3 results about "Tangential point" patented technology

The present application belongs to the field of gear design, and particularly relates to a design method of a drum-shaped modification curve of gear tooth direction, comprising: 1) constructing a whole C 2 smoothly continuous double circular-arc spline drum-shaped modification curve; 2) obtaining the coordinates of the common tangent point F i of the i-th double circular-arc segment of the double circular-arc spline drum-shaped modification curve; 3) constructing a multi-element nonlinear equation set; 4) obtaining an initial solution by solving the linear term of the equation set, and iteratively calculating the accurate solution of the multi-element nonlinear equation set; and 5) obtaining the drum-shaped modification curve of the gear tooth direction according to the accurate value of the intermediate variable chord tangent angle of the i-th double circular-arc segment. The drum-shaped modification curve of the gear tooth direction obtained by the present application adopts segmented low-order interpolation, can avoid the "Runge" effect of high-order interpolation, and has good properties of the first and second order derivatives of the drum-shaped curve. The curve has high fitting accuracy, is continuous and smooth, reduces the impact and vibration in the gear transmission process, improves the tooth surface contact state, and improves the gear transmission performance.

The application discloses a shear strength parameter calculation method and an evaluation method thereof, and relates to the field of geotechnical engineering, aiming at fast and accurate shear strength parameters. The technical scheme adopted by the application is as follows: the shear strength parameter calculation method is used to calculate the cohesion and the internal friction angle according to constraint condition one and constraint condition two through at least two groups of triaxial test data. Constraint condition one: the sum of the vector distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to each Mohr stress circle to the to-be-solved failure strength line is 0. Constraint condition two: the sum of the distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to each Mohr stress circle to the to-be-solved failure strength line is minimum. The application further provides an evaluation method of the shear strength parameter calculation method, which is used to determine the cohesion and the internal friction angle according to the above method, and then to evaluate the quality through the maximum distance ratio δ. The application is used for calculating and evaluating the shear strength parameters according to the triaxial test data.

This invention discloses a mathematical method for solving the inscribed circle of a Bezier-type flow channel, comprising the following steps: S1, obtaining curves 1 and 2 of the Bezier-type parameters on both sides of the flow channel; S2, establishing a mathematical model of the inscribed circle with "equal radius + tangency" geometric constraints based on the Bezier curve equation and its first derivative equation; S3, deriving a functional expression for the parameters by simultaneously applying two tangent and perpendicular constraints; S4, substituting the functional expression into the equal radius constraint to construct a single-variable nonlinear equation = 0; S5, solving the single-variable nonlinear equation = 0 using a numerical iteration method for the current input value; S6, calculating the coordinates of the inscribed circle center O(x,y), the coordinates of the tangency point T1 on curve 1, and the coordinates of the tangency point T2 on curve 2; S7, repeating steps S1 to S6 until traversing the interval [0,1], and outputting a set of geometric parameters for a series of inscribed circles.