JP2012021538A - Design program for gear meshing with pinion, method for manufacturing die by the design program and die manufactured by the method for manufacturing the die, method for manufacturing gear meshing with pinion by design program and gear meshing with pinion manufactured by method for manufacturing the gear - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a design program by which a pinion and a tooth flank and/or a bottom of a mating gear do not interfere with each other.SOLUTION: In a design program for a gear meshing with a pinion, a locus of a pinion is determined by a function f(u, θ, Φ) of a parameter u in a pinion facewidth direction, a parameter θ of a pinion pressure angle and a parameter Φ of rotational motion of the pinion, and with respect to a function f(Φ) of coordinates z of a plurality of intersections of the locus of the pinion of an optional cross section of the function f(θ, Φ) and y=y*, the design program has a first step for extracting ranges where three equinoctial points a, b and c in an optional section (a, c) satisfy a<b<c, f(b)<f(a) and f(b)<f(c), a second step for specifying an intermediate point between b and c as d and extracting the minimum value existent section of the function f(Φ) as a section (a, d) and a section (b, c), respectively, when f(b)<f(d), a<b<d, f(b)<f(a) and f(b)<f(d) are satisfied and when f(d)<f(b), b<d<c, f(d)<f(b) and f(d)<f(c) are satisfied and a third step for replacing the minimum value existent section in the second step into a section (a, c), The minimum value of the function f(Φ) is employed as a standard of the coordinate z of the tooth flank and/or bottom of the gear 2 by repeating the second and third steps.

Description

  The present invention relates to a design program for a gear meshing with a pinion, a method for producing a mold by the design program, a mold produced by the production method, a method for producing a gear meshing with a pinion by the design program, and the production method. Relates to a gear meshing with a pinion.

  Conventionally, as a method for calculating the tooth surface coordinates of a pinion and a gear meshing with the pinion, a method of solving and calculating an equation including a pitch circle radius, a pressure angle of a gear pair, and a curvature radius is known.

  Further, as a design method for calculating the bottom coordinate of the pinion and the gear meshing with the pinion, the value obtained by the above-mentioned equation is calculated by a gear design expert with a maximum relative curvature equal to a predetermined percentage (for example, 51%). A method for obtaining it is known (see Patent Document 1).

JP-T-2001-519013

  However, in the method of calculating the tooth surface coordinates by the equation of the pitch circle radius, the pressure angle of the gear pair, and the radius of curvature, only the tooth surface coordinates of the gear meshing with the pinion and the pinion can be accurately calculated. That is, since the gear bottom coordinate is set by the gear designer with a maximum relative curvature equal to a predetermined percentage, depending on the set value, the gear bottom meshing with the pinion may interfere with the pinion.

  The present invention has been made in view of the above circumstances, and reproduces the locus of the tooth surface or root of the pinion, calculates the tooth surface coordinate or the tooth bottom coordinate of the gear meshing with the pinion from this locus, and calculates the tooth surface of the pinion. Alternatively, a design program for a gear that meshes with a pinion that does not interfere with the tooth surface or the tooth bottom of a gear that meshes with the pinion and the pinion, with the tooth surface or the tooth bottom meshing with the pinion and the tooth surface or the tooth bottom having a similar shape. It is an object of the present invention to provide a mold manufacturing method according to the present invention, a mold manufactured by the manufacturing method, a manufacturing method of a gear meshing with a pinion by the design program, and a gear meshing with a pinion manufactured by the manufacturing method.

  The design program for the gear meshing with the pinion of the present invention is such that the pinion tooth width direction parameter is u, the pinion pressure angle parameter is θ, the pinion rotational motion parameter is Φ, and the pinion locus is a function f (u, The parameter u in the tooth width direction is made arbitrary by considering an arbitrary cross section, and y = y * in the arbitrary cross section determined by the function f (θ, Φ). With respect to the function f (Φ) representing the z-coordinates of a plurality of intersections obtained by the following, in the first step, the trisection points a, b, c are a <b <c in the arbitrary section (a, c), b) Processing for extracting a range where <f (a) and f (b) <f (c), and in the second step, between the points b and c in the extracted arbitrary section (a, c) Let f be d and calculate f (d). b) <f (d), and the triple points a, b, d are a <b <d and f (b) <f (a) and f (b) <f (d) The interval in which the minimum value of the function f (Φ) exists is (a, d), f (d) <f (b), and the triple points b, d, c are b <d <c and f When (d) <f (b) and f (d) <f (c), a process of extracting a minimum value section in which a section where the minimum value of the function f (Φ) exists is (b, c); In the third step, the process of replacing the section having the new minimum value extracted in the second step as the section (a, c), the second step and the third step are repeated, and finally the section (a , C), the minimum value of the function f (Φ) at y = y * is determined by a calculation process called the trichodum method of determining the minimum value of the function f (Φ) in The first, characterized in that and calculates as a reference z-coordinate in the y = y * of the tooth surface or tooth bottom of the gear meshing.

  A second feature of the design program for the gear meshing with the pinion of the present invention is that both the tooth surface coordinate and the tooth bottom coordinate are calculated as a reference for the z coordinate at y = y *.

  The third feature of the design program for the gear meshing with the pinion according to the present invention is that the tooth surface coordinate is obtained by a mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear meshing with the pinion and the pinion are orthogonal to each other. And

  The design program for a gear meshing with a pinion according to the present invention has a fourth feature that the gear meshing with the pinion is a face gear.

  In the method of manufacturing a mold for a gear meshing with a pinion according to the present invention, the pinion tooth width direction parameter is u, the pinion pressure angle parameter is θ, the pinion rotational motion parameter is Φ, and the pinion locus is a function f. The parameter u in the tooth width direction is determined by considering an arbitrary cross section determined by (u, θ, Φ), and the pinion trajectory in an arbitrary cross section determined by the function f (θ, Φ) and y = Regarding the function f (Φ) representing the z-coordinates of a plurality of intersections obtained by y *, in the first step, the trisection points a, b, c are a <b <c in an arbitrary section (a, c), In the process of extracting a range where f (b) <f (a) and f (b) <f (c), and in the second step, points b and c in the extracted arbitrary section (a, c) F (d) is calculated using the intermediate point d of f (d) ) <F (d), and the triple points a, b, d are functions when a <b <d and f (b) <f (a) and f (b) <f (d). An interval where the minimum value of f (Φ) exists is (a, d), f (d) <f (b), and the three-quarter points b, d, c are b <d <c and f (d When d) <f (b) and f (d) <f (c), a process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists; In the third step, the process of replacing the section having the new minimum value extracted in the second step as the section (a, c), the second step and the third step are repeated, and finally the section (a, c The minimum value of the function f (Φ) at y = y * is obtained by a calculation process called the trichodum method of obtaining the minimum value of the function f (Φ) in c), and the minimum value is used as a pinion. The tooth surface of the meshing gear or the root of the gear is calculated as a reference for the z coordinate at y = y *, the tooth surface shape or the tooth bottom shape of the gear meshing with the pinion is calculated from the calculated coordinates, and the gear meshing with the pinion is calculated. The first feature is to manufacture a mold from a tooth surface shape or a tooth bottom shape.

  The method for producing a mold for a gear meshing with a pinion according to the present invention has a second feature in that both the tooth surface coordinates and the tooth bottom coordinates are calculated with reference to the z coordinate at y = y *.

  According to the manufacturing method of a gear mold that meshes with a pinion according to the present invention, the tooth surface coordinates are obtained by a mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear and the pinion that mesh with the pinion are orthogonal to each other. Three features.

  The fourth aspect of the method for manufacturing a mold for a gear meshing with a pinion according to the present invention is that the gear meshing with the pinion is a face gear.

  A mold for a gear meshing with a pinion according to the present invention is manufactured by the above-described mold manufacturing method.

  In the method of manufacturing a gear meshing with a pinion according to the present invention, the pinion tooth width direction parameter is u, the pinion pressure angle parameter is θ, the pinion rotational motion parameter is Φ, and the pinion locus is a function f (u, By considering an arbitrary cross section determined by θ, Φ), the parameter u in the tooth width direction becomes arbitrary, and the pinion trajectory in an arbitrary cross section determined by the function f (θ, Φ) and y = y * Regarding the function f (Φ) representing the z-coordinates of the plurality of intersections obtained, in the first step, the trisection points a, b, c are a <b <c in the arbitrary section (a, c), and f (b ) <F (a) and f (b) <f (c) are extracted, and in the second step, in the extracted arbitrary section (a, c), an intermediate point between points b and c d, f (d) is calculated, and f (b) < If (d), and the three-points a, b, d are a <b <d and f (b) <f (a) and f (b) <f (d), then the function f (Φ ) Is a section where the minimum value exists (a, d), and f (d) <f (b), and the trisection points b, d, c are b <d <c and f (d) < When f (b) and f (d) <f (c), a process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists, and a third step , The process of replacing the section having the new minimum value extracted in the second step as the section (a, c), the second step and the third step are repeated, and finally the section (a, c) The minimum value of the function f (Φ) is obtained by calculating the minimum value of the function f (Φ), and the minimum value of the function f (Φ) at y = y * is obtained. The gear tooth surface or the tooth bottom is calculated as a reference for the z coordinate at y = y *, and the gear tooth surface shape or the tooth bottom shape meshing with the pinion is calculated from the calculated coordinates, and the gear is engaged with the pinion. The first feature is to manufacture a mold that manufactures a mold from the tooth surface shape or the bottom shape of the gear, and to manufacture a gear that meshes with the pinion by the mold.

  The manufacturing method of the gear meshing with the pinion according to the present invention has a second feature that both the tooth surface coordinate and the tooth bottom coordinate are calculated as the reference of the z coordinate at y = y *.

  The third feature of the method for manufacturing a gear meshing with a pinion according to the present invention is that the tooth surface coordinates are obtained by a mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear meshing with the pinion and the pinion are orthogonal to each other. And

  A fourth feature of the method of manufacturing a gear meshing with a pinion according to the present invention is that the gear meshing with the pinion is a face gear.

  The gear meshing with the pinion according to the present invention is manufactured by the method of manufacturing the gear meshing with the pinion.

  According to the first aspect of the present invention, according to the design program for the gear meshing with the pinion that calculates the tooth surface coordinate or the tooth bottom coordinate of the gear meshing with the pinion, the pinion tooth width direction parameter is u, and the pinion pressure angle parameter is Is θ, the pinion rotational motion parameter is Φ, the pinion trajectory is determined by the function f (u, θ, Φ), the parameter u in the tooth width direction becomes arbitrary by considering an arbitrary cross section, and the function f With respect to the function f (Φ) representing the pinion trajectory in an arbitrary cross section determined by (θ, Φ) and the z coordinates of a plurality of intersections obtained by y = y *, in the first step, an arbitrary section (a, a process of extracting a range in which c is a third point a, b, c is a <b <c, and f (b) <f (a) and f (b) <f (c); In the step, the extracted arbitrary district In (a, c), an intermediate point d between points b and c is used, and f (d) is calculated, and f (b) <f (d). If b <d, and f (b) <f (a) and f (b) <f (d), the interval where the minimum value of the function f (Φ) exists is (a, d), and f (D) <f (b), where the three-points b, d, c are b <d <c, and f (d) <f (b) and f (d) <f (c) , A process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists, and a section having a new minimum value extracted in the second step in the third step. The three-point method in which the processing to be replaced as the section (a, c) and the second step and the third step are repeated to finally obtain the minimum value of the function f (Φ) in the section (a, c). Calculation process To obtain the minimum value of the function f (Φ) at y = y * and calculate the minimum value as a reference for the z coordinate of the tooth surface or the bottom of the gear meshing with the pinion at y = y *. The tooth surface or root shape of the meshing gear can be reproduced, and the tooth surface or tooth bottom of the gear meshing with the pinion has a similar shape to the locus of the pinion tooth surface or tooth tip, and meshes with the pinion tooth tip and pinion. It is possible to provide a design program for a gear that meshes with a pinion in which a tooth surface or a tooth bottom shape of the gear does not interfere.

  According to the gear design program for calculating the tooth surface coordinate or the tooth bottom coordinate of the gear meshing with the pinion of the second feature of the present invention, both the tooth surface and the tooth bottom are calculated as the reference of the z coordinate at y = y *. Therefore, the coordinates of both the tooth surface and the tooth bottom of the gear meshing with the pinion are calculated by the same calculation method, and the clearance between the tooth surface and the tooth bottom of the gear meshing with the pinion can be seamlessly connected without any step.

  According to the gear design program for calculating the tooth surface coordinate or the tooth bottom coordinate of the gear meshing with the pinion of the second feature of the present invention, the tooth surface coordinate is the relative value of the gear and the pinion meshing with the normal vector of the tooth surface and the pinion. Since the three-point method is an iterative calculation and requires computation time because it is determined by the mechanical requirement that the velocity vectors are orthogonal, the tooth surface coordinates are the relative velocity of the gear and pinion meshing with the tooth surface normal vector and the pinion. The calculation time can be shortened by obtaining by the mechanical essential condition that the calculation time that the vectors are orthogonal is short and by obtaining only the root coordinate by the three-point method.

  According to the third feature of the present invention, according to the design program for the gear meshing with the pinion which calculates the tooth surface coordinate or the tooth bottom coordinate of the gear meshing with the pinion, since the gear meshing with the pinion is a face gear, the offset amount, the twist angle As for the face gear that has a complex mesh, the accurate tooth surface shape and root shape can only be reproduced with a cutting tool that molds the pinion that meshes with the face gear. Surface shape and root shape can be reproduced by a gear design program.

  According to the manufacturing method of the gear mold that meshes with the pinion of the first feature of the present invention, the pinion tooth width direction parameter is u, the pinion pressure angle parameter is θ, and the pinion rotational motion parameter is Φ. The pinion trajectory is determined by the function f (u, θ, Φ), and by considering the arbitrary cross section, the parameter u in the tooth width direction is arbitrary, and the arbitrary cross section determined by the function f (θ, Φ) For the function f (Φ) representing the pinion trajectory and the z-coordinates of a plurality of intersections obtained by y = y *, in the first step, the trisection points a, b, c are a process of extracting a range where a <b <c, and f (b) <f (a) and f (b) <f (c), and in the second step, the extracted arbitrary sections (a, c ), The intermediate point d between points b and c is f (d F (b) <f (d), and the three-points a, b, d are a <b <d and f (b) <f (a) and f (b) <f In the case of (d), the interval where the minimum value of the function f (Φ) exists is (a, d), f (d) <f (b), and the three-points b, d, c are b < When d <c, and f (d) <f (b) and f (d) <f (c), the minimum of (b, c) is the interval where the minimum value of the function f (Φ) exists The process of extracting the value section, the process of replacing the section with the new minimum value extracted in the second step as the section (a, c) in the third step, and the second step and the third step are repeated. Then, finally, the minimum value of the function f (Φ) at y = y * is obtained by a calculation process called a three-point method in which the minimum value of the function f (Φ) in the section (a, c) is obtained, Calculate the minimum value as a reference for the z coordinate of the tooth surface or bottom of the gear meshing with the pinion at y = y *, and calculate the tooth surface shape or the tooth bottom shape of the gear meshing with the pinion from the calculated coordinate. To produce a mold from the tooth surface shape or the bottom shape of the gear meshing with the pinion, the tooth surface or the tooth bottom of the gear meshing with the pinion has a similar shape to the tooth surface of the pinion or the locus of the tooth tip, and the gear meshes with the pinion and the pinion. A mold for forming a gear that meshes with a pinion that does not interfere with the tooth surface or the tooth bottom shape can be manufactured.

  According to the second aspect of the present invention, the gear mold for meshing with the pinion calculates both the tooth surface coordinate and the root coordinate as the reference of the z coordinate at y = y *, and therefore the gear meshed with the pinion. Coordinates of both tooth surface and tooth bottom of the gear are calculated by the same calculation method, and a gear mold that meshes with the pinion is seamlessly connected without gap between the tooth surface and the tooth bottom of the gear meshing with the pinion. Can do.

  According to the third aspect of the present invention, the method for manufacturing a mold for a gear meshing with a pinion is such that the tooth surface coordinate is orthogonal to the normal vector of the tooth surface and the relative velocity vector of the gear meshing with the pinion and the pinion. Since the three-point method is an iterative calculation because it is calculated according to the essential conditions, it takes time to calculate the tooth surface coordinates, and the tooth surface normal vector and the gear meshing with the pinion and the relative velocity vector of the pinion are orthogonal. It is possible to reduce the calculation time and to obtain the mold manufacturing method in which the mold design time is shortened by obtaining the root essential coordinates by the three-point method.

  According to the fourth aspect of the present invention, the gear mold for meshing with the pinion is a face gear. Therefore, the face gear having complicated meshing such as an offset amount and a torsion angle is a face gear. The exact tooth surface shape and root shape can only be reproduced with a cutting tool that has a pinion that meshes with the pinion, but the exact tooth surface shape and root shape of the face gear can be reproduced. It can be reproduced by a design program, and a face gear mold can be manufactured by the design program.

  According to the mold of the gear meshing with the pinion of the present invention, the tooth surface or the tooth bottom of the gear meshing with the pinion has a shape similar to the locus of the tooth surface or tip of the pinion, and the tooth surface or tooth of the gear meshing with the pinion and the pinion A mold that molds a gear that meshes with a pinion that does not interfere with the bottom shape can be manufactured, and a gear that meshes with the pinion can be mass-produced with the mold.

  According to the manufacturing method of the gear meshing with the pinion of the first feature of the present invention, the pinion tooth width direction parameter is u, the pinion pressure angle parameter is θ, the pinion rotational motion parameter is Φ, The trajectory is determined by the function f (u, θ, Φ), and by considering an arbitrary cross section, the parameter u in the tooth width direction is arbitrary, and the pinion at an arbitrary cross section determined by the function f (θ, Φ) For the function f (Φ) representing the z-coordinates of a plurality of intersections obtained from the locus of y and y = y *, the minimum value of the function f (Φ) at y = y * is obtained by the three-point method, and the minimum value is obtained. The design of the gear meshing with the pinion is calculated as a reference of the Z coordinate at y = y * of the tooth surface or the tooth bottom of the gear meshing with the pinion, and designing the tooth surface shape or the tooth bottom shape of the gear meshing with the pinion from the calculated coordinate Process And the manufacturing process of the mold for manufacturing the mold from the tooth surface shape or the root shape of the gear meshing with the pinion, and the tooth surface or the tooth bottom of the gear meshing with the pinion are manufactured in order to manufacture the gear meshing with the pinion by the mold. A gear meshing with the pinion that has a shape similar to the locus of the tooth surface or tip of the pinion and does not interfere with the tooth surface or bottom shape of the gear meshing with the pinion and the pinion can be manufactured by the mold.

  According to the manufacturing method of the gear meshing with the pinion according to the second aspect of the present invention, both the tooth surface coordinate and the tooth bottom coordinate are calculated as the reference of the z coordinate at y = y *. Therefore, the tooth surface of the gear meshing with the pinion In addition, the coordinates of both the tooth bottom and the tooth bottom are calculated by the same calculation method, and the gear meshing with the pinion seamlessly connected without gap between the tooth surface and the tooth bottom of the gear meshing with the pinion can be manufactured.

  According to the third aspect of the present invention, the tooth surface coordinates are determined by the mechanical requirement that the normal vector of the tooth surface and the relative velocity vector of the gear and the pinion meshing with each other are orthogonal to each other. Therefore, since the three-point method is an iterative calculation, it takes time to calculate, so the tooth surface coordinate is a mechanical prerequisite that the normal vector of the tooth surface, the gear meshing with the pinion, and the relative velocity vector of the pinion are orthogonal By obtaining the root coordinates by the three-point method, the calculation time can be shortened, and a method of manufacturing a gear meshing with a pinion with a reduced mold design time can be realized.

  According to the fourth aspect of the present invention, the gear that meshes with the pinion is a face gear. Therefore, the face gear that engages in a complicated manner such as an offset amount and a torsion angle meshes with the pinion. The exact tooth surface shape and root shape can only be reproduced with a cutting tool that has been molded, but this is a design program for gears that mesh the exact tooth surface shape and bottom shape of the face gear with the pinion. The face gear can be manufactured by a mold according to the design program.

  According to the gear meshing with the pinion of the present invention, since the gear surface meshing with the pinion is manufactured by the manufacturing method of the gear meshing with the pinion, the tooth surface or the tooth bottom of the gear meshing with the pinion has a shape similar to the locus of the pinion tooth surface or the tooth tip. It is possible to manufacture a mold for molding a gear that meshes with the pinion without interference of the tooth surface or the root shape of the gear that meshes with the pinion, and it is possible to mass-produce gears that mesh with the pinion.

  1 to 5 show a first embodiment of the present invention. FIG. 1 is a perspective view of the pinion and face gear of the present invention, and FIG. 2 shows a coordinate system of the pinion and face gear of the present invention. FIG. 3 is a diagram showing a pinion curve group and an envelope in an arbitrary x cross section of the present invention, FIG. 4 is a diagram showing a function f (Φ) and a ternary point, and FIG. It is a figure showing the tooth gear surface and tooth bottom point sequence obtained by the dividing point method.

  First, the face gear as the gear 2 meshing with the pinion 1 and the pinion 1 transmits the rotation by the staggered shaft as shown in FIG. Therefore, the rotation shafts of the pinion 1 and the face gear are in a twisted position as shown in FIG. The subscript 1 in FIG. 2 represents the pinion 1, the subscript 2 represents the face gear, and the one without the subscript represents the frame coordinate system. Here, Φ represents a rotational motion parameter, Cy represents an offset amount, and Cx represents a parameter for determining the setting position of the pinion 1 together with the offset amount.

  The coordinate conversion from the coordinate system S1 of the pinion 1 to the coordinate system S2 of the face gear is expressed by the following formula 1. At this time, Expression 2 is satisfied.

  Next, determination of the pinion tooth surface will be described. In creating the face gear tooth surface, the tooth surface of the pinion 1 must first be determined. Assuming that a cylindrical involute gear is used for the pinion 1, the origin of the pinion coordinate system is the tooth gap and the center of the tooth width, and the involute tooth profile is a function expressed using the pressure angle parameter θ. Here, db represents the basic circle diameter. Further, the involute function is expressed by Equation 4.

  A formula obtained by converting the involute tooth profile of Formula 4 using a rotation matrix so that the y1 axis is located at the center of the tooth gap is expressed by Formula 5. Here, ηb represents the center angle of the tooth gap width on the basic circle, and decoding represents the left and right sides of the tooth surface, with the upper side on the left side and the lower side on the right side.

  The pinion tooth surface is determined by two parameters, a parameter u in the tooth width direction and a parameter θ of the pressure angle. Therefore, if the tooth width of the pinion 1 is b1, the value range of the parameter u in the tooth width direction is given by Equation 6.

  When the pinion 1 is a spur gear, the tooth profile of Formula 5 may be expanded as it is in the tooth width direction, but it is not easy with a helical gear. Therefore, the tooth surface of a helical gear having a helix angle β using the parameter u in the tooth width direction is expressed by Equation 7. The coordinate matrix given by Equation 7 is applied to Equation 5. Here, ψ is expressed by Equation 8. L represents a lead. The lead L is given by Equation 9 using the reference circle diameter d and the twist angle β. Here, the sign of the twist angle represents the left twist and the right twist, respectively. Therefore, the involute part of the pinion 1 is expressed by Expression 11 according to Expression 10.

  When calculating the root of the face gear from the locus of the pinion 1, the shape of the tooth tip of the pinion 1 is important. The tooth tip is expressed by Equation 12, but the shape of the tooth tip of the pinion 1 can be obtained by giving Equation 15 of the arc in contact with the involute portion. Here, rc is the radius of the arc, αa is the pressure angle in the tip circle, ψa is the center angle of the tip width, and θc is the angle formed by the x axis and rc, and is given by Equation 14. The curved surface group by the pinion tooth surface is expressed by Formula 1 and Formula 11 to Formula 13.

  Here, by making the parameter u in the tooth width direction optional, Equation 13 becomes a function of θ and Φ. Furthermore, the variable θ is set to a sufficient range for obtaining one tooth surface of the face gear, and the variable Φ is changed at a constant interval, thereby making it possible to obtain a group of curves (the tooth tip, tooth surface and pinion of the pinion 1) as shown in FIG. The locus of the root) and the envelope (the locus of the lowest point in the tooth tip, tooth surface, and root locus of the pinion 1) can be obtained. This envelope is the cross-sectional shape of the face gear that is similar to the locus of the tooth tip, tooth surface, and tooth bottom of the pinion 1 that is about to be obtained. Furthermore, the face gear cross-sectional shape in each cross section, that is, the face gear tooth surface shape, can be obtained by changing the arbitrary parameter u in the tooth width direction.

  Since it is difficult to obtain the above-described envelope curve (the locus of the minimum value of the Z coordinate in the tooth tip, tooth surface, and tooth bottom locus of the pinion 1) as a function, the face gear can be obtained by obtaining a point sequence on the envelope. Find the cross-sectional shape. The procedure for obtaining this point sequence will be described below. Arbitrary y = y * is set as shown in FIG. A point A at which the z coordinate of the intersection with the tooth tip, tooth surface and root locus of the pinion 1 determined by the function f (Φ) representing the z coordinate at y = y * is a point on the envelope, That is, it is a point to obtain in order to obtain a face gear tooth surface shape that is similar to the locus of the tooth tip, tooth surface, and tooth bottom of the pinion 1. Furthermore, if y * is changed at regular intervals, a point sequence on the envelope can be obtained.

  Next, a method for obtaining the minimum value of the function f (Φ) representing the z coordinate at y = y * (minimum value of the z coordinate in the locus of the tooth tip, tooth surface, and tooth bottom of the pinion 1) by the three-point method will be described. To do. For example, when the function f (Φ) at y = y * draws a non-singular curve as shown in FIG. 4, with respect to the function f (Φ), in the first step, the trisection point in the arbitrary interval (a, c) a, b, c are in a range where a <b <c, f (b) <f (a) and f (b) <f (c), and the minimum value of the function f (Φ) is an arbitrary interval (a , C), and in the second step, in the extracted arbitrary section (a, c), an intermediate point d between the points b and c is calculated and f (d) is calculated. f (b) <f (d), and the triple points a, b, d are a <b <d and f (b) <f (a) and f (b) <f (d). In this case, the interval in which the minimum value of the function f (Φ) exists is (a, d), f (d) <f (b), and the trisection points b, d, c are b <d <c and , F (d) <f (b) and f ( d) If f <c (c), extract the minimum value section with (b, c) as the section where the minimum value of the function f (Φ) exists, and extract in the second step in the third step The process of replacing the section having the new minimum value as the section (a, c) and the second step and the third step are repeated, and finally the value of the function f (Φ) in the section (a, c) The minimum value of the z coordinate in the locus of the tooth tip, tooth surface, and tooth bottom of the pinion 1 is obtained by a calculation process called the three-point method for obtaining the minimum value of.

  The tooth surface of the face gear, the tooth tip, which is in contact with the lowest point of the z coordinate in each coordinate of the tooth surface, the tooth tip, and the locus of the root of the pinion 1 obtained by the design program that performs the calculation process referred to as the above-described three-point method. The tooth bottom shape is shown in FIG. Here, by setting a predetermined backlash in the pinion 1 in advance, the tooth face, the tooth tip, and the tooth bottom shape of the obtained face gear can obtain a predetermined clearance with respect to the actual pinion 1.

  Since the three-point method is an iterative calculation, it requires calculation time, so the tooth surface coordinates are mechanistically essential that the normal vector of the tooth surface and the relative velocity vector of the gear 2 and the pinion 1 meshing with the pinion are orthogonal to each other. It is also possible to reduce the calculation time by obtaining the condition and obtaining the tooth bottom coordinates by the three-point method. At this time, a clearance is given between the tooth surface and the tooth bottom, and pinion 1 is obtained by C1 continuation (one continuous differentiation is possible with respect to the target function, and the first derivative exists and is continuous). The gap between the tooth surface and the tooth bottom of the gear 2 meshing with each other can be seamlessly connected without any step.

  A method for obtaining the tooth surface coordinates based on the mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear 2 meshing with the pinion 1 and the pinion 1 are orthogonal to each other will be described. When both tooth surfaces rotating on the respective rotating shafts are in contact with each other, both tooth surfaces can be said to be conjugate if they satisfy an equation called a meshing equation. The meshing formula is obtained by obtaining a common normal vector N at the contact point of both tooth surfaces and a relative velocity vector (slip velocity) (V (12)) at that point. When the inner product of these vectors is 0, that is, when the relative velocity vector is orthogonal to the normal vector as shown in FIG. 6, both tooth surfaces are conjugate. Therefore, the meshing formula is expressed by Formula 16.

  This is nothing but the mechanical requirement of the geometry of the gear 2 meshing with the pinion 1. If this meshing expression is not 0, the relative velocity vector of the tooth surface has a component in the normal direction, so that the next two tooth surfaces are either separated or bite. Therefore, it can be said that two contact points in contact state are conjugate if Expression 16 is satisfied.

  Subsequently, the normal vector and the principal curvature of the conjugate tooth surface will be described. When considering a regular curved surface given by Expression 17, the unit normal vector is expressed by Expression 18.

  The direction of the normal vector at each contact point of the curved surface conjugate to the regular curved surface is equal to the direction of the normal vector of the contact point of the regular curved surface. That is, the vector in the opposite direction to the tooth surface outward normal of the pinion 1 becomes the outward normal vector of the conjugate tooth surface. Therefore, the normal vector of the conjugate tooth surface can be obtained by setting the sign of the tooth surface outward normal of the pinion 1 to-. The first basic form of the curved surface is defined as Equation 19. However, Expression 20 and Expression 21 are satisfied.

  Further, the second basic format is also defined in Equation 22. However, Expression 23 is satisfied.

  The main curvatures κf and κh are in the relationship of Equation 24 using Equations 23 and 25.

  Therefore, the principal curvature at an arbitrary point on the pinion tooth surface can be obtained by simultaneously solving the two expressions of Expression 24. When the obtained principal curvatures κf and κh of the pinion tooth surface are used, the principal curvatures κq and κs of the tooth surface conjugate with the pinion 1 are in a relationship as shown in Equation 25, Equation 26, and Equation 27. However, Expression 28, Expression 29, and Expression 30 are satisfied.

  Of these symbols, n is a unit normal vector, ω (12) is a relative angular velocity vector, e is a unit vector in the main direction, vtr is a velocity vector of a contact point with respect to the absolute coordinate system, and R is a gear from the origin of the pinion coordinate system. A vector to an arbitrary point on the rotation axis, σ is an angle formed by ef and eh, subscript f means main direction 1 (pinion 1), and subscript h means main direction 2 (pinion 1). Therefore, the principal curvature of the conjugate tooth surface can be obtained by simultaneously solving the three expressions of Expression 25, Expression 26, and Expression 27.

  Next, a method of manufacturing a face gear mold that meshes with the pinion 1 will be described. First, a hot or cold forging die for forming the face gear is prepared. As a method for manufacturing this forging die for final molding, the face gear tooth surface, tooth tip and root shape data obtained by the above design program are input to the NC processing machine, and the forging die for final molding. This is done by cutting the mold. In addition, in order to manufacture a forging die for final molding, the face surface, tooth tip, and root shape of the face gear obtained by the above design program are supplied to the NC processing machine, and the face gear teeth are generated by the NC processing machine. An electrode tooth profile that reproduces the surface, tooth tip, and tooth bottom shape is produced, and the forging die for final molding is electrodischarge processed with this electrode tooth shape to reproduce the face surface, tooth tip, and tooth bottom shape of the face gear. Alternatively, a forging die for final molding may be manufactured.

  Next, a method for manufacturing a face gear will be described. First, a forging device for forming a predetermined shape material and face gear is prepared. In addition, it is not necessary to have one forging die device, and it is general to prepare a forging device having a plurality of stages. First, a raw material is placed on a forging die of a forging device, forged, and forged in a plurality of stages to obtain a rough face gear close to the face gear shape. Next, the face gear is placed on a forging die for final molding of a forging apparatus for final molding and forged to form the tooth surface, tooth tip, and tooth bottom shape of the face gear. Finally, the necessary cutting process is performed to complete the face gear molding. Thereafter, predetermined heat treatment is performed to complete the manufacture of the face gear.

  As described above, according to the design program of the gear 2 meshing with the pinion 1 for calculating the tooth surface coordinate or the tooth bottom coordinate of the face gear, u is the parameter in the tooth width direction of the pinion 1 and θ is the parameter of the pressure angle of the pinion 1. , The parameter of the rotational motion of the pinion 1 is Φ, the locus of the pinion 1 is determined by the function f (u, θ, Φ), the parameter u in the tooth width direction is arbitrary by considering an arbitrary cross section, and the function f In relation to the function f (Φ) representing the locus of the pinion 1 in an arbitrary cross section determined by (θ, Φ) and the z coordinates of a plurality of intersections obtained by y = y *, in the first step, an arbitrary section (a , C), a process of extracting a range where the three-points a, b, c are a <b <c, and f (b) <f (a) and f (b) <f (c); In two steps, the extracted arbitrary section ( , C), an intermediate point d between the points b and c is calculated, and f (d) is calculated, and f (b) <f (d), and the ternary points a, b, d are a <b < When d and f (b) <f (a) and f (b) <f (d), the interval where the minimum value of the function f (Φ) exists is defined as (a, d), and f (d ) <F (b), and the triple points b, d, c are b <d <c and f (d) <f (b) and f (d) <f (c) In the third step, a section having a new minimum value extracted in the second step is defined as a section ((b, c)). A calculation called a three-point method in which the processing to be replaced as a, c), the second step and the third step are repeated, and the minimum value of the function f (Φ) in the section (a, c) is finally obtained. By processing Therefore, the minimum value of the function f (Φ) at y = y * is obtained, and the minimum value is calculated as a reference for the z coordinate of the tooth surface or the tooth bottom of the gear 2 meshing with the pinion 1 at y = y *. The shape of the tooth surface or the tooth bottom of the gear can be reproduced.

  Further, according to the design program of the gear 2 meshing with the pinion 1 for calculating the tooth surface coordinate or the tooth bottom coordinate of the face gear, both the tooth surface and the tooth bottom are calculated as the reference of the z coordinate at y = y *. Since the coordinates of both the tooth surface and the tooth bottom of the gear 2 meshing with the pinion 1 are calculated by the same calculation method, the clearance between the tooth surface and the tooth bottom of the gear 2 meshing with the pinion 1 can be seamlessly connected without any step. Further, it is possible to suppress a minute shift due to a difference in calculation method.

  Furthermore, according to the design program of the gear 2 meshed with the pinion 1 for calculating the tooth surface coordinate or the tooth bottom coordinate of the face gear, the tooth surface coordinate is the relative value of the gear 2 and the pinion 1 meshed with the normal vector of the tooth surface and the pinion 1. Since the three-point method is an iterative calculation because it is determined by the mechanical requirement that the velocity vectors are orthogonal, the operation time is required. Therefore, the tooth surface coordinates are the gear 2 meshed with the tooth surface normal vector and the pinion 1. The calculation time can be shortened by obtaining by the mechanical essential condition that the relative velocity vectors of the pinion 1 are orthogonal, and by obtaining the root coordinate by the three-point method.

  In addition, according to the design program for the gear 2 meshing with the pinion 1 for calculating the tooth surface coordinate or the tooth bottom coordinate of the face gear, the gear 2 meshing with the pinion 1 is a face gear, so that the offset amount, the twist angle, and the like are complicated. As for the face gear that is in mesh, the pinion 1 that meshes with the face gear can only be reproduced with a cutting tool that is shaped, but the exact tooth surface shape and root shape can only be reproduced. The tooth bottom shape can be reproduced by the design program of the gear 2 meshing with the pinion 1.

  According to the face gear mold manufacturing method, the pinion 1 tooth width direction parameter is u, the pinion 1 pressure angle parameter is θ, the pinion 1 rotational motion parameter is Φ, and the pinion 1 trajectory is a function. The parameter u in the tooth width direction is determined by considering an arbitrary cross section, determined by f (u, θ, Φ), and the trajectory of the pinion 1 at an arbitrary cross section determined by the function f (θ, Φ) And the function f (Φ) representing the z-coordinates of a plurality of intersections obtained by y = y *, in the first step, the trisection points a, b, c are a <b <c in the arbitrary section (a, c). In the second step, a point b is extracted in the extracted arbitrary section (a, c) in the process of extracting a range where f (b) <f (a) and f (b) <f (c) And f (d) is calculated as an intermediate point d between point c and point c. ) <F (d), and the triple points a, b, d are functions when a <b <d and f (b) <f (a) and f (b) <f (d). An interval where the minimum value of f (Φ) exists is (a, d), f (d) <f (b), and the three-quarter points b, d, c are b <d <c and f (d When d) <f (b) and f (d) <f (c), a process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists; In the third step, the process of replacing the section having the new minimum value extracted in the second step as the section (a, c), the second step and the third step are repeated, and finally the section (a, c The minimum value of the function f (Φ) at y = y * is determined by a calculation process called the trichotomy method of determining the minimum value of the function f (Φ) in c), and the minimum value is set to the pinion 1 The tooth surface of the meshing gear 2 or the tooth bottom is calculated as a reference for the z coordinate at y = y *, and the tooth surface shape or the tooth bottom shape of the gear 2 meshing with the pinion 1 is calculated from the calculated coordinates. In order to manufacture a mold from the tooth surface shape or the tooth bottom shape of the gear 2 meshing with the pinion 1, the tooth surface or tooth bottom of the gear 2 meshing with the pinion 1 has a shape similar to the locus of the tooth surface or tooth tip of the pinion 1, and the pinion 1 Thus, it is possible to manufacture a mold for molding a face gear in which the tooth surface or the tooth bottom shape of the gear 2 meshing with the pinion 1 does not interfere.

  According to the manufacturing method of the face gear mold, both the tooth surface coordinate and the tooth bottom coordinate are calculated as the reference of the z coordinate at y = y *, and therefore both the tooth surface and the tooth bottom of the gear 2 meshing with the pinion 1 are used. Are calculated using the same calculation method, and the gap between the tooth surface and the tooth bottom of the gear 2 meshing with the pinion 1 can be seamlessly connected without any step. Can be manufactured.

  According to the manufacturing method of the face gear mold, according to the manufacturing method of the gear 2 meshing with the pinion 1, the tooth surface coordinates are relative to the normal vector of the tooth surface and the gear 2 and the pinion 1 meshing with the pinion 1. Since the three-point method is an iterative calculation because it is determined by the mechanical requirement that the velocity vectors are orthogonal, the operation time is required. Therefore, the tooth surface coordinates are the gear 2 meshed with the tooth surface normal vector and the pinion 1. By obtaining the mechanical requirement that the relative velocity vectors of the pinion 1 are orthogonal, and by obtaining the root coordinate by the ternary point method, the calculation time can be shortened, and the mold design time is shortened. The manufacturing method can be realized.

  According to the method of manufacturing the mold of the gear 2 that meshes with the pinion 1, the gear 2 that meshes with the pinion 1 is a face gear. Therefore, the face gear that has complicated meshing such as an offset amount and a torsion angle meshes with the face gear. The accurate tooth surface shape and root shape can be reproduced only by cutting with a cutting tool that has been shaped, but the gear 2 is designed to mesh with the pinion 1 with the exact tooth surface shape and bottom shape of the face gear. It can be reproduced by a program, and a face gear mold can be manufactured by the design program.

  According to the mold of the face gear, the tooth surface or bottom of the face gear has a shape similar to the locus of the tooth surface or tip of the pinion 1, and the tooth surface or bottom of the gear 2 that meshes with the pinion 1 and the pinion 1. A mold for molding the gear 2 that meshes with the pinion 1 without interference can be manufactured, and the face gear can be mass-produced with the mold.

  According to the manufacturing method of the face gear, u is the parameter in the tooth width direction of the pinion 1, θ is the parameter of the pressure angle of the pinion 1, and Φ is the parameter of the rotational motion of the pinion 1, and the locus of the pinion 1 is a function f (u , θ, Φ), and by considering an arbitrary cross section, the parameter u in the tooth width direction becomes arbitrary, and the locus of the pinion 1 in an arbitrary cross section determined by the function f (θ, Φ) and y = Regarding the function f (Φ) representing the z-coordinates of a plurality of intersections obtained by y *, in the first step, the trisection points a, b, c are a <b <c in an arbitrary section (a, c), In the process of extracting a range where f (b) <f (a) and f (b) <f (c), and in the second step, points b and c in the extracted arbitrary section (a, c) F (d) is calculated using the intermediate point d of f (b) < If (d), and the three-points a, b, d are a <b <d and f (b) <f (a) and f (b) <f (d), then the function f (Φ ) Is a section where the minimum value exists (a, d), and f (d) <f (b), and the trisection points b, d, c are b <d <c and f (d) < When f (b) and f (d) <f (c), a process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists, and a third step , The process of replacing the section having the new minimum value extracted in the second step as the section (a, c), the second step and the third step are repeated, and finally the section (a, c) The minimum value of the function f (Φ) at y = y * is obtained by a calculation process called a three-point method in which the minimum value of the function f (Φ) is obtained, and the minimum value is engaged with the pinion 1 A gear meshing with the pinion 1 that calculates the tooth surface shape or the tooth bottom shape of the gear 2 that meshes with the pinion 1 based on the calculated coordinates and calculated as the reference of the z coordinate at the tooth surface or the tooth bottom of the gear wheel 2 In order to manufacture the gear 2 that meshes with the pinion 1 by the mold, and the manufacturing process of the mold that manufactures the mold from the tooth surface shape or the tooth bottom shape of the gear 2 that meshes with the pinion 1, The tooth surface or bottom of the tooth is similar to the locus of the tooth surface or tip of the pinion 1, and the gear 2 that meshes with the pinion 1 without interference of the tooth surface or the bottom of the face gear is manufactured by a mold. can do.

  According to the manufacturing method of the face gear, since both the tooth surface coordinate and the tooth bottom coordinate are calculated as the reference of the z coordinate at y = y *, the coordinates of both the tooth surface and the tooth bottom of the gear 2 meshing with the pinion 1 are obtained. The gap between the tooth surface of the gear 2 and the tooth bottom calculated by the same calculation method and meshing with the pinion 1 can be seamlessly connected without any step, so there is no fine deviation due to the difference in the calculation method, and the tooth surface of the face gear A face gear that is seamlessly connected between the tooth bottom and the tooth bottom can be manufactured by a mold.

  According to the manufacturing method of the face gear, the tooth surface coordinates are obtained by the mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear 2 and the pinion 1 meshing with the pinion 1 are orthogonal to each other. Since it is an iterative calculation, calculation time is required. Therefore, the tooth surface coordinate is obtained by a mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear 2 and the pinion 1 meshing with the pinion 1 are orthogonal to each other. By obtaining the base coordinates by the trichotomy method, the calculation time can be shortened, and a method of manufacturing the gear 2 meshing with the pinion 1 with a shortened mold design time can be realized.

  According to the manufacturing method of the gear 2 that meshes with the pinion 1, the gear 2 that meshes with the pinion 1 is a face gear. Therefore, the face gear that is complicatedly meshed such as the offset amount and the torsion angle takes the pinion 1 that meshes with the face gear. The exact tooth surface shape and root shape can only be reproduced by cutting with the cutting tool, but with the design program for the gear 2 that meshes the exact tooth surface shape and the tooth bottom shape of the face gear with the pinion 1. The face gear can be manufactured by a mold according to the design program.

  Since the face gear is manufactured by the method for manufacturing the face gear, the face gear has a shape similar to the tooth surface or tooth tip locus of the pinion 1, and the tooth surface or the tooth bottom shape of the pinion 1 does not interfere with each other. A mold for molding the gear 2 meshing with the pinion 1 can be manufactured, and the face gear can be mass-produced with the mold.

  In this embodiment, the face gear is mainly described as the gear 2 that meshes with the pinion 1, but the spur gear, the helical gear, the helical gear, the rack, the bevel gear, the pinion 1 and the gear 2 that meshes with the pinion 1, You may use for a crown gear, a worm gear, and a hypoid gear.

It is a perspective view of the pinion and face gear of the present invention. It is a figure showing the coordinate system of the pinion and face gear of this invention. It is a figure showing the curve group and envelope of the pinion in arbitrary x cross sections of the present invention. It is a figure showing the function f ((PHI)) and the half point of this invention. It is a figure showing the tooth | gear surface of a face gear obtained by the three point method of this invention, and the point sequence of a tooth base. It is a figure showing the relationship between the relative velocity vector of a tooth surface of this invention, and a normal vector.

1 Pinion 2 Gear meshing with pinion

Claims (14)

In the design program of the gear meshing with the pinion for calculating the tooth surface coordinate or the tooth bottom coordinate of the gear (2) meshing with the pinion (1),
The pinion (1) tooth width direction parameter is u, the pinion (1) pressure angle parameter is θ, the pinion (1) rotational motion parameter is Φ, and the pinion (1) trajectory is a function f (u, The parameter u in the tooth width direction is determined by considering an arbitrary cross section, and the locus of the pinion (1) at an arbitrary cross section determined by the function f (θ, Φ) and y = Function f (Φ) representing z coordinates of a plurality of intersection points obtained by y *
In the first step, in the arbitrary section (a, c), the third points a, b, c are a <b <c, and f (b) <f (a) and f (b) <f (c) A process of extracting a range;
In the second step, in the extracted arbitrary section (a, c), f (d) is calculated by setting an intermediate point d between the points b and c, and f (b) <f (d). The dividing points a, b, and d have a minimum value of the function f (Φ) when a <b <d and f (b) <f (a) and f (b) <f (d). Let the interval be (a, d),
f (d) <f (b), and the triple points b, d, c are b <d <c and f (d) <f (b) and f (d) <f (c). A process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists;
In the third step, a process of replacing the section having the new minimum value extracted in the second step as the section (a, c);
By repeating the second step and the third step, and finally calculating the minimum value of the function f (Φ) in the section (a, c), a calculation process called a trichotomy method,
The minimum value of the function f (Φ) at y = y * is obtained, and the minimum value is calculated as a reference for the z coordinate of the tooth surface or the bottom of the gear (2) meshing with the pinion (1) at y = y *. A design program for a gear that meshes with a pinion.   2. The design program for a gear meshing with a pinion according to claim 1, wherein both the tooth surface coordinate and the tooth bottom coordinate are calculated as a reference for the z coordinate at y = y *.   The tooth surface coordinates are obtained by a mechanical essential condition that the normal vector of the tooth surface and the relative velocity vector of the gear (2) and the pinion (1) meshing with the pinion (1) are orthogonal to each other. Design program for gears that mesh with the described pinion.   The gear (2) meshing with the pinion (1) is a face gear, and the design program for the gear meshing with the pinion according to any one of claims 1 to 3. In the manufacturing method of the mold of the gear (2) meshing with the pinion (1),
The pinion (1) tooth width direction parameter is u, the pinion (1) pressure angle parameter is θ, the pinion (1) rotational motion parameter is Φ, and the pinion (1) trajectory is a function f (u, The parameter u in the tooth width direction is determined by considering an arbitrary cross section, and the locus of the pinion (1) at an arbitrary cross section determined by the function f (θ, Φ) and y = Function f (Φ) representing z coordinates of a plurality of intersection points obtained by y *
In the first step, in the arbitrary section (a, c), the third points a, b, c are a <b <c, and f (b) <f (a) and f (b) <f (c) A process of extracting a range;
In the second step, in the extracted arbitrary section (a, c), f (d) is calculated by setting an intermediate point d between the points b and c, and f (b) <f (d). The dividing points a, b, and d have a minimum value of the function f (Φ) when a <b <d and f (b) <f (a) and f (b) <f (d). Let the interval be (a, d),
f (d) <f (b), and the triple points b, d, c are b <d <c and f (d) <f (b) and f (d) <f (c). A process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists;
In the third step, a process of replacing the section having the new minimum value extracted in the second step as the section (a, c);
By repeating the second step and the third step, and finally calculating the minimum value of the function f (Φ) in the section (a, c), a calculation process called a trichotomy method,
The minimum value of the function f (Φ) at y = y * is obtained, and the minimum value is calculated as a reference for the z coordinate of the tooth surface or the bottom of the gear (2) meshing with the pinion (1) at y = y *. ,
The tooth surface shape or the root shape of the gear (2) meshing with the pinion (1) is calculated from the calculated coordinates, and the mold is calculated from the tooth surface shape or the tooth bottom shape of the gear (2) meshing with the pinion (1). The manufacturing method of the metal mold | die of the gear meshing | engaged with a pinion characterized by manufacturing this.   6. The method for producing a mold for a gear meshing with a pinion according to claim 5, wherein both the tooth surface coordinate and the tooth bottom coordinate are calculated as a reference for the z coordinate at y = y *.   The tooth surface coordinates are obtained by a mechanical requirement that the normal vector of the tooth surface and the relative velocity vector of the gear (2) and the pinion (1) meshing with the pinion (1) are orthogonal to each other. The manufacturing method of the metal mold | die of the gear which meshes with the pinion of description.   The method for manufacturing a mold for a gear meshing with a pinion according to any one of claims 6 to 7, wherein the gear (2) meshing with the pinion (1) is a face gear.   The gear mold for meshing with the pinion according to any one of claims 5 to 8, wherein the mold is manufactured by the method for manufacturing the mold. In the manufacturing method of the gear (2) meshing with the pinion (1),
The pinion (1) tooth width direction parameter is u, the pinion (1) pressure angle parameter is θ, the pinion (1) rotational motion parameter is Φ, and the pinion (1) trajectory is a function f (u, The parameter u in the tooth width direction is determined by considering an arbitrary cross section, and the locus of the pinion (1) at an arbitrary cross section determined by the function f (θ, Φ) and y = Function f (Φ) representing z coordinates of a plurality of intersection points obtained by y *
In the first step, in the arbitrary section (a, c), the third points a, b, c are a <b <c, and f (b) <f (a) and f (b) <f (c) A process of extracting a range;
In the second step, in the extracted arbitrary section (a, c), f (d) is calculated by setting an intermediate point d between the points b and c, and f (b) <f (d). The dividing points a, b, and d have a minimum value of the function f (Φ) when a <b <d and f (b) <f (a) and f (b) <f (d). Let the interval be (a, d),
f (d) <f (b), and the triple points b, d, c are b <d <c and f (d) <f (b) and f (d) <f (c). A process of extracting a minimum value section having (b, c) as a section where the minimum value of the function f (Φ) exists;
In the third step, a process of replacing the section having the new minimum value extracted in the second step as the section (a, c);
By repeating the second step and the third step, and finally calculating the minimum value of the function f (Φ) in the section (a, c), a calculation process called a trichotomy method,
The minimum value of the function f (Φ) at y = y * is obtained, and the minimum value is calculated as a reference for the z coordinate of the tooth surface or the bottom of the gear (2) meshing with the pinion (1) at y = y *. ,
The design step of the gear (2) meshing with the pinion (1) for designing the tooth surface shape or the root shape of the gear (2) meshing with the pinion (1) from the calculated coordinates, and the gear meshing with the pinion (1) ( 2) A manufacturing process of a mold for manufacturing a mold from a tooth surface shape or a tooth bottom shape, and a gear (2) that meshes with the pinion (1) by the mold. Production method.   11. The method of manufacturing a gear meshing with a pinion according to claim 10, wherein both the tooth surface coordinate and the tooth bottom coordinate are calculated as a reference for the z coordinate at y = y *.   The tooth surface coordinates are obtained by a mechanical requirement that the normal vector of the tooth surface and the relative velocity vector of the gear (2) and the pinion (1) meshing with the pinion (1) are orthogonal to each other. The manufacturing method of the gear which meshes with the pinion of description.   The gear manufacturing method according to any one of claims 10 to 12, wherein the gear (2) meshing with the pinion (1) is a face gear.   14. The gear meshing with the pinion according to claim 10, wherein the gear meshing with the pinion is manufactured by a manufacturing method of the gear (2) meshing with the pinion (1).

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