Tooth Profile Equation Research Articles

Center Distance Change of Silent Chain Drive Effect on Sprocket Tooth Profile Modification

The principle of modified gear was applied to silent chain transmission, and tooth profile equation of the involute sprocket was derived, then method of processing gear using imaginary rack cutter solved modification coefficient of involute sprocket. When Center distance of silent chain drive changed smaller, processing method of sprocket modification coefficient and range of modification coefficient values were analysed. The method by changing the modification coefficient of involute sprocket solves the problem that the chain links are increased or decreased in the actual application to be unable to meet the requirements of specific center distance, thus improve transmission performance of silent chain.

Design of a Novel Cycloid Drive with a Cycloid-arc Gear and Analysis of Its Meshing Characteristic

Cycloid drive is used widely in many industrial areas for both power transmission and precision transmission. In this paper a novel cycloid drive is proposed and its meshing characteristics are analyzed. The conjugated gear pair of this novel cycloid drive is composed by an external cycloid-arc gear and an internal ring gear. Firstly, the idea of this novel cycloid drive is described and the tooth profile equation of the external cycloid-arc gear is presented. Secondly, based on coordinate transformation and gear geometry theory, the meshing equation for this novel cycloid drive is established, the equation of the conjugated tooth profile and the formula of induced normal curvature are also derived. Thirdly, the meshing characteristics are analyzed based on a numerical example: the drawing of the conjugated tooth pair is presented and compared with the conventional cycloid drive and the double-enveloping cycloid drive; the contact lines between one tooth pair at different meshing positions are illustrated. Finally, the induced normal curvature is calculated and compared with that of the conventional cycloid drive and the double-enveloping cycloid drive, which shows good characteristic of this novel cycloid drive.

Meshing Theory of New Epicycloids Gear Drive

In order to realize the pure rolling, improve the contact ratio, remove the backlash and raise the life, a new epicycloids gear drive is put forward. The drive part of the particular mechanism is a wheel with the roller tooth and is called the roller gear. And the driven part is the epicycloids gear. The tooth profile equation is achieved and meshing characteristics is also studied. The basic parameters of the new mechanism are researched and the 3D model is achieved. The research result shows that the new drive is workable and the new mechanism has a wide application prospect.

Generation and investigation of a new cycloid drive with double contact

A new cycloid drive with double contact lines between one tooth pair is presented in this paper. The new conjugated tooth profile is generated by applying double-enveloping gear theory in cycloid drives. Based on coordinate transformation and gear geometry theory, the meshing equation for this new cycloid drive is established at first, then the equation of tooth profile and meshing line and the formula of induced normal curvature are also derived. The meshing characteristics are investigated by theoretical analysis and numerical examples: the double contact characteristic is revealed by that the meshing function can be resolved into two independent factors; the contact lines at different instant and meshing line are illustrated based on a numerical example; the superior characteristics of the new conjugated tooth profile is represented by comparison of induced normal curvature with conventional cycloid drives. The physical prototype is trial-produced and the transmission error of the prototype is also tested, which shows that double-enveloping theory can be applied for cycloid drives.

Study and Experimental Analysis of Oval Bevel Gear Transmission

Oval bevel gear is introduced as a new gear transmission type of intersecting axes, in which high-order, denaturing and eccentric one are included. Based on the theory of spatial engagement, spatial spherical coordinate system of the noncircular bevel gearing was developed and a generalized tooth profile equation of noncircular bevel gears was also proposed. The gear profile can be enveloped for the generating movement between conical cutter and oval bevel gear according to the envelope principle of conjugate profiles. Then a new and general parametric design method for oval bevel gear was founded. The classification and gear variability condition of oval bevel gear were discussed. Meanwhile, its pitch curve, addendum and dedendum curve were studied, and the corresponding equations were deduced. A roll check experiment is performed on the prototype workpiece. Then the influences of motor speed and load on transmission ratio were analyzed. Finally, the design method, profile generation method and manufacture method of oval bevel gear were certified as correct by comparing experimental curve of transmission ratio with theoretical one.

Optimization of New Type Sintering Machine’s Sprocket Wheel with Even-Number Teeth

Comprehensive consideration the even teeth sintering machine’s pallet car and the smooth and continuous meshing of variable acceleration segment of the sprocket wheel’s tooth profile, puts forward a new type sprocket wheel’s tooth profile to make variable acceleration segment’s unified equation. According to the displacement, velocity and acceleration’s curves of the pallet car in the stage of variable acceleration, with the method of locus of the contact new tooth profile’s equation is deduced. The sprocket wheel which is derived by this method is stability in variable speed process, concise, easy to manufacture and analyze the characteristics equation of tooth profile.

Research on Geometry Relationship of Pin-Rack Gearing

The pin-rack gearing is a particular type of cycloidal gearing which transforms a rotation motion to a linear one. Comparing with rack and pinion gearing and hydraulic swing cylinder, the pin-rack gearing has a more compact structure, less mass and lower cost. Nevertheless, designers always worry about vibration, noise and low use life as pin-rack mechanism working caused by deficiency of design theory. The present research derived the pin-rack gearing tooth profile equation and studied the geometry relationship among design parameters. The results can help to improve the pin-rack gearing design.

Tooth Profile Synthesis and Strength Computation of Swing Movable Teeth Drives

The tooth profile synthesis of swing movable teeth drives was performed. The tooth profile equation of the internal teeth ring was established. The analysis result shows the deformation distribution of the movable tooth in the normal direction at the contact point of the wave generator is a sine function. Furthermore, the forces of the wave generator, the movable tooth pin and the internal teeth ring acting on the movable tooth were analyzed. Based on the Hertz theory and material mechanics, the contact strength calculation methods for the meshing pairs of the movable tooth and the wave generator as well as the movable tooth and the internal teeth ring were discussed. The calculation method for the bending strength of the pin was also derived. The research result provides a theoretical basis for designing and applying swing movable teeth drives.

An Optimization Approach to the Displacement Volumes for External Spur Gear Pumps

To increase volume displacement is always concerning in designing external gear pumps (EGPs). Therefore, an approach of optimization analysis intending to enhance their displacement capability is proposed in this study. Through that, design parameters of the spur gears in the pumps are systematically resulted to achieve their optimal volume displacements. Parametrically, a CAD model to visualize the designed gear of the optimal design is also created. Firstly, the study derives tooth profile equations by using the coordinate transformation and equation of meshing for gears on a rack cutter profile. Then, an analytic formula represented the enveloping area by an involute curve is derived. Next, volumes of output and trapped backflow of the EGP are achieved. Therefore the net output volume can be calculated accurately and efficiently. After that, the optimization analysis to maximize the volume displacement is performed. Through that, optimal design parameters for the pumps are achieved under assigned constraints for considerations of design and manufacturing. Additionally, influences of module, pressure angle, and addendum correction factor for the gears in the pumps on their displacement capability are also investigated. Additionally, flowrate fluctuation characteristics under different pressure angles of gears are finally discussed.

Meshing theory and simulation of noninvolute beveloid gears

Based on the space engagement theory, a special type of noninvolute beveloid gears meshing with line contact between intersecting axes has been studied in this paper for the first time. The engagement equation and tooth profile equation have been presented by applying the theory of gearing. Meanwhile the tooth profile errors and axial errors have been calculated by means of numerical analysis in this paper. As a numerical example, the three-dimensional simulation of beveloid gears between intersecting axes has been finished by means of the CAD system, Pro/Engineer.