Gears

Gear Stress

Bending and contact stress of a spur gear pair by the Lewis equation with the Barth velocity factor and by the AGMA 2001-D04 rating method as presented in Shigley's Mechanical Engineering Design (Chapter 14): pitch-line velocity and transmitted load from the power and speed, the dynamic factor from the quality number, the size, load-distribution (C_mc, C_pf, C_pm, C_ma, C_e), rim-thickness, reliability and temperature factors, the stress-cycle factors Y_N and Z_N for the life, the hardness-ratio factor, the geometry factors I and J (J entered from the AGMA chart or computed by the AGMA 908-B89 tooth layout), the elastic coefficient, the allowable bending and contact stress numbers by material grade and Brinell hardness, the AGMA safety factors S_F and S_H for pinion and gear (with S_H squared for the comparison on a load basis), the power rating at unit safety factor, margins of safety, a drawing of the pinion tooth with the Lewis parabola and the dynamic-factor chart. Default inputs are Shigley's Example 14-4 (17-tooth pinion at 1,800 rev/min driving a 52-tooth gear, 4 hp, 10 teeth/in, 1.5-in face, Q_v 6, grade 1 through-hardened steels at 240 and 200 HB).

1 worked example reproduced, listed on the tool page.

Spur and Helical Gear Geometry

Involute geometry of a spur or helical gear pair, external or internal, from the normal module (or diametral pitch), the tooth numbers, the normal pressure angle, the helix angle, the rack addendum and dedendum coefficients and the profile shifts: transverse pressure angle and module, reference, base, tip and root diameters, pitches and lead, the standard centre distance and the zero-backlash working centre distance with the working pressure angle from the involute function (Newton), the backlash produced by an entered centre distance (exact from the tooth-thickness equation beside the 2 Δa tan α estimate of NASA RP-1152), tooth thickness at any diameter, tip thickness and the pointing diameter, chordal thickness and height for a gear-tooth caliper, the span measurement over k teeth (base tangent length), the measurement over pins or balls with the pin-contact pressure angle solved from its involute equation, the transverse, overlap and total contact ratios with the path of contact, the specific sliding and sliding-velocity ratio along the line of action, the undercut check (minimum teeth, minimum profile shift, rack-generated form diameter), the involute-interference check of both members and the trochoid-interference scan of an internal pair; a drawing of the two teeth meshing at the pitch point generated from the involute equations; and a gear-train analysis (compound trains in series, simple and compound epicyclic trains by the tabular Willis method with the assembly and planet-spacing conditions, speeds and torques). The default pair (20 and 40 teeth, 2.5 mm module, 20°, 15° helix) is illustrative; the method is checked against Buckingham's 1928 worked problems, the NAVEDTRA 12204 caliper example and the contact ratios of NASA TM 83725.

1 worked example reproduced, listed on the tool page.

Other Mechanical Design sections

Shafts · Bearings · Springs · Fasteners and Power Screws · Pressure Vessels · Tolerances · Mass Properties · Vibration · Acoustics · Brakes, Clutches and Belts · Machining and Manufacturing · Lubrication and Wear