Multi-axis turning machining path planning method for worm

Abstract

The invention discloses a multi-shaft turning machining path planning method for a worm, which applies a multi-shaft precision turning technology to finish machining of the worm and expands the scheme of finish machining of the worm. According to the method, precise turning and five-axis linkage machining characteristics are considered, a tooth profile equation of the toroidal worm is combined, planning and fairness optimization are conducted on a tool path, and a reliable scheme for conducting turning machining on the curved surface of the toroidal worm through a multi-axis machine tool is provided. Specifically, a traditional worm machining mode needs to be carried out on a special machine tool with a rotary table, during machining, the center distance is adjusted by moving the rotary table in the radial direction of a worm, and the transmission ratio is adjusted by arranging a change gear; the problems of complicated machine tool adjustment, long processing period and high cost exist in the prior art. According to the machining method, the multi-axis precision turning technology is adopted, and the machining precision is improved by reducing datum conversion in multi-axis machining; in the whole machining process, the part only needs to be clamped at one time, and constant precision can be kept.

Description

Technical Field

[0001] The invention belongs to the technical field of worm gear pairs, and specifically relates to a worm multi-axis turning machining path planning method. Background Art

[0002] The enveloping worm pair is one of the basic mechanical transmission elements, which is widely used in the pressing device of the rolling mill, the reducer of the elevator, the lifting device of the naval gun and the mining machinery. Compared with the ordinary worm transmission, the enveloping worm pair has the characteristics of multi-tooth meshing, instantaneous double-line contact, wide working tooth surface, large load-bearing capacity, good lubrication conditions, etc., which conforms to the development trend of the worm pair. However, these excellent properties of the enveloping worm pair must be guaranteed by high manufacturing and installation precision. For example, for the worm pair with a center distance greater than 400mm, the radial runout of the worm and the pitch error of the worm wheel shall not exceed 0.015ram, and the center distance error and the center plane offset of the worm wheel also need to be controlled within a very small range, otherwise the actual meshing performance will be different from the theoretical analysis results, such as the double-line contact degenerated into point contact, and the simultaneous meshing of multiple teeth degenerated into single-tooth meshing at the entrance of the worm.

[0003] In the prior art, the processing method of the annular envelope worm pair generally adopts the dual modeling method. Under this processing method, due to the complex process, it is difficult to solve the chronic problem of poor precision, and it is impossible to find a fundamental solution to the complications of high cost and short life caused by it. These problems limit the promotion and popularization of the annular envelope worm pair, and the advantages of this worm pair are not fully utilized. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a worm multi-axis turning machining path planning method, which can realize the machining of the toroidal worm by using the multi-axis turning machining technology to improve the machining accuracy and efficiency of the toroidal worm.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] A worm multi-axis turning machining path planning method comprises the following steps:

[0007] Step 1: Parameterization of worm tooth surface

[0008] 11) In the Cartesian coordinate system, construct the helical trajectory equation of any point on the worm tooth surface;

[0009] 12) The starting point and end point of the helical trajectory of any two points on the worm tooth surface are respectively located in the radial plane perpendicular to the worm axis. By introducing the phase angle, the complete helical trajectory equation of the worm tooth surface is obtained;

[0010] 13) Based on the complete helical trajectory equation, the upper tooth surface helical trajectory equation and the lower tooth surface helical trajectory equation of the worm gear are obtained;

[0011] Step 2: Solving the contact points of turning trajectory cutters

[0012] 21) Projecting the spiral trajectory points in the radial plane onto the machining surface in the axial direction to generate the spiral tool trajectory equation;

[0013] 22) Discretize the spiral tool trajectory equation to obtain the spiral tool trajectory contact point;

[0014] Step 3: Tool pose optimization

[0015] Tool arc wrap angle limit: Considering the influence of tool arc wrap angle, calculate the machining angle set of tool axis in the axial direction;

[0016] Machining interference limitation: To prevent interference between the tool and the machining surface during machining, the tool swing angle set for each working section is calculated;

[0017] Get the intersection of the machining angle set and the tool swing angle sum;

[0018] Step 4: Solve the knife position

[0019] The tool tip radius compensation is performed on the tool contact points that are spirally distributed on the worm tooth surface. The compensation direction is the normal vector direction at the tool contact point, and the tool position point trajectory equation is obtained. The tool position point trajectory equation is discretized to obtain the tool position point coordinates.

[0020] Step 5: Smoothness of tool axis vector change

[0021] Considering the machining efficiency and the smoothness of the tool axis vector angle transformation, the worm surface is discretized into multiple spiral lines to obtain the overall path of the tool position point.

[0022] Furthermore, in step 11), the helical trajectory equation of any point on the worm tooth surface is:

[0023]

[0024] Where: a is the center distance of the worm pair; R is the spiral radius; A is the worm swing angle; i 传 is the transmission ratio; the X-axis and the Y-axis are located in the radial direction of the worm, and the Z-axis is the rotation axis coaxial with the axis of the worm.

[0025] Further, in step 12), the helical trajectory equation of the worm tooth surface is:

[0026]

[0027] Among them: b is the boundary size; t is the rotation angle parameter of the rotation axis; f is the phase angle, which is determined by the positions of the four end points of the radial section of the worm tooth.

[0028] Further, in step 13), the trajectory equation of the upper tooth surface helix is:

[0029]

[0030] Where: R 1 R is the radius of the tooth tip circle; 2 is the tooth root circle radius; θ 1 is the phase angle of the tooth top point on the upper tooth surface; θ 2 is the phase angle of the tooth bottom end point on the upper tooth surface; ξ 1 is the ratio coefficient of the change of tooth thickness on the upper tooth surface to the change of phase angle;

[0031] The helix trajectory equation of the lower tooth surface is:

[0032]

[0033] Where: θ 3 is the phase angle of the tooth bottom end point of the lower tooth surface; θ 4 is the phase angle of the tooth top point on the lower tooth surface; ξ 2 It represents the ratio coefficient of the change of tooth thickness on the lower tooth surface to the change of phase angle.

[0034] Further, in step 21), the spiral tool trajectory equation is:

[0035]

[0036] Wherein: k = 1 or 3, and: when k = 1, it is the upper tooth surface; when k = 3, it is the lower tooth surface.

[0037] Furthermore, in step 22), the parameter b affecting the worm tooth thickness is discretized into n parts, and the obtained spiral trajectory knife contact point is:

[0038]

[0039] Where: q i is the i-th knife contact point obtained by discretization; (x i ,y i ,z i ) is the knife contact q i Coordinates of m i Knife contact q i From the tip circle R 1 The radial distance of i Knife contact q i Distance to the center of the worm gear; f i Knife contact q i The phase angle of .

[0040] Further, in step three, the machining angle set of the tool axis in the axial direction is:

[0041] ψ=(0,ψ 1 )∪(ψ 2 ,π)

[0042] Where: 1 Q is the point between the tool and the tooth top of the upper tooth surface 1 and the upper tooth surface tooth bottom end point Q 2 When the line segments between them contact, the angle between the tool axis vector and the worm axis at the boundary point of the tool wrap angle; ψ 2 The cutter axis vector and the bottom end point Q of the lower tooth surface 3 and the tooth top point Q on the lower tooth surface 4 When the line segments between them contact, the angle between the tool axis vector and the worm axis at the boundary point of the tool wrap angle is:

[0043]

[0044]

[0045] Where: δ is the half wrap angle of the tool arc; For line segment Q 1 Q 2 The angle between the worm axis and the worm shaft; For line segment Q 3 Q 4 The angle between the worm axis and the worm shaft axis; and:

[0046]

[0047] Where: y 1 and z 1 They are the top point Q of the upper tooth surface 1 The Y-axis and Z-axis coordinates of y 2 and z 2 The upper tooth surface and the tooth bottom end point Q 2 The Y-axis and Z-axis coordinates of y 3 and z 3 The bottom end point Q of the lower tooth surface is 3 The Y-axis and Z-axis coordinates of y 4 and z 4 The tooth top point Q of the lower tooth surface is 4 The Y-axis and Z-axis coordinates.

[0048] Furthermore, in step 3, the tool swing angle set of each working section is:

[0049] ε=(ε 2 , ε 1 )∪(ε 2 ′,ε 1 ′)

[0050] Where: 1 is the angle between the straight line BC and the axis of the worm; ε 2 is the angle between the straight line BD and the worm axis; ε 1 ′ is the angle between the straight line B′C and the worm axis; ε 2 ' is the angle between the straight line B'D and the worm axis; point B is along the straight line Q 1 Q 2 The tool position point that satisfies the tool swing angle limit after the normal direction is translated by the maximum machining depth; point B′ is along the straight line Q 3 Q 4 The tool position point that meets the tool swing angle limit after the normal direction is translated by the maximum machining depth; point C is the tooth top point Q on the upper tooth surface 1 Along the straight line Q 1 Q 2 Normal direction translation d 1 / 2; point D is the point Q at the top of the lower tooth surface 4 Along the straight line Q 3 Q 4 Normal direction translation d 1 / 2; and:

[0051]

[0052] Where: y B and z B is the coordinate value of point B on the Y axis and Z axis; B′ and z B′ The coordinates of point B' on the Y and Z axes; C and z C is the coordinate value of point C on the Y axis and Z axis; D and z D are the coordinate values ​​of point D on the Y and Z axes.

[0053] Furthermore, in step 4, tool tip radius offset compensation is performed along the contact point normal direction, which is expressed as:

[0054] z N′ =z N ―rcosα i

[0055] y N′ =y N +rsinα i

[0056] Where: y N and z N is the coordinate value of the knife contact point N in the Y-axis and Z-axis directions; N′ and z N′is the coordinate value of the tool position point in the Y-axis and Z-axis directions after tool nose radius offset compensation; r is the tool nose radius; α i is the angle between the normal vector of different touch points and the Z axis;

[0057] The tool position trajectory equation is:

[0058]

[0059] Where: (x i ,y i ,z i ) is the coordinate of the i-th knife contact point; (x i+1 ,y i+1 ,z i+1 ) is the coordinate of the i+1th knife contact point; (x j ,y j ,z j ) is the coordinate of the tool position point.

[0060] Furthermore, in step 5, the overall path of the tool position point is:

[0061]

[0062] Where: (x i ,y i ,z i ) is the coordinate of the i-th knife contact point; (x P ,y P ,z P ) is the coordinate of the tool position point; τ is the feed amount of each tool cutting in the Y-axis direction; λ is the thickness of each tool cutting; m is the number of discretization parts; b i is the distance from the knife contact point to the center point of the worm gear;

[0063] For the upper tooth surface:

[0064]

[0065] Where: γ 1 ′ is the single transformation angle of the tool axis vector when machining the upper tooth surface;

[0066] For the lower tooth surface:

[0067]

[0068] Where: γ 2 'When machining the upper tooth surface, the tool axis vector changes angle once.

[0069] The beneficial effects of the present invention are:

[0070] The worm multi-axis turning machining path planning method of the present invention applies multi-axis precision turning technology to the finishing of worms, expanding the solution for finishing worms. The present invention considers the characteristics of precision turning and five-axis linkage machining, combines the tooth profile equation of the toroidal worm, plans the tool path and optimizes the smoothness, and proposes a reliable solution for turning the curved surface of the toroidal worm using a multi-axis machine tool. Specifically, the traditional method of machining worms needs to be carried out on a special machine tool with a turntable. During machining, the center distance is adjusted by moving the turntable along the radial direction of the worm, and the transmission ratio is adjusted by the matching wheel; this type of machine tool is usually a cylindrical grinder style, a lathe style or a gear hobbing machine style in terms of structural style, and there are problems such as cumbersome machine tool adjustment, long machining cycle and high cost. In the present invention, by adopting multi-axis precision turning technology, multi-axis machining improves machining accuracy by reducing reference conversion; during the entire machining process, the parts only need to be clamped once, which helps to maintain constant accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0072] Figure 1 It is a flow chart of an embodiment of a method for planning a machining path for multi-axis turning of a worm gear according to the present invention;

[0073] Figure 2 It is a two-dimensional analysis diagram of the spiral trajectory;

[0074] Figure 3 It is a three-dimensional analysis diagram of the spiral trajectory;

[0075] Figure 4 It is the phase angle analysis diagram;

[0076] Figure 5 is the worm gear profile diagram;

[0077] Figure 6 It is the spatial spiral diagram of the tooth profile;

[0078] Figure 7 is the worm gear profile diagram;

[0079] Figure 8 This is a schematic diagram of the knife contact point;

[0080] Fig. 9 It is the cross-sectional tooth profile diagram;

[0081] Fig.10 It is the vector limit diagram of the cutter axis on the upper tooth surface;

[0082] Fig.11 It is the vector limit diagram of cutter axis on lower tooth surface;

[0083] Fig.12 is the tool tip radius offset diagram;

[0084] Fig.13 is the tooth surface curve diagram;

[0085] Fig.14 Schematic diagram of tool processing. DETAILED DESCRIPTION

[0086] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0087] like Figure 1 As shown, the worm multi-axis turning machining path planning method of this embodiment includes the following steps.

[0088] Step 1: Parameterization of worm tooth surface

[0089] 11) In the Cartesian coordinate system, construct the helical trajectory equation for any point on the worm tooth surface.

[0090] like Figure 2 As shown in the figure, the shaded part is the axial section of the worm gear after the material is removed by the material removal method. The four corner points of the section are the four endpoints of the tooth shape, which are marked as 1, 2, 3, and 4 in the figure. The trajectory curves of these four points are drawn. Then, after using boundary blending, surface merging and solidification, the worm gear profile can be obtained. Now, take a point trajectory as an example for derivation. In the two-dimensional plane shown in the figure, the center distance a is the center distance of the worm gear transmission, and the equation of the arc should be:

[0091] (y+a) 2 +z 2 =R 2

[0092] y=RcosA,z=RsinA

[0093] Now let's rotate the arc around the Z axis, that is:

[0094]

[0095] Then the equation of the three-dimensional surface is:

[0096]

[0097] Point P(z,y) becomes point P(x,y,z). The actual point P is moving relative to the X-Y plane while rotating around the Z axis. Figure 3The projection of point P on the X-Z plane is point M. Connect OM and extend it, and it intersects with the circle formed by rotating (0, a) around the X axis at point N. Here, ∠MNP is called the swing angle and is recorded as A, and ∠MOY is called the rotation angle and is recorded as B. The distance from point P to the X axis is OM, which is determined by the swing angle A. Figure 3 It can be concluded that:

[0098] OM=a―RcosA

[0099] On the X-Y plane, we can get That is:

[0100] x 2 +y 2 =(a-RcosA) 2

[0101] x and y are functions of OM and the rotation angle B. Let:

[0102]

[0103] Then we have:

[0104]

[0105] The relationship between angle A and angle B is determined by the transmission ratio i, which is:

[0106] B=iA

[0107] Combining the above formulas, the helical trajectory equation of any point on the worm tooth surface with respect to angle A can be obtained as:

[0108]

[0109] Where: a is the center distance of the worm pair; R is the spiral radius; A is the worm swing angle; i 传 is the transmission ratio; the X-axis and the Y-axis are located in the radial direction of the worm, and the Z-axis is the rotation axis coaxial with the axis of the worm.

[0110] 12) The starting point and end point of the helical trajectory of any two points on the worm tooth surface are respectively located in the radial plane perpendicular to the worm axis. By introducing the phase angle, the complete helical trajectory equation of the worm tooth surface is obtained.

[0111] The above is just an expression for the helical trajectory of the worm gear transmission. The specific modeling and processing must also consider the change of the phase angle. Because it is necessary to ensure that the starting points of the four lines are in the same plane passing through the worm axis, and at the same time, it is necessary to ensure that the end points of the four lines are also in the same plane passing through the worm axis. This is very important and will affect the success of modeling and processing. Figure 4 The shape of the worm shaft section is represented by, θ 1 ,θ 2,θ 3 ,θ 4 are the phase angles of the four spiral lines, let θ 1 =0,θ 2 ,θ 3 ,θ 4 It is determined by the shape of the cross section that needs to be cut off, and can be obtained by drawing or calculation.

[0112] Taking the phase angle into account, the helix trajectory equation of the worm tooth surface is:

[0113]

[0114] Among them: b is the boundary size; t is the rotation angle parameter of the rotation axis; f is the phase angle, which is determined by the positions of the four end points of the radial section of the worm tooth.

[0115] 13) Based on the complete helical trajectory equation, the upper tooth surface helical trajectory equation and the lower tooth surface helical trajectory equation of the worm gear are obtained.

[0116] like Figure 5 As shown, the tooth surface of the worm is divided into an upper tooth surface and a lower tooth surface. The upper tooth surface is the line segment Q 1 Q 2 The set in three-dimensional space, the lower tooth surface is the line segment Q 3 Q 4 Set in three-dimensional space.

[0117] When the generated helix is ​​the tooth top, b is R 1 , f takes θ 2 and θ 3 ; When the generated helix is ​​the tooth bottom, b is R 2 , f takes θ 3 and θ 4 The change of phase angle refers to the change of swing angle π(t―f), while the rotation angle iπt has no change of phase angle, so as to ensure that the starting points of the four lines are in the same plane passing through the axis of the worm, and at the same time ensure that the end points of the four lines are in the same plane passing through the axis of the worm.

[0118] In this way, the helical trajectory equation of the upper tooth surface is:

[0119]

[0120] Where: R 1 R is the radius of the tooth tip circle; 2 is the tooth root circle radius; θ 1 is the phase angle of the tooth top point on the upper tooth surface; θ 2 is the phase angle of the tooth bottom end point on the upper tooth surface; ξ 1 is the ratio coefficient of the change of tooth thickness on the upper tooth surface to the change of phase angle;

[0121] The helix trajectory equation of the lower tooth surface is:

[0122]

[0123] Where: θ 3 is the phase angle of the tooth bottom end point of the lower tooth surface; θ 4 is the phase angle of the tooth top point on the lower tooth surface; ξ 2 It is the ratio coefficient of the change of tooth thickness on the lower tooth surface to the change of phase angle.

[0124] Step 2: Solving the contact points of turning trajectory cutters

[0125] 21) Project the spiral trajectory points in the radial plane onto the machining surface in the axial direction to generate the spiral tool trajectory equation.

[0126] Specifically, the value range of t is (-1, 1), so substitute Figure 4 Middle Q 1 , Q 2 , Q 3 , Q 4 The R and f values ​​corresponding to the four points, in three-dimensional space, the generated tooth profile spiral line is as follows Figure 6 As shown;

[0127] In multi-axis turning, the key is to project the Archimedean spiral points on the X-Y plane onto the machining surface of the Z axis, and the toroidal worm tooth surface can also be regarded as a collection of projections of plane spiral lines in the vertical direction. The spiral tool trajectory equation is:

[0128]

[0129] Wherein: k = 1 or 3, and: when k = 1, it is the upper tooth surface; when k = 3, it is the lower tooth surface.

[0130] 22) Discretize the spiral tool trajectory equation to obtain the spiral trajectory tool contact point.

[0131] Specifically, the parameter b that affects the worm tooth thickness is discretized into n parts, and the spiral trajectory knife contact point is obtained as follows:

[0132]

[0133] Where: q i is the i-th knife contact point obtained by discretization; (x i ,y i ,z i ) is the knife contact q i Coordinates of m i Knife contact q i From the tip circle R 1 The radial distance ofi Knife contact q i The distance to the center of the worm gear is Figure 3 The point (0,a,0) in i Knife contact q i The phase angle of .

[0134] Step 3: Tool pose optimization

[0135] After solving the tool contact trajectory, in order to avoid local and global interference, it is necessary to judge the tool posture interference and smooth the tool axis vector.

[0136] When t=0, the coordinates of the four points are Q 1 (0,y 1 , z 1 ), Q 2 (0,y 2 , z 2 ), Q 3 (0,y 3 , z 3 ), Q 4 (0,y 4 , z 4 ), connect the four adjacent points to build a network that passes through the knife contact point z 1 , Q 2 , Q 3 , Q 4 The plane G(x i ,y i ,z i ), which is used to solve the feasible interval of the tool axis swing angle, such as Figure 7 shown.

[0137] (1) Tool arc angle limit

[0138] Considering the influence of the tool arc wrap angle, the machining angle set of the tool axis in the axial direction is calculated.

[0139] During the machining process, the tool itself can only achieve good results if the cutting edge is within the tool arc wrap angle range, so the influence of the tool arc wrap angle needs to be considered. Let the tool arc half wrap angle be δ. When the machining passes through Q 1 Q 2 and Q 3 Q 4 When the helical surface is formed, the tool is placed at the limit position, such as Figure 8 As shown, line segment Q 1 Q 2 and line segment Q 3 Q 4 The angles with the Z axis are:

[0140]

[0141] Where: y 1 and z 1 They are the top point Q of the upper tooth surface 1 The Y-axis and Z-axis coordinates of y 2 and z 2 The upper tooth surface and the tooth bottom end point Q 2 The Y-axis and Z-axis coordinates of y 3 and z 3 The bottom end point Q of the lower tooth surface is 3 The Y-axis and Z-axis coordinates of y 4 and z 4 The tooth top point Q of the lower tooth surface is 4 The Y-axis and Z-axis coordinates.

[0142] Tool and line segment Q 1 Q 2 The contact point F is a boundary point of the tool wrap angle, and the angle between the tool and the Z axis is ψ 1 , from the geometric relationship we can get:

[0143]

[0144] The machining angle range between the tool axis and the Z axis is (0, ψ 1 ).

[0145] Tool and line segment Q 3 Q 4 Contact point E is another boundary point of the tool wrap angle. At this time, the angle between the tool and the Z axis is ψ 2 , from the geometric relationship we can get:

[0146]

[0147] Then the machining angle range between the tool axis and the Z axis is (ψ 2 , π).

[0148] Where: δ is the half wrap angle of the tool arc; For line segment Q 1 Q 2 The angle between the worm axis and the worm shaft; For line segment Q 3 Q 4 The angle between the worm and the axis of the worm.

[0149] The angle range can be obtained in other planes by the same method. Therefore, on the entire tooth surface, considering the influence of the tool arc wrap angle, the machining angle set of the tool axis in the axial direction is:

[0150] ψ=(0,ψ 1)∪(ψ 2 ,π)

[0151] Where: 1 and ψ 2 Respectively represent ψ 1i With ψ 2i The set of 1 Q is the point between the tool and the tooth top on the upper tooth surface 1 and the upper tooth surface tooth bottom end point Q 2 When the line segments between them contact, the angle between the tool axis vector and the worm axis at the boundary point of the tool wrap angle; ψ 2 The cutter axis vector and the bottom end point Q of the lower tooth surface 3 and the tooth top point Q on the lower tooth surface 4 When the line segments between them contact, the angle between the tool axis vector and the worm axis at the boundary point of the tool wrap angle;

[0152] (2) Processing interference limitation

[0153] In order to prevent the tool from interfering with the machining surface during machining, the tool swing angle set of each working section is calculated.

[0154] Fig. 9 In the Z-Y plane, the vector:

[0155]

[0156] Take Q 1 With Q 2 The midpoint is A(z A ,y A ), perpendicular to line segment Q 1 Q 2 The normal vector along the positive Y axis is:

[0157]

[0158] Then the unit normal vector is:

[0159]

[0160] The angle between this vector and the Z axis is

[0161]

[0162] Then the normal vector through point A is:

[0163]

[0164] Assume the radius of the cutter head is r and the diameter of the handle is d 1 , then the line segment Q 1 Q 2 As the base, the normal vector through point A The coordinates of the cutting position are A′(z A +rsinα,y A +rcosα).

[0165] In order to prevent the tool from interfering with the machining surface during machining, the angular range of tool swing for each working section is calculated. Fig.10 As shown in the figure, when the tool position point is at point B, it is the maximum depth of machining. If the tool swing angle limit is met at this time, then in the entire machining process Q 1 Q 2 There will be no interference on the upper tooth surface. At this time, the maximum angle of the tool is the tool handle and point Q 1 With Q 4 Here we can make point Q 1 With Q 4 Move toward the middle along the lines perpendicular to each other The distance to point C(z C ,y C ), point D(z D ,y D ), then BC and BD coincide with the tool axis vector, and we have:

[0166]

[0167] The angle between BC and the Z axis is ε 1 :

[0168]

[0169] The angle between BD and the Z axis is ε 2 :

[0170]

[0171] Then the swing angle range of the tool axis about the Z axis is (ε 2 , ε 1 ).

[0172] Where: y B and z B is the coordinate value of point B on the Y axis and Z axis; C and z C is the coordinate value of point C on the Y axis and Z axis; D and z D are the coordinate values ​​of point D on the Y and Z axes.

[0173] Similarly, it can be inferred that the processed line segment Q 3 Q 4 When the lower tooth surface Fig.11 As shown, the tool axis vector is:

[0174]

[0175] The deepest knife point is B′(z 3 +rsinα,y 3 +rcos α), the angle between B′C and the Z axis is ε 1 ′:

[0176]

[0177] The angle between B′D and the Z axis is

[0178]

[0179] Then the swing angle range of the tool axis about the Z axis is (ε 2 ′,ε 1 ′).

[0180] Where: y B′ and z B′ The coordinate values ​​of point B' on the Y and Z axes.

[0181] According to the above method, the limit swing angle of the tool axis corresponding to the i-th (i=1, 2…, n) tool contact point is judged in turn, and the feasible interval ε of the tool axis swing angle corresponding to the tool contact points of the whole path is obtained, which is specifically expressed as:

[0182] ε=(ε 2 , ε 1 )∪(ε 2 ′,ε 1 ′)

[0183] Here ε 2 , ε 1 , ε 2 ′,ε 1 ′ respectively represents ε 2i , ε 1i , ε 2i ′,ε 1i ′’s collection.

[0184] Where: 1 is the angle between the straight line BC and the axis of the worm; ε 2 is the angle between the straight line BD and the worm axis; ε 1 ′ is the angle between the straight line B′C and the worm axis; ε 2 ' is the angle between the straight line B'D and the worm axis; point B is along the straight line Q 1 Q 2 The tool position point that satisfies the tool swing angle limit after the normal direction is translated by the maximum machining depth; point B′ is along the straight line Q 3 Q 4The tool position point that meets the tool swing angle limit after the normal direction is translated by the maximum machining depth; point C is the tooth top point Q on the upper tooth surface 1 Along the straight line Q 1 Q 2 Normal direction translation d 1 / 2; point D is the point Q at the top of the lower tooth surface 4 Along the straight line Q 3 Q 4 Normal direction translation d 1 / 2 after the point.

[0185] Get the intersection of the machining angle set and the tool swing angle:

[0186] γ=[(ε 2 , ε 1 )∩(0,ψ 1 )]∪[(ε 2 ′,ε 1 ′)∩(ψ 2 ,π)]

[0187] Step 4: Solve the knife position

[0188] The tool tip radius compensation is performed on the spirally distributed tool contact points on the worm tooth surface. The compensation direction is the normal vector direction at the tool contact point, and the tool position point trajectory equation is obtained. The tool position point trajectory equation is discretized to obtain the tool position point coordinates.

[0189] Specifically, in order to achieve high-efficiency and high-precision machining, solving the tool position point and generating a smooth tool path are the key tasks of multi-hybrid CNC machining.

[0190] For the precision turning of curved surfaces, according to the machining characteristics, the tool tip radius compensation can be directly performed on the spirally distributed tool contact points on the curved surface. The compensation direction is the normal vector direction at the tool contact point, such as Fig.12 In the tool tip radius offset compensation is performed along the contact point normal direction, which is expressed as:

[0191] z N′ =z N ―r cos α i

[0192] y N′ =y N +rsinα i

[0193] Where: y N and z N is the coordinate value of the knife contact point N in the Y-axis and Z-axis directions; N′ and z N′is the coordinate value of the tool position point in the Y-axis and Z-axis directions after tool nose radius offset compensation; r is the tool nose radius; α i is the angle between the normal vector of different touch points and the Z axis.

[0194] Combined with the discrete equation of the spiral trajectory tool contact point, the tool position trajectory equation is obtained as follows:

[0195]

[0196] Where: (x i ,y i ,z i ) is the coordinate of the i-th knife contact point; (x i+1 ,y i+1 ,z i+1 ) is the coordinate of the i+1th knife contact point; (x j ,y j ,z j ) is the coordinate of the tool position point.

[0197] The knife position (X p ,Y p ,Z p ) coordinates are:

[0198]

[0199] Step 5: Smoothness of tool axis vector change

[0200] Considering the machining efficiency and the smoothness of the tool axis vector angle transformation, the worm surface is discretized into multiple spiral lines to obtain the overall path of the tool position point.

[0201] Depend on Fig.13 It can be seen that the tooth surface of the worm is composed of spatial spiral lines. Considering the processing efficiency and the smoothness of the tool axis vector angle change, it is necessary to reasonably discretize the worm surface into multiple curves to ensure that all areas of the surface are processed without excessive repetition of processing, and the tool angle change between each path will not be too large, thereby improving the smoothness of the tool axis angle change.

[0202] Taking the machining of the upper tooth surface as an example, in the tool position trajectory equation, the parameter controlling the root circle and the top circle is b, and its range is (R 1 , R 2 ).like Fig.14 As shown, on each plane perpendicular to the Z axis, the worm gear tooth profile can have Q 1 , Q 2 , Q 3 , Q 4 Four points, assuming the thickness of each cutting is λ:

[0203] Fig.14The green line in the middle (the one parallel to the Y axis) is the distance perpendicular to the Z axis, indicating the feed amount τ of each cutting in the Y axis direction:

[0204]

[0205] The number of discretizations is:

[0206]

[0207] The expression of b is:

[0208] b i =R 1 +i,i∈[1,m]

[0209] When machining the upper tooth surface, the tool axis angle change range is γ 1 =(ε 2 , ε 1 )∩(0,ψ 1 ), and also make it discretized into m parts, then the single transformation angle of the tool axis vector can be expressed as:

[0210]

[0211] Similarly, when machining the lower tooth surface, the tool axis angle γ 2 =(ε 2 ′,ε 1 ′)∩(ψ 2 ,π), a single angle transformation can be expressed as:

[0212]

[0213] Combining the above equations, the overall path of the tool position point is obtained as:

[0214]

[0215] Where: (x i ,y i ,z i ) is the coordinate of the i-th knife contact point; (x P ,y P ,z P ) is the coordinate of the tool position point; τ is the feed amount of each tool cutting in the Y-axis direction; λ is the thickness of each tool cutting; m is the number of discretization parts; b i is the distance from the knife contact point to the center point of the worm gear, such as Figure 3 As shown, the center point of the worm gear is point (0, a, 0).

[0216] For the upper tooth surface:

[0217]

[0218] Where: γ 1 ′ is the single transformation angle of the tool axis vector when machining the upper tooth surface;

[0219] For the lower tooth surface:

[0220]

[0221] Where: γ 2 'When machining the upper tooth surface, the tool axis vector changes angle once.

[0222] The angle transformation of the tool axis is consistent with the discretization of the path spacing, and the synchronous transformation is maintained, which is beneficial to the smoothness of the overall path of the machining process. Combining the tool position coordinates obtained by the tool position solution and the interference-free machining posture sequence obtained by interference judgment, a complete five-axis turning machining path can be obtained. Based on these data, some series of post-processing are performed to convert the path into the G code required for machine tool processing.

[0223] The above-described embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or changes made by those skilled in the art based on the present invention are within the protection scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A worm multi-axis turning machining path planning method, characterized in that: The steps include: Step 1: Parameterization of worm tooth surface 11) In the Cartesian coordinate system, construct the helical trajectory equation of any point on the worm tooth surface; 12) The starting point and end point of the helical trajectory of any two points on the worm tooth surface are respectively located in the radial plane perpendicular to the worm axis. By introducing the phase angle, the complete helical trajectory equation of the worm tooth surface is obtained; 13) Based on the complete helical trajectory equation, the upper tooth surface helical trajectory equation and the lower tooth surface helical trajectory equation of the worm gear are obtained; Step 2: Solving the contact points of turning trajectory cutters 21) Projecting the spiral trajectory points in the radial plane onto the machining surface in the axial direction to generate the spiral tool trajectory equation; 22) Discretize the spiral tool trajectory equation to obtain the spiral tool trajectory contact point; Step 3: Tool pose optimization Tool arc wrap angle limit: Considering the influence of tool arc wrap angle, calculate the machining angle set of tool axis in the axial direction; Machining interference limitation: To prevent interference between the tool and the machining surface during machining, the tool swing angle set for each working section is calculated; Get the intersection of the machining angle set and the tool swing angle sum; Step 4: Solve the knife position The tool tip radius compensation is performed on the tool contact points that are spirally distributed on the worm tooth surface. The compensation direction is the normal vector direction at the tool contact point, and the tool position point trajectory equation is obtained. The tool position point trajectory equation is discretized to obtain the tool position point coordinates. Step 5: Smoothness of tool axis vector change Considering the machining efficiency and the smoothness of the tool axis vector angle transformation, the worm surface is discretized into multiple spiral lines to obtain the overall path of the tool position point.

2. The worm multi-axis turning machining path planning method according to claim 1, characterized in that: In step 11), the helical trajectory equation of any point on the worm tooth surface is: Where: a is the center distance of the worm pair; R is the spiral radius; A is the worm swing angle; i 传 is the transmission ratio; the X-axis and the Y-axis are located in the radial direction of the worm, and the Z-axis is the rotation axis coaxial with the axis of the worm.

3. The worm multi-axis turning machining path planning method according to claim 2, characterized in that: In the step 12), the helical trajectory equation of the worm tooth surface is: Where: b is the boundary size; t is the rotation angle parameter of the rotation axis; f is the phase angle.

4. The worm multi-axis turning machining path planning method according to claim 3, characterized in that: In step 13), the trajectory equation of the upper tooth surface helix is: Where: R1 is the radius of the tooth tip circle; R2 is the radius of the tooth root circle; θ1 is the phase angle of the top point of the upper tooth surface; θ2 is the phase angle of the bottom point of the upper tooth surface; ξ1 is the ratio coefficient of the change of the tooth thickness of the upper tooth surface to the change of the phase angle; The helix trajectory equation of the lower tooth surface is: Among them: θ3 is the phase angle of the tooth bottom end point of the lower tooth surface; θ4 is the phase angle of the tooth top point of the lower tooth surface; ξ2 is the ratio coefficient of the change of tooth thickness of the lower tooth surface to the change of phase angle.

5. The worm multi-axis turning machining path planning method according to claim 1, characterized in that: In the step 21), the spiral tool trajectory equation is: Wherein: k = 1 or 3, and: when k = 1, it is the upper tooth surface; when k = 3, it is the lower tooth surface.

6. The worm multi-axis turning machining path planning method according to claim 5, characterized in that: In step 22), the parameter b affecting the worm tooth thickness is discretized into n parts, and the obtained spiral track knife contact point is: Where: q i is the i-th knife contact point obtained by discretization; (x i ,y i ,z i ) is the knife contact q i Coordinates of m i Knife contact q i Radial distance from the tooth tip circle R1; b i Knife contact q i Distance to the center of the worm gear; f i Knife contact q i The phase angle of .

7. The worm multi-axis turning machining path planning method according to claim 1, characterized in that: In step 3, the machining angle set of the tool axis in the axial direction is: ψ=(0,ψ1)∪(ψ2,π) Where: ψ1 is the angle between the tool axis vector and the worm axis at the boundary point of the tool wrap angle when the tool contacts the line segment between the upper tooth surface tooth top point Q1 and the upper tooth surface tooth bottom end point Q2; ψ2 is the angle between the tool axis vector and the worm axis at the boundary point of the tool wrap angle when the tool contacts the line segment between the lower tooth surface tooth bottom end point Q3 and the lower tooth surface tooth top point Q4; and: Where: δ is the half wrap angle of the tool arc; is the angle between the line segment Q1Q2 and the worm axis; is the angle between line segment Q3Q4 and the worm axis; and: Among them: y1 and z1 are the Y-axis and Z-axis coordinates of the tooth top point Q1 on the upper tooth surface; y2 and z2 are the Y-axis and Z-axis coordinates of the tooth bottom end point Q2 on the upper tooth surface; y3 and z3 are the Y-axis and Z-axis coordinates of the tooth bottom end point Q3 on the lower tooth surface; y4 and z4 are the Y-axis and Z-axis coordinates of the tooth top point Q4 on the lower tooth surface.

8. The worm multi-axis turning machining path planning method according to claim 1, characterized in that: In step 3, the tool swing angle set of each working section is: ε=(ε2, ε1)∪(ε2′, ε1′) Among them: ε1 is the angle between the straight line BC and the axis of the worm; ε2 is the angle between the straight line BD and the axis of the worm; ε1′ is the angle between the straight line B′C and the axis of the worm; ε2′ is the angle between the straight line B′D and the axis of the worm; Point B is the tool position point that satisfies the tool swing angle restriction after being translated along the normal direction of the straight line Q1Q2 by the maximum processing depth; Point B′ is the tool position point that satisfies the tool swing angle restriction after being translated along the normal direction of the straight line Q3Q4 by the maximum processing depth; Point C is the point position of the tooth top point Q1 on the upper tooth surface after being translated d1 / 2 along the normal direction of the straight line Q1Q2; Point D is the point position of the tooth top point Q4 on the lower tooth surface after being translated d1 / 2 along the normal direction of the straight line Q3Q4; and: Where: y B and Z B is the coordinate value of point B on the Y axis and Z axis; B′ and Z B′ The coordinates of point B' on the Y and Z axes; C and z C is the coordinate value of point C on the Y axis and Z axis; D and z D are the coordinate values ​​of point D on the Y and Z axes.

9. The worm multi-axis turning machining path planning method according to claim 1, characterized in that: In the step 41), tool tip radius offset compensation is performed along the contact point normal direction, which is expressed as: With N′ =from N ―r cos α i and N′ =and N +r sin α i Where: y N and z N is the coordinate value of the knife contact point N in the Y-axis and Z-axis directions; N′ and z N′ is the coordinate value of the tool position point in the Y-axis and Z-axis directions after tool nose radius offset compensation; r is the tool nose radius; α i is the angle between the normal vector of different touch points and the Z axis; The tool position trajectory equation is: Where: (x i ,y i ,z i ) is the coordinate of the i-th knife contact point; (x i+1 ,y i+1 ,z i+1 ) is the coordinate of the i+1th knife contact point; (x j ,y j ,z j ) is the coordinate of the tool position point.

10. The worm multi-axis turning machining path planning method according to claim 9, characterized in that: In step 5, the overall path of the tool position point is: Where: (x i ,y i ,z i ) is the coordinate of the i-th knife contact point; (x P ,y P ,z P ) is the coordinate of the tool position point; τ is the feed amount of each tool cutting in the Y-axis direction; λ is the thickness of each tool cutting; m is the number of discretization parts; b i is the distance from the knife contact point to the center point of the worm gear; For the upper tooth surface: Where: γ1′ is the single transformation angle of the tool axis vector when machining the upper tooth surface; For the lower tooth surface: Among them: γ2′ is the angle of single change of the tool axis vector when machining the upper tooth surface.

Images