechnet, daher ist es sofort und privat. Ideal für App-Entwickler im Maschinenbau, Hydraulik, Pneumatik, Vakuum- und Produktdesign, Dichtungsauswahl- und Nutdesign-Tools sowie CAD-Plugins. Reine lokale Berechnung – kein Key, kein Drittanbieter-Service, sofort. Zoll oder Millimeter. Live, nichts gespeichert. 3 Compute-Endpunkte.

api.oanor.com/oring-api

Gear-train ratio, speed and torque maths as an API, computed locally and deterministically. The ratio endpoint computes the gear ratio of a single pair from the driver and driven tooth counts (or pitch diameters), ratio = N_driven/N_driver, classifies it as a reduction (more torque, less speed) or an overdrive, and — given an input speed and torque — returns the output speed (input/ratio) and the output torque (input·ratio·efficiency). The train endpoint computes a compound gear train: the overall ratio is the product of the individual stage ratios, and it returns each stage ratio, the output speed and torque, noting that idler gears change only the direction of rotation, not the ratio. The solve endpoint finds the missing one of the input speed, the output speed and the ratio from the other two — for example, the ratio needed to drop a 1500 rpm motor to a 500 rpm output. Everything is computed locally and deterministically, so it is instant and private. Ideal for drivetrain, robotics and machine-design tools, gearbox and transmission selection, bicycle and vehicle gearing, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is gear-train ratio and torque; for spur-gear tooth geometry use a spur-gear API.

api.oanor.com/gearratio-api

Belt-conveyor design maths as an API, computed locally and deterministically. The capacity endpoint computes the throughput of a belt conveyor — the volumetric capacity Q = A·v·3600 (m³/h) from the belt cross-section and speed, and the mass capacity Q·ρ/1000 (t/h) from the bulk density — and, when only the belt width is given, estimates the cross-section as A ≈ load_factor·width². The power endpoint computes the drive power as the sum of the horizontal friction power, μ·g·(material + 2·belt + idler mass per metre)·length·speed, and the vertical lift power, ṁ·g·height, then divides by the drive efficiency to give the motor power. The tension endpoint computes the belt tensions from the effective tension Te = P/v: the tight-side tension T1 = Te·e^(μθ)/(e^(μθ)−1) and the slack-side tension T2 = T1 − Te, using the Euler-Eytelwein grip of the belt on the drive pulley. Everything is computed locally and deterministically, so it is instant and private. Ideal for bulk-materials-handling, mining and plant-design tools, conveyor selection and motor sizing, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is a simplified belt-conveyor model; for rope/belt capstan friction use a capstan API and for belt-drive geometry use a belt-drive API.

api.oanor.com/conveyor-api

Pulley and block-and-tackle mechanics as an API, computed locally and deterministically. The advantage endpoint computes the mechanical advantage of a pulley system — the ideal MA equals the number of rope parts supporting the load, which is also the velocity ratio — and returns the effort needed to hold or raise a load, effort = load/(n·efficiency), the length of rope that must be pulled (n times the lift height) and the work in and out. The friction endpoint models a real block and tackle where every sheave loses a little tension: the mechanical advantage becomes MA = e·(1−eⁿ)/(1−e) for a per-sheave efficiency e (≈0.96 for a plain bearing, ≈0.98 for a ball bearing), so it returns the true MA, the overall efficiency and the extra effort friction costs you. The solve endpoint takes any two of the load, the effort and the number of rope parts and returns the third — for example, how many parts you need so a given person can raise a given load, or the heaviest load a winch can lift. Everything is computed locally and deterministically, so it is instant and private. Ideal for rigging, lifting and hoist-design tools, sailing, climbing and theatre-rigging apps, crane and winch sizing, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is pulley and block-and-tackle mechanics; for lever and moment balance use a lever API and for rope-around-a-drum capstan friction use a capstan API.

api.oanor.com/pulley-api

Bolted-joint torque, preload and stress maths as an API, computed locally and deterministically for ISO metric fasteners. The torque endpoint applies the torque-tension relation T = K·D·F — the tightening torque equals the nut factor times the nominal diameter times the bolt preload — and solves either way: the torque needed for a target preload, or the preload achieved by a given torque, with the nut factor K capturing the lubrication condition (≈0.20 plain, 0.16 plated, 0.12 lubricated). The stressarea endpoint computes the tensile stress area from the thread geometry, As = π/4·(d − 0.9382·P)² — the effective cross-section that carries the load — together with the nominal shank area and, given a proof or yield stress, the proof and yield loads of the bolt. The preload endpoint sets the clamp force as a percentage of the proof load (75 % is the usual target for reusable joints), F = (percent/100)·σproof·As, and returns the resulting tensile stress and, with a diameter and nut factor, the tightening torque. Grade proof stresses for 8.8, 10.9 and 12.9 bolts are documented. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-design, assembly and maintenance tools, torque-spec generation, fastener selection and structural-bolting apps, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is bolt tightening and preload mechanics; for thread pitch/lead geometry use a thread API and for bolt-circle hole patterns use a bolt-circle API.

api.oanor.com/bolttorque-api

Slider-crank (piston-crank) mechanism kinematics as an API, computed locally and deterministically. The position endpoint takes the crank radius, the connecting-rod length and the crank angle from top dead centre and returns the exact piston displacement from TDC, x = r(1−cosθ) + l(1 − √(1−λ²sin²θ)) with λ = r/l, the piston-pin distance from the crank axis, the connecting-rod swing angle φ = asin(λ·sinθ), the stroke (2r), the rod ratio n = l/r and the fraction of stroke travelled. The velocity endpoint adds the crank speed (as rpm or angular velocity) and returns the exact piston velocity, v = ω·[r·sinθ + r·λ·sinθcosθ/√(1−λ²sin²θ)], and the piston acceleration from the standard two-term approximation a ≈ r·ω²·(cosθ + λ·cos2θ) — the inertia term engine designers use for balancing. The geometry endpoint summarises the whole mechanism: the stroke, the rod ratio, the top- and bottom-dead-centre positions, the maximum connecting-rod angle asin(λ), and — with a speed — the mean piston speed 2·stroke·(rev/s). Everything is computed locally and deterministically, so it is instant and private. Ideal for engine, compressor and pump-mechanism design tools, robotics and linkage simulation, CNC and animation, and mechanical-engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is slider-crank linkage kinematics; for rotational energy use a flywheel API and for shaft torsion use a torsion API.

api.oanor.com/crankslider-api

Matemáticas de vida útil de rodamientos de elementos rodantes (ISO 281) como una API, calculada local y determinísticamente. El endpoint de vida calcula la vida nominal básica de un rodamiento de bolas o rodillos, L10 = (C/P)^p — donde p es 3 para rodamientos de bolas y 10/3 para rodamientos de rodillos — a partir de la capacidad de carga dinámica C y la carga equivalente P, reportando la vida en millones de revoluciones y, dada una velocidad en rpm, en horas y días; también funciona en reversa, resolviendo la capacidad de carga dinámica mínima necesaria para una vida objetivo, o la carga máxima que un rodamiento puede soportar para alcanzarla. El endpoint de carga calcula la carga dinámica equivalente P = X·Fr + Y·Fa a partir de las cargas radial y axial y los factores X e Y del rodamiento, el valor de carga único que necesita la fórmula de vida. El endpoint de confiabilidad aplica el factor de modificación de vida a1 de la ISO 281 para dar la vida nominal ajustada Lna = a1·L10 para cualquier probabilidad de supervivencia desde 90 % hasta 99.95 %, interpolado de la tabla de confiabilidad estándar. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de ingeniería mecánica, mantenimiento y confiabilidad, diseño de máquinas y trenes de potencia, aplicaciones de mantenimiento predictivo y costeo de vida útil, y educación en ingeniería. Cálculo local puro — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esta es la vida nominal de rodamientos; para esfuerzo de torsión en ejes use una API de torsión y para energía rotacional use una API de volante de inercia.

api.oanor.com/bearing-api

Torque de embreagem de fricção e freio a disco como uma API, calculado local e deterministicamente. O endpoint de embreagem calcula o torque que uma embreagem de placa (disco) pode transmitir a partir do coeficiente de atrito, da força de aperto axial e dos raios interno e externo da face de atrito, por ambas as teorias padrão — desgaste uniforme, T = n·μ·F·(Ro+Ri)/2, e pressão uniforme, T = ⅔·n·μ·F·(Ro³−Ri³)/(Ro²−Ri²) — para qualquer número de superfícies de atrito (uma embreagem multi-disco multiplica o torque), além da potência máxima em uma dada velocidade. O endpoint cônico faz o mesmo para uma embreagem cônica, T = n·μ·F·Rm/sin α, onde o ângulo de cunha amplifica a força normal por 1/sin α. O endpoint de freio fornece o torque de frenagem de um freio a disco, T = n·μ·F·R_eff, a potência dissipada em uma velocidade e — dada uma inércia rotativa e sua velocidade — a desaceleração angular, o tempo e o número de revoluções para parar, e a energia cinética convertida em calor. Tudo é calculado local e deterministicamente, portanto é instantâneo e privado. Ideal para ferramentas de trem de força, automotivas e de projeto de máquinas, engenharia de embreagens, freios e guinchos, e educação em engenharia mecânica. Cálculo puramente local — sem chave, sem serviço de terceiros, instantâneo. Ao vivo, nada armazenado. 3 endpoints. Este é o torque de embreagem e freio de fricção rotativa; para tensão de torção de eixo, use uma API de torção e para fricção de cabo/correia em tambor, use uma API de capstan.

api.oanor.com/clutch-api

Matemáticas de fricción de cabrestante y correa (la ecuación de Euler-Eytelwein) como una API, calculada local y determinísticamente. El endpoint de cabrestante aplica T1/T2 = e^(μ·β) — la relación entre la tensión del lado tenso y el lado flojo de una cuerda o correa enrollada alrededor de un tambor depende solo del coeficiente de fricción y el ángulo de envoltura, no del diámetro del tambor — y resuelve para cualquiera de las dos tensiones, la fricción o el ángulo de envoltura que omitas, con el ángulo de envoltura dado en grados, radianes o vueltas completas. El endpoint de sujeción muestra el efecto cabrestante: cómo una fuerza pequeña sostiene o mueve una carga grande, fuerza de sujeción = Carga·e^(−μβ) y fuerza de tracción = Carga·e^(+μβ) — unas pocas vueltas de cuerda alrededor de una bita permiten que una persona sostenga un barco. El endpoint de correa dimensiona una transmisión por correa: a partir de la tensión máxima del lado tenso, la fricción y el ángulo de envoltura, proporciona la tensión del lado flojo, la tensión efectiva (neta) T1 − T2 que impulsa la carga y, con la velocidad de la correa, la potencia máxima transmisible antes de que la correa deslice. Todo se calcula local y determinísticamente, por lo que es instantáneo y privado. Ideal para herramientas de ingeniería mecánica y marina, diseño de transmisiones por correa, cabrestantes, polipastos y frenos de banda, aplicaciones de escalada y aparejos, y educación en física. Cálculo local puro — sin clave, sin servicio de terceros, instantáneo. En vivo, nada almacenado. 3 endpoints. Esto es fricción de correa y cuerda; para longitud de correa, ángulo de envoltura y relación de velocidad, usa una API de transmisión por correa.

api.oanor.com/capstan-api

Pascal's-principle hydraulics as an API, computed locally and deterministically. The press endpoint computes the force multiplication of a hydraulic press, jack or master/slave cylinder: a pressure P = F/A acts equally throughout a connected fluid, so a small input force on a small piston becomes a large output force on a large piston, F2 = F1·A2/A1, with the mechanical advantage A2/A1 — areas given directly or as piston diameters, and the pressure in pascals, bar and psi. The stroke endpoint applies volume conservation, A1·d1 = A2·d2: the big piston moves less the more force it gains, and the work F·d is the same on both sides. The cylinder endpoint gives the push and pull force of a hydraulic cylinder at a pressure, F = P·A on the bore side and F = P·(A_bore − A_rod) on the rod (annulus) side. Everything is computed locally and deterministically, so it is instant and private. Ideal for hydraulics and fluid-power engineering tools, press, jack and lift design, brake and machine apps, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Pascal-principle force multiplication; for pressure at depth and force on a submerged wall use a hydrostatics API and for pump power use a pump API.

api.oanor.com/hydraulic-api

Shaft torsion as an API, computed locally and deterministically. The stress endpoint computes the maximum torsional shear stress in a circular shaft, τ = T·r/J — torque times the outer radius divided by the polar moment of inertia — for a solid shaft (J = π·d⁴/32) or a hollow tube (J = π·(D⁴−d⁴)/32), and solves the torque a shaft can carry for an allowable stress. The twist endpoint computes the angle of twist along the shaft, θ = T·L/(G·J), in radians and degrees, from the torque, length and the shear modulus (given directly or from a built-in material table — steel, aluminium, copper, titanium and more), plus the torsional stiffness G·J/L. The power endpoint relates the power a rotating shaft transmits to its torque and speed, P = T·ω = T·2πN/60, and solves any of the three, reporting power in watts, kilowatts and horsepower. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical and drivetrain engineering tools, shaft, axle and coupling design, motor and gearbox apps, and machine-design education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is circular-shaft torsion; for axial stress-strain use a Young's-modulus API and for the 2D stress state use a Mohr-circle API.

api.oanor.com/torsion-api

Tensão axial, deformação e módulo de Young como uma API, calculados local e deterministicamente. O endpoint de tensão relaciona as três grandezas de um membro carregado axialmente — a tensão σ = F/A, a deformação ε = ΔL/L e o módulo de Young E = σ/ε — e resolve para qualquer uma que você omitir, tomando o módulo diretamente, em gigapascals, ou de uma tabela de materiais embutida (aço, alumínio, cobre, titânio, concreto, vidro e mais), com a tensão reportada em pascals, MPa e GPa. O endpoint de alongamento calcula o quanto uma barra se estica sob uma carga axial, δ = F·L/(A·E), a partir da força, comprimento e seção transversal (área ou diâmetro) e do material ou módulo, juntamente com a tensão, deformação e a rigidez axial k = A·E/L. O endpoint de Poisson trabalha com o coeficiente de Poisson ν: a deformação lateral que acompanha uma deformação axial, e o módulo de cisalhamento G = E/(2(1+ν)) e o módulo volumétrico K = E/(3(1−2ν)) derivados do módulo de Young. Tudo é calculado local e deterministicamente, portanto é instantâneo e privado. Ideal para ferramentas de engenharia mecânica, civil e de materiais, aplicações de projeto estrutural e de máquinas, testes de materiais e educação. Cálculo local puro — sem chave, sem serviço de terceiros, instantâneo. Ao vivo, nada armazenado. 3 endpoints. Esta é a deformação axial de materiais; para o estado 2D de tensão (tensões principais, círculo de Mohr) use uma API de círculo de Mohr e para flambagem de colunas use uma API de flambagem.

api.oanor.com/youngmodulus-api

Single-degree-of-freedom vibration (spring-mass-damper) maths as an API, computed locally and deterministically. The natural endpoint gives the undamped natural frequency of a spring-mass system, ωn = √(k/m), fn = ωn/2π and the period T = 1/fn, and solves for whichever of the stiffness, mass or natural frequency you leave out. The damped endpoint analyses a damped system from the stiffness, mass and either a damping coefficient or a damping ratio: it returns the critical damping coefficient cc = 2√(km), the damping ratio ζ = c/cc, the classification (underdamped, critically damped or overdamped), and — for an underdamped system — the damped natural frequency ωd = ωn·√(1−ζ²), its period, and the logarithmic decrement δ = 2πζ/√(1−ζ²). The pendulum endpoint gives the period and frequency of a simple pendulum, T = 2π·√(L/g), and solves the length from a target period, with gravity adjustable. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, structural and earthquake-engineering tools, machine-condition-monitoring and isolation-design apps, instrument and clock design, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is discrete spring-mass-damper vibration; for standing waves on strings and in air columns use a standing-wave API.

api.oanor.com/vibration-api

Euler column buckling as an API, computed locally and deterministically. The critical-load endpoint computes the Euler critical (buckling) load of a slender column, Pcr = π²·E·I / (K·L)², from the Young's modulus, the second moment of area, the length and the end conditions — pinned-pinned (K=1), fixed-fixed (K=0.5), fixed-pinned (K≈0.7) or fixed-free / cantilever (K=2), or a custom effective-length factor — and, given the cross-section area, also the radius of gyration, slenderness ratio and critical buckling stress. The section endpoint returns the area, the second moment of area about both axes and the radius of gyration for a solid circle, a hollow circle or tube, or a rectangle, and highlights the weak-axis value that governs buckling. The slenderness endpoint computes the slenderness ratio λ = K·L/r and, given the modulus and yield strength, the transition slenderness λ1 = π·√(2E/σy) that separates long Euler columns from short and intermediate ones, classifies the column and returns both the Euler and the J.B. Johnson critical stresses. Everything is computed locally and deterministically, so it is instant and private. Ideal for structural, mechanical and aerospace engineering tools, strut and frame design, machine-design and stability-analysis apps, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is column buckling and stability; for beam bending, shear and deflection use a beam-statics API.

api.oanor.com/buckling-api

Mohr's circle and 2D (plane) stress transformation as an API, computed locally and deterministically. The principal endpoint takes a plane-stress state — the normal stresses σx and σy and the shear stress τxy — and returns the principal stresses σ1 and σ2 = (σx+σy)/2 ± √(((σx−σy)/2)² + τxy²), the maximum in-plane shear stress, the orientation of the principal and maximum-shear planes, the centre and radius of Mohr's circle, and the von Mises and Tresca equivalent stresses (treating plane stress with the third principal σ3 = 0). The transform endpoint rotates the stress state onto a plane at any angle θ, returning σx', σy' and τx'y' using the standard transformation equations, and confirms the σx+σy invariant. The safety endpoint computes the factor of safety against a material's yield strength under either the von Mises (distortion-energy) or the Tresca (maximum-shear) criterion, from a full stress state or from principal stresses directly. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical, structural and aerospace engineering tools, finite-element pre- and post-processing, machine-design and stress-analysis apps, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is stress-state analysis; for fillet-weld throat sizing use a weld API and for helical-spring rates use a spring API.

api.oanor.com/mohr-api

Flywheel and rotational-energy dynamics as an API, computed locally and deterministically. The energy endpoint computes the rotational kinetic energy stored in a spinning body, E = ½·I·ω², together with its angular momentum L = I·ω, in joules, kilojoules and watt-hours — from a moment of inertia (given directly, or worked out from a shape, mass and dimension) and an angular speed given as rpm, radians per second or hertz, which it reports in all three. The inertia endpoint returns the moment of inertia about the central axis for the common shapes — solid disk and cylinder (½·m·r²), thin ring and hoop (m·r²), hollow cylinder (½·m·(r_out²+r_in²)), solid sphere (⅖·m·r²), hollow sphere (⅔·m·r²) and a rod about its centre (1/12·m·L²) or end (⅓·m·L²) — from a mass and a radius, diameter or length. The flywheel endpoint sizes a flywheel: give a target energy and an operating speed and it returns the required inertia I = 2E/ω², or give an inertia and a maximum and minimum rpm and it returns the energy delivered between them, ΔE = ½·I·(ω₁²−ω₂²), with the coefficient of fluctuation. Everything is computed locally and deterministically, so it is instant and private. Ideal for mechanical-engineering and energy-storage tools, motor, engine and powertrain design, kinetic-energy-recovery and physics-education apps. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is rotational energy and inertia; for bolt tightening torque use a torque API and for power-screw mechanics use a screw-jack API.

api.oanor.com/flywheel-api