A design system and method for the backlash angle of broaches used in involute spline machining

Abstract

This invention discloses a design system for machining the backlash angle of a spline broach based on an involute curve. The system includes a broach original tooth profile parameter input module for inputting basic parameters of the broach spline tooth profile; a new involute parameter calculation module for calculating and outputting new involute parameters of the broach spline teeth based on the basic parameters of the broach spline tooth profile; a gauge bar parameter calculation module for calculating and outputting gauge bar parameters based on the new involute parameters of the broach spline teeth; and a broach tooth profile parameter update output module for outputting tooth profile parameters related to the new involute curve used for the backlash angle of the broach spline teeth from the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline teeth, and the gauge bar parameters. The new involute curve obtained through this design system allows for direct machining of the backlash angle of the broach spline teeth. This backlash angle machining can be achieved without changing the fixture, while ensuring machining accuracy.

Description

Technical Field

[0001] This invention relates to the field of broach machining design technology, specifically to a design system and method for the side clearance angle of a broach used for machining splines based on involute curves. Background Technology

[0002] To reduce friction between the broach teeth of the involute spline and the workpiece surface being machined, and to lower the surface roughness of the spline hole, the involute teeth that do not participate in cutting need to be ground away to obtain a new tooth profile after the clearance angle is opened (see...). Figure 1 When machining the backlash angle, the grinding wheel enters from the broach's calibration tooth section and grinds towards the cutting tooth section, lowering the grinding wheel's position height tooth by tooth to ensure that each cutting tooth retains a side cutting width of 0.6–0.8 mm and a maximum backlash value of approximately 0.2–0.3 mm at the root. Currently, domestic tool manufacturers calculate the grinding wheel's machining angle based on the backlash value in the drawings, and then dress the grinding wheel according to the machining angle (straight line). Ordinary spline broach grinding machines require a special fixture for dressing involute grinding wheels. This special fixture is not interchangeable with the fixture for dressing straight lines. After changing the fixture, the center of the fixture for dressing involute grinding wheels must be re-aligned, severely affecting the grinding efficiency of the broach spline tooth backlash angle.

[0003] The backlash of broach splines is 0.2–0.3 mm. This backlash value is difficult to measure at the bottom of the broach spline, making it impossible for the operator to determine the actual backlash during machining and also impossible to measure after machining. Insufficient backlash affects the broaching quality of the workpiece, resulting in poor surface roughness of the splines and, in severe cases, surface burrs. Excessive backlash weakens the strength of the broach teeth. Therefore, machining the backlash angle of broach splines according to the involute curve has always been a technical challenge that the cutting tool industry needs to solve. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the aforementioned background technology and provide a design system and method for machining the backlash angle of spline broaches without changing the fixture, simply by calling an involute-based shaping program on a CNC machine tool.

[0005] To achieve this objective, the present invention provides a design system for the backlash angle of a broach used for machining splines based on involute curves. This system is characterized by comprising a broach original tooth profile parameter input module, a new involute parameter calculation module, a gauge bar parameter calculation module, and a broach tooth profile parameter update output module.

[0006] The broach original tooth profile parameter input module is used to input the basic parameters of the broach spline tooth profile;

[0007] The new involute parameter output module is used to calculate and output the new involute parameters of the broach spline tooth based on the basic parameters of the broach spline tooth profile.

[0008] The gauge bar parameter output module is used to calculate and output the gauge bar parameters based on the new involute parameters of the broach spline teeth.

[0009] The broach tooth profile parameter update output module is used to output the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline tooth, and the tooth profile parameters related to the new involute used for the side clearance angle of the broach spline tooth in the parameters of the gauge bar.

[0010] Furthermore, the new involute parameter output module includes a broach original opening angle parameter calculation module and a broach new involute parameter calculation module;

[0011] The broach original opening angle parameter calculation module is used to calculate the broach spline profile parameters related to the new involute of the broach based on the basic parameters of the broach spline profile.

[0012] The broach new involute parameter calculation module is used to calculate the broach new involute parameters based on the broach spline tooth profile parameters and new involute constraint conditions related to the broach new involute.

[0013] The basic parameters of the broach spline tooth profile include the broach module, broach calibration tooth diameter, broach pitch angle, broach spline minor diameter, broach pitch arc tooth thickness, broach spline tooth side cutting width, broach spline number of teeth, and broach spline minor diameter backlash.

[0014] Furthermore, the broach spline tooth profile parameters related to the new involute of the broach include the minimum effective starting circle diameter of the broach spline teeth after opening the side clearance angle according to the original involute and the arc tooth thickness at the minimum effective starting circle diameter of the spline teeth after opening the side clearance angle according to the original involute.

[0015] Furthermore, the new involute constraint conditions include that the intersection of the new involute and the original involute of the broach is located on the smallest effective starting circle after the backlash angle of the broach spline teeth is opened according to the original involute; and that the distance between the new involute and the original involute at the minor diameter of the broach spline is the same as the backlash size of the minor diameter of the broach spline.

[0016] Furthermore, the gauge bar parameter output module includes a new broaching tool arc tooth thickness calculation module, a gauge bar diameter calculation module, and a gauge bar spacing calculation module;

[0017] The new broach segmented arc tooth thickness calculation module is used to calculate the broach segmented arc tooth thickness according to the new involute curve of the broach.

[0018] The measuring rod diameter calculation module is used to calculate the measuring rod diameter according to the measuring rod diameter constraint conditions.

[0019] The bar spacing calculation module is used to calculate the bar spacing.

[0020] Furthermore, the diameter constraint conditions of the gauge bar include that the contact point between the gauge bar and the broach spline teeth is on the new involute of the broach; and that the gauge bar does not interfere with the circular contour line of the minor diameter of the broach spline.

[0021] Furthermore, the condition for determining whether the contact point between the measuring bar and the broach spline is on the new involute of the broach is that the diameter of the contact circle of the measuring bar is smaller than the minimum effective starting circle diameter of the broach spline after the side clearance angle is opened according to the original involute.

[0022] Furthermore, the criterion for determining that the measuring bar and the circular outline of the broach spline minor diameter do not interfere is that the distance between the lowest points of the measuring bar is greater than the broach spline minor diameter.

[0023] Furthermore, the design method for the backlash angle of the broach used for machining involute splines includes the following steps:

[0024] Step 1: Input the basic parameters of the broach spline tooth profile;

[0025] Step 2: Calculate and output the new involute parameters of the broach spline teeth based on the basic parameters of the broach spline tooth profile;

[0026] Step 3: Calculate and output the parameters of the gauge bar based on the new involute parameters of the broach spline teeth;

[0027] Step 4: Output the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline teeth, and the tooth profile parameters of the gauge bar that are related to the new involute used for the backlash angle of the broach spline teeth.

[0028] The beneficial effects of this invention are as follows: The new involute spline broach backlash angle obtained through the design system of this invention can be directly machined using a new involute spline. This machining of the backlash angle can be achieved without changing the fixture, ensuring machining accuracy, effectively controlling the broach side cutting edge width and tooth root backlash value, and improving the machining quality of the broach. This creates a new and efficient solution for the mass production of broaches. Before the implementation of this invention, machining based on experience required approximately 1.5 hours; now it only takes less than 0.5 hours, an efficiency improvement of at least 3 times. This invention can be applied to the mass production process of all involute spline broaches and can be widely promoted and applied both within and outside the industry. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the module connection of the design system for the backlash angle of the broach used for machining splines according to the involute curve in this invention;

[0030] Figure 2 This is a schematic diagram of the broach opening angle in this invention;

[0031] Figure 3This is a schematic diagram of the tooth profile dimensions after the broach has its side clearance angle opened in this invention;

[0032] Figure 4 This is a schematic diagram of the fit between the gauge bar and the spline teeth of the broach in this invention;

[0033] Figure 5 This is a simplified diagram for calculating the span distance in this invention;

[0034] Among them, 1—Broach original tooth profile parameter input module, 2—New involute parameter calculation module (2.1—Broach original clearance angle parameter calculation module, 2.2—Broach new involute parameter calculation module), 3—Gauge bar parameter calculation module (3.1—New broach segmented arc tooth thickness calculation module, 3.2—Gauge bar diameter calculation module, 3.3—Gross spacing calculation module), 4—Broach tooth profile parameter update output module, 5—Gauge bar. Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0036] like Figure 1 The design system shown, based on the involute machining of spline broach backlash angle, includes: a broach original tooth profile parameter input module 1 for inputting the basic parameters of the broach spline tooth profile; a new involute parameter calculation module 2 for calculating and outputting the new involute parameters of the broach spline teeth based on the basic parameters of the broach spline tooth profile; a gauge bar parameter calculation module 3 for calculating and outputting the gauge bar parameters based on the new involute parameters of the broach spline teeth; and a broach tooth profile parameter update output module 4 for outputting the tooth profile parameters related to the new involute used for the broach spline tooth backlash angle from the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline teeth, and the gauge bar parameters. The new involute parameter output module 2 includes a broach original clearance angle parameter calculation module 2.1 for calculating broach spline tooth profile parameters related to the new involute of the broach based on the basic parameters of the broach spline tooth profile, and a new involute parameter calculation module 2.2 for calculating the new involute parameters of the broach based on the broach spline tooth profile parameters and new involute constraint conditions related to the new involute of the broach. The gauge bar parameter output module 3 includes a new broach segmented arc tooth thickness calculation module 3.1 for calculating the broach segmented arc tooth thickness according to the new involute of the broach, a gauge bar diameter calculation module 3.2 for calculating the gauge bar diameter based on the gauge bar diameter constraint conditions, and a gauge bar spacing calculation module 3.3 for calculating the gauge bar spacing.

[0037] The basic parameters of the broach spline profile mentioned above include the broach module, broach calibration tooth diameter, broach pitch angle, broach spline minor diameter, broach pitch arc tooth thickness, broach spline side cutting width, broach spline number of teeth, and broach spline minor diameter backlash. The broach spline profile parameters related to the new involute curve include the minimum effective starting circle diameter after the broach spline teeth have their backlash angle adjusted according to the original involute curve, and the arc tooth thickness at the minimum effective starting circle diameter after the spline teeth have their backlash angle adjusted according to the original involute curve.

[0038] The aforementioned constraints on the new involute curve include: the intersection of the new involute curve and the original involute curve of the broach lies on the minimum effective starting circle after the backlash angle of the broach spline teeth is adjusted according to the original involute curve; and the distance between the new involute curve and the original involute curve at the minor diameter of the broach spline is the same as the backlash size of the minor diameter of the broach spline. The gauge bar diameter constraints include: the contact point between the gauge bar and the broach spline teeth lies on the new involute curve of the broach; and the circular profiles of the gauge bar and the minor diameter of the broach spline do not interfere. The criterion for determining that the contact point between the gauge bar and the broach spline teeth lies on the new involute curve is: the diameter of the contact circle of the gauge bar is smaller than the diameter of the minimum effective starting circle after the backlash angle of the broach spline teeth is adjusted according to the original involute curve. The criterion for determining that the circular profiles of the gauge bar and the minor diameter of the broach spline do not interfere is: the distance between the lowest points of the gauge bar is greater than the minor diameter of the broach spline.

[0039] Based on the above-mentioned design system for the side clearance angle of a broach used for machining splines using involute curves, the design method for the side clearance angle of a broach used for machining splines using involute curves in this invention includes the following steps:

[0040] Step 1: Input the basic parameters of the broach spline tooth profile;

[0041] Step 2: Calculate and output the new involute parameters of the broach spline teeth based on the basic parameters of the broach spline tooth profile;

[0042] Step 3: Calculate and output the parameters of the gauge bar based on the new involute parameters of the broach spline teeth;

[0043] Step 4: Output the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline teeth, and the tooth profile parameters related to the new involute used for the backlash angle of the broach spline teeth in the parameters of the gauge bar.

[0044] The above methods are explained in detail below:

[0045] (1) Determine the basic parameters of the broach spline tooth profile:

[0046] Mt = Module, Z = Number of broach teeth, af1 = Pitch angle, Sf1 = Pitch arc tooth thickness, di = Broach minor diameter, Cx = Backlash on broach minor diameter.

[0047] Crimping diameter Df1=Mt×Z

[0048] Base circle diameter d01 = Df1 × Cos(af1)

[0049] Involute function invaf1 = tg(af1) - af1

[0050] (2) Determine the minimum effective starting circle diameter dyj after determining the broach opening angle:

[0051] dyj=dyxz-2×(0.6-0.8), dyxz=diameter of broach calibration teeth

[0052] Calculate the tooth thickness Syj at the minimum effective starting circle diameter dyj after the broach clearance angle:

[0053] The pressure angle at the original involute circle dyj is ayj = arccos(d01 / dyj).

[0054] invayj = tg(ayj) - ayj

[0055] Syj=(Sf1 / Df1+invaf1-invayj)×dyj

[0056] (3) The pressure angle of the new involute used to determine the broaching tool opening angle is af2.

[0057] The new involute must satisfy two constraints: ① It intersects the original involute at a diameter dyj; ② The two involutes are separated by a distance Cx at the minor diameter di of the broach.

[0058] The initial pressure angle for the bisector of the new involute is af2 = af1 - 1.5°.

[0059] The diameter of the dividing circle, Df2, is equal to Mt × Z.

[0060] The new base circle diameter d02 = Df2 × Cos(af2)

[0061] Involute function invaf2 = tg(af2) – af2

[0062] The pressure angle ai1 on the diameter di of the original involute is given by arccos(d01 / di).

[0063] invai1=tg(ai1)-ai1

[0064] The thickness of the arc tooth at the root of the original involute tooth is Si1 = (sf1 / Df1 + invaf1 - invai1) × di

[0065] The pressure angle ai2 on the diameter di of the new involute is given by arccos(d02 / di).

[0066] invai2=tg(ai2)-ai2

[0067] The thickness of the arc tooth at the root of the new involute tooth is Si2 = (syj / dyj + invayj - invai2) × di

[0068] Since this is a transcendental equation, multiple iterative calculations are required to determine the bisection pressure angle af2 of the new involute, ultimately satisfying the dimensional requirements.

[0069] (Si1-Si2) / 2 = side clearance value (Cx±0.02) can be obtained.

[0070] (4) Calculate the diameter dp of the measuring rod after the side clearance angle is opened.

[0071] The diameter dp of the gauge bar has two constraints: ① The contact circle djy of the gauge bar is on a new involute; ② The gauge bar does not interfere with the minor diameter of the broach.

[0072] (4-1) Recalculate the tooth thickness Sf2 of the piecing arc according to the new involute.

[0073] invaf2=tg(af2)–af2

[0074] Sf2=Df2×(syj / dyj+invayj—invaf2)

[0075] (4-2) Formula for calculating the span M value

[0076] like Figure 5 As shown, construct the auxiliary involute O1E, then the line segment NAO1 = arc length NDE. The basic formula for the value of M is derived as follows:

[0077] Cos(aj)=d02 / dj, dj=2×0A, d02=2×0N, dj is the diameter of the contact circle of the measuring rod, and Sj is the thickness of the arc tooth on the dj circle.

[0078] invaj = tg(aj) - aj(1)

[0079] ax=aj+(π / Z-sj / dj)(2)

[0080] tg(ax)=tg(aj)+Dp / d02(3)

[0081] Sj / dj+invaj=Sf2 / df2+invaf2(4)

[0082] Combining (3)-(2) with (1) and (4), we get invax=Sf2 / df2+invaf2+Dp / d02-π / Z

[0083] The iterative method is used to find ax = arcinv(invax).

[0084] Odd number of teeth: Mji=d02 / cos(ax)×cos(π / 2 / Z)+Dp

[0085] Even number of teeth: Mou = d0² / cos(ax) + Dp

[0086] The final formula is unified as: M=d02 / cos(ax)×cos((π / 2 / Z)×(1-(-1)) Z ) / 2) / 2))+Dp

[0087] (4-3) Select the diameter dp1 of the measuring rod

[0088] Initially, the diameter of the measuring rod is dp1 = π × Df2 / Z – Sf2

[0089] am1 = Atn(tg(af2) + dp1 / d02), the pressure angle aj = am1 when the contact point of the gauge bar is located on the pitch circle.

[0090] invam1 = tg(am1) - am1

[0091] invax1=invaf2+Sf2 / Df2+(dp1 / d02-π / Z)

[0092] If invax1 < 0, then dp1 = dp1 + 0.0001

[0093] If Abs(invax1-invam1)>0.00001, then dp1=dp1+0.0001

[0094] The calculation continues iteratively until invax1 > 0.

[0095] Dp = dp1

[0096] Rem5-4: Calculation of span distance M and interference verification

[0097] invax=invaf2+Sf2 / Df2+(Dp / d02-π / Z)

[0098] Using the iterative method, the pressure angle AM ​​= arcinv(invax) that satisfies the involute function invax can be calculated in reverse.

[0099] The new gauge span Mdp = d02 / Cos(AM)×Cos((π / 2 / Z)×(1-(-1)) Z ) / 2))+Dp(that is, the above formula M=d02 / cos(ax)×cos((π / 2 / Z)×(1-(-1)) Z ) / 2) / 2))+Dp)

[0100] In △OAO1, the diameter djy of the contact circle of the new gauge rod can be calculated according to the law of cosines.

[0101] djy = Sqr(Dp) 2 +(d02 / Cos(AM)) 2 -Dp×d02×tg(AM)×2)

[0102] After verifying whether the gauge bar meets the first two constraints, the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline tooth, and the tooth profile parameters of the gauge bar related to the new involute used for the broach spline tooth clearance angle can be output.

[0103] The above method will be described below with reference to specific embodiments.

[0104] Determine the basic tooth profile parameters of the broach:

[0105] Module Mt = 3.5, number of broach teeth Z = 39, pressure angle of the piecing circle af1 = 30°, tooth thickness of the piecing circle arc Sf1 = 5.729, broach calibration tooth diameter dyxz = 139.88, broach minor diameter di = 132.15, backlash on the broach minor diameter Cx = 0.2, and side cutting width f = 0.6.

[0106] The diameter of the original magnifying circle, Df1, is equal to Mt × Z, which is 136.5.

[0107] The diameter of the primitive circle d01 = Df1 × Cos(af1) = 118.2125

[0108] The original involute function invaf1 = tg(af1) - af1 = 0.05375149

[0109] The minimum effective starting circle diameter dyj after determining the broach clearance angle:

[0110] dyj=dyxz-2×(0.6-0.8)=139.88-2×0.6=138.68

[0111] Calculate the tooth thickness Syj at the minimum effective starting circle diameter dyj after the broach clearance angle:

[0112] The pressure angle at the diameter of the original involute dyj is ayj = arccos(d01 / dyj) = 0.5502157.

[0113] invayj=tg(ayj)-ayj=0.06318632

[0114] Syj=(Sf1 / Df1+invaf1-invayj)×dyj=4.512

[0115] Find the new involute dividing circle pressure angle af2 used for the broaching tool opening angle:

[0116] The new involute must satisfy two constraints: ① It intersects the original involute at a diameter dyj; ② The two involutes are separated by a distance Cx at the minor diameter di of the broach.

[0117] The pressure angle of the new involute is af2 = 27.305° (this is the accurate pressure angle after iteration).

[0118] The new dividing circle diameter Df2 = Mt × Z = 136.5

[0119] The new base circle diameter d02 = Df2 × Cos(af2) = 121.2908

[0120] The new involute function invaf2 = tg(af2) – af2 = 0.03968688

[0121] The pressure angle at the diameter di of the original involute is ai1 = arccos(d01 / di) = 0.463412011

[0122] invai1=tg(ai1)-ai1=0.036293526

[0123] The thickness of the arc teeth on the minor diameter of the broach is Si1 = (sf1 / Df1 + invaf1 - invai1) × di = 7.85439

[0124] The pressure angle at the diameter of the new involute dyj is ayj2=arccos(d02 / dyj)=0.5502157

[0125] invayj2=tg(ajy2)-ayj2=0.06318632

[0126] The pressure angle at the diameter di of the new involute is ai² = arccos(d₀² / di) = 0.40822579

[0127] invai2=tg(ai2)-ai2=0.02429767313

[0128] The arc tooth thickness Si2 after the backlash angle of the broach minor diameter is calculated as follows: Si2 = (syj / dyj + invayj2 - invai2) × di = 7.45439

[0129] The broach backlash value (Si1-Si2) / 2 = 0.20 meets the drawing requirements.

[0130] Find the diameter dp of the measuring rod after the clearance angle is opened:

[0131] The diameter dp of the gauge bar should meet the following two constraints: ① The contact circle djy of the gauge bar is on a new involute; ② The gauge bar does not interfere with the minor diameter of the broach.

[0132] Recalculate the tooth thickness Sf2 of the new involute curve:

[0133] invaf2=tg(af2)–af2=0.03968688

[0134] Sf2=Df2×(syj / dyj+invayj-invaf2)=5.59914

[0135] Select the diameter Dp of the measuring rod:

[0136] Initially, the diameter of the measuring rod is dp1 = π × Df2 / Z – Sf2 = 5.396

[0137] To simplify the process, we directly give the result dp1 = 6.20143 after iteration, which satisfies the requirement.

[0138] am1=Atn(tg(af2)+dp1 / d02)=0.516087,when the contact point of the gauge bar is located on the pitch circle, aj′=am1

[0139] invam1=tg(am1)-am1=0.05129066

[0140] invax1=invaf2+Sf2 / Df2+(dp1 / d02-π / Z)=0.051281

[0141] If invax1 < 0, then dp1 = dp1 + 0.0001

[0142] If Abs(invax1-invam1)>0.00001, then dp1=dp1+0.0001

[0143] The calculation continues iteratively until invax1 > 0.

[0144] Rounding dp1 = 6.20143, we get Dp = 7.0.

[0145] Calculate the new span M:

[0146] invax=invaf2+Sf2 / Df2+(Dp / d02-π / Z)=0.05786512

[0147] Pressure angle Am = arc(invax) = 0.53560225

[0148] The new gauge span M = d0² / Cos(AM) × Cos((π / 2 / Z) × (1-(-1))Z ) / 2)+Dp=147.93

[0149] The contact circle diameter of the new gauge bar is djy = Sqr(Dp) 2 +(d02 / Cos(AM)) 2 -Dp×d02×tg(AM)×2)=137.6013

[0150] The contact circle diameter of the new gauge bar is djy = 137.6013 < 139.88 - 2 × 0.8 = 138.28, indicating that the contact point of the gauge bar is on the new involute tooth profile.

[0151] The lowest point of the measuring rod is 147.93 - 2 × 7 = 133.93 > 132.15 (bottom diameter), indicating that there is no interference between the measuring rod and the bottom of the groove.

[0152] In summary, the new involute tooth profile parameters used for the open clearance angle are as follows:

[0153]

[0154] After dressing the grinding wheel according to the new parameters in the table above, and controlling the span distance M = 147.93 (gauge diameter dp = 7.0), the following can be guaranteed:

[0155] The broach side cutting edge width f = 0.6, and the side clearance on the minor diameter Cx = 0.2.

[0156] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the structure of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A design system for the backlash angle of a broach used for machining splines based on involute curves, characterized in that: It includes a broach original tooth profile parameter input module, a new involute parameter calculation module, a gauge bar parameter calculation module, and a broach tooth profile parameter update output module; The broach original tooth profile parameter input module is used to input the basic parameters of the broach spline tooth profile; The new involute parameter calculation module is used to calculate and output the new involute parameters of the broach spline teeth based on the basic parameters of the broach spline tooth profile. The new involute parameter calculation module includes a broach original clearance angle parameter calculation module and a broach new involute parameter calculation module. The broach original clearance angle parameter calculation module is used to calculate the broach spline tooth profile parameters related to the new involute based on the basic parameters of the broach spline tooth profile. The broach new involute parameter calculation module is used to calculate the new involute parameters based on the broach spline tooth profile parameters related to the new involute and the new involute constraint conditions. The broach spline tooth profile parameters related to the new involute include the minimum effective starting circle diameter of the broach spline teeth after opening the clearance angle according to the original involute and the arc tooth thickness at the minimum effective starting circle diameter after opening the clearance angle according to the original involute. The new involute must satisfy two constraints: the new involute intersects the original involute at a diameter dyj, and the new involute is Cx apart from the original involute at the minor diameter di of the broach. The initial pressure angle of the new involute's bisection is af2 = af1 - 1.5°; The diameter of the dividing circle, Df2, is equal to Mt × Z; The diameter of the new base circle is d02 = Df2 × Cos(af2); The involute function invaf2 = tg(af2) – af2; The pressure angle ai1 on the original involute diameter di is given by arccos(d01 / di). The involute function invai1 = tg(ai1) - ai1; The thickness of the arc tooth at the root of the original involute tooth is Si1 = (sf1 / Df1 + invaf1 - invai1) × di; The pressure angle on the diameter of the new involute di is ai2=arccos(d02 / di); The involute function invai2 = tg(ai2) - ai2; The thickness of the arc tooth at the root of the new involute tooth is Si2 = (syj / dyj + invayj - invai2) × di; After multiple iterative calculations, the pressure angle af2 of the new involute circle was obtained, and the final size requirement was met: (Si1-Si2) / 2=side clearance value Cx±0.

02. Where, af1 is the pressure angle of the parting circle, Mt is the module, Z is the number of broach teeth, Df2 is the parting circle diameter, di is the minor diameter of the broach, d01 is the base circle diameter, sf1 is the tooth thickness of the parting circle arc, Df1 is the original parting circle diameter, d02 is the new base circle diameter, syj is the tooth thickness at the minimum effective starting circle diameter dyj after the broach clearance angle, dyj is the minimum effective starting circle diameter after the broach clearance angle, and ayj is the pressure angle at the original involute diameter dyj. The gauge bar parameter calculation module is used to calculate and output the gauge bar parameters based on the new involute parameters of the broach spline teeth. The gauge bar parameter calculation module includes a new broach parting arc tooth thickness calculation module, a gauge bar diameter calculation module, and a span-bar distance calculation module. The new broach parting arc tooth thickness calculation module is used to calculate the broach parting arc tooth thickness according to the new involute of the broach. The gauge bar diameter calculation module is used to calculate the gauge bar diameter based on the gauge bar diameter constraint conditions. The span-bar distance calculation module is used to calculate the span-bar distance of the gauge bar. The gauge bar diameter constraint conditions include that the contact point between the gauge bar and the broach spline teeth is on the new involute of the broach; and that the gauge bar does not interfere with the circular contour line of the minor diameter of the broach spline. The broach tooth profile parameter update output module is used to output the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline tooth, and the tooth profile parameters related to the new involute used for the side clearance angle of the broach spline tooth in the parameters of the gauge bar.

2. The design system for the backlash angle of a broach used for involute spline machining as described in claim 1, characterized in that: The basic parameters of the broach spline tooth profile include the broach module, broach calibration tooth diameter, broach pitch angle, broach spline minor diameter, broach pitch arc tooth thickness, broach spline tooth side cutting width, broach spline number of teeth, and broach spline minor diameter backlash.

3. The design system for the backlash angle of a broach used for involute spline machining as described in claim 1, characterized in that: The new involute constraint condition includes that the intersection of the new involute of the broach and the original involute of the broach is located on the smallest effective starting circle after the broach spline tooth opens the side clearance angle according to the original involute. Furthermore, the distance between the new involute curve and the original involute curve at the minor diameter of the broach spline is the same as the side clearance of the minor diameter of the broach spline.

4. The design system for the backlash angle of a broach used for involute spline machining as described in claim 1, characterized in that: The condition for determining whether the contact point between the gauge bar and the broach spline is on the new involute of the broach is that the contact circle diameter of the gauge bar is smaller than the minimum effective starting circle diameter of the broach spline after the side clearance angle is opened according to the original involute.

5. The design system for the backlash angle of a broach used for involute spline machining as described in claim 4, characterized in that: The condition for determining that the measuring bar and the circular outline of the minor diameter of the broach spline do not interfere is that the distance between the lowest points of the measuring bar is greater than the minor diameter of the broach spline.

6. A method for designing the backlash angle of a broach used for machining splines based on involute curves, characterized in that: It includes the following steps: Step 1: Input the basic parameters of the broach spline tooth profile; Step 2: Calculate and output the new involute parameters of the broach spline teeth based on the basic parameters of the broach spline tooth profile; this includes calculating the broach spline tooth profile parameters related to the new involute based on the basic parameters of the broach spline tooth profile, and calculating the new involute parameters based on the broach spline tooth profile parameters related to the new involute and the new involute constraint conditions; the broach spline tooth profile parameters related to the new involute include the minimum effective starting circle diameter of the broach spline teeth after opening the backlash angle according to the original involute and the arc tooth thickness at the minimum effective starting circle diameter of the broach spline teeth after opening the backlash angle according to the original involute; The new involute must satisfy two constraints: the new involute intersects the original involute at a diameter dyj, and the new involute is Cx apart from the original involute at the minor diameter di of the broach. The initial pressure angle of the new involute's bisection is af2 = af1 - 1.5°; The diameter of the dividing circle, Df2, is equal to Mt × Z; The diameter of the new base circle is d02 = Df2 × Cos(af2); The involute function invaf2 = tg(af2) – af2; The pressure angle ai1 on the original involute diameter di is given by arccos(d01 / di). The involute function invai1 = tg(ai1) - ai1; The thickness of the arc tooth at the root of the original involute tooth is Si1 = (sf1 / Df1 + invaf1 - invai1) × di; The pressure angle on the diameter of the new involute di is ai2=arccos(d02 / di); The involute function invai2 = tg(ai2) - ai2; The thickness of the arc tooth at the root of the new involute tooth is Si2 = (syj / dyj + invayj - invai2) × di; After multiple iterative calculations, the pressure angle af2 of the new involute circle was obtained, and the final size requirement was met: (Si1-Si2) / 2=side clearance value Cx±0.

02. Where, af1 is the pressure angle of the parting circle, Mt is the module, Z is the number of broach teeth, Df2 is the parting circle diameter, di is the minor diameter of the broach, d01 is the base circle diameter, sf1 is the tooth thickness of the parting circle arc, Df1 is the original parting circle diameter, d02 is the new base circle diameter, syj is the tooth thickness at the minimum effective starting circle diameter dyj after the broach clearance angle, dyj is the minimum effective starting circle diameter after the broach clearance angle, and ayj is the pressure angle at the original involute diameter dyj. Step 3: Calculate and output the parameters of the gauge bar based on the new involute parameters of the broach spline teeth; including calculating the broach parting arc tooth thickness according to the new involute, calculating the gauge bar diameter according to the gauge bar diameter constraint conditions, and calculating the gauge bar span; the gauge bar diameter constraint conditions include that the contact point between the gauge bar and the broach spline teeth is on the new involute of the broach; and that the gauge bar does not interfere with the circular contour line of the minor diameter of the broach spline. Step 4: Output the basic parameters of the broach spline tooth profile, the new involute parameters of the broach spline teeth, and the tooth profile parameters related to the new involute used for the backlash angle of the broach spline teeth in the parameters of the gauge bar.

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