Study On Geometrical Design Theory Of Polyhedral Helix Curve Meshing Wheel Reducer

Gear reducers are widely used between prime motors and working mechanisms withinmodern machines to change values and directions of rotation speeds. Commonly usingtraditional space curve meshing gears as transmission components, classical gear reducers arestuck with their structures and sizes as well as their limited output shafts.The Space Curve Meshing Wheel (SCMW) is an innovative gear, which has possesseddecent design theory and fabrication foundation. Progresses have been achieved in manyaspects like meshing equations, contact ratio, elastic deformation criterion, manufacturingtechnology and assembly accuracy. It has begun to be applied in the fields like micro reducers.The Helix Curve Meshing Wheel (HCMW) is the most common SCMW with the mostmatured technology.Based on the HCMW, a micro reducer with multiple output shafts named PolyhedralHelix Curve Meshing Wheel Reducer (Polyhedral HCMWR) was proposed in thisdissertation, and its design theory was studied from geometrical perspectives. The features ofthis reducer include the application of the transmission train, the polyhedral3D geometriclayout of the input and output shafts, and single input and multiple outputs in either singlestage reducer of parallel transmissions or multiple stage reducer of mixed transmissions. Witha small size, light weight and high flexibility, this reducer is very suitable to serve in a smalldevice.Specifically speaking, the followings were concerned in the dissertation:(1) Design of the HCMW with unequal tine radii. The design fundamental based on thecontact curves were expounded, the meshing equation of the SCMW was solved in the spacecurve meshing coordinates as well as its contact curves and center curves. As an illustration,equations of the HCMW were derived, the driving and driven wheels were simulated with3Dmodeling software, and its transmission continuity was testified by virtual simulation andpractical experiment.(2) Component layout specification and installation dimension chains formulation for thePolyhedral HCMWR. The installation chains of the HCMW were analyzed according to threedifferent cases (intersecting axis, vertical axis, or parallel axis), respectively; the HCMW trainwith a single driving wheel and multiple driven wheels was designed; the initial installationangle of the HCMW train was studied; the mesh requirement was proposed after the analysisof the mesh status in the HCMW train; and based on the HCMW train, the concept of the Polyhedral HCMWR and its component layout specification were defined, and the designformulas of the transmission system and the box structure were derived.(3) Geometrical constrain demarcations and interference-proof condition deductions inthe Polyhedral HCMWR. The geometric constraints were defined and calculated in the threeaspects: contact curves, HCMW pair and HCMW train; the interference-proof conditionswere proposed in the same three aspects. As a practical example, the parameter selection of atetrahedron HCMWR with HCMW trains was illustrated to show the process of determiningthe feasibility range of the position parameters.(4) Selection criterion and calculation formulas of the position parameters based on thesliding rates. With the slide rates of classical space conjugate surfaces referred, the slide ratesof two conjugate curves in the space were defined and calculated, and subsequently those ofthe contact curves in the SCMW and the HCMW were derived; and optimal meshingcondition and position-parameter selection criterion of the HCMW were obtained based onthe analysis of the monotonicity and feasible region of its sliding rates.