CN116638158A - Involute enveloping worm tooth surface turning tool confirmation method - Google Patents
Involute enveloping worm tooth surface turning tool confirmation method Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23F—MAKING GEARS OR TOOTHED RACKS
- B23F23/00—Accessories or equipment combined with or arranged in, or specially designed to form part of, gear-cutting machines
Abstract
The invention provides a method for confirming a turning cutter for a tooth surface of an involute enveloping worm, which comprises the following steps: s1, determining an involute enveloping worm to be processed; s2, determining an external meshing involute cylindrical gear A, wherein the external meshing involute cylindrical gear A is meshed with an involute toroidal worm to form a transmission pair; s3, generating an involute intermediate gear with zero thickness based on the external meshing involute cylindrical gear A, wherein the involute intermediate gear is provided with external teeth and internal teeth, and the tooth surface parameters of the internal teeth and the external teeth of the involute intermediate gear are the same as the tooth surface parameters of the external meshing involute cylindrical gear A; s4, determining an external meshing involute cylindrical gear B, wherein the external meshing involute cylindrical gear B is meshed with the internal teeth of the involute medium gear to form a transmission pair; s5, processing the external meshing involute cylindrical gear B to obtain the turning cutter of the involute toroidal worm to be processed.
Description
Technical Field
The invention relates to the field of machining of enveloping worms, in particular to a method for confirming a turning tool for a tooth surface of an involute enveloping worm.
Background
The involute enveloping worm drive is used as a multi-tooth line/point contact drive mechanism, and has the advantages of large drive ratio, stable drive, small noise impact, adjustable backlash and the like; at present, two types mainly exist, namely, equal tooth thickness involute gear enveloping worm transmission and variable tooth thickness involute gear enveloping worm transmission, and the transmission mechanism is widely applied to the fields of aerospace, strategic equipment, intelligent manufacturing, wind power heat energy and other national emerging industries and strategic deployment, and has important research significance and application value in the field of precise heavy-load driving transmission.
At present, the involute toroidal worm is mainly formed by turning, but cannot be formed by precise grinding, so that the machining precision and efficiency are greatly reduced. The turning gear processing method is widely applied to gear tooth surface processing in gear transmission, the efficiency of the turning gear processing method is 4-6 times of that of a hobbing, 6-10 times of that of a gear shaping, and the precision of the turning gear processing method can reach 4-6 levels, but due to the complexity of the tooth surface of an enveloping worm, a turning gear cutter in the prior art cannot be applied to processing of the enveloping worm.
Therefore, in order to solve the above-mentioned technical problems, a new technical means is needed.
Disclosure of Invention
Therefore, the invention aims to provide a method for confirming the turning tool of the tooth surface of the involute enveloping worm, which can determine the machining tool for machining the turning of the involute enveloping worm, thereby effectively improving the machining efficiency and the machining precision of the enveloping worm.
The invention provides a method for confirming a turning cutter for a tooth surface of an involute enveloping worm, which comprises the following steps:
s1, determining an involute enveloping worm to be processed;
s2, determining an external meshing involute cylindrical gear A, wherein the external meshing involute cylindrical gear A is meshed with an involute toroidal worm to form a transmission pair;
s3, generating an involute intermediate gear with zero thickness based on the external meshing involute cylindrical gear A, wherein the involute intermediate gear is provided with external teeth and internal teeth, and the tooth surface parameters of the internal teeth and the external teeth of the involute intermediate gear are the same as the tooth surface parameters of the external meshing involute cylindrical gear A;
s4, determining an external meshing involute cylindrical gear B, wherein the external meshing involute cylindrical gear B is meshed with the internal teeth of the involute medium gear to form a transmission pair;
s5, processing the external meshing involute cylindrical gear B to obtain the turning cutter of the involute toroidal worm to be processed.
Further, in step S2, the external engagement involute cylindrical gear a is determined by the following method:
construction space fixing standard sigma u (O u -x u ,y u ,z u ) And space fixing standard sigma v (O v -x v ,y v ,z v ) Wherein:
space fixing standard sigma u (O u -x u ,y u ,z u ) For the initial position of the external engagement involute cylindrical gear A, a space fixing bracket sigma v (O v -x v ,y v ,z v ) Enveloping the initial position of the toroidal worm for the involute surface to be processed;
construction of a spatial movement frame sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) And space motion frame sigma 2 (O 2 -x 2 ,y 2 ,z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein: space motion standard sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixedly connected with an external meshing involute cylindrical gear A and wound around z 1 The shaft rotates and its instantaneous rotational displacement isSpace motion standard sigma 2 (O 2 -x 2 ,y 2 ,z 2 ) Fixedly connected with the involute toroidal worm and wound around z 2 The shaft rotates and its instantaneous rotational displacement is +.>The center distance between the external meshing involute cylindrical gear A and the involute toroidal worm is a, and the intersecting angle of the shaft is zero;
based on space differential geometry and gear meshing principle, in space motion standard sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) In the step (a), the external tooth surface equation r of the external meshing involute cylindrical gear A is obtained 1 I ：
Wherein: τ is the sum of the spreading angle and the pressure angle of the external meshing involute cylindrical gear A; θ is the spiral parameter of the external meshing involute cylindrical gear A; delta is the base circle half angle of the external meshing involute cylindrical gear A;the base radius of the external meshing involute cylindrical gear A is the base radius of the external meshing involute cylindrical gear A; p is the spiral parameter of the external engagement involute cylindrical gear A, and +.>Beta is the helix angle of the external engagement involute cylindrical gear A, alpha t The end face pressure angle of the external meshing involute cylindrical gear A is set; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear A are respectively; i.e 1 、j 1 And k 1 Respectively coordinate axes x 1 、y 1 And z 1 Is included in the vector.
Further, in step S1, the involute enveloping worm to be processed is determined by the following method:
according to the gear meshing principle, the involute enveloping worm tooth surface can be obtained in the space movement standard frame sigma through coordinate transformation and bottom vector conversion 2 (O 2 -x 2 ,y 2 ,z 2 ) Tooth surface equation in (a)The method comprises the following steps:
wherein: phi II Is the meshing function of the involute enveloping worm tooth surface,i 21 ＝1/i 12 ＝Z 1 /Z 2 ；Z 1 for the number of teeth, Z, of the external engagement involute cylindrical gear A 2 The number of heads of the toroidal worm is the involute envelope; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear A are respectively; i.e 2 、j 2 And k 2 Respectively coordinate axes x 2 、y 2 And z 2 Is included in the vector.
Further, the tooth surface equation of the external engagement involute cylindrical gear B is determined by the following method:
construction space fixing standard sigma w (O w -x w ,y w ,z w ) Wherein the space is fixed by a standard sigma w (O w -x w ,y w ,z w ) The initial position of the external meshing involute cylindrical gear B;
construction of a spatial movement frame sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) Wherein, the space motion frame sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) Fixedly connected with an external meshing involute cylindrical gear B and winds around z 3 The shaft rotates and a certain instantaneous rotational displacement isThe center distance between the external meshing involute cylindrical gear B and the involute medium gear is B, and the intersecting angle of the external meshing involute cylindrical gear B and the involute medium gear is zero; the wheelbase between the external meshing involute cylindrical gear B and the involute toroidal worm is c;
based on space differential geometry and gear meshing principle, in space motion standard sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) In the above step, the tooth surface equation of the external engagement involute cylindrical gear B is obtained
Wherein: τ and θ are tooth surface parameters of the external meshing involute cylindrical gear B; delta is the base circle half angle of the external meshing involute cylindrical gear B;the base radius of the external meshing involute cylindrical gear B is the base radius of the external meshing involute cylindrical gear B; p is the spiral parameter of the external meshing involute cylindrical gear B; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear B are respectively; i.e 3 、j 3 And k 3 Respectively coordinate axes x 3 、y 3 And z 3 Is included in the vector.
Further, the following conditions need to be satisfied between the turning tool of the involute enveloping worm to be processed and the blank of the involute enveloping worm to be processed:
wherein: omega c The rotating speed of the worm turning tool rotating around the central axis of the worm turning tool in the process of machining the annular worm; omega 3 The theoretical rotating speed of the external meshing involute cylindrical gear B; v is the feeding cutting movement speed of the worm turning gear cutter moving up and down along the central axis of the worm turning gear cutter; f (omega) o ) As to the rotational speed omega o When the number of teeth of the worm turning gear is equal to the number of teeth of the involute cylindrical gear in conjugate engagement with the worm to be machined, f (ω) o )＝0。
The invention has the beneficial effects that: the processing tool for processing the teeth of the involute enveloping worm can be determined, so that the processing efficiency and the processing precision of the enveloping worm are effectively improved, and the processing tool is high in adaptability and can be suitable for the involute enveloping worm with equal tooth thickness and the involute enveloping worm with variable tooth thickness.
Drawings
The invention is further described below with reference to the accompanying drawings and examples:
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a schematic diagram of the meshing of the involute toroidal worm with the external meshing involute cylindrical gear a.
Fig. 3 is a schematic diagram of the meshing of the external meshing cylindrical gear B, the involute intermediate gear and the involute toroidal worm.
Fig. 4 is a schematic view of the turning gear cutter according to the present invention.
Fig. 5 is a schematic diagram of involute enveloping worm gear machining.
Fig. 6 is a schematic diagram of the turning of the tooth surface of the full conjugate involute enveloping worm.
Detailed Description
The present invention is further described in detail below:
the invention provides a method for confirming a turning cutter for a tooth surface of an involute enveloping worm, which comprises the following steps:
s1, determining an involute enveloping worm to be processed;
s2, determining an external meshing involute cylindrical gear A, wherein the external meshing involute cylindrical gear A is meshed with an involute toroidal worm to form a transmission pair;
s3, generating an involute intermediate gear with zero thickness based on the external meshing involute cylindrical gear A, wherein the involute intermediate gear is provided with external teeth and internal teeth, and the tooth surface parameters of the internal teeth and the external teeth of the involute intermediate gear are the same as the tooth surface parameters of the external meshing involute cylindrical gear A;
s4, determining an external meshing involute cylindrical gear B, wherein the external meshing involute cylindrical gear B is meshed with the internal teeth of the involute medium gear to form a transmission pair;
s5, processing the external meshing involute cylindrical gear B to obtain a turning cutter of the involute toroidal worm to be processed; by the method, the processing tool for processing the teeth of the involute toroidal worm can be determined, so that the processing efficiency and the processing precision of the enveloping toroidal worm are effectively improved, and the method is high in adaptability and can be suitable for the involute toroidal worm with equal tooth thickness and the involute toroidal worm with variable tooth thickness.
In this embodiment, in step S2, the external meshing involute cylindrical gear a is determined by the following method:
construction space fixing standard sigma u (O u -x u ,y u ,z u ) And space fixing standard sigma v (O v -x v ,y v ,z v ) Wherein:
space fixing standard sigma u (O u -x u ,y u ,z u ) For the initial position of the external engagement involute cylindrical gear A, a space fixing bracket sigma v (O v -x v ,y v ,z v ) Enveloping the initial position of the toroidal worm for the involute surface to be processed;
construction of a spatial movement frame sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) And space motion frame sigma 2 (O 2 -x 2 ,y 2 ,z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein: space motion standard sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixedly connected with an external meshing involute cylindrical gear A and wound around z 1 The shaft rotates and its instantaneous rotational displacement isSpace motion standard sigma 2 (O 2 -x 2 ,y 2 ,z 2 ) Fixedly connected with the involute toroidal worm and wound around z 2 The shaft rotates and its instantaneous rotational displacement is +.>The center distance between the external meshing involute cylindrical gear A and the involute toroidal worm is a, and the intersecting angle of the shaft is zero;
based on space differential geometry and gear meshing principle, in space motion standard sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) In the step (a), the external tooth surface equation r of the external meshing involute cylindrical gear A is obtained 1 I ：
Wherein: τ is the sum of the spreading angle and the pressure angle of the external meshing involute cylindrical gear A; θ is the spiral parameter of the external meshing involute cylindrical gear A; delta is the base circle half angle of the external meshing involute cylindrical gear A;the base radius of the external meshing involute cylindrical gear A is the base radius of the external meshing involute cylindrical gear A; p is the spiral parameter of the external engagement involute cylindrical gear A, and +.>Beta is the helix angle of the external engagement involute cylindrical gear A, alpha t The end face pressure angle of the external meshing involute cylindrical gear A is set; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear A are respectively; i.e 1 、j 1 And k 1 Respectively coordinate axes x 1 、y 1 And z 1 Wherein, as shown in fig. 2, 2 is an external meshing involute cylindrical gear a in fig. 2, 1 is an involute toroidal worm, and conjugate meshing is carried out between the external meshing involute cylindrical gear a and the involute toroidal worm.
In this embodiment, in step S1, the involute enveloping worm to be processed is determined by the following method:
according to the gear meshing principle, the involute enveloping worm tooth surface can be obtained in the space movement standard frame sigma through coordinate transformation and bottom vector conversion 2 (O 2 -x 2 ,y 2 ,z 2 ) Tooth surface equation in (a)The method comprises the following steps:
wherein: phi II Is the meshing function of the involute enveloping worm tooth surface,i 21 ＝1/i 12 ＝Z 1 /Z 2 ；Z 1 for the number of teeth, Z, of the external engagement involute cylindrical gear A 2 The number of heads of the toroidal worm is the involute envelope; />And->Tooth surface seats of external-meshing involute cylindrical gear A respectivelyMarking values; i.e 2 、j 2 And k 2 Respectively coordinate axes x 2 、y 2 And z 2 Is included in the vector.
In this embodiment, the tooth surface equation of the external-meshing involute cylindrical gear B is determined by the following method:
construction space fixing standard sigma w (O w -x w ,y w ,z w ) Wherein the space is fixed by a standard sigma w (O w -x w ,y w ,z w ) The initial position of the external meshing involute cylindrical gear B;
construction of a spatial movement frame sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) Wherein, the space motion frame sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) Fixedly connected with an external meshing involute cylindrical gear B and winds around z 3 The shaft rotates and a certain instantaneous rotational displacement isThe center distance between the external meshing involute cylindrical gear B and the involute medium gear is B, and the intersecting angle of the external meshing involute cylindrical gear B and the involute medium gear is zero; the wheelbase between the external meshing involute cylindrical gear B and the involute toroidal worm is c;
based on space differential geometry and gear meshing principle, in space motion standard sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) In the above step, the tooth surface equation of the external engagement involute cylindrical gear B is obtained
Wherein: τ and θ are tooth surface parameters of the external meshing involute cylindrical gear B; delta is the base circle half angle of the external meshing involute cylindrical gear B;is engaged gradually to the outsideThe base radius of the open-line cylindrical gear B; p is the spiral parameter of the external meshing involute cylindrical gear B; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear B are respectively; i.e 3 、j 3 And k 3 Respectively coordinate axes x 3 、y 3 And z 3 Is defined by the three vectors of (a); wherein, because the parameters of the internal tooth and the external tooth of the involute intermediate gear are the same, the equations of the internal tooth surface of the involute intermediate gear and the external tooth surface of the involute intermediate gear are the same, the internal tooth of the involute intermediate gear is meshed with the external meshing involute cylindrical gear B, as shown in figure 3, and in figure 3, the 1-involute enveloping ring worm; 4-external meshing involute cylindrical gear B; 5-involute intermediate gear; the involute intermediate gear and the involute toroidal worm are in complete conjugate engagement, and the involute intermediate gear and the external engagement involute cylindrical gear B are in complete conjugate engagement, and in view of the fact that the involute intermediate gear is a face gear with zero thickness, according to the lambda theorem, after the involute intermediate gear is removed, the involute toroidal worm and the external engagement involute cylindrical gear B are in equivalent local conjugate engagement, and the wheelbase between the external engagement involute cylindrical gear B and the involute toroidal worm is c.
The external meshing involute cylindrical gear B is processed to form a turning gear cutter, the structure of which is shown in fig. 4, wherein the cutter comprises the following structure: 6-worm turning gear knife; 61-a cutter handle; 62-cutter body; 63—knife edge face; 64-tool weight reduction cavity, the worm gear turning knife has the same axial intersection angle (zero in the example of the invention) with the involute medium gear in the process of generating the turning teeth for machining and enveloping the toroidal worm blank to obtain the involute enveloping toroidal worm, as shown in fig. 5. At the same time, the toroidal worm blank has only feed cutting movement rotating around the central line axis of the toroidal worm blank, and the worm turning gear knife is except around the central line axis z of the toroidal worm blank 3 Rotary main cutting movement (rotational speed omega c ) In addition, there is also a direction z 3 Up-and-down motion of the shaft (velocity v) and around z 1 Shaft rotation (rotation speed omega) o ) Is provided.
And (3) taking the external meshing involute cylindrical gear B as a worm turning gear knife obtained by a prototype, and performing conjugate motion with a processed blank body through enveloping motion to complete continuous indexing generation processing of the involute enveloping worm tooth surface. According to the conjugate relation among the worm turning gear knife, the medium gear and the processed toroidal worm, the correct processing condition of the involute toroidal worm can be known as follows: the worm turning gear knife is the same as the modulus, the pressure angle, the helix angle and the axiality angle of the medium gear; the number of teeth of the worm turning gear is not greater than that of involute cylindrical gears which are in conjugate engagement with the worm to be processed.
When the number of teeth of the worm turning gear is equal to the number of teeth of the involute cylindrical gear which is in conjugate engagement with the worm to be processed, namely the worm turning gear obtained by taking the external engagement involute cylindrical gear A as a prototype, the worm turning gear is wound around the central axis z of the worm turning gear 1 Rotary main cutting movement (rotational speed omega c ) In addition, there is only one feed cutting movement along z 1 The shaft moves up and down (speed v) as shown in fig. 6.
In this embodiment, the following conditions need to be satisfied between the turning tool of the involute enveloping worm to be processed and the blank of the involute enveloping worm to be processed:
wherein: omega c The rotating speed of the worm turning tool rotating around the central axis of the worm turning tool in the process of machining the annular worm; omega 3 The theoretical rotating speed of the external meshing involute cylindrical gear B; v is the feeding cutting movement speed of the worm turning gear cutter moving up and down along the central axis of the worm turning gear cutter; f (omega) o ) As to the rotational speed omega o Is a function of the existing one, and is not described in detail here, f (ω) when the number of teeth of the worm turning gear is equal to the number of teeth of the involute cylindrical gear in conjugate engagement with the worm to be machined o )＝0。
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.
Claims (5)
1. A method for confirming a turning cutter of a involute enveloping worm tooth surface is characterized in that: the method comprises the following steps:
s1, determining an involute enveloping worm to be processed;
s2, determining an external meshing involute cylindrical gear A, wherein the external meshing involute cylindrical gear A is meshed with an involute toroidal worm to form a transmission pair;
s3, generating an involute intermediate gear with zero thickness based on the external meshing involute cylindrical gear A, wherein the involute intermediate gear is provided with external teeth and internal teeth, and the tooth surface parameters of the internal teeth and the external teeth of the involute intermediate gear are the same as the tooth surface parameters of the external meshing involute cylindrical gear A;
s4, determining an external meshing involute cylindrical gear B, wherein the external meshing involute cylindrical gear B is meshed with the internal teeth of the involute medium gear to form a transmission pair;
s5, processing the external meshing involute cylindrical gear B to obtain the turning cutter of the involute toroidal worm to be processed.
2. The involute enveloping worm tooth surface turning tool identification method according to claim 1, characterized in that: in step S2, the external meshing involute cylindrical gear a is determined by the following method:
construction space fixing standard sigma u (O u -x u ,y u ,z u ) And space fixing standard sigma v (O v -x v ,y v ,z v ) Wherein:
space fixing standard sigma u (O u -x u ,y u ,z u ) For the initial position of the external engagement involute cylindrical gear A, a space fixing bracket sigma v (O v -x v ,y v ,z v ) Enveloping the initial position of the toroidal worm for the involute surface to be processed;
construction of a spatial movement frame sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) And space motion frame sigma 2 (O 2 -x 2 ,y 2 ,z 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Wherein: space motion standard sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) Fixedly connected with an external meshing involute cylindrical gear A and wound around z 1 The shaft rotates and its instantaneous rotational displacement isSpace motion standard sigma 2 (O 2 -x 2 ,y 2 ,z 2 ) Fixedly connected with the involute toroidal worm and wound around z 2 The shaft rotates and its instantaneous rotational displacement is +.>The center distance between the external meshing involute cylindrical gear A and the involute toroidal worm is a, and the intersecting angle of the shaft is zero;
based on space differential geometry and gear meshing principle, in space motion standard sigma 1 (O 1 -x 1 ,y 1 ,z 1 ) In the step (a), the external tooth surface equation r of the external meshing involute cylindrical gear A is obtained 1 I ：
Wherein: τ is the sum of the spreading angle and the pressure angle of the external meshing involute cylindrical gear A; θ is the spiral parameter of the external meshing involute cylindrical gear A; delta is the base circle half angle of the external meshing involute cylindrical gear A;the base radius of the external meshing involute cylindrical gear A is the base radius of the external meshing involute cylindrical gear A; p is the spiral parameter of the external engagement involute cylindrical gear A, and +.>Beta is the helix angle of the external engagement involute cylindrical gear A, alpha t The end face pressure angle of the external meshing involute cylindrical gear A is set; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear A are respectively; i.e 1 、j 1 And k 1 Respectively coordinate axes x 1 、y 1 And z 1 Is included in the vector.
3. The involute toroidal worm tooth surface turning tool identification method according to claim 2, characterized in that: in step S1, the involute enveloping worm to be processed is determined by the following method:
according to the gear meshing principle, the involute enveloping worm tooth surface can be obtained in the space movement standard frame sigma through coordinate transformation and bottom vector conversion 2 (O 2 -x 2 ,y 2 ,z 2 ) Tooth surface equation in (a)The method comprises the following steps:
wherein: phi II Is the meshing function of the involute enveloping worm tooth surface,i 21 ＝1/i 12 ＝Z 1 /Z 2 ；Z 1 for the number of teeth, Z, of the external engagement involute cylindrical gear A 2 The number of heads of the toroidal worm is the involute envelope; />And->The tooth surface coordinate values of the external meshing involute cylindrical gear A are respectively; i.e 2 、j 2 And k 2 Respectively coordinate axes x 2 、y 2 And z 2 Is included in the vector.
4. The involute toroidal worm tooth surface turning tool identification method according to claim 3, characterized in that: the tooth surface equation of the external meshing involute cylindrical gear B is determined by the following method:
construction space fixing standard sigma w (O w -x w ,y w ,z w ) Wherein the space is fixed by a standard sigma w (O w -x w ,y w ,z w ) The initial position of the external meshing involute cylindrical gear B;
construction of a spatial movement frame sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) Wherein, the space motion frame sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) Fixedly connected with an external meshing involute cylindrical gear B and winds around z 3 The shaft rotates and a certain instantaneous rotational displacement isThe center distance between the external meshing involute cylindrical gear B and the involute medium gear is B, and the intersecting angle of the external meshing involute cylindrical gear B and the involute medium gear is zero; the wheelbase between the external meshing involute cylindrical gear B and the involute toroidal worm is c;
based on space differential geometry and gear meshing principle, in space motion standard sigma 3 (O 3 -x 3 ,y 3 ,z 3 ) In the above step, the tooth surface equation of the external engagement involute cylindrical gear B is obtained
Wherein: τ and θ are tooth surface parameters of the external meshing involute cylindrical gear B; delta is the base circle half angle of the external meshing involute cylindrical gear B;the base radius of the external meshing involute cylindrical gear B is the base radius of the external meshing involute cylindrical gear B; p is the spiral parameter of the external meshing involute cylindrical gear B;and->The tooth surface coordinate values of the external meshing involute cylindrical gear B are respectively; i.e 3 、j 3 And k 3 Respectively coordinate axes x 3 、y 3 And z 3 Is included in the vector.
5. The method for confirming the involute toroidal worm tooth surface turning tool according to claim 4, characterized in that: the following conditions need to be met between a turning cutter of the involute enveloping worm to be processed and a blank of the involute enveloping worm to be processed:
wherein: omega c The rotating speed of the worm turning tool rotating around the central axis of the worm turning tool in the process of machining the annular worm;
ω 3 the theoretical rotating speed of the external meshing involute cylindrical gear B; v is the feeding cutting movement speed of the worm turning gear cutter moving up and down along the central axis of the worm turning gear cutter; f (omega) o ) As to the rotational speed omega o When the number of teeth of the worm turning gear is equal to the number of teeth of the involute cylindrical gear in conjugate engagement with the worm to be machined, f (ω) o )＝0。
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| CN202310532389.3A CN116638158A (en) | 2023-05-10 | 2023-05-10 | Involute enveloping worm tooth surface turning tool confirmation method |
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| CN202310532389.3A CN116638158A (en) | 2023-05-10 | 2023-05-10 | Involute enveloping worm tooth surface turning tool confirmation method |
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