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Technical Documents - Documentos Técnicos: Nomenclatura de los engranajes

NOMENCLATURA DE ENGRANAJES

Los engranajes constituyen uno de los mejores medios disponibles para transmitir movimiento, cuando en las máquinas la transmisión de potencia se hace de un eje a otro paralelo cercano a él.

De entre los diferentes tipos de engranajes son los cilíndricos de dientes rectos los más usuales, los cuales se caracterizan porque son ruedas dentadas cuyos dientes son rectos y paralelos al eje del árbol.

Es importante destacar que la gran duración de las transmisiones con engranajes va acompañada de un diseño, un análisis y una fabricación complejos, que es preciso conocer.

Antes de comenzar su estudio es interesante ofrecer la terminología característica usada en estos elementos.

Fig. 1 - Nomenclatura de los engranajes

La nomenclatura presentada en la figura anterior tiene las siguientes definiciones:

  • Circunferencia de paso o primitiva es la de contacto entre los dientes que determina la relación de transmisión. Las circunferencias primitivas de dos engranajes son tangentes entre sí.
  • Paso circular es la distancia medida sobre la circunferencia primitiva entre un determinado punto de un diente y el punto correspondiente de un diente inmediato. Según se aprecia en la figura anterior el paso circular o simplemente paso es igual a la suma del grueso del diente y el ancho entre los dientes consecutivos.
  • Módulo es el cociente del diámetro de la circunferencia primitiva y el número de dientes.
  • Paso diametral es la razón entre el número de dientes y el diámetro de paso. Evidentemente módulo y paso diametral son inversos.
  • Adendo es la distancia radial entre el tope del diente y la circunferencia primitiva.
  • Dedendo es la distancia radial desde la circunferencia primitiva hasta la circunferencia de base.
  • Altura total es la suma del dedendo mas el adendo.
  • Circunferencia de holgura es la circunferencia tangente a la del adendo mando los dientes están conectados.
  • Holgura es la diferencia entre el dedendo y el adendo.
  • Juego es la diferencia entre el ancho del espacio y el grueso del diente.
  • Anchura de cara es la longitud de los dientes en la dirección axial.
  • Cara es la superficie lateral del diente limitada por la circunferencia primitiva y la circunferencia de adendo.
  • Flanco es la superficie lateral del diente limitada por la circunferencia primitiva y la circunferencia de dedendo.
  • Superficie de fondo es la superficie de la parte inferior del espacio comprendido entra dientes contiguos.
  • Radio de entalle es el radio de la cuna de empotramiento del diente en el engranaje.
  • Angulo de acción es el ángulo que gira el engranaje desde que entran en contacto un par de dientes hasta que termina su contacto.
  • Angulo de aproximación es el ángulo que gira un engranaje desde el instante en el que dos dientes entran en contacto, hasta que ambos dientes entran en contacto en el punto correspondiente al diámetro primitivo.
  • Ángulo de alejamiento es el ángulo que gira un engranaje desde que los dientes están en contacto en el punto correspondiente al diámetro primitivo hasta que se separan.
  • Ángulo de sección = ángulo de aproximación + ángulo de alejamiento

Gear Terminology

addendum: The radial distance between the top land and the pitch circle.

addendum circle: The circle defining the outer diameter of the gear.

circular pitch: The distance along the pitch circle from a point on one tooth to a corresponding point on an adjacent tooth. It is also the sum of the tooth thickness and the space width, measured in inches or millimeters.

clearance: The radial distance between the bottom land and the clearance circle.

contact ratio: The ratio of the number of teeth in contact to the number of those not in contact.

dedendum circle: The theoretical circle through the bottom lands of a gear.

dedendum: The radial distance between the pitch circle and the dedendum circle.

depth: A number standardized in terms of pitch. Full-depth teeth have a working depth of 2/P. If the teeth have equal addenda (as in standard interchangeable gears), the addendum is 1/P. Full-depth gear teeth have a larger contact ratio than stub teeth, and their working depth is about 20% more than that of stub gear teeth. Gears with a small number of teeth might require undercutting to prevent one interfering with another during engagement.

diametral pitch (P): The ratio of the number of teeth to the pitch diameter.

A measure of the coarseness of a gear, it is the index of tooth size when U.S. units are used, expressed as teeth per inch.

pitch: A standard pitch is typically a whole number when measured as a diametral pitch (P). Coarse-pitch gears have teeth larger than a diametral pitch of 20 (typically 0.5 to 19.99). Fine-pitch gears usually have teeth of diametral pitch greater than 20. The usual maximum fineness is 120 diametral pitch, but involute-tooth gears can be made with diametral pitches as fine as 200, and cycloidal tooth gears can be made with diametral pitches to 350.

pitch circle: A theoretical circle upon which all calculations are based.

pitch diameter: The diameter of the pitch circle, the imaginary circle that rolls without slipping with the pitch circle of the mating gear, measured in inches or millimeters.

pressure angle: The angle between the tooth profile and a line perpendicular to the pitch circle, usually at the point where the pitch circle and the tooth profile intersect. Standard angles are 20 and 25º. The pressure angle affects the force that tends to separate mating gears. A high pressure angle decreases the contact ratio, but it permits the teeth to have higher capacity and it allows gears to have fewer teeth without undercutting.

Gear Dynamics Terminology

backlash: The amount by which the width of a tooth space exceeds the thickness of the engaging tooth measured on the pitch circle. It is the shortest distance between the noncontacting surfaces of adjacent teeth.

gear efficiency: The ratio of output power to input power, taking into consideration power losses in the gears and bearings and from windage and churning of lubricant.

gear power: A gear’s load and speed capacity, determined by gear dimensions and type. Helical and helical-type gears have capacities to approximately 30,000 hp, spiral bevel gears to about 5000 hp, and worm gears to about 750 hp.

gear ratio: The number of teeth in the gear (larger of a pair) divided by the number of teeth in the pinion (smaller of a pair). Also, the ratio of the speed of the pinion to the speed of the gear. In reduction gears, the ratio of input to output speeds.

gear speed: A value determined by a specific pitchline velocity. It can be increased by improving the accuracy of the gear teeth and the balance of rotating parts.

undercutting: Recessing in the bases of gear tooth flanks to improve clearance.

Gear Classification

External gears have teeth on the outside surface of a disk or wheel.

Internal gears have teeth on the inside surface of a cylinder.

Spur gears are cylindrical gears with teeth that are straight and parallel to the axis of rotation. They are used to transmit motion between parallel shafts.

Rack gears have teeth on a flat rather than a curved surface that provide straight-line rather than rotary motion.

Helical gears have a cylindrical shape, but their teeth are set at an angle to the axis. They are capable of smoother and quieter action than spur gears. When their axes are parallel, they are called parallel helical gears, and when they are at right angles they are called helical gears.

Herringbone and worm gears are based on helical gear geometry.

Herringbone gears are double helical gears with both right-hand and left-hand helix angles side by side across the face of the gear. This geometry neutralizes axial thrust from helical teeth.

Worm gears are crossed-axis helical gears in which the helix angle of one of the gears (the worm) has a high helix angle, resembling a screw.

Pinions are the smaller of two mating gears; the larger one is called the gear or wheel.

Bevel gears have teeth on a conical surface that mate on axes that intersect, typically at right angles. They are used in applications where there are right angles between input and output shafts. This class of gears includes the most common straight and spiral bevel as well as the miter and hypoid.

Straight bevel gears are the simplest bevel gears. Their straight teeth produce instantaneous line contact when they mate. These gears provide moderate torque transmission, but they are not as smooth running or quiet as spiral bevel gears because the straight teeth engage with full-line contact. They permit medium load capacity.

Spiral bevel gears have curved oblique teeth. The spiral angle of curvature with respect to the gear axis permits substantial tooth overlap.

Consequently, teeth engage gradually and at least two teeth are in contact at the same time. These gears have lower tooth loading than straight bevel gears, and they can turn up to eight times faster. They permit high load capacity.

Miter gears are mating bevel gears with equal numbers of teeth and with their axes at right angles.

Hypoid gears are spiral bevel gears with offset intersecting axes.

Face gears have straight tooth surfaces, but their axes lie in planes perpendicular to shaft axes. They are designed to mate with instantaneous point contact. These gears are used in right-angle drives, but they have low load capacities.

Designing a properly sized gearbox is not a simple task and tables or manufacturer’s recommendations are usually the best place to look for help. The amount of power a gearbox can transmit is affected by gear size, tooth size, rpm of the faster shaft, lubrication method, available cooling method (everything from nothing at all to forced air), gear materials, bearing types, etc. All these variables must be taken into account to come up with an effectively sized gearbox. Don’t be daunted by this. In most cases the gearbox is not designed at all, but easily selected from a large assortment of off-the-shelf gearboxes made by one of many manufacturers.

Let’s now turn our attention to more complicated gearboxes that do more than just exchange speed for torque.

 

 


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