A hob for machining external beveled taper teeth and its design method

Abstract

The present invention provides a hob for machining externally inclined inverted bevel gears and a design method thereof, which relates to the field of machining externally inclined inverted bevel gears. The actual helix angle β of the left tooth surface of the externally inclined inverted bevel gear to be machined is determined by using the helix angle and the indexing cone angle of the externally inclined inverted bevel gear to be machined. 1L and the actual helix angle β of the right tooth surface 1R According to β 1L and β 1R , as well as its helix angle and normal module, determine the actual normal module m of its left tooth surface n1L and the actual normal module m of the right tooth surface n1R According to β 1L and β 1R , as well as its helix angle and normal pressure angle, determine the actual normal pressure angle α of its left tooth surface n1L and the actual normal pressure angle α of the right tooth surface n1R ; According to its normal modulus, m n1L , α n1L , and m n1R and α n1R Determine the left tooth surface pressure angle α of the hob respectively n0L and right tooth surface pressure angle α n0R , and then determine the remaining parameters of the hob. According to this design, the hob precision of the processed external beveled inverted cone gear is high.

Description

Technical Field

[0001] The present invention relates to the field of machining external beveled and tapered teeth, and specifically to a hob for machining external beveled and tapered teeth and its design method. Background Art

[0002] After adopting the transmission structure with external beveled and tapered teeth in a transmission, the shift synchronization mechanism can be integrated with the planetary transmission structure, the transmission chain is shortened, the size of the transmission is significantly reduced, and the transmission efficiency and synchronization efficiency are improved. It is a new type of transmission structure for transmissions.

[0003] In the hobbing process of external beveled and tapered gears, generally the method of gradually changing the center distance is used to form the tooth thickness taper. Since the center distance and the helix angle change simultaneously compared with the nominal parameters, different errors of the normal base pitch of the externally hobbed beveled and tapered gears are generated on different radius sections, and further a large error is generated in the machined tooth profile, Ha The error can reach more than 20μm, and further the transmission of the transmission cannot operate normally.

[0004] As a tooth structure of a new type of gear, external beveled and tapered teeth are currently generally machined by gear shaping in both domestic and foreign countries. However, gear shaping equipment has not been popularized yet, and advanced high-precision gear shaping equipment needs to be purchased for machining, resulting in a very high machining cost for external beveled and tapered teeth. In order to reduce costs, alternative solutions need to be found, such as Figure 1 As shown, the tooth profile detection accuracy of the external beveled and tapered teeth machined by a hob using the conventional design method is very poor, and the main error is Ha the error, with a value between 86 - 133μm, exceeding the 12th-level accuracy specified in the gear accuracy standard GB10095. Figure 2 Namely, the schematic diagram of the tooth profile error of the current external beveled and tapered teeth caused by the normal base pitch error. It can be seen that there is a large difference between the theoretical tooth profile and the actual tooth profile. Currently, there are reports on the tooth profile design of a hob for rough grooving of helical gear shaper cutters (whose structure is similar to that of external beveled and tapered teeth). Specifically, in the book "Gear Cutter Design Manual" (edited by Yuan Junzhe, etc.), the calculation process of the tooth profile of the hob for rough grooving of helical gear shaper cutters is mentioned. It uses the method of cross-section projection for calculation to obtain the tooth profile design method of the hob for rough grooving of helical gear shaper cutters, but it still cannot meet the requirements of fine machining of external beveled and tapered teeth, and the calculation process is relatively complex. Summary of the Invention

[0005] Aiming at the problems existing in the prior art, the present invention provides a hob for machining external beveled and tapered teeth and its design method. The external beveled and tapered teeth machined with the hob have the same hobbing accuracy as normal gears, high accuracy, and small theoretical machining error, which can reach below the 7th level.

[0006] The present invention is realized through the following technical solutions:

[0007] A design method for a hob for machining external oblique taper teeth, comprising the following steps:

[0008] S1. Determine the actual helix angle β of the left tooth surface of the external oblique taper gear to be machined by using the helix angle and pitch cone angle of the external oblique taper gear to be machined 1L and the actual helix angle β of the right tooth surface 1R , where β 1L is located on the left side of the tooth thickness center line of the gear, and β 1R is located on the right side of the tooth thickness center line of the gear;

[0009] S2. According to β 1L and β 1R , as well as the helix angle and normal module of the gear described in S1, determine the actual normal module m of the left tooth surface of the gear described in S1 n1L and the actual normal module m of the right tooth surface n1R ;

[0010] According to β 1L and β 1R , as well as the helix angle and normal pressure angle of the gear described in S1, determine the actual normal pressure angle α of the left tooth surface of the gear described in S1 n1L and the actual normal pressure angle α of the right tooth surface n1R ;

[0011] where m n1L and α n1L are both located on the left side of the tooth thickness center line of the gear described in S1, and m n1R and α n1R are located on the right side of the tooth thickness center line of the gear;

[0012] S3. According to the normal module of the gear described in S1, m n1L , α n1L , as well as m n1R and α n1R , respectively determine the pressure angle α of the left tooth surface of the hob n0L and the pressure angle α of the right tooth surface n0R , and then determine the remaining parameters of the hob to complete the design of the hob for machining external oblique taper teeth;

[0013] where α n0L is located on the left side of the tooth thickness center line of the hob, and α n0R is located on the right side of the tooth thickness center line of the hob.

[0014] Preferably, β described in S1 1L is obtained by the following formula:

[0015] Among them, β1 is the helix angle of the external bevel gear to be machined, and δ is the pitch cone angle of the external bevel gear to be machined. When the large end of the tooth thickness of the gear is at the lower part, take +, and when the large end of the tooth thickness of the gear is at the upper part, take -.

[0016] Preferably, β in S1 1R is obtained by the following formula:

[0017] Among them, β1 is the helix angle of the external bevel gear to be machined, and δ is the pitch cone angle of the external bevel gear to be machined. When the large end of the tooth thickness of the gear is at the lower part, take -, and when the large end of the tooth thickness of the gear is at the upper part, take +.

[0018] Preferably, m in S2 n1L is obtained by the following formula:

[0019] Among them, m n and β1 are the normal module and helix angle of the gear described in S1 respectively.

[0020] Preferably, m in S2 n1R is obtained by the following formula:

[0021] Among them, m n and β1 are the normal module and helix angle of the gear described in S1 respectively.

[0022] Preferably, α in S2 n1L is obtained by the following formula:

[0023] Among them, α n and β1 are the normal pressure angle and helix angle of the gear described in S1 respectively.

[0024] Preferably, α in S2 n1R is obtained by the following formula:

[0025] Among them, α n and β1 are the normal pressure angle and helix angle of the gear described in S1 respectively.

[0026] Preferably, α in S3 n0L is obtained by the following formula:

[0027] Among them, m n is the normal module of the gear described in S1.

[0028] Preferably, α in S3 n0R is obtained by the following formula:

[0029] Among them, m nIt is the normal module of the gear described in S1.

[0030] A hob for machining external helical beveloid teeth obtained by the design method of the hob for machining external helical beveloid teeth described in any one of the above.

[0031] Compared with the prior art, the present invention has the following beneficial technical effects:

[0032] For the design method of a hob for machining external helical beveloid teeth of the present invention, first, according to the pitch cone angle and helix angle of the external helical beveloid gear to be machined, the actual helix angles of the left and right tooth surfaces of the gear are obtained respectively. Then, further combined with the normal module of the gear, the actual normal module and actual normal pressure angle of its left and right tooth surfaces can be obtained. Finally, according to the principle that the normal base pitch of the hob is equal to the nominal normal base pitch of the gear, and combined with the normal module of the gear for pressure angle transformation, the pressure angles of the left and right tooth surfaces of the hob can be obtained. Since only the pressure angle needs to be improved, the design process of the remaining parameters of the hob is the same as that of the conventional hob, and thus the design of the hob for machining external helical beveloid teeth can be completed. For the external helical beveloid teeth machined by this design method, the normal base pitch error caused by helical generation and gradual change of the center distance in the machining of external helical beveloid teeth is completely eliminated, and the final machining tooth profile error of the external helical beveloid teeth is equivalent to the normal gear hobbing accuracy, with high precision and small theoretical machining error, reaching below grade 7.

[0033] The hob obtained by the design method of the present invention simultaneously realizes the design of increasing the pressure angle of the tooth profile of the hob, thereby reducing the root cone angle of the external helical beveloid teeth during machining, reducing the tooth height of the hob, increasing the effective diameter of the hob, reducing the maximum cutting depth and cutting force, and improving the machining performance of the hob. Brief Description of the Drawings

[0034] Figure 1 It is the tooth profile detection accuracy diagram of the external helical beveloid teeth machined by the hob using the conventional design method.

[0035] Figure 2 It is the schematic diagram of the tooth profile error of the current external helical beveloid teeth caused by the normal base pitch error.

[0036] Figure 3 It is the tooth profile accuracy diagram of the external helical beveloid teeth machined by the hob designed by this method.

[0037] Figure 4 It is the schematic diagram of the gear parameter conversion relationship described in the present invention.

[0038] Figure 5 It is the schematic diagram of the normal tooth profile of the hob described in the present invention.

[0039] Figure 6 It is the schematic diagram of the actual helix angle of the left tooth surface and the actual helix angle of the right tooth surface described in the present invention. Detailed implementation manners

[0040] The following further describes the present invention in detail with reference to specific embodiments, which is an explanation rather than a limitation of the present invention.

[0041] For the design method of a hob for machining external beveloid teeth of the present invention, the tooth parameters of the external beveloid gear to be machined need to be known, namely the normal module m n , the normal pressure angle α n , the normal base pitch P bn1 , the helix angle β1 and the pitch cone angle δ.

[0042] Essentially, the design of the hob for machining external beveloid teeth is to obtain the left tooth surface pressure angle and the right tooth surface pressure angle of the hob. Among them, the pressure angle corresponding to the left side of the tooth thickness center line of the hob is the left tooth surface pressure angle, and the pressure angle corresponding to the right side is the right tooth surface pressure angle. The design processes of the remaining parameters are the same as those of the existing hob.

[0043] Specifically, the design processes of the left tooth surface pressure angle α n0L and the right tooth surface pressure angle α n0R are as follows:

[0044] Step 1, as Figure 6 shown, the actual helix angle β 1L of the left tooth surface and the actual helix angle β 1R of the right tooth surface of the external beveloid gear to be machined can be determined by using the helix angle and the pitch cone angle of the external beveloid gear to be machined, where β 1L is located on the left side of the tooth thickness center line of the gear, and β 1R is located on the right side of the tooth thickness center line of the gear;

[0045] Specifically, the following formulas are used to determine the actual helix angle β 1L of the left tooth surface and the actual helix angle β 1R of the right tooth surface respectively:

[0046] (Take + when the large end of the gear tooth thickness is at the bottom, and take - when it is at the top)

[0047] (Take - when the large end of the gear tooth thickness is at the bottom, and take + when it is at the top)

[0048] Step 2, according to β 1L and β 1R , as well as the helix angle and the normal module of the external beveloid gear to be machined, determine the actual normal module m n1L of the left tooth surface and the actual normal module m n1R of the right tooth surface;

[0049] Specifically, the following formula is used to further determine the actual normal module m of the left tooth surface of the gear by using the results of Step 1n1L and the actual normal module \(m\) of the right tooth surface n1R :

[0050]

[0051]

[0052] Step 3: According to \(\beta\) 1L and \(\beta\) 1R , as well as the helix angle and normal pressure angle of the external helical bevel gear to be machined, determine the actual normal pressure angle \(\alpha\) n1L of its left tooth surface and the actual normal pressure angle \(\alpha\) n1R of its right tooth surface;

[0053] Specifically, the following formula is used to further determine the actual normal pressure angle \(\alpha\) n1L of the left tooth surface and the actual normal pressure angle \(\alpha\) n1R of the right tooth surface respectively by using the results of Step 1:

[0054]

[0055]

[0056] In Steps 2 and 3, \(m\) n1L and \(\alpha\) n1L are both located on the left side of the tooth thickness center line of the external helical bevel gear to be machined, and \(m\) n1R and \(\alpha\) n1R are located on the right side of the tooth thickness center line;

[0057] Figure 4 The normal parameters in can specifically be the normal module \(m\) n or the normal pressure angle \(\alpha\) n . Therefore, the left correction parameter in the figure is the actual normal module or the actual normal pressure angle of the left tooth surface, and the right correction parameter is the actual normal module or the actual normal pressure angle of the right tooth surface.

[0058] Figure 5 This is a schematic diagram of the normal tooth profile of the hob of the present invention. The left pressure angle therein is the pressure angle of the left tooth surface, and the right pressure angle is the pressure angle of the right tooth surface.

[0059] Step 4: Using the results of Steps 2 and 3, and based on the principle that the normal base pitch of the hob is equal to the normal base pitch of the gear, and finally combined with the normal module of the external helical bevel gear to be machined, the left tooth surface pressure angle \(\alpha\) n0L and the right tooth surface pressure angle \(\alpha\) n0R of the hob can be determined respectively:

[0060] Based on the above principle, the following two formulas can be obtained:

[0061] Pbn1 = π * m n * cos(α n0L ) = π * m n1L * cos(α n1L )

[0062] P bn1 = π * m n * cos(α n0R ) = π * m n1R * cos(α n1R )

[0063] It should be noted that: when the root cone angle design is not performed, the normal module of the hob is equal to the normal module of the external bevel gear to be machined (after the root cone angle is changed, only their normal base pitches are equal). Therefore, the normal module of the external bevel gear to be machined is used on the right side of the first equal sign in the above two formulas.

[0064] Specifically, the pressure angles α n0L of the left tooth surface and α n0R of the right tooth surface of the hob can be further obtained from the above two formulas respectively:

[0065]

[0066]

[0067] The remaining parameters of the hob are all designed by the existing hob design method. Thus, the design of the hob for machining the external bevel gear can be completed.

[0068] After machining according to the finally obtained hob parameters, the hob for machining the external bevel gear can be obtained.

[0069] Figure 3 Figure of the machining tooth profile accuracy of the external bevel gear of the hob designed by this method. It can be seen that the error value of f Ha is 0.0 - 6.8 μm, which is reduced by one order of magnitude compared with the error in Figure 1 , and reaches within the 6th grade accuracy given by the gear accuracy standard GB10095.

[0070] The following uses an example to specifically illustrate the solution process of the pressure angle α n0L of the left tooth surface and α n0R of the right tooth surface of the hob:

[0071] Example

[0072] Given the tooth parameters of the gear: the normal module m n is 3.56, the helix angle β1 is -13° (left-handed), and the normal pressure angle is α nis 20°, the pitch cone angle δ is 6.5°, and when machining, the tooth thickness at the large end of the external bevel gear with reverse taper is at the lower end.

[0073] Step 1 uses the following process to respectively determine the actual helix angle β of the left tooth surface 1L , the actual helix angle β of the right tooth surface 1R :

[0074]

[0075]

[0076] Step 2 uses the following process to further respectively determine the actual normal module m of the left tooth surface of the gear n1L , the actual normal module m of the right tooth surface n1R :

[0077]

[0078]

[0079] Step 3 uses the following process to further respectively determine the actual normal pressure angle α of the left tooth surface n1L , the actual normal pressure angle α of the right tooth surface n1R :

[0080]

[0081]

[0082] Step 4 finally uses the following process to respectively obtain the pressure angle α of the left tooth surface of the hob n0L , the pressure angle α of the right tooth surface n0R :

[0083]

[0084]

Claims

1. A design method for a hob for machining external inclined taper teeth, characterized in that, It includes the following steps: S1. Determine the actual helix angle β of the left tooth surface of the bevel gear to be machined using the helix angle and pitch cone angle of the bevel gear to be machined 1L and the actual helix angle β of the right tooth surface 1R , where β 1L is located on the left side of the tooth thickness center line of the gear, and β 1R is located on the right side of the tooth thickness center line of the gear; S2. According to β 1L and β 1R , as well as the helix angle and normal module of the bevel gear to be machined, determine the actual normal module m n1L of the left tooth surface and the actual normal module m n1R of the right tooth surface of the gear described in S1; According to β 1L and β 1R , as well as the helix angle and normal pressure angle of the externally beveled and inverted cone gear to be machined, determine the actual normal pressure angle α n1L of the left tooth surface and the actual normal pressure angle α n1R of the right tooth surface; where m n1L and α n1L are both located on the left side of the tooth thickness center line of the gear described in S1, m n1R and α n1R are located on the right side of the tooth thickness center line of the said gear; S3. Determine, according to the normal module m n1L , α n1L , and m n1R and α n1R respectively determine the left flank pressure angle α n0L and the right flank pressure angle α n0R of the hob. Then determine the remaining parameters of the hob to complete the design of the hob for machining the external beveled taper gear; where α n0L is on the left side of the tooth thickness center line of the hob, and α n0R is on the right side of the tooth thickness center line of the hob.

2. The design method of the hob for machining external beveled taper teeth according to claim 1, characterized in that, β as described in S1 1L Obtained according to the following formula: Where β1 is the helix angle of the external bevel gear to be machined, and δ is the pitch cone angle of the external bevel gear to be machined. When the large end of the tooth thickness of the gear is at the bottom, take +, and when the large end of the tooth thickness of the gear is at the top, take -.

3. The design method of the hob for machining external beveled taper teeth according to claim 1, characterized in that, β as described in S1 1R Obtained according to the following formula: Wherein, β1 is the helix angle of the external bevel gear to be machined, and δ is the pitch cone angle of the external bevel gear to be machined. When the large end of the tooth thickness of the gear is at the lower part, take "-", and when the large end of the tooth thickness of the gear is at the upper part, take "+".

4. The design method of the hob for machining external inclined taper teeth according to claim 1, characterized in that, m as described in S2 n1L obtained according to the following formula: where m n and β1 are respectively the normal module and helix angle of the externally bevel inverted cone gear to be machined.

5. The design method of the hob for machining external beveled taper teeth according to claim 1, characterized in that, m as described in S2 n1R Obtained according to the following formula: where m n and β1 are respectively the normal module and helix angle of the bevel gear with an external inclined inverted cone to be machined.

6. The design method of the hob for machining external beveled taper teeth according to claim 1, characterized in that, α as described in S2 n1L Obtained according to the following formula: where α n and β1 are the normal pressure angle and helix angle of the external bevel gear with an inclined inverted cone to be machined, respectively.

7. The design method of the hob for machining external inclined bevel gears according to claim 1, characterized in that, α as described in S2 n1R Obtained according to the following formula: where α n and β1 are the normal pressure angle and helix angle of the external bevel gear with an inclined reverse taper to be machined, respectively.

8. The design method of the hob for machining external beveled taper teeth according to claim 1, characterized in that, α as described in S3 n0L Obtained according to the following formula: where m n is the normal module of the external bevel gear to be machined.

9. The design method of the hob for machining external beveled taper teeth according to claim 1, characterized in that, α as described in S3 n0R obtained according to the following formula: where m n is the normal module of the externally beveled and tapered gear to be machined.

10. A hob for machining external beveled taper teeth obtained by the design method of the hob for machining external beveled taper teeth described in any one of claims 1-9.

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