CN111079233A - Elastic deformation optimization gear shaving cutter design method - Google Patents

Elastic deformation optimization gear shaving cutter design method Download PDF

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CN111079233A
CN111079233A CN201911142792.5A CN201911142792A CN111079233A CN 111079233 A CN111079233 A CN 111079233A CN 201911142792 A CN201911142792 A CN 201911142792A CN 111079233 A CN111079233 A CN 111079233A
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shaving cutter
gear
gear shaving
elastic deformation
calculating
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CN111079233B (en
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金伟峰
严鉴铂
赵艳文
林鸥
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Xian Fast Auto Drive Co Ltd
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Xian Fast Auto Drive Co Ltd
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Abstract

The invention relates to a design method of an elastic deformation optimization gear shaving cutter. Aims to inhibit or reduce the phenomenon of shaving concavity generated in the prior shaving process. The method comprises the steps of 1) setting an initial meshing angle parameter a _ nh0, and calculating an initial parameter of the gear shaving cutter through a _ nh 0; step 2) calculating elastic deformation delta corresponding to each stress point at any moment of the gear shaving cutter tooth part through the initial parameters of the gear shaving cutter in the step 1)0tAnd calculating the elastic deformation delta of each stress point on the gear meshed with the tooth part at the corresponding moment1t(ii) a Then calculating the comprehensive elastic deformation delta corresponding to each stress pointt(ii) a Step 3) drawing comprehensive elastic deformation deltatThe dynamic distribution diagram of elastic deformation between the pressure angles of the corresponding stress points is calculated, and the comprehensive elastic deformation range R is calculatedδ(ii) a Step 4) adjusting the meshing angle parameter a _ nh0, and repeating the steps 2) to 3) when R is equal toδA _ nh0 at less than or closest to 10 μm is the final design engagement angle parameter. And other parameter designs of the gear shaving cutter are completed according to the final design a _ nh0 value.

Description

Elastic deformation optimization gear shaving cutter design method
Technical Field
The invention relates to a gear shaving cutter, in particular to a design method of an elastic deformation optimized gear shaving cutter.
Background
In the past, the design of parameters of the gear shaving is most important to determine the meshing angle a _ nh0 of the gear shaving cutter, the meshing angle a _ nh0 which is usually suitable can reduce or inhibit the formation of concave parts in the gear shaving, and the gear shaving cutter is generally designed by adopting a small meshing angle or a balanced gear shaving meshing angle; however, the shaving cutter designed by the two methods sometimes still enters a better meshing state in the second half of the life cycle, and the phenomenon is caused because the rigidity of the shaving cutter is reduced due to a small meshing angle or balanced shaving meshing, and more bending deformation is generated during the shaving cutter processing, so that the middle area of the tooth surface with higher comprehensive rigidity has the smallest cutter yielding and the largest processing amount, and the shaving dents are generated.
Disclosure of Invention
The invention aims to inhibit or reduce the phenomenon of shaving concavity generated in the shaving process in the prior art, and provides a design method of an elastic deformation optimized shaving cutter.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention discloses a design method of an elastic deformation optimization gear shaving cutter, which is characterized by comprising the following steps: the method comprises the following steps: the method comprises the following steps:
step 1) setting an initial meshing angle parameter a _ nh0, and calculating an initial parameter of the gear shaving cutter through the initial meshing angle parameter a _ nh 0;
step 2) calculating elastic deformation delta corresponding to each stress point at any moment of the gear shaving cutter tooth part through the initial parameters of the gear shaving cutter in the step 1)0tAnd calculating the elastic deformation delta of each stress point on the gear meshed with the tooth part at the corresponding moment1t(ii) a Then calculating the comprehensive elastic deformation delta corresponding to each stress pointt；
Step 3) drawing comprehensive elastic deformation deltatThe dynamic distribution diagram of elastic deformation between the pressure angles of the corresponding stress points is calculated, and the comprehensive elastic deformation range R is calculatedδ；
Step 4) adjusting the meshing angle parameter a _ nh0, and repeating the steps 2) to 3) to enable R to be in a state of being in a certain rangeδLess than 10 μm, the corresponding meshing angle parameter a _ nh0 is the final design meshing angle parameter for the shaver, if R isδThe mesh angle parameter a _ nh0 is always larger than 10 mu m, and the parameter closest to 10 mu m is taken as the final design mesh angle parameter;
and completing other parameter design of the gear shaving cutter according to the final design meshing angle parameter a _ nh 0.
Further, the step 2) specifically includes:
step 2.1) establishing a coordinate system by taking the center of the gear shaving cutter as an origin, taking the center line of the tooth part along the radius of the gear shaving cutter as an X axis and taking the radius of the gear shaving cutter which is vertical to the X axis and is vertical to the axial direction of the gear shaving cutter as a Y axis;
step 2.2) the tooth part is sequentially divided into a plurality of parts with the width b (b) along the X axis<0.001mm) and continuous rectangles, calculating the height y of each rectangleiWherein i ═ 1, 2, 3 … …, or n:
Figure BDA0002281409250000021
wherein ,
Figure BDA0002281409250000022
xiis yiThe vertical distance of the corresponding rectangle from the origin; r isxiIs xiThe distance from one end of the rectangle to the origin along the height direction; r is0The reference circle radius of the gear shaving cutter; stα for the gear shaving cutter dividing circle end face arc tooth thicknessrxiIs rxiPressure angle on circle αtThe pressure angle of the end face of the reference circle of the gear shaving cutter is set; r isxkThe distance from the center of a gear shaving cutter withdrawal hole to the original point is obtained; srxkIs rxkThe tooth thickness on the circle; stifThe thickness of the arc teeth on the end surface of the involute starting circle of the gear shaving cutter is equal to the thickness of the arc teeth on the end surface of the involute starting circle of the gear shaving cutter; r isfThe radius of the gear root circle of the gear shaving cutter; srfThe arc tooth thickness of the round end surface of the gear shaving cutter tooth root;
Figure BDA0002281409250000023
α is the radius of the tool withdrawal holefiIs radius rxiThe included angle with the X axis; z0The number of the gear shaving cutter teeth; rhorl is a circular secant function calculated according to the height of the chord bow;
step 2.3) calculating the contact force F of the surfaces of the two sides of the tooth part of the gear shaving cutter at any time t1t and F2t：
Figure BDA0002281409250000031
Figure BDA0002281409250000032
wherein ,Ev1Is equivalent elastic modulus of the gear shaving cutter; r isF1The distance from the meshing point of the gear shaving cutter to the origin; n is a radical ofv1Is rF1tEffective contact pair number when the circles are engaged; snrF1tIs rF1tThe thickness of the circular arc tooth; a isrF1tIs rF1tA pressure angle on circle; rhovrF1tIs rF1tInstantaneous composite radius of curvature of contact when the circles are engaged; r isF2tThe distance from the meshing point on the other side of the gear shaving cutter to the origin; n is a radical ofv2Is rF2tEffective contact pair number when the circles are engaged; snrF2tIs rF2tThe thickness of the circular arc tooth; a isrF2Is rF2tA circular pressure angle; rhovrF2tIs rF2tInstantaneous composite radius of curvature of contact when the circles are engaged; delta is the radial feed of each stroke of gear shaving;
step 2.4) calculating the contact forces F respectively1t、F2tAt xiAmount of bending deformation δ generated in squarexi1t、δxi2t(the effect of the shaving cutter base circle helix angle is not considered):
Figure BDA0002281409250000033
aF1tyis F1tIncluded angle with Y axis; a isF1txIs F1tIncluded angle with the X axis; x is the number ofF1tIs F1tAn operative X-axis coordinate; bv1Effective tooth width of the gear shaving cutter; a isF2tyIs F2tIncluded angle with Y axis; a isF2txIs F2tIncluded angle with the X axis; x is the number ofF2tIs F2tAn operative X-axis coordinate;
step 2.5) calculating F separately1t、F2tAt xF1tAmount of bending deformation δ ofF1tw and δF2tw：
Figure BDA0002281409250000034
wherein ,
Figure BDA0002281409250000035
xrfis the X-axis coordinate of the rectangular center at the tooth root; when F is present2tX-axis coordinate of not less than F1tIn the X-axis coordinate of (1), n2＝n1(ii) a When F is present2tX axis coordinate of<F1tIn the X-axis coordinate of (a),
Figure BDA0002281409250000041
step 2.6) calculating the contact force F1tTotal bending deformation delta corresponding to action pointFtw：
a. When the gear-shaving cutter is stressed on one side, F2tThe amount of bending deformation generated is 0, then:
δFtw＝δF1tw；
b. when the gear shaving cutter is stressed on both sides, and F2tX-axis coordinate of not less than F1tX-axis coordinate of (a), then:
δFtw＝δF1tw-δF2tw；
c. when the gear shaving cutter is stressed on both sides, and F2tX axis coordinate of<F1tX-axis coordinate of (a), then:
δFtw＝δF1tw-δF2tw-θF2t·(xF1t-xF2t)
wherein ,
Figure BDA0002281409250000042
step 2.7) calculating F on the gear shaving cutter1tContact deformation of point of action
Figure BDA0002281409250000043
Figure BDA0002281409250000044
Step 2.8) calculating the tooth contact force F according to the results obtained in step 2.6) and step 2.7)1tAmount of total elastic deformation δ at point of action0t：
δ0t＝δFtw+δFtc
Step 2.9) similarly, calculating the contact force F on the gear meshed with the gear shaving cutter through the calculation methods from the step 2.1) to the step 2.8)1tTotal elastic deformation delta at corresponding position of action point1t：
δ1t＝δF1tw+δF1tc
wherein ,δF1twIs the contact force F on the gear1tAmount of bending deformation, δ, at corresponding position of action pointF1tcIs the contact force F on the gear1tThe contact deformation amount of the corresponding position of the action point;
step 2.10) calculating the comprehensive elastic deformation delta of the gear shaving cutter and the gear at the time tt：
δt＝δ0t+δ1t；
Step 2.11) calculating the comprehensive elastic deformation of different stress points when the gear shaving cutter and the gear interact with each other by the methods from the step 2.1) to the step 2.10).
Further, the step 3) is specifically as follows:
step 3.1) finding out the maximum value delta of the comprehensive elastic deformation in the elastic deformation dynamic distribution diagrammaxAnd finding out the minimum value delta of the comprehensive elastic deformation except the starting point and the end point of the involutemin；
Step 3.2) calculating comprehensive elastic deformation range Rδ：
Rδ＝δmax-δmin。
Further, the other initial parameters in the step 1) comprise the thickness of the rounding teeth, the outer diameter, the center distance, the top clearance, the length of an actual meshing line, the diameter of the tool retracting hole and the distribution diameter of the tool retracting hole;
further, the other parameters in the step 4) include the thickness of the rounding teeth, the outer diameter, the center distance, the top clearance, the length of the actual meshing line, the diameter of the tool retracting hole and the distribution diameter of the tool retracting hole.
The invention has the beneficial effects that:
according to the invention, in the design of the gear shaving cutter, the elastic variable in gear shaving processing is optimized by adjusting the relevant parameters of the gear shaving cutter, the optimal meshing angle parameter a _ nh0 and the relevant parameters of the gear are found, so that the elastic deformation difference of each part of the meshing tooth surface in the gear shaving processing is minimized, and the effects of inhibiting the concave in the gear shaving, reducing the grinding difficulty of the gear shaving cutter, improving the gear shaving processing quality and prolonging the service life of the gear shaving cutter are achieved.
Drawings
FIG. 1 is a schematic view of the construction of a gear shaving cutter according to the present invention;
FIG. 2 is a schematic diagram illustrating a tooth structure of the shaving cutter of the present invention;
FIG. 3 shows the combined elastic deformation δ of the present inventiontThe elastic deformation dynamic distribution diagram between the pressure angle and the corresponding stress point;
FIG. 4 is a dynamic distribution diagram of elastic deformation between the integrated elastic deformation and the corresponding force-bearing point pressure angle after the meshing angle parameters are optimized.
In the figure, 1-tooth part and 2-tool withdrawal hole.
Detailed Description
To make the objects, advantages and features of the present invention more apparent, a method for designing an elastically deformable optimized shaver according to the present invention will be described in detail with reference to the accompanying drawings and specific embodiments. The advantages and features of the present invention will become more apparent from the following detailed description. It should be noted that: the drawings are in simplified form and are not to precise scale, the intention being solely for the convenience and clarity of illustrating embodiments of the invention; second, the structures shown in the drawings are often part of actual structures.
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a design method of an elastic deformation optimized gear shaving cutter, which has the working principle as follows:
the technical principle adopted by the invention is that through adjusting relevant parameters of the gear shaving cutter in the gear shaving cutter design, the elastic deformation difference at each position of the tooth surface of the meshing gear in the gear shaving processing is minimized, so that the effects of inhibiting the concave in the gear shaving, reducing the grinding difficulty of the gear shaving cutter, improving the gear shaving processing quality and prolonging the service life of the gear shaving cutter are achieved.
The invention discloses a design method of an elastic deformation optimization gear shaving cutter, which comprises the following design and calculation processes:
step 1) setting an initial meshing angle parameter a _ nh0, and calculating an initial shaving cutter parameter through the initial meshing angle parameter a _ nh 0: the thickness, the outer diameter, the center distance, the top clearance, the length of an actual meshing line, the diameter of a tool retracting hole and the distribution diameter of the tool retracting hole are measured;
step 2) calculating elastic deformation delta corresponding to each stress point at any moment of the gear shaving cutter tooth part through the initial parameters of the gear shaving cutter in the step 1)0tAnd calculating the elastic deformation delta of each stress point on the gear meshed with the tooth part at the corresponding moment1t(ii) a Then calculating the comprehensive elastic deformation delta corresponding to each stress pointt；
As shown in fig. 1 and 2, the following are specific:
step 2.1) establishing a coordinate system by taking the center of the gear shaving cutter as an origin, taking the center line of the tooth part along the radius of the gear shaving cutter as an X axis and taking the radius of the gear shaving cutter which is vertical to the X axis and is vertical to the axial direction of the gear shaving cutter as a Y axis;
step 2.2) the tooth part is sequentially divided into a plurality of parts with the width b (b) along the X axis<0.001mm) and continuous rectangles, calculating the height y of each rectangleiWherein i ═ 1, 2, 3 … …, or n:
Figure BDA0002281409250000071
wherein ,
Figure BDA0002281409250000072
xiis yiThe vertical distance of the corresponding rectangle from the origin; r isxiIs xiThe distance from one end of the rectangle to the origin along the height direction; r is0The reference circle radius of the gear shaving cutter; stFor gear shaving cuttersThickness of the teeth of the reference circle end face αrxiIs rxiPressure angle on circle αtThe pressure angle of the end face of the reference circle of the gear shaving cutter is set; r isxkThe distance from the center of a gear shaving cutter withdrawal hole to the original point is obtained; srxkIs rxkThe tooth thickness on the circle; stifThe thickness of the arc teeth on the end surface of the involute starting circle of the gear shaving cutter is equal to the thickness of the arc teeth on the end surface of the involute starting circle of the gear shaving cutter; r isfThe radius of the gear root circle of the gear shaving cutter; srfThe arc tooth thickness of the round end surface of the gear shaving cutter tooth root;
Figure BDA0002281409250000073
α is the radius of the tool withdrawal holefiIs radius rxiThe included angle with the X axis; z0The number of the gear shaving cutter teeth; rhorl is a circular secant function calculated according to the height of the chord bow;
step 2.3) calculating the contact force F of the surfaces of the two sides of the tooth part of the gear shaving cutter at any time t1t and F2t：
Figure BDA0002281409250000074
Figure BDA0002281409250000075
wherein ,Ev1Is equivalent elastic modulus of the gear shaving cutter; r isF1The distance from the meshing point of the gear shaving cutter to the origin; n is a radical ofv1Is rF1tEffective contact pair number when the circles are engaged; snrF1tIs rF1tThe thickness of the circular arc tooth; a isrF1tIs rF1tA pressure angle on circle; rhovrF1tIs rF1tInstantaneous composite radius of curvature of contact when the circles are engaged; r isF2tThe distance from the meshing point on the other side of the gear shaving cutter to the origin; n is a radical ofv2Is rF2tEffective contact pair number when the circles are engaged; snrF2tIs rF2tThe thickness of the circular arc tooth; a isrF2Is rF2tA circular pressure angle; rhovrF2tIs rF2tInstantaneous composite radius of curvature of contact when the circles are engaged; delta is the radial feed of each stroke of gear shaving;
step 2.4) calculating the contact forces F respectively1t、F2tAt xiBending produced on a rectangleAmount of deformation deltaxi1t、δxi2t：
Figure BDA0002281409250000081
aF1tyIs F1tIncluded angle with Y axis; a isF1txIs F1tIncluded angle with the X axis; x is the number ofF1tIs F1tAn operative X-axis coordinate; bv1Effective tooth width of the gear shaving cutter; a isF2tyIs F2tIncluded angle with Y axis; a isF2txIs F2tIncluded angle with the X axis; x is the number ofF2tIs F2tAn operative X-axis coordinate;
step 2.5) calculating F separately1t、F2tAt xF1tAmount of bending deformation δ ofF1tw and δF2tw：
Figure BDA0002281409250000082
wherein ,
Figure BDA0002281409250000083
xrfis the X-axis coordinate of the rectangular center at the tooth root; when F is present2tX-axis coordinate of not less than F1tIn the X-axis coordinate of (1), n2＝n1(ii) a When F is present2tX axis coordinate of<F1tIn the X-axis coordinate of (a),
Figure BDA0002281409250000084
step 2.6) calculating the contact force F1tTotal bending deformation delta corresponding to action pointFtw：
a. When the gear-shaving cutter is stressed on one side, F2tThe amount of bending deformation generated is 0, then:
δFtw＝δF1tw；
b. when the gear shaving cutter is stressed on both sides, and F2tX-axis coordinate of not less than F1tX-axis coordinate of (a), then:
δFtw＝δF1tw-δF2tw；
c. when the gear shaving cutter is stressed on both sides, and F2tX axis coordinate of<F1tX-axis coordinate of (a), then:
δFtw＝δF1tw-δF2tw-θF2t·(xF1t-xF2t)
wherein ,
Figure BDA0002281409250000085
step 2.7) calculating F on the gear shaving cutter1tContact deformation of point of action
Figure BDA0002281409250000086
Figure BDA0002281409250000091
Step 2.8) calculating the tooth contact force F according to the results obtained in step 2.6) and step 2.7)1tAmount of total elastic deformation δ at point of action0t：
δ0t＝δFtw+δFtc
Step 2.9) similarly, calculating the contact force F on the gear meshed with the gear shaving cutter through the calculation methods from the step 2.1) to the step 2.8)1tTotal elastic deformation delta at corresponding position of action point1t：
δ1t＝δF1tw+δF1tc
wherein ,δF1twIs the contact force F on the gear1tAmount of bending deformation, δ, at corresponding position of action pointF1tcIs the contact force F on the gear1tThe contact deformation amount of the corresponding position of the action point;
step 2.10) calculating the comprehensive elastic deformation delta of the gear shaving cutter and the gear at the time tt：
δt＝δ0t+δ1t；
Step 2.11) calculating the comprehensive elastic deformation of different stress points when the gear shaving cutter and the gear interact with each other by the methods from the step 2.1) to the step 2.10).
Step 3) as shown in FIG. 3, the comprehensive elastic deformation amount δ is plottedtThe dynamic distribution diagram of elastic deformation between the pressure angles of the corresponding stress points is calculated, and the comprehensive elastic deformation range R is calculatedδ(ii) a The method comprises the following specific steps:
step 3.1) finding out the maximum value delta of the comprehensive elastic deformation in the elastic deformation dynamic distribution diagrammaxAnd finding out the minimum value delta of the comprehensive elastic deformation except the starting point and the end point of the involutemin；
Step 3.2) calculating comprehensive elastic deformation range Rδ：
Rδ＝δmax-δmin。
Step 4) adjusting the meshing angle parameter a _ nh0, and repeating the steps 2) to 3) to enable R to be in a state of being in a certain rangeδLess than 10 μm, the corresponding meshing angle parameter a _ nh0 is the final design meshing angle parameter for the shaver, if R isδThe mesh angle parameter a _ nh0 is always larger than 10 mu m, and the parameter closest to 10 mu m is taken as the final design mesh angle parameter;
and (3) designing the thickness, the outer diameter, the center distance, the top clearance, the actual meshing line length, the tool retracting hole diameter and the tool retracting hole distribution diameter of the gear shaving cutter rounding teeth according to the final designed meshing angle parameter a _ nh0, wherein the optimized elastic deformation dynamic distribution diagram is shown in FIG. 4.
Reference is made to handbooks for designing and selecting gear cutters for methods for calculating initial parameters and other parameters.

Claims (5)

1. A design method of an elastic deformation optimization shaving cutter is characterized by comprising the following steps:
step 1) setting an initial meshing angle parameter a _ nh0, and calculating an initial parameter of the gear shaving cutter through the initial meshing angle parameter a _ nh 0;
step 2) calculating elastic deformation delta corresponding to each stress point at any moment of the gear shaving cutter tooth part through the initial parameters of the gear shaving cutter in the step 1)0tAnd calculating the elastic deformation delta of each stress point on the gear meshed with the tooth part at the corresponding moment1t(ii) a Then calculating the comprehensive elastic deformation delta corresponding to each stress pointt；
Step 3) drawing comprehensive elastic deformation deltatThe dynamic distribution diagram of elastic deformation between the pressure angles of the corresponding stress points is calculated, and the comprehensive elastic deformation range R is calculatedδ；
Step 4) adjusting the meshing angle parameter a _ nh0, and repeating the steps 2) to 3) to enable R to be in a state of being in a certain rangeδLess than 10 μm, the corresponding meshing angle parameter a _ nh0 is the final design meshing angle parameter for the shaver, if R isδThe mesh angle parameter a _ nh0 is always larger than 10 mu m, and the parameter closest to 10 mu m is taken as the final design mesh angle parameter;
and completing other parameter design of the gear shaving cutter according to the final design meshing angle parameter a _ nh 0.
2. The method for designing an elastic deformation optimized shaving cutter according to claim 1, wherein the step 2) specifically comprises:
step 2.1) establishing a coordinate system by taking the center of the gear shaving cutter as an origin, taking the center line of the tooth part along the radius of the gear shaving cutter as an X axis and taking the radius of the gear shaving cutter which is vertical to the X axis and is vertical to the axial direction of the gear shaving cutter as a Y axis;
step 2.2) the tooth part is sequentially divided into a plurality of parts with the width b (b) along the X axis<0.001mm) and continuous rectangles, calculating the height y of each rectangleiWherein i ═ 1, 2, 3 … …, or n:
Figure FDA0002281409240000011
wherein ,
Figure FDA0002281409240000021
xiis yiThe vertical distance of the corresponding rectangle from the origin; r isxiIs xiThe distance from one end of the rectangle to the origin along the height direction; r is0The reference circle radius of the gear shaving cutter; stα for the gear shaving cutter dividing circle end face arc tooth thicknessrxiIs rxiPressure angle on circle αtThe pressure angle of the end face of the reference circle of the gear shaving cutter is set; r isxkFor the distance from the center of the tool retracting hole of the gear shaving cutter to the originSeparating; srxkIs rxkThe tooth thickness on the circle; stifThe thickness of the arc teeth on the end surface of the involute starting circle of the gear shaving cutter is equal to the thickness of the arc teeth on the end surface of the involute starting circle of the gear shaving cutter; r isfThe radius of the gear root circle of the gear shaving cutter; srfThe arc tooth thickness of the round end surface of the gear shaving cutter tooth root;
Figure FDA0002281409240000024
α is the radius of the tool withdrawal holefiIs radius rxiThe included angle with the X axis; z0The number of the gear shaving cutter teeth; rhorl is a circular secant function calculated according to the height of the chord bow;
step 2.3) calculating the contact force F of the surfaces of the two sides of the tooth part of the gear shaving cutter at any time t1t and F2t：
Figure FDA0002281409240000022
Figure FDA0002281409240000023
wherein ,Ev1Is equivalent elastic modulus of the gear shaving cutter; r isF1The distance from the meshing point of the gear shaving cutter to the origin; n is a radical ofv1Is rF1tEffective contact pair number when the circles are engaged; snrF1tIs rF1tThe thickness of the circular arc tooth; a isrF1tIs rF1tA pressure angle on circle; rhovrF1tIs rF1tInstantaneous composite radius of curvature of contact when the circles are engaged; r isF2tThe distance from the meshing point on the other side of the gear shaving cutter to the origin; n is a radical ofv2Is rF2tEffective contact pair number when the circles are engaged; snrF2tIs rF2tThe thickness of the circular arc tooth; a isrF2Is rF2tA circular pressure angle; rhovrF2tIs rF2tInstantaneous composite radius of curvature of contact when the circles are engaged; delta is the radial feed amount of each stroke of gear shaving;
step 2.4) calculating the contact forces F respectively1t、F2tAt xiAmount of bending deformation δ generated in squarexi1t、δxi2t：
Figure FDA0002281409240000031
aF1tyIs F1tIncluded angle with Y axis; a isF1txIs F1tIncluded angle with the X axis; x is the number ofF1tIs F1tAn operative X-axis coordinate; bv1Effective tooth width of the gear shaving cutter; a isF2tyIs F2tIncluded angle with Y axis; a isF2txIs F2tIncluded angle with the X axis; x is the number ofF2tIs F2tAn operative X-axis coordinate;
step 2.5) calculating F separately1t、F2tAt xF1tAmount of bending deformation δ ofF1tw and δF2tw：
Figure FDA0002281409240000032
wherein ,
Figure FDA0002281409240000033
xrfis the X-axis coordinate of the rectangular center at the tooth root; when F is present2tX-axis coordinate of not less than F1tIn the X-axis coordinate of (1), n2＝n1(ii) a When F is present2tX axis coordinate of<F1tIn the X-axis coordinate of (a),
Figure FDA0002281409240000034
step 2.6) calculating the contact force F1tTotal bending deformation delta corresponding to action pointFtw：
a. When the gear-shaving cutter is stressed on one side, F2tThe amount of bending deformation generated is 0, then:
δFtw＝δF1tw；
b. when the gear shaving cutter is stressed on both sides, and F2tX-axis coordinate of not less than F1tX-axis coordinate of (a), then:
δFtw＝δF1tw-δF2tw；
c. when the gear shaving cutter is stressed on both sides, and F2tX axis coordinate of<F1tX-axis coordinate of (a), then:
δFtw＝δF1tw-δF2tw-θF2t·(xF1t-xF2t)
wherein ,
Figure FDA0002281409240000035
step 2.7) calculating F on the gear shaving cutter1tContact deformation of point of action
Figure FDA0002281409240000036
Figure FDA0002281409240000037
Step 2.8) calculating the tooth contact force F according to the results obtained in step 2.6) and step 2.7)1tAmount of total elastic deformation δ at point of action0t：
δ0t＝δFtw+δFtc
Step 2.9) similarly, calculating the contact force F on the gear meshed with the gear shaving cutter through the calculation methods from the step 2.1) to the step 2.8)1tTotal elastic deformation delta at corresponding position of action point1t：
δ1t＝δF1tw+δF1tc
wherein ,δF1twIs the contact force F on the gear1tAmount of bending deformation, δ, at corresponding position of action pointF1tcIs the contact force F on the gear1tThe contact deformation amount of the corresponding position of the action point;
step 2.10) calculating the comprehensive elastic deformation delta of the gear shaving cutter and the gear at the time tt：
δt＝δ0t+δ1t；
Step 2.11) calculating the comprehensive elastic deformation of different stress points when the gear shaving cutter and the gear interact with each other by the methods from the step 2.1) to the step 2.10).
3. A method according to claim 1 or 2, wherein the step 3) is specifically:
step 3.1) finding out the maximum value delta of the comprehensive elastic deformation in the elastic deformation dynamic distribution diagrammaxAnd finding out the minimum value delta of the comprehensive elastic deformation except the starting point and the end point of the involutemin；
Step 3.2) calculating comprehensive elastic deformation range Rδ：
Rδ＝δmax-δmin。
4. The method as claimed in claim 1, wherein the other initial parameters in step 1) include partial circle tooth thickness, outer diameter, center distance, tip clearance, actual meshing line length, relief hole diameter, and relief hole distribution diameter.
5. The method as claimed in claim 1, wherein the other parameters in step 4) include partial circle tooth thickness, outer diameter, center distance, tip clearance, actual meshing line length, relief hole diameter, and relief hole distribution diameter.
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112861286A (en) * 2021-03-02 2021-05-28 西安建筑科技大学 Gear shaving machining parameter global optimization design method

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106611080A (en) * 2016-11-10 2017-05-03 西安建筑科技大学 Shaving cutter design method based on analysis on meshing contact property of shaving gears
WO2017215621A1 (en) * 2016-06-16 2017-12-21 南通慧幸智能科技有限公司 Tooth profile design method for three-dimensional high-rigidity harmonic speed reducer
CN109710969A (en) * 2018-11-15 2019-05-03 西安建筑科技大学 A kind of shaving profile error prediction technique

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2017215621A1 (en) * 2016-06-16 2017-12-21 南通慧幸智能科技有限公司 Tooth profile design method for three-dimensional high-rigidity harmonic speed reducer
CN106611080A (en) * 2016-11-10 2017-05-03 西安建筑科技大学 Shaving cutter design method based on analysis on meshing contact property of shaving gears
CN109710969A (en) * 2018-11-15 2019-05-03 西安建筑科技大学 A kind of shaving profile error prediction technique

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
华成丽;: "剃齿变形量计算与刀具修形曲线拟合应用" *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112861286A (en) * 2021-03-02 2021-05-28 西安建筑科技大学 Gear shaving machining parameter global optimization design method
CN112861286B (en) * 2021-03-02 2023-04-18 西安建筑科技大学 Gear shaving machining parameter global optimization design method

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