Study On Conjugate Theory Of Constant-depth Tooth Logarithmic Spiral Bevel Gear

Spiral bevel gear in automotive, aircraft, a large number of applications is widely inengineering machinery, is one of the important parts, mechanical transmission is the keypoint of design research. Of logarithmic spiral bevel gear of the new gear with tooth allpoint to the line delay spiral Angle is equal to good engineering characteristics, will bevery good solution currently in the process of the spiral bevel spiral gear angle at differentmeshing transmission of point is not equal to the transmission is not smooth, friction wearserious, low transmission efficiency problem. The meet the conjugate transmissionaccurately theoretical tooth surface calculation is an important problem facing.Paper first gives the space meshing theory analysis used in the basic concept, thispaper discusses the space bevel gear transmission principle, on the basis of clarified thelogarithmic spiral bevel gear tooth surface formation principle, and discretization toothsurface is established. In this paper, the logarithmic spiral polar coordinates equation oflogarithmic spiral and logarithmic spiral bevel gear tooth surface formation, rolling basewith the base curve surface of spherical involute forming principle as the foundation, tocoordinate transform again, and through the right. Angle coordinate system and polarcoordinate transformation between spherical involute and accurate logarithmic spiral planein the conical surface rolling contact line, the combination of form the tooth surface ofconjugate condition, get the discrete tooth surface data point. When spherical involutescanning angle of start and end value determine, cone logarithmic spiral equation can beobtained, the only depending on a parameter range, namely, to establish a sphericalinvolute logarithmic spiral surface boundary conditions.Through MATLAB language programming, based on the discrete form accurate toothsurface coordinates. Theory of spherical involute accurate logarithmic spiral bevel geartooth surface by MTALAB language programming calculation, find out the tooth surfacecoordinates of points, and import it into complete tooth surface formed in the Pro/E. This kind of method to establish the discrete point conjugate tooth surface has good features,shape is more accurate, easier to tooth surface analysis and calculation.Along with the discretization of tooth surface formation, resolve conjugate surfacetheory can not meet the needs of the design, therefore, need to apply digital method basedon the discrete form of conjugate surface, to establish digital model of conjugate surface.Based on the digitized method of conjugate surface and its solving principle, the traditionalanalytic conjugate theory, its characteristic is that regardless of the previous theory ofconjugate curved surface of complicated derivation and the matrix transformation, appliedonly to the relationship between the structure framework of conjugate condition, usingdigital means, use the computer to help to solve the various problems in the theory ofconjugate curved surface. This method not only can solve the problem of the conjugatecalculation of digital surface, can also solve the problem of analytic conjugate curvedsurface of the calculation, which can realize the computation of overall\"digital\" willmake known to surface the coordinates of the points measured, conjugate curved surface tosolve cohesion into close organic entirety.