TWI254658B - A manufacture method for a spherical gear with ring-involute teeth - Google Patents

Abstract

A method is presented for manufacturing the ring-involute teeth of spherical gears including convex and concave teeth. Based on this method, a mathematical model of the meshing principles of a cutter meshed with a gear that has either convex teeth or concave teeth is presented. The spherical gear mechanism was determined with the aid of the proposed mathematical model. A pair of spherical gears with ring-involute teeth including convex and concave teeth which in the opposite spherical gears dispose continuously and orderly in a scattered way and engage reverse teeth each other.

Description

1254658 IX. Description of the Invention: [Technical Field] The present invention has a method for manufacturing a spherical gear having a ring-shaped involute gear. A method for manufacturing a ring-shaped involute including a convex tooth and a concave tooth Spherical gear of the tooth. The application of the space common vehicle surface is obtained by the two-parameter surface family envelope theory method, which is processed by a circular involute tool, so that the involute tooth profile is distributed on the spherical surface and the convex or concave convex teeth are formed. The spherical wheel of the concave tooth. [Prior Art]

Gears are a very important transmission component that is widely used in everyday life and in a variety of different drive system towels. The rotation between the rotation axes of the wheel can be divided into spur gears, helical gears, herringbone gears, etc., which are applied to the parallel shaft transmission; used for the interlaced shaft to transmit the shouting gear, the worm gear group, and the interlaced (four) rotary recording; Straight bevel gears, worm wire bevel gears transmitted by intersecting axes, etc. As the machine rotates at a higher speed and requires high precision and low cost, the design and addition of the gear are important. At present, the common gear cutting methods are _rolling and rolling gears, scraping and grinding are more common, but grinding the reel, = tool milling gear and _ various special machine cutting gears, etc.; : It has its advantages and disadvantages' and the occasions that apply are different. However, the main purpose of various gears 2, /, is to produce low-cost, high-precision (four) efficiency::: hobbing and gearing is the most commonly used coarse (four) type, precision machining is due to its high cost. Equipment investment is expensive, 5 !254658 ^ Unless the accuracy of the gear is high, most of the gears are still finished by scraping. The scraper is a soft tooth surface machining program. After scraping the teeth, heat treatment is performed. It is a hard tooth surface machining that needs to be processed after the gear is heat treated. Involute gears have been widely used in the tooth profile of various gears due to their high precision and easy machining. They have replaced the Cycl〇id Teeth gears. In addition, the involute spur gear and the helical gear have the advantage of not generating Kinematic Errors when there is an assembly error in the center distance of the Gear Pair. Popular. Gears are very important components in mechanical systems and structures. They are not only an important part of all kinds of machinery, but almost all mechanical internal structures are indispensable for gears. The quality of its gears is more stringent. If the gears are bad, the machine will not run smoothly. Gears can be widely used today. The main reason for this is that the range of transmission horsepower is very wide. The method of classifying the most f is based on the #axing axis. The parallel axis (Parallel Axes) is the intersecting axis (Intersecting Axes). Two types of methods. The gear can be matched with the number of teeth to obtain the 'Renith and correct turn ratio, and the position of the relationship between the light can be appropriately changed by increasing or decreasing the number of gear combinations. For example, in the first figure, the wrist joint mechanism 2 of the wrist joint used by the mouth paint robot produced by Norwegian Plus Company has only two degrees of freedom, and its structure is mainly composed of the following components: _ wheel u, external gear η, ring-shaped 6 1254658 column 13, split ring 14, positioning control connector 15 and offset control connector 16. Norwegian Trallfa first developed the transmission of spherical gears to the flexible wrist mechanism of industrial robots. The concept of this gear can be used for two degrees of freedom, gear mechanism, as shown in Figure 2. Referring to Figures 1 and 2, it can be seen that the wrist joint of the traditional-machine arm requires many elements and components to achieve its function, and the joints can be seen in the figure, with only two degrees of freedom. The action that it can operate, 0 is still not fine enough and smooth. [Summary of the invention] The surface parameter equation; at the same time, it provides a feasible theoretical analysis and addition for the addition of the spherical gear. Because of the wheel lion's line, it has a good heavy load capacity. The spherical gear of the open gear tooth has great application value in the bionic robot. In order to make the spherical contour at the same time and the discrete and discrete distribution of the tooth shape, the present invention applies the two-parameter female enveloping theory of the space common vehicle surface, and analyzes the geometric frequency of the ball-wheel surface with a circular involute tool. To develop the design and manufacturing technology of the professional wheel of the robotic flexible joint. Trial establishment of a spherical gear

3 Through research, it is found that there are three main degrees of freedom of motion of the spherical gear transmission: the first = the gear wheel - the wheel is _ moving, the second is the rotation of the wheel, and the third is the axis rotation. Therefore, to completely solve the problem of the spherical gear tooth profile, we must weave the original hand, use the tooth line that satisfies the rim fit law, and distribute the wheel to the 7 1254658 so that the involute tooth teeth are on the spherical surface. Invention _ ring fine line cutter, cloth on the spherical surface to solve the problem of gear tooth distribution. The main advantage of the gear teeth according to the involute distribution is that the thin wire is formed by only one line. = The involute gear only requires the modulus scale, for the case of installation error.

=:=, maintaining a stable angular velocity ratio, the angular velocity ratio will not change like the cycloid ω 乂, and the error of 5 ~ distance, affecting the transmission quality. The circumferential section is a point corresponding to the two teeth along the pitch circle, and the length '(4) can also be defined as the vertical distance of the corresponding side of the adjacent phase tooth', so it is also called a knuckle. The value of the week is equal to the important length of the throttling circumference divided by the pitch circle and the circumference of the involute gear. The gear is fixed after it is made. 'If the _ wheel can be made well (four), its week or The modulus must be the same. Based on the above concept, the present invention proposes a circular involute tool to machine a spherical thin wire gear having a discrete and continuously distributed gear form to establish a mathematical mode of a ring involute ball _ wheel. According to this mathematical mode, The geometric model of the circular involute spherical gear is extracted. The method for manufacturing a spherical surface of a lion's fine-toothed tooth has a ring-shaped involute tooth of a spherical wheel that is disposed on a spherical surface by discretely distributing a lion thin wire. From the geometric point of view, it is the common (four) surface salivation problem. Therefore, according to the two-parameter curved surface Wei Luo theory, the circular fine line cutter is used to study the moving mechanism of the spherical gear; and the lion thin ball gambling mechanism is , Entering a total of the teeth of the secret synthesis 'Try to establish a township gradually-available ball axle round face mathematical model 8 1254658 Equation 0 to i M ^ surface day guard 'we can be known by the surface equation, and two === The relative position of the tooth-shaped surface is determined by the tooth-shaped curve, and the two curved surfaces are mutually required to achieve a common curved surface. In the middle, when the return wheel is in the mouth and the drive is turned, the two ball balls are purely rolled. Therefore, in the merging 2' two-wheel profile is always point contact only when the two-wheel polar axis coincides position, since the private paste line is relatively distributed on the (four) surface recording, the present invention uses the == line t-tools to create The convex gear tooth surface is gradually opened _ wheel, and the (four) wheel t produces a spherical tooth gear with a different concave tooth profile, so that the current direction of the two-axis is purely rolling, and the connection between the two-pole axis and the two centers is always the same = It is the normal plane of the tooth profile, and the spray point is always along the plane. Therefore, the merging point (4) must be decorated as _ relative rotifer 0, and the spherical gear made by the ring axis tooth is green. Propose a system two::: two packs: a convex involute spherical gear composed of a convex tooth and a concave tooth. Based on this method, the proposed _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Using the developed mathematical model and fine analysis of the gear teeth, the motion error is based on the existence of the combination _, the designed _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ The gear tooth of the gear of the invention has the gear teeth of the bad involute gear tooth manufacturing method, and compares with each other, and found that the v〇n-Mises stress of the gear proposed by the invention is smaller than that of the conventional spur gear. . With the aid of the mathematical mode, the spherical gear mechanism after the speed ratio is determined. Using a rapid prototyping and manufacturing technique, a ball _ surface 1^ wheel mechanism with a convex gear and a concave gear was designed. Rapid Prototyping provides a full-scale solid model for analysis and further development. The results of these mathematical modes can be applied to the design of a spherical gear mechanism. [Embodiment] The method for manufacturing a spherical gear having annular involute teeth is described by a mathematical model, and the mathematical symbol is as shown in Fig. 3. φ The present invention uses a tool to obtain the convex and concave teeth of a spherical gear. It has been found that the shape of the involute teeth has an important advantage. The influence of the error of the middle distance between the center of the gear on the gear ratio is irrelevant. For the spherical gear proposed by Lin invention, the influence of the assembly error on the motion error can be achieved by using the tooth contact analysis method (TCA) to simulate the motion error of the assembled gear with axial deviation and center distance error. The invention relates to a method for manufacturing a spherical gear with a ring involute tooth. Some embodiments are known as the case of '5i• different gears, and the △ coffee indicates the pair of spherical teeth; . Figure 4 shows the composition of the w-center distance error. Using the tooth contact analysis method (10)), the motion error is obtained. The purpose of the stress analysis is that the mosquitoes have a circumstantial equation.

According to the gear concept proposed by the invention, it can be known that the spur gear and the present stress are smaller than the Von-Mises stress of the conventional spur gear. The wheel shifting heart S mathematical ^^^^ can derive a spherical surface having an involute tooth shape The material of the window wheel is two. Wheel theory, the spherical gear mechanism can be obtained by arranging the spherical surface in a circumferential manner and using a cutter to paste the outer layer of the material. Obtained: convex tooth of the layered spherical gear. A discrete volume is then obtained on the partial sphere. Outer layer. A six-toothed tooth is distributed in the first one, and twelve teeth are in the second ring. In the above manner, a convex spherical gear having annular involute teeth is obtained. A concave spherical gear is obtained in a similar manner. One of the advantages of Benming's method of manufacturing a spherical gear with annular involute gears is the ability to provide a geometric model of a fast (four) single spherical gear. The developed computer cymbal can be used to determine the geometric characteristics of the tooth contact analysis. From the above results, the opened tool can be used for gear machining. Finally, take the schedule! A geometric model of a gear with a gear ratio of 3:2. 1254658 The convex gear consists of the same contour of a continuous convex w. Similarly, the shape of the involute gear teeth, each of the teeth has a w-face gear consisting of _, slamming, and the design of the tool for each of the rounds of the 'focal lion's gear tooth gear is to be saki. , Display #—a convex gear and a concave shape are composed of two straight lines, which are shown in Fig. 5. The design parameters of the tool's shape cutting tool. The force angle of the shaft is also. Variables, representatives to produce a convex __ shank gear bottom, paste 2 consideration. In the gear and tool curve? In terms of area, the surface of the attachment can be made into the shape of a material. Therefore, the α6, 6c, and g regions are only considered in the generation process of the annular involute convex gear. Similarly, a stone, and the generation process of the concave gear only in the annular involute are considered. From the description of this part, the coordinate system of the tool is expressed as 弋 slave, ~ 尺, ~), 々 superscript g is used to represent the 3, & 3 and _ areas of the tool. As shown in Fig. 5, the αδ region produces a convex gear bottom. The variable number is the parameter of the tool curve. ^The equation of the region is represented by the coordinate system s, which can be expressed as:

Rab = <b 0 ' yf nm/2-Xb zf 1 -cic +rsin^c -r 1 1 1 〇<<w ^ (1) αΧ-(10) is a design parameter, what is the pressure angle, meaning And ~ X tool design parameters. The parameter w is as shown in Figure 5. The vector in the equation is 12 1254658

Tool position vector. The upper right corner represents the 3F eight clothing field. The subscript c indicates the position vector of the coordinate system 乂. The parameter m is the modulus. Each factory = 〇·2. The radius of the guide circle of the root of the female tooth produces the guide _ of the ring-shaped fine tooth, and λ represents the design parameter of the knife. In order to generate the complete rim of the tool, the equation of the _ domain is expressed as a coordinate system, which can be expressed as:

Rbc 2 4 Γ ybcc <c 1 0 纥+ac tan 么+rcos 么—rsinXc ~ac +rsin^c -rcosXc 1 ' 0<λο <π/2-φ(:ι (2) , β tool pressure angle , and ^ is the tool design parameter. The circular guide surface of the tooth root is half-controlled. The parameter is the modulus. In order to produce the side of the gear tooth working surface, use the flat edge of the tool g. In • represents the design of the tool curve The parameter of the 3 region is represented by the coordinate system & and can be expressed as: R:d = M ' 0 " Less r bc-Xh sin^ K(10)Φ. 1 -1 _ , -τηλπι2 <Xh < m2m3 ? (3) 13 1254658 Most and 2 claws 3 represent the straight edges of the tool. Depending on the geometry of the tool, the parameters formed can be determined by ^ = a /e.喰 and ^, /e.垅. A and A are design parameters. As shown in Figure 5. The stone area is the crest of the tool curve to create the bottom of the concave tooth. As shown in Figure 5, the equation for the stone area is represented by the coordinate system fork, 玎:

〇 -at tan φα~τ cos φ€^γ sin Xd at -rsin^c +rcosXd 1

〇<λί/ <π!2-φ^ (4) • 埒 is the position vector of the tool, and the superscript letter g symbolizes the equations (1)-(4), π, ^ 6c, and 叾 regions. The subscript symbol c represents the equation in the coordinate system & As shown in Fig. 6 and Fig. 7, the coordinate system & cut, heart, and, represent the coordinate system fixed on the tool. The fixed coordinate system ~ (eight), X /, ~ Z /) is tightly connected to the structure of the φ tool. The tool is transferred along the linear displacement. Two fixed reference coordinate systems & (α, X", where, ZJ and \ team, X" Λ, respectively, are closely connected to the structure of the concave spherical gear and the convex spherical gear. Coordinate system & (02, bh, y The mouth 5 丨 (Ο, x, yx A) are attached to the concave spherical gear and the convex spherical gear respectively. Seat wheel; 糸 & and A-wrap axis and X-axis rotation & && Angle. As shown in Fig. 6 and Fig. 7, α is the angle of rotation, and its area is 〇^. It is rotated around the center line of the tooth to simulate the rotation surface of the tooth. In order to generate the tool curve 14 1254658 outside the group Alternatively, the equipotential matrix conversion from the coordinate system\to the coordinate system & and the power matrix transformation for coordinate transformation, the matrix a can be obtained by: cosa -sin a 0 0 sin a cos φλ cos a cos^ -sin φλ 0 sin a sin φλ cos a sin φλ cos^ 0 A Ssinacos do +' sinasin private -^cosacos^ +rA cosasin^ S sin ψλ + rp] cos φχ (5) The relationship between S and color is S = , ~ represents the standard pitch radius of the convex gear. Similarly, the matrix I is converted from the equivalence to the equivalence matrix of the heart. , matrix & can be expressed as: Μ 2(^2)= cos or — sin a 0 sin a cos φ2 cos a cos φ2 sin 0 -sin a sin φ2 -cos a sin cos 0 -*S sin a cos 2 + sin a sin more 2 a Scosacos + ~cosasin^ -*Ssin<i2 -~2 cos "2 1 (6) The relationship between 5* and A is s = , and ~ represents the standard pitch half of the concave gear

path. Using the equations (1) to (4) and the equipotential matrix to convert the tool curve group can be expressed by the following equation α? Φ^ΜΜκξ^) (7) The variable λ7 is the design parameter, and the vector 埒(λ, α, is the tool curve group. The meanings of the text are 3, 5, 叾, and 忑. 圮 is the tool position vector, as expressed by equations 〇) to (4). The subscript symbol / is / and 2. Apply the double envelope potential theory to the tool parameter curve group, as expressed by equation (7). The mathematical mode of the gear teeth of each spherical gear must satisfy the equation (7) of 15 1254658 and the following equations.

(8): Equations (1) to (3) generations of light (7) and (8), mouths are obtained by the 彳疋刀兴四, 界々八群--the convex tooth mathematical model Σ1. . Substituting equations (3) and (4) into the equation () (8) can be obtained from the tool curve group—concave spherical teeth of the concave spherical gear mathematics _. _ Equation (3) produces a convex wheel and a concave tooth ς2. Using the formulas (3), (7), and (8), the mixed formula can be expressed by the following equation: φχ -Ά rpx ^Φα and (9) rPl ^Φα (10) In order to approximate the contours of the convex and concave teeth, use the computer program The complete contour of the convex and concave teeth. The geometry of the spherical surface _ size parameter, as shown in the attached table 1. As shown in Figures 8 and 9, 〇. _18(). , 6 (). _ take and m? E y β — The 怿 line has it. But 疋30. -210. , 90. —27〇. And 15 baht. —33〇. The three lines have 2 " 30. ^ History.乂 2 of those ~210,90. -270. And 150. -330. The three lines reproduce the contours of the six teeth of the temple, which is the result of the central wheel of the wheel: the production of the central wheel (four) of the complex 16 16254658, which is obtained by the previous gear meshing theory. . As shown in Figure 8, it is obtained. A side view of the wheel of the wheel of the Nagasaki group of 77 Sakya groups. Such as the 9th _: - a tooth. Here, the figure 9 shows that the angle of the cloth is 2~. The 7"' is viewed from the side, and the first ring is divided as shown in Figure 9. The first round is recorded. Subscript text, the shape is (10)'. It is known that the wheel mechanism represents the wheel gear of the concave gear. Subscript text (four) face gear. The phase: t: this can be used to obtain the convex spherical teeth of the annular involute teeth.告f, go and rapid prototyping technology, assembly of convex gears and concave two "> When the transmission is actuated, the driving gear teeth of the central gear are idling = tooth_minute_, this (four) person test light hypothesis: (1) Inelastic delivery, U) The effect of temperature, friction, and power can be neglected; (3) A pair of inspection materials can be considered. Listening to the age of the ear, can calculate the impact of the error of 34 skills _ incoming material clock _ record _ loading error. As shown in Figure 10, &, establish a coordinate system ^, to explore the pair of spherical gears with assembly errors χ s (χ, ("巧' ζ 》, A% 6, 4), heart (z ,,r,,ζγ) and Α Α' A'2J° coordinate system && respectively, next to the convex spherical gear and the concave spherical surface 17 1254658. The coordinate system is used to analyze the assembly error. The convex ball wind is private to study the assembly error. Paper and "retain the original parameters have group = face silk and weave, replaced by heart. If there is no body (four), 4 secret ~ and 0 heavy #. Coordinate money "% For the reference block t system, the estimated miscellaneous error. Coordinate money (four) parameters and positioning, can estimate the center distance between the ten convex spherical surface # and the concave spherical gear _ sensitivity and tilting of the tilting vehicle such as 'coordinate system The origin q of Sj and the origin 0 of the coordinate system ~ have a complementary difference. Compensation 010/=Λ"... indicates the error of the center distance between the spherical gears, as shown in Fig. 10. = Angle and vertical offset The angle of the corner. In order to obtain the two offsets "and, the seat grabs the angle of rotation of the fine angle 1 of the U. A biasing system (iv) State two web track (11) (12)

Rlf = ΜβΜηι^1 , R2f = Μ nR2 , n^L^n The matrix ~ and ~ indicate the coordinate change _ via %. She I divide 1254658 and don't be ~ and ~ 3x3 submatrix. The matrix % transform coordinate system & y is the same as the %3X3 submatrix. Position vector = convex spherical gear in the middle. The position vector is shown in the coordinate system. Inward A (/=1, 2) indicates 夂 (ί=12) in the coordinate system ^. Vector, a normal vector is the same at the point of contact. Therefore, when applying the obtained model tooth contact analysis, 'because the two contact faces are tangent, the following equations a, .d γ must be noted. , ❽ <-#i; (13) (14) The amount indicates that the convex spherical gear and the concave spherical gear position are respectively located in the coordinate money ~ in the middle normal line. The vector plane coordinate system has five unique habits, and the Η+ rhyme (10) and (10) production can be regarded as changing money. These five equations have six unknowns, among them. Because r==(TGA) is exhausted, it generates an input variable, and rotates her function, which can be expressed as /4 is nonlinear, and the error comes from the linear function track, which is the tooth 19 1254658 round The motion error 'is defined as shown below

(8)) = (κ°) - # (κ°) is the gear ratio. (7=1, 2) is the most accurate and angular position of the convex and concave gears. The item (10)) indicates the motion error of the pair of gears, which can be derived from the assembly error. The following examples are used to calculate the difference of the gear engagement. Fig. 2 shows the components of these embodiments '~ and 岣 indicate the distance error of the pair of spherical gears. Embodiment 1 shows the motion error in the case of ideal assembly (e.g., 々 '> with assembly error). In this case, the motion error is zero. Substituting Example 2 into equations (13) through (15) 'The motion error of the spherical gear assembled by the convex tooth and the concave tooth can be estimated using a computer program, as shown in Fig. 11. As shown in Figure 11, the motion error between the maximum and minimum values is almost zero. This is the same as the case of ideal assembly. The motion errors from the embodiment 1 and 2' spherical gears are similar to those of the spur gears with involute teeth. In other words, the sensitivity of the center distance error of the convex and concave teeth is zero. The change in the center distance between the convex spherical gear and the concave spherical gear does not include the motion error at the time of rotation. Substituting Examples 3 to 9 into equations (13) to (15), a computer program can be used to estimate the motion error of the spherical gear assembled by the convex tooth and the concave tooth, as shown in Figs. 12 to 18. 1254658 » 12 ® to 18th The motion error will increase in the transition county; therefore, the tooth (four) tone sum is He Wei. The 12th 18th motion error is good. The motion error of the ^^35 object line function is more than the motion error of the linear function. 纟° In the no-designed chiropractic error function, the occupational wheel concept can be known. Parabolic function. As shown in Fig. 19, an embodiment of all motion errors is summarized. The vibrations of the movements of the embodiments & $ and Lu 6 are almost zero as shown in Fig. 19. In other words, the motion errors of Embodiments 2, 5, and 6 are insensitive, while other motion errors are sensitive. Because the convex surface and the _ ball are healthy, there is an involute profile produced by the (four) theory. Other cross sections not only satisfy the combined motion. For a face gear with a small offset angle of 5, a small motion error will result. Therefore, the spherical window wheel can be used not only for the movement of the robot hand f. Moreover, the spherical gear can also replace the (10) person. The stress analysis presented in the following section can ant the stress distribution of the gear Φ transmission. The most effective way to determine accurate dexterity and writhing is the finite element analysis, which assumes that there is no assembly error between the convex and concave gears. Called by the finite element record and the general computer, it can be called the stress analysis of the _ wheel crane device. The computer program can be run under the Windows XP operating system to obtain the value of the force transmission analysis of the gear transmission. The convex and concave recording materials can be assumed to be isotropic and homogeneous 'with Young's modulus of steel (Y〇ung, s coffee & 沁 (eight) 21 1254658 five _ 207 Gpa Poisson ratio u = 0.3. The partial distribution of the convex and concave gears is used to determine the stress distribution of the gear. The model can be obtained from a CAD computer program and then subjected to finite element analysis by MSYS Workbench. In this analysis, the convex gear assumes a concave surface with a fixed moment. The gear rotates about its axis. A counterclockwise torque acts on the convex gear, causing contact between the convex gear and the concave gear. The torque acting on the convex gear is 250 Nm. > Figure 20 A model diagram of two meshing gears of a degree of freedom, meshing the surfaces of the two meshing gears to provide elastic sandbox derivation and plausible use for numerical simulation or pilot production. As shown in Fig. 20, the concave surface A part of the wheel line of the wheel can be rotated around its axis. At the same time, part of the wheel of the convex gear can be rotated around its axis. The two gears are fanned in a convex manner. The rim and the concave spherical gear 2 are arranged in a relative manner, and when the teeth of the surface are in motion, the convex surface spherical gear teeth 11 and the concave spherical gear teeth 21 are combined in opposite directions. The diameter of the pitch circle may be equal or - large-small, the axis of the gear may be parallel; the surface of the t, the convex spherical gear 丨 and the concave spherical gear 2 _ gear are meshed. Figure 21, concave surface The distribution of the Von_Mises stress of the gear. As shown in the figure, the three-degree stress distribution of the convex gear should be read by to-Mises. The maximum stress of Von-Mises is 4.6〇8xio9iv/w2. 22 1254658 The gear tooth profile of the spherical gear manufacturing method with the circular involute gear teeth has greater strength than the involute gear teeth of the conventional spur gear, and the gear tooth stress analysis of the spur gear and the gear of the present invention, as in the 23rd Fig. 24 and Fig. 24. The elastic modulus and the Poisson ratio (p〇issonrati〇) of the brothers 23 and 24 are respectively the heart 207 coffee ' ϋ = 0·3. In the 23rd and 24th figures, The bottom node of the tooth can be regarded as fixed. In Figure 21, there are 21563 Element, 31252 nodes. In Figure 24, there are 16598 elements, 24276 nodes. The 10-node has four-sided elements to form a grid of two gear-solid geometries. It is assumed that the spur gear and the present invention The structural torque of the gear is 25 〇Nm. Comparing Fig. 23 and Fig. 24, it can be observed that the stress distribution of Von-Mises stress is different. The Von-Mises stress of the tooth of the present invention is higher than that of the conventional spur gear. The 〇n-Mises stress is small. In the method for manufacturing a spherical gear with annular involute gear teeth, the motion error is simulated by the gear tooth stress analysis. The combined error of the motion error to the center-to-center distance is dull φ and is also sensitive to the misalignment angle μ. The proposed gear concept can obtain a parabolic motion error function without pre-designing a parabolic error function. Moreover, the three-degree stress analysis of the proposed gear concept can be explored. Here, the TurboCH programming language and the Solidw〇rks software are used to generate the geometric model of the spherical tooth surface, and the cutting simulation of the spherical gear is made by his software. To show the movement of the spherical gear mechanism, s〇lidw〇rksx is used to combine the spherical gears of the convex and concave teeth. The speed forming method and manufacturing technology can produce spherical teeth 23 1254658 round convex ball = wheel and concave spherical surface, fast fine method can include reverse work and private law ° after taking 'to computer program, - electric hard design Program and a computer === the gear mechanism of the present invention. The tooth of the annular involute tooth is proposed. The mathematics (4) analysis is useful for the design and production of the hybrid red. According to the above, the two-parameter surface family envelope theory of the involute tool calls for the establishment of a spherical gear profile to provide a convenient and versatile tool. In the method for manufacturing a spherical gear having a meandering involute tooth of the present invention, a mathematical formula, an equation, and a parameter formula of the cutter are used to obtain a spherical ring gear system of a discrete annular involute tooth profile. Geometric shapes and mathematical modes of spherical gears in the form of discrete annular involutes have also been established. - A spherical record structure (4) Her pieces are also assembled. The spherical gear is continuously rotated on both axes, and the spherical gear of the convex tooth is processed. Transfer the Maste·Drawing Silk to the number of Jianguan bed machine to the king of the engine (four) gear. Qing computer-aided designer is called the program language. Solidlks and Mastered are developing and producing ball-wheels and forming the basis for the design and manufacture of ball gears. Finally, the present invention has a circular involute ball. The method of manufacturing the face tooth is also useful for those who design the spherical gear. The previous discrete ring-shaped _-forms have a tool simulation process to perform _. _Tool_ is an unknown number but the number of workpieces in the wheel is 24 1254658. The model is as described above. Therefore, it is very easy to make a gear tool simulation. By using the Mastercam software, it is easier to get, the tool cutting process of the spherical gear = machining road plus graphics, as shown in Figure 25. The invention relates to a method for manufacturing a spherical gear with annular involute gear teeth, which can make a spherical gear with convex or concave gear teeth into a spherical gear with a spherical appearance and a spherical appearance, so as to be applicable to various types. combination. The use of the method for manufacturing the spherical involute gear of the present invention and the yoke example are one of the preferred embodiments of the present invention, and are not intended to limit the features of the present invention. , the side of the ship, should be within the scope of the invention and patent application of the present invention. , 'T, above, the invention has the effect of the spherical involute gear of the circular involute gear, which can meet the requirements of the invention patent, and the French fishing court submits the invention patent of the present invention. The application, the tribute to the Xiaoxuan Bureau and the reviewing committee of the review, and the early grant of the invention patent of the case, the real sense of virtue. 25 1254658 [Simple description of the diagram] Figure 1 is a schematic diagram of the wrist joint of a conventional robot. Figure 2 is a schematic view of a conventional spherical gear mechanism. Figure 3 is a schematic diagram of the main design parameters of the spherical gear. Figure 4 is a schematic diagram of the types of combined errors. Figure 5 is a schematic diagram of the tool curve design. Figure 6 is a schematic view of a method of producing a concave spherical gear. Figure 7 is a schematic diagram of a method of producing a convex spherical gear. Figure 8 is a schematic view showing the distribution of convex and concave teeth on the spherical surface. Figure 9 is a side view of the tooth distribution. Figure 10 is a schematic diagram of a coordinate system for analog combined error. Figure 11 is a schematic diagram of the motion error of the second embodiment. Figure 12 is a schematic diagram of the motion error of the third embodiment. Figure 13 is a schematic diagram of the motion error of the fourth embodiment. Figure 14 is a schematic diagram of the motion error of the fifth embodiment. Fig. 15 is a view showing the motion error of the embodiment 6. Figure 16 is a schematic diagram of the motion error of the seventh embodiment. 26 1254658 Figure 17 is a schematic diagram of the motion error of the embodiment 8. Figure 18 is a schematic diagram of the motion error of the embodiment 9. Figure 19 is a schematic illustration of the motion error of all embodiments. Figure 20 is a schematic view of two spray gears. Figure 21 is a schematic view showing the stress distribution of the Von-Mises of the concave gear. Figure 22 is a schematic diagram showing the stress distribution of the Von-Mises of the convex gear. B Figure 23 shows the Von-Mises stress distribution of conventional spur gear teeth. Figure 24 is a diagram showing the Von-Mises stress distribution of the gear teeth of the present invention. ^ Figure 25 is a simulation diagram of a spherical gear made using the software of the present invention.

27 1254658 [Description of main component symbols] 1 convex spherical gear 11 convex spherical gear tooth 2 concave spherical gear 21 concave spherical gear tooth

3 grid

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Claims (1)

1254658 X. Patent application scope: 制造%-shaped involute gear spherical gear manufacturing side, including the gear of the convex tooth and the tooth of the concave tooth. The convex ring of the involute tooth is gradually opened. The reel is aged, each phase has a phase, the * wheel consists of a continuous concave gear from a continuous concave annular involute m rim; the same 'the same contour; to obtain a convex gear and a concave gear The purpose of the tool is to cut the outer layer of the material, its knife & ancient saying... 1 shape field two straight lines, these straight _ Cheng Li Lai angle; In addition, Wei Wei _ cutter set the number of revolutions 'by this' can produce convex The gear bottom, side, round and top surfaces, and the bottom, side and rounded surfaces of the gear teeth of the gear teeth. The method for manufacturing a spherical involute gear spherical gear according to the scope of the invention, wherein the bottom of the gear tooth of the convex tooth is represented by μ, the variable number is a parameter of the tool curve; and the equation of the ice zone is a coordinate system fork. Representation can be expressed as: Μ a 0 ' yf Kb 1 = fine /2 — λ6 ~~cic +rsin^c ' 1 〇<λό <w9 . A Man "-reo is a design parameter, what is The pressure angle is the tool design parameter; the < vector in the equation is the position vector; the upper right corner represents the area; the subscript C represents the position vector of the coordinate system & the parameter m is the modulus; the root of each tooth The radius of the guide circle is added. 29 1254658 3. If you apply for the method of manufacturing the red ball gear of the first round of the special Ma Ma, the guiding surface of the convex tooth is represented by skill, ^ represents the design parameter of the tool; The temple, [the equation of the region is expressed by the coordinates, which can be expressed as follows: XcC _ 0 - bc +ac tan^c +rcos^c -rsinXc - 0C +rsin$c -rcosXc 1 ' 0<XC <tt /2 — 1 1 What is the tool's pressure angle ά is the tool design parameter; the root radius of the tooth root is r = 0.2w, and the parameter is the modulus. The spherical gear of the ring-shaped involute gear described in the scope of the patent application is manufactured, wherein the side of the convex tooth is represented by g, and the tool is used to generate the tooth of the wheel. ] flat edge; represents the design of the tool curve, the equation of the w region is represented by the coordinate system fork, which can be expressed as: Kd y.Cd ' r Xc fly, Cd o - yc ^.cd bc Zc 1 K c〇 s^c 1 . 1 -mxm2 <Xh <m2m3, the number of tables ^4 can be the straight edge of the tool; according to the geometry of the tool, the formation of the reference; decision; Yihe is the design parameter. 1254658, the spherical involute gear of the ring-shaped tooth described in the first item of the scope of the application of the j-li range is made of Γ田, and the tooth bottom of the concave tooth is represented by %; the stone area is the crest of the tool curve for cutting _ The bottom of the equation; the equation of the domain is represented by the remainder β, which can be expressed by the following formula: c 4e 0 Ί yd: ^de = *dtan0c~rcos<^+rsin, Zc 1 at +rcos^^ ' °<λ ^ <π/2-φ(: 0 1 -1 6 , such as the application of the paste 1 嶋丨 嶋 四 四 四 四 四 四 四 四 四 四 四 四 四 四 四 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造 制造The structure; the tool is moved along the axis misalignment; the two _ reference reference seat ', the first 77 is tightly connected to the convex spherical gear and the concave spherical gear; the other two coordinate systems are closely attached to the convex spherical gear and the concave spherical surface 7. As in the patent application, the spherical involute gear of the involute gear described in Item 1 is called ', ', and 'Haidao'. In order to generate the rake of the tool curve family, the coordinate system can also be utilized. Alternate matrix conversion to coordinate system & application with same-screen matrix transformation For coordinate transformation, the matrix I can be obtained by: cos a -sin a 0 0 sin a cos ^ sin a sin ^ cos a cos ^ cos a sin ^ a sin do not cos do 0 0 -iSsinacos^ sinasin^ —Scosacos is + 'Cosasin is 5 sin +' cos is the relationship between u, ~ represents the standard pitch of the convex gear 31 1254658 radius, the matrix is converted from the sense to the S2 matrix; therefore, the matrix 1 can be expressed as: Cos a sin a cos φ2 -sin a sin - S sin a cos φ2 + rpi sin a sin φ2 sin a cos a cos φ2 - cos a sin φ2 - S cos a cos φ2 + rp cos a sin φ2 -*SsinA c〇 s 矣0 0 sin 0 C〇S^2 0 The relationship between Xi and 02 is S = rp2A, and ~ represents the convex gear radius. The moment is the moment 8. The ring involute as described in the patent application scope. The ball method of the wheel guard, wherein the tool curve group can be expressed by the following formula: ', the face gear manufacturing iff (λ7, a, ¢).) = Mic(φ. )r^ [χ.) The variable number λ7 is a design parameter , vector (Li Μ λ,, a, table) is the knife mark superscript text g is <& and 3,, curve,; and do.埒 is the knife. The subscript symbol i· is / and 2. >, 薏 vector, 9, as applied for the manufacturing method of the Gu Di , item, in which the spherical vibration of the spherical surface of each needle and long involute tooth ~ dRg spherical gear can satisfy the equation at 6, / Equation making method, Cai, will be the bottom of the bottom of the ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ (λ, «, ^ ^ ^ ^ φ # ^ ^ ^ ^ Desire /^=〇, an outer layer Σ1 can be obtained from the tool curve group; in addition, the layer Σ1 is called the convex surface tooth of the convex spherical gear. The method for making a spherical gear of a circular involute tooth', in which the equation of the side center is expressed, the equation of the tooth is shown by the equation, the equation of the tool curve group is expressed by the equation 'u) = the spider, and the equation of the spherical spherical gear Unusual = 〇, the outer layer Σ 2 can be obtained from the tool curve group. The additional layer Σ 2 is called the concave tooth of the concave spherical gear. 2) a method for manufacturing a ring-shaped wire-toothed tooth, which comprises a gear of a convex tooth and a gear of a concave tooth; a convex gear is a "connected"; a convex ring involute Tooth composition 'Every wheel has the same wheel; sample:: Wheel:: Concave concave ring involute gear teeth and pass a convex gear and a concave gear manufacturing method, with 2 之外 outer layer, its tool The shape consists of two straight lines: these two:: two variable angles; the other 'variable number represents the design parameters of the cutting tool; thereby, the bottom of the convex tooth, the (four), the circular and top surfaces and the concave teeth : bottom, side and rounded surface, thus obtaining the central tooth; copying the six teeth from the central wheel obtained by the younger brother; likewise, the second ring by the central wheel: 33 1254658 copying twelve rounds tooth. 13. The method of manufacturing a spherical involute gear of the circular involute tooth according to claim 12, wherein the first ring replicates six teeth, and the first is set. -18〇°, 60. -240. And 120. -300° three lines with a pitch; use the tool curve along 30 ° - 210 °, 90. - 270° and 150. - The 330° three lines produce the contours of the six teeth of the second toroid, and the contours of the twelve teeth will be reproduced from the contour of the central tooth of the resulting gear. 34