CN110977054B - Machining and manufacturing method of gear rack gear shaping with variable transmission ratio - Google Patents

Machining and manufacturing method of gear rack gear shaping with variable transmission ratio Download PDF

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CN110977054B
CN110977054B CN201911268360.9A CN201911268360A CN110977054B CN 110977054 B CN110977054 B CN 110977054B CN 201911268360 A CN201911268360 A CN 201911268360A CN 110977054 B CN110977054 B CN 110977054B
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rack
gear
gear shaping
cutter
variable transmission
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CN110977054A (en
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韩星会
华林
徐曼
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Wuhan University of Technology WUT
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Wuhan University of Technology WUT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
    • B23F5/12—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by planing or slotting
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F1/00—Making gear teeth by tools of which the profile matches the profile of the required surface
    • B23F1/04—Making gear teeth by tools of which the profile matches the profile of the required surface by planing or slotting
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
    • B23F5/12—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by planing or slotting
    • B23F5/14—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by planing or slotting the tool having the same profile as a tooth or teeth of a rack

Abstract

The invention discloses a method for processing and manufacturing gear shaping of a variable transmission ratio rack, which comprises the following steps: s1, establishing a gear shaper cutter tooth profile model according to the gear shaper cutter parameters and the geometric shape; s2, obtaining a transmission ratio function; s3, obtaining an envelope motion coordinate transformation matrix from a pinion cutter coordinate system to a processed rack coordinate system; s4, transforming the coordinates of the pinion cutter mathematical model into a coordinate system of the processed rack to obtain an enveloping mathematical model of the variable transmission ratio rack; s5, converting the tool enveloping motion track into machine tool processing codes according to the conversion relation between the tool location point instruction and each motion axis; and S6, according to the obtained machining code, the gear shaping machine tool with the four shafts in triple linkage realizes the gear shaping machining of the variable transmission rack. The invention combines design and process, converts the enveloping motion track of the cutter into machine tool processing codes, and finally realizes the gear shaping processing of the variable transmission ratio rack.

Description

Machining and manufacturing method of gear rack gear shaping with variable transmission ratio
Technical Field
The invention belongs to the technical field of gear shaping processing technology, and particularly relates to a variable transmission ratio rack gear shaping processing and manufacturing method.
Background
The variable transmission ratio rack is used as a non-standard rack, is a key part of a mechanical variable transmission ratio steering gear, and has important significance in solving the balance problem of steering portability and steering sensitivity in the driving process of the automobile steering gear. Due to the need to achieve varying gear ratios, variable ratio racks have complex varying non-standard tooth profiles along the length, resulting in high manufacturing difficulties for variable ratio racks. The existing manufacturing process for the variable transmission ratio rack mainly comprises forging and rotary forging, and although the machining efficiency is high, the large-size variable transmission ratio rack cannot be machined with high precision. The gear shaping process is used as a mechanical processing process, can process various complex tooth shapes without the limitation of the geometric shape of a workpiece, has high processing precision, is widely applied to the field of gear processing, and has mature development, so the gear shaping process has important practical significance in processing the variable transmission ratio rack. At present, no report about processing the variable transmission ratio rack by adopting a gear shaping process exists.
Disclosure of Invention
The invention aims to provide a variable transmission ratio rack gear shaping processing and manufacturing method, which is characterized in that an enveloping motion mathematical model corresponding to the actual gear shaping processing process of a variable transmission ratio rack is established based on the motion relation of each shaft of a four-shaft triple-linkage gear shaping processing machine tool, and the enveloping motion track of a cutter is converted into a machine tool processing code based on the conversion relation of a machine tool processing instruction and the feed rate of a cutter shaft workpiece shaft, so that the gear shaping processing of the variable transmission ratio rack is realized.
The technical scheme adopted by the invention for solving the technical problems is as follows: a method for processing and manufacturing gear shaping of a variable transmission ratio rack is constructed, and comprises the following steps:
s1, obtaining a gear shaping cutter mathematical model for gear shaping processing of the variable transmission ratio rack according to the gear shaping cutter parameters and the geometric relationship thereof
Figure GDA0002715599100000011
S2, obtaining a variable transmission ratio function according to the transmission requirement and the motion parameters
Figure GDA0002715599100000012
S3, obtaining a variable transmission ratio function according to the machine tool shaft motion relation in the variable transmission ratio rack gear shaping process and the variable transmission ratio function obtained in S2
Figure GDA0002715599100000013
Obtaining an envelope motion coordinate transformation matrix M from a gear shaper cutter coordinate system TCS to a processed rack coordinate system WCSW-T；
S4, transforming matrix M through envelope motion coordinate obtained in S3W-TA mathematical model of the slotting cutter obtained in S1
Figure GDA0002715599100000021
Transforming the coordinates to a rack coordinate system WCS to be processed to obtain an enveloping mathematical model of the rack with variable transmission ratio
Figure GDA0002715599100000022
S5, converting the tool enveloping motion track into a corresponding machine tool processing code according to the relation between the machine tool feed rate and the circumferential motion rate of the tool and the moving rate of the workbench, and using the machine tool processing code to process the gear rack with variable transmission ratio by the gear shaping machine tool;
and S6, according to the processing code obtained in the step S5, the gear shaping machine tool with four shafts in three-linkage is fed for multiple times, and the gear shaping processing of the gear rack with the variable transmission ratio is realized by changing the feeding amount.
In the scheme, the mathematical model of the slotting cutter in S1
Figure GDA0002715599100000023
Calculated by the following formula:
Figure GDA0002715599100000024
wherein
Figure GDA0002715599100000025
Is the tooth top part of the gear shaper cutter, the tooth profile angle range is
Figure GDA0002715599100000026
And the number of teeth i is e [0, z ]]；Rk(rb,αk) Is a left involute and a right involute of a gear shaping cutter, and the pressure angle range of the involute is alphak∈[0,αa]；
Figure GDA0002715599100000027
Is the tooth root part of the gear shaping cutter, and the tooth form angle range is
Figure GDA0002715599100000028
And the number of teeth i is e [0, z ]]. Respectively calculated by the following formula:
Figure GDA0002715599100000029
Figure GDA00027155991000000210
Figure GDA00027155991000000211
in the formula (2), raFor the addendum circle radius of the pinion cutter, other parameters are calculated by the following formula:
r＝mz (5)
Figure GDA00027155991000000212
Figure GDA00027155991000000213
Figure GDA00027155991000000214
Figure GDA00027155991000000215
Figure GDA00027155991000000216
Figure GDA0002715599100000031
Figure GDA0002715599100000032
wherein m is the module of the gear shaping cutter, z is the number of teeth of the gear shaping cutter,
Figure GDA0002715599100000033
is the tooth crest height coefficient of the pinion cutterbIs the base circle radius of the gear shaper cutter, and alpha is the base circle pressure angle.
In formula (3), each parameter is calculated from the following formula:
Figure GDA0002715599100000034
u＝tanαk (14)
in the formula (4), rfThe radius of the root circle of the gear shaper cutter is obtained by calculating the following parameters:
Figure GDA0002715599100000035
wherein, c*The coefficient of the headspace is.
In the above solution, in S2, the rotation angle range of the slotting cutter is
Figure GDA0002715599100000036
Variable transmission ratio function
Figure GDA0002715599100000037
The expression is as follows:
Figure GDA0002715599100000038
in the above scheme, S3 specifically is: envelope motion coordinate transformation matrix M from gear shaping cutter shaft coordinate system (TCS) to machined rack coordinate system (WCS)W-TExpressed by the following formula:
Figure GDA0002715599100000039
wherein s is the transverse horizontal movement stroke of the processed rack and is obtained by the following formula:
Figure GDA00027155991000000310
in the above scheme, S4 specifically is: obtaining an enveloping mathematical model of the variable transmission ratio rack through an enveloping motion coordinate transformation matrix
Figure GDA00027155991000000311
The following were used:
Figure GDA00027155991000000312
in the above scheme, S5 specifically is: the machine tool machining instruction feed rate F indicates the feed rate of the tool position point and the circumferential feed rate F of the same tool shaft B shaftBAnd workpiece axis X-axis infeed rate FXThe following calculated relationship exists:
Figure GDA00027155991000000313
Figure GDA0002715599100000041
wherein, Δ B is the circumferential feeding increment of the tool shaft, and the relationship with the circumferential corner increment δ B of the tool is as follows: Δ B is δ B, Δ X is the workpiece axis horizontal feed increment, and the relationship with the workpiece horizontal displacement increment δ X is: Δ X ═ δ X, and according to the transmission mesh relationship:
Figure GDA0002715599100000042
the tool location displacement increment Δ S can be calculated by the following formula:
Figure GDA0002715599100000043
and converting the tool enveloping motion track into a corresponding machine tool machining code according to the relation for gear shaping machining of the variable transmission ratio rack.
In the above scheme, S6 specifically is: inputting the machining code obtained in the fifth step into a four-axis triple-linkage gear shaping machine tool, setting different feeding cycles, and performing gear shaping on the rack by changing the feeding amount.
The implementation of the variable transmission ratio rack gear shaping processing and manufacturing method has the following beneficial effects:
based on the motion relation of each shaft of the machine tool in the variable transmission ratio rack gear shaping processing process, an enveloping motion mathematical model corresponding to the actual gear shaping processing process of the variable transmission ratio rack is established based on the tooth profile forming principle, the enveloping motion track of the cutter is converted into a machine tool processing code based on the calculation relation of the machine tool processing instruction and the cutter shaft workpiece shaft feed rate, the design and the process are combined, and the gear shaping processing of the variable transmission ratio rack is finally realized.
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic representation of a cutter tooth profile according to an embodiment of the present invention;
FIG. 3 is a schematic view of the movement of the axes of the gear shaper machine according to an embodiment of the present invention;
FIG. 4 is a schematic view of the coordinates of the cutter and the workpiece of the gear shaping machine in an embodiment of the present invention;
FIG. 5 is a schematic diagram of a variable gear ratio rack envelope model according to an embodiment of the present invention;
fig. 6 is a practical machining diagram of the variable transmission ratio rack in the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Taking a variable transmission ratio rack as an example, the variable transmission ratio rack is processed and manufactured by the method. The basic parameters of the slotting cutter are shown in table 1:
TABLE 1 basic parameters of the gear shaping tool
Figure GDA0002715599100000051
The variable ratio function parameters of the variable ratio racks being machined are shown in table 2 below:
TABLE 2 variable ratio function parameters
Figure GDA0002715599100000052
The parameter settings of the multiple variable feed amount in the gear shaping process are shown in the following table 3:
TABLE 3 feed amount settings
Figure GDA0002715599100000053
The up-and-down reciprocating speed of the main shaft of the pinion cutter is 240DS/min, and the feeding rate of a machine tool is 21 mm/min.
The method for processing and manufacturing the gear shaping of the variable transmission ratio rack is shown in fig. 1-6 and comprises the following steps:
s1, obtaining a gear shaping cutter mathematical model for gear shaping processing of the variable transmission ratio rack according to the gear shaping cutter parameters and the geometric relationship thereof
Figure GDA0002715599100000054
S2, obtaining a variable transmission ratio function according to the transmission requirement and the motion parameters
Figure GDA0002715599100000055
S3, obtaining a variable transmission ratio function according to the machine tool shaft motion relation in the variable transmission ratio rack gear shaping process and the variable transmission ratio function obtained in S2
Figure GDA0002715599100000056
Obtaining an envelope motion coordinate transformation matrix M from a gear shaper cutter coordinate system TCS to a processed rack coordinate system WCSW-T；
S4, transforming matrix M through envelope motion coordinate obtained in S3W-TA mathematical model of the slotting cutter obtained in S1
Figure GDA0002715599100000057
Transforming the coordinates to a rack coordinate system WCS to be processed to obtain an enveloping mathematical model of the rack with variable transmission ratio
Figure GDA0002715599100000058
S5, converting the tool enveloping motion track into a corresponding machine tool processing code according to the relation between the machine tool feed rate and the circumferential motion rate of the tool and the moving rate of the workbench, and using the machine tool processing code to process the gear rack with variable transmission ratio by the gear shaping machine tool;
and S6, according to the processing code obtained in the step S5, the gear shaping machine tool with four shafts in three-linkage is fed for multiple times, and the gear shaping processing of the gear rack with the variable transmission ratio is realized by changing the feeding amount.
In the above embodiment step S1, the mathematical model of the slotting cutter
Figure GDA0002715599100000061
Calculated by the following formula:
Figure GDA0002715599100000062
wherein
Figure GDA0002715599100000063
Is the tooth top part of the gear shaper cutter, the tooth profile angle range is
Figure GDA0002715599100000064
And the number of teeth i is e [0, z ]]；Rk(rb,αk) Is a left involute and a right involute of a gear shaping cutter, and the pressure angle range of the involute is alphak∈[0,αa]；
Figure GDA0002715599100000065
Is the tooth root part of the gear shaping cutter, and the tooth form angle range is
Figure GDA0002715599100000066
And the number of teeth i is e to 0,z]. Respectively calculated by the following formula:
Figure GDA0002715599100000067
Figure GDA0002715599100000068
Figure GDA0002715599100000069
in the formula (2), raFor the addendum circle radius of the pinion cutter, other parameters are calculated by the following formula:
r＝mz (5)
Figure GDA00027155991000000610
Figure GDA00027155991000000611
Figure GDA00027155991000000612
Figure GDA00027155991000000613
Figure GDA00027155991000000614
Figure GDA00027155991000000615
Figure GDA00027155991000000616
wherein m is the module of the gear shaping cutter, z is the number of teeth of the gear shaping cutter,
Figure GDA00027155991000000617
is the tooth crest height coefficient of the pinion cutterbIs the base circle radius of the gear shaper cutter, and alpha is the base circle pressure angle.
In formula (3), each parameter is calculated from the following formula:
Figure GDA00027155991000000618
u＝tanαk (14)
in the formula (4), rfThe radius of the root circle of the gear shaper cutter is obtained by calculating the following parameters:
Figure GDA0002715599100000071
wherein, c*The coefficient of the headspace is.
The step S2 of the above embodiment is specifically: the rotation angle range of the gear shaping cutter is
Figure GDA0002715599100000072
Obtaining a variable ratio function
Figure GDA0002715599100000073
Figure GDA0002715599100000074
The step S3 of the above embodiment is specifically: envelope motion coordinate transformation matrix M from gear shaping cutter shaft coordinate system (TCS) to machined rack coordinate system (WCS)W-TObtained by the following formula:
Figure GDA0002715599100000075
wherein s is the transverse horizontal movement stroke of the processed rack and is obtained by the following formula:
Figure GDA0002715599100000076
the step S4 of the above embodiment is specifically: obtaining an enveloping mathematical model of the variable transmission ratio rack through an enveloping motion coordinate transformation matrix
Figure GDA0002715599100000077
Calculated by the following formula:
Figure GDA0002715599100000078
the step S5 of the above embodiment is specifically: the machine tool machining instruction feed rate F indicates the feed rate of the tool position point and the circumferential feed rate F of the same tool shaft B shaftBAnd workpiece axis X-axis infeed rate FXThe following calculated relationship exists:
Figure GDA0002715599100000079
Figure GDA00027155991000000710
wherein, Δ B is the circumferential feeding increment of the tool shaft, and the relationship with the circumferential corner increment δ B of the tool is as follows: Δ B is δ B, Δ X is the workpiece axis horizontal feed increment, and the relationship with the workpiece horizontal displacement increment δ X is: Δ X ═ δ X, and according to the transmission mesh relationship:
Figure GDA00027155991000000711
the tool location displacement increment Δ S can be calculated by the following formula:
Figure GDA00027155991000000712
and converting the tool enveloping motion track into a corresponding machine tool machining code according to the relation for gear shaping machining of the variable transmission ratio rack.
The step S6 of the above embodiment is specifically: and (4) inputting the machining code obtained in the step (S5) into a four-shaft three-linkage gear shaping machine tool, setting different feeding cycles, and performing gear shaping machining on the rack by changing the feeding amount.
While the present invention has been described with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, which are illustrative and not restrictive, and it will be apparent to those skilled in the art that various changes and modifications can be made therein without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (7)

1. A method for processing and manufacturing gear shaping of a variable transmission ratio rack is characterized by comprising the following steps:
s1, obtaining a gear shaping cutter mathematical model for gear shaping processing of the variable transmission ratio rack according to the gear shaping cutter parameters and the geometric relationship thereof
Figure FDA0002715599090000011
S2, obtaining a variable transmission ratio function according to the transmission requirement and the motion parameters
Figure FDA0002715599090000012
S3, obtaining a variable transmission ratio function according to the machine tool shaft motion relation in the variable transmission ratio rack gear shaping process and the variable transmission ratio function obtained in S2
Figure FDA0002715599090000013
Obtaining an envelope motion coordinate transformation matrix M from a gear shaper cutter coordinate system TCS to a processed rack coordinate system WCSW-T；
S4, transforming matrix M through envelope motion coordinate obtained in S3W-TTransforming the coordinates of the pinion cutter mathematical model R obtained in the step S1 into a rack coordinate system WCS to be processed to obtain an envelope mathematical model R of the rack with variable transmission ratiow；
S5, converting the tool envelope motion track into a corresponding machine tool processing code according to the relationship between the machine tool feed rate and the circumferential motion rate of the tool and the moving rate of the workbench;
and S6, according to the machine tool machining code obtained in the S5, the gear shaping machining of the gear rack with the variable transmission ratio is realized on the gear shaping machine tool with the four-shaft triple-linkage.
2. The method for manufacturing a gear ratio-variable rack gear according to claim 1, wherein in step S1, the mathematical model of the gear shaper cutter
Figure FDA0002715599090000014
Calculated by the following formula:
Figure FDA0002715599090000015
wherein
Figure FDA0002715599090000016
Is the tooth top part of the gear shaper cutter, the tooth profile angle range is
Figure FDA0002715599090000017
And the number of teeth i is e [0, z ]]；Rk(rb,αk) Is a left involute and a right involute of a gear shaping cutter, and the pressure angle range of the involute is alphak∈[0,αa]；
Figure FDA0002715599090000018
Is the tooth root part of the gear shaping cutter, and the tooth form angle range is
Figure FDA0002715599090000019
And the number of teeth i is e [0, z ]](ii) a Respectively calculated by the following formula:
Figure FDA00027155990900000110
Figure FDA00027155990900000111
Figure FDA00027155990900000112
in the formula (2), raFor the addendum circle radius of the pinion cutter, the parameters in the formula (2) are calculated by the following formula:
r＝mz (5)
Figure FDA0002715599090000021
Figure FDA0002715599090000022
Figure FDA0002715599090000023
Figure FDA0002715599090000024
Figure FDA0002715599090000025
Figure FDA0002715599090000026
Figure FDA0002715599090000027
wherein m is the module of the gear shaping cutter, z is the number of teeth of the gear shaping cutter,
Figure FDA0002715599090000028
is the tooth crest height coefficient of the pinion cutterbIs the base circle radius of the gear shaper cutter, and alpha is the base circle pressure angle;
in formula (3), each parameter is calculated from the following formula:
Figure FDA0002715599090000029
u＝tanαk (14)
in the formula (4), rfThe radius of the root circle of the gear shaper cutter is obtained by calculating the following parameters:
Figure FDA00027155990900000210
wherein, c*The coefficient of the headspace is.
3. The method according to claim 1, wherein in step S2, the rotation angle of the slotting cutter is within the range of
Figure FDA00027155990900000211
Obtaining a variable ratio function
Figure FDA00027155990900000212
Figure FDA00027155990900000213
4. The method for manufacturing a gear ratio-variable rack gear according to claim 1, wherein in step S3, the transformation matrix M of the enveloping motion coordinate from the gear shaping spindle coordinate system (TCS) to the processed rack coordinate system (WCS) is usedW-TObtained by the following formula:
Figure FDA00027155990900000214
wherein s is the transverse horizontal movement stroke of the processed rack and is obtained by the following formula:
Figure FDA0002715599090000031
5. the method for manufacturing a gear shaping rack according to claim 1, wherein in step S4, the enveloping mathematical model of the gear shaping rack is obtained by enveloping the motion coordinate transformation matrix
Figure FDA0002715599090000032
Calculated by the following formula:
Figure FDA0002715599090000033
6. the method according to claim 1, wherein in step S5, the machine tool machining command feed rate F indicates the feed rate of the tool position, and the circumferential feed rate F is equal to the circumferential feed rate of the B-axis of the tool shaftBAnd workpiece axis X-axis infeed rate FXThe following calculated relationship exists:
Figure FDA0002715599090000034
Figure FDA0002715599090000035
wherein, Δ B is the circumferential feeding increment of the tool shaft, and the relationship with the circumferential corner increment δ B of the tool is as follows: Δ B is δ B, Δ X is the workpiece axis horizontal feed increment, and the relationship with the workpiece horizontal displacement increment δ X is: Δ X ═ δ X, and according to the transmission mesh relationship:
Figure FDA0002715599090000036
the displacement increment deltaS of the tool location is calculated by the following formula:
Figure FDA0002715599090000037
and converting the tool enveloping motion track into a corresponding machine tool machining code according to the relation for gear shaping machining of the variable transmission ratio rack.
7. The method for machining and manufacturing the gear-ratio-variable rack gear according to claim 1, wherein step S6 is specifically: and (4) inputting the machining code obtained in the step (S5) into a four-shaft three-linkage gear shaping machine tool, setting different feeding cycles, and performing gear shaping machining on the rack by changing the feeding amount.
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