A study of teeth generation for arbitrary-shaped sprockets

ABSTRACTIn the noncircular sprocket designing process, drawing the teeth cannot be automatically performed using any function in the drawing software, and it needs complicated manual operations and adjustments. The accuracy and time waste are big problems here. This paper proposes a procedure to automatically generate a complete 3D sprocket design from a set of sprocket pitch coordinates. Japanese standard tooth profile (JIS B 1801) is used as an example model in the procedure development. First, the tooth profile equation is derived using the theory of gearing in a particular coordinate system. Subsequently, the coordinate transformation matrix is built to attach the tooth profile on every sprocket pitch coordinate in the correct direction, remove some coordinates surpassing the outer diameter limit, and build the complete 3D sprocket profile. The proposed procedure can be implemented into programming languages with the sprocket pitch coordinate file as the input and the set of sprocket teeth coordinate as the output. With the proposed procedure, a 3D design of any shape sprocket can be generated quickly and accurately.CO EDITOR-IN-CHIEF: HsiauShu-SanASSOCIATE EDITOR: JengYeau-RenKEYWORDS: Coordinate transformationsprocket teeth generationteeth design process Nomenclature B=bottom tooth flank angleDr=chain roller diameterE=radius of the bottom tooth flanke=moving vector of segment 3 of the tooth profileF=top tooth flank radiusf=moving vector of segment 5 of the tooth profileg=tooth side reliefH=maximum tooth heighth=tooth side heightK=horizontal position of the center of the top tooth flank radiusMpf, Mtp=Matrices 3 × 3for transformation from Sf to Sp and Sp to StN=number of teethp=chain pitch valueQ=horizontal position of the center of the bottom tooth flank profileR=chain seating radiusRc=tooth side radiusr=moving vector of segment 2 of the tooth profiles=line vector of segment 4 of the tooth profileSf , Sp, St=tooth profile, sprocket, and pitch coordinate systemT=vertical position of the center of the bottom tooth flank profilet=tooth widthU=line profile connecting the chain seating radius on the right and left sideu=line vector of segment 1 of the tooth profileV=vertical position of the center of the top tooth flank radiusyz=line profile connecting the bottom and top tooth flankα=moving angle of vector rβ=moving angle of vector eφ=moving angle of vector fθn=normal angle of the n-pitch coordinateψn=n-pitch line angleDisclosure statementNo potential conflict of interest was reported by the author(s).AcknowledgmentsThis research was funded by the Ministry of Science and Technology of the ROC – Taiwan, grant number MOST 110-2221-E-150-029. The sprocket prototype manufacturing was supported by SAMOX company Taiwan.Additional informationFundingThis research was supported by the Ministry of Science and Technology of Taiwan [MOST 110-2221-E-150-029].