Accurate modeling of logarithmic spiral bevel gear based on the tooth flank formation and Boolean addition operation

Abstract

The logarithmic spiral bevel gear is a new type of spiral bevel gear and has received great attention in the industry for its excellent engineering characteristics. The objective of this study is to develop an accurate geometric model for the logarithmic spiral bevel gear. Based on the gear tooth flank formation mechanism, a conical logarithmic spiral curve with a constant spiral angle was constructed as the tooth trace curve. The profiles for the exterior and interior transverse of the tooth were built with an accurate involutes curve, with transition being circular arcs and straight lines. The first tooth model was established by sweeping the tooth profile accurately along the tooth trace curve, and the rest of the teeth were created by an array operation. The accurate three-dimensional model of logarithmic spiral bevel gear was finally obtained by means of a Boolean addition operation among all of the gear teeth and the root cone. An experimental study was carried out for such a gear whose number of teeth was 37, with modules being 4.5 mm, normal pressure angle being 20° and spiral angle being 35°. A DMU 40 monoBLOCK five-axis computer numerical control milling machine tool was used to produce the prototype, and a Zeiss CONTURA G3 three-dimensional coordinate instrument was employed to measure the exterior transverse addendum diameter. The linear error between the theoretical model value and the measured average value was 0.0027 mm, indicating the effectiveness and practicability of this modeling method, which provides an accurate geometric model for design and for subsequent tasks like computer-aided engineering analysis and manufacturing.

Geometrical design of variable ratio tooth profile based on Boolean subtraction operation and a novel modification method

“…The novel gear pair with VRTP still follows conjugate meshing characteristics, so the design [11] , modeling [12,13] , analysis [14,15] and manufacturing [16,17] methods for traditional gears are also applicable. Meshing theory has played a momentous role in gear geometry.…”

Five-Axis Numerical Control Machining of the Tooth Flank of a Logarithmic Spiral Bevel Gear Pinion

“…Logarithmic spiral bevel gear (LSBG) is a new kind of SBG with the characteristics of using a conical logarithmic spiral curve as the tooth trace curve and an involute as the tooth profile curve [15][16]. The spiral angle at a point defined by the angle between the tangent direction of the conical logarithmic spiral curve and the cone generatrix direction is constant [17]. The LSBGs have better transmission characteristics compared with the conventional SBGs [18][19][20] because of the constant spiral angle.…”

Computing Algorithm for the Gear Tooth Space Points Cloud Envelope Generated by the Mixed Cad Method

“…The virtual solid or surface models of gears [1,2,3,4,5,6,7,9], virtual gearing [8,9] or virtual manufacturing process studies of the gears [3] are the less expensive methods to develop and study new gearing solutions. Working in virtual environment needs specific models (solid, surface, assembly, FEA etc.)…”

“…Numerous software products were developed to solve particular cases [1,3,8], beside the well-known universally applicable modeling methods: solid or surface modeling using the teeth surface equations deduced with the meshing theory, Boolean Subtracting or Additive methods, the use of the relative movements of the workpiece and the tool etc.…”