A non-orthogonal face gear machining method based on a four-axis machine tool

Abstract

The present invention relates to a method for machining non-orthogonal face gears based on a four-axis machine tool, and belongs to the field of non-orthogonal face gear machining. Before machining, the present invention adjusts the installation angle of the workpiece to be machined to a first set angle. During a tooth profile cutting process, the following steps are repeated until the termination condition is met: the gear cutting cutter is moved so that the origin of the first coordinate system is moved to the spatial coordinates of the vertex of the cone of the face gear located in the machine tool coordinate system. During the machining process, the present invention tilts the face gear to be machined at a certain angle through equivalent modeling, so that the four-axis machine tool can also perform gear cutting on non-orthogonal face gears, effectively reducing costs.

Description

Technical Field

[0001] The invention relates to a non-orthogonal face gear machining method based on a four-axis machine tool, and belongs to the field of non-orthogonal face gear machining. Background Art

[0002] Non-orthogonal face gear transmissions are gear pairs in which the angle between the face gear and the cylindrical gear axis ranges from 0° to 15°. These are a special type of non-orthogonal face gear transmission that boasts high transmission efficiency, low noise, long life, compact structure, low axial force, good flow diversion, and insensitivity to installation errors. They have demonstrated significant advantages in transmission structures such as helicopters and ships. However, traditional gear shaping and milling processes suffer from low efficiency and poor precision, making them impractical for high-volume, high-precision production.

[0003] In comparison, gear turning is significantly more efficient and can efficiently complete the processing of non-orthogonal face gears while ensuring accuracy. Gear turning of non-orthogonal face gears is a method of gear processing based on the principle of meshing of spatially staggered axis gears. During processing, the cutting motion occurs at the contact point between the edge of the tool cutting edge and the outer surface of the workpiece blank. Unlike processing methods such as gear shaping and gear milling, the spatial position of the tool and the workpiece are constantly changing during the entire gear turning process, causing the position of the tool cutting edge involved in the processing to change accordingly. This causes the linear speed at any point on the tool cutting edge to continuously change as the gear turning process progresses. Due to the particularity of the structure of non-orthogonal face gears, six-axis machine tools are often required for processing. Due to the high cost of six-axis machine tools, the processing capabilities within the industry are limited, which seriously restricts the promotion and application of non-orthogonal spur face gears. Summary of the Invention

[0004] The purpose of the present invention is to provide a non-orthogonal face gear skiving method based on a four-axis machine tool, so as to solve the problem of high cost when using a six-axis machine tool to skive non-orthogonal face gears.

[0005] To achieve the above object, the solution of the present invention includes:

[0006] A non-orthogonal face gear turning method based on a four-axis machine tool of the present invention comprises the following steps: mounting a face gear to be processed on a workpiece mounting seat to be processed of the four-axis machine tool, the workpiece mounting seat to be processed having a first degree of freedom of horizontal rotation and a second degree of freedom of rotation around the axial direction of the face gear to be processed; the four-axis machine tool comprises a rotating shaft on which a gear turning cutter is mounted, the rotating shaft is arranged on a Y-axis moving mechanism, the Y-axis moving mechanism is arranged on an X-axis moving mechanism, and the workpiece mounting seat to be processed is arranged on a Z-axis moving mechanism; adjusting the mounting angle between the spindle axis of the workpiece box and the X-axis to a first set angle by adjusting the first degree of freedom, the first set angle being obtained according to the unit vector of the axis of the gear turning cutter in the first coordinate system and the unit vector of the axis of the face gear in the face gear coordinate system after being transformed into the first coordinate system; establishing a first coordinate system according to the X, Y, and Z axes, with the origin being the intersection of the front cutting face of the gear turning cutter and the axis of the gear turning cutter;

[0007] During a single cutting process of the face gear by the gear skiving cutter, if the termination condition is not satisfied, the following steps are repeated: the origin of the first coordinate system of the gear skiving cutter is moved to the spatial coordinates of the vertex of the face gear cone in the machine tool coordinate system; a transformation matrix from the first coordinate system to the machine tool coordinate system is obtained according to a second set angle, wherein the second set angle is obtained according to the X-axis component and the Y-axis component of the unit vector of the axis of the face gear in the first coordinate system;

[0008] The termination condition is: the radial distance between the contact point between the gear cutting cutter and the face gear and the axis of the face gear is greater than the large end pitch circle radius of the face gear.

[0009] Furthermore, the spatial coordinates are also superimposed with the tooth direction feed vector of the gear skiving cutter and / or the tooth depth feed vector of the gear skiving cutter.

[0010] Furthermore, the first set angle is obtained by the following formula:

[0011] δ a =arccos(e t2 e a2 )

[0012] Among them, δ a is the first setting angle, e t2 is the unit vector of the axis of the gear cutting tool in the first coordinate system, e a2 is a vector.

[0013] Furthermore, the second set angle is obtained by the following formula:

[0014]

[0015] in, Set the angle for the second time, -e a2(2) is the component of the unit vector of the face gear axis in the first coordinate system in the Y-axis direction of the first coordinate system, e a2 (1) is the component of the unit vector of the face gear axis in the first coordinate system in the X-axis direction of the first coordinate system.

[0016] Furthermore, the first setting vector is obtained by the following formula:

[0017] e lY =T Y2 e l2

[0018] Among them, e lY is the tooth feed vector of the gear cutting tool, e l2 is the tooth feed direction corresponding to the tangent point between the gear cutting cutter and the face gear, T Y2 To obtain a conversion matrix according to the second set angle.

[0019] Furthermore, the second setting vector is obtained by the following formula:

[0020] e dY =T Y2 e d2

[0021] Among them, e dY is the tooth depth feed vector of the gear cutting tool, e d2 It is the tooth depth feed direction corresponding to the tangent point between the gear cutting cutter and the face gear.

[0022] The present invention has the following beneficial effects: This invention is a pioneering innovation that adjusts the mounting angle of the workpiece to be machined to a first set angle before machining. During a single tooth profile cutting process, the following steps are repeated until a termination condition is satisfied: the gear skiving cutter is moved so that the origin of the first coordinate system is moved to the spatial coordinates of the face gear's cone apex located in the machine tool coordinate system. During machining, the present invention uses equivalent modeling to tilt the face gear to a certain angle, enabling a four-axis machine tool to skive non-orthogonal face gears, effectively reducing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a schematic diagram of a four-axis machine tool model of the present invention;

[0024] Figure 2 This is a schematic diagram of theoretical positions for gear skiving according to the present invention;

[0025] Figure 3 This is a schematic diagram of the gear skiving position after equivalent conversion according to the present invention;

[0026] Figure 4 It is a schematic diagram of a mathematical model for gear turning according to the present invention.

[0027] In the figure: 1. Y-axis moving mechanism; 2. X-axis moving mechanism; 3. Z-axis moving mechanism; 4. Gear cutting cutter; 5. Face gear to be machined; 6. Workpiece box; 7. Workpiece installation angle. DETAILED DESCRIPTION

[0028] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0029] The idea of ​​the present invention is that when using a four-axis machine tool to turn non-orthogonal face gears, the gear cutting cutter is controlled to perform processing according to the gear cutting model after equivalent modeling, thereby equivalently achieving the tool tilting capability of a six-axis machine tool.

[0030] Method Example:

[0031] This embodiment provides a non-orthogonal face gear turning method based on a four-axis machine tool. The four-axis machine tool model on which the present invention relies is as follows: Figure 1 As shown, it includes a workpiece box (6), a face gear (5) to be processed is installed on the main shaft (A axis) of the workpiece box (6), a workpiece installation angle (7) that rotates the workpiece box to a certain angle, and a rotation axis C axis installed with a gear cutter (4), the rotation axis is set on the Y axis moving mechanism (1), the Y axis moving mechanism (1) is set on the X axis moving mechanism (2), and the workpiece box (6) is set on the Z axis moving mechanism (3), the Y axis is in the vertical direction, the Z axis is in the same direction as the axis of the tool box, the X axis is perpendicular to the Y axis and the Z axis at the same time, and the movement of the Z axis realizes the feeding of the workpiece to be processed. After the machine tool is equipped with an electronic gear box function, the A axis can realize follow-up linkage with the C axis; wherein, the Y axis is in the vertical direction, the Z axis is in the same direction as the axis of the rotation axis, and the X axis is perpendicular to the Y axis and the Z axis at the same time.

[0032] In order to achieve the equivalent effect of a four-axis machine tool and a six-axis machine tool when machining non-orthogonal face gears, the following steps are included:

[0033] 1. Adjustment of the gear cutting machine and realization of gear cutting motion. Before gear cutting, manually adjust the workpiece installation angle to adjust the installation angle of the gear to be processed to the first set angle δ a , that is, the angle formed by the axis of the A-axis and the X-axis is adjusted to the first set angle. The follow-up linkage relationship of the A-axis relative to the C-axis is set based on the function of the electronic gearbox. During gear cutting, the tooth profile of the face gear is processed by the follow-up movement of the A-axis relative to the C-axis. This linkage runs through the entire gear cutting process. By controlling the gear cutting cutter to enter from the outer end and exit from the inner end of the face gear to be processed, or to enter from the inner end and exit from the outer end of the face gear to be processed, the intersection of the front cutting face of the gear cutting cutter and the axis of the gear cutting cutter is moved to the spatial coordinate of the vertex of the cone of the face gear located in the machine tool coordinate system, and the above process is repeated until the full tooth depth is processed and the processing termination condition is met.

[0034] 2. Equivalent realization of gear turning. In order to meet the requirement of collinearity between the gear turning cutter tooth direction and the face gear tooth direction, the gear turning cutter and the face gear must have a helix angle difference, so the gear turning cutter needs to be tilted in the vertical direction to achieve the processing requirements. The position relationship between the two is as follows: Figure 2 As shown in the figure, a virtual cylindrical gear is added to illustrate the transition relationship between the gear cutting cutter and the face gear to be machined. Since cylindrical gears were used in the past, a virtual cylindrical gear was added as a reference when the model was established. At this time, the plane L formed by the axis of the face gear and the axis of the virtual cylindrical gear is a horizontal plane, and there is an angle between the axis of the gear cutting cutter and this plane. Obviously, a six-axis machine tool can achieve this ability to tilt the gear cutting cutter, while a four-axis machine tool does not have this "tool tilting" capability. Therefore, an effective equivalent conversion must be performed before a four-axis machine tool can be used to cut non-orthogonal face gears. Therefore, the relative positions of the gear cutting cutter and the face gear need to be equivalently converted according to the machine tool structure.

[0035] During equivalent conversion, the axis of the virtual gear cutting tool is aligned with the axis of the gear cutting tool in the actual machine tool. Figure 4 The Z2 direction of the gear cutting tool axis is Figure 1 The axis of the gear cutting tool in the Figure 4 The X3 direction in Figure 1 The X-axis direction of the machine tool coincides with the Z-axis direction of the workpiece. f The component of the direction along the vertical direction of the machine tool is not 0 (posture such as Figure 2 shown), does not conform to Figure 1 The model structure in , then we can Figure 4 The tool and the face gear rotate as a whole around the tool axis by a second set angle At this time, the axis of the face gear is guaranteed to be parallel to the horizontal plane. Figure 3 As shown, this conforms to Figure 1 The model structure in . Figure 1 The machine tool installation angle in the needs to be adjusted to the first setting angle δ a , to ensure the spatial angle relationship between the axis of the gear cutting cutter and the axis of the face gear. Through the above conversion relationship, it can be determined Figure 4 The tool origin O2 and the workpiece cone vertex O f exist Figure 1 The relative coordinate positions of X, Y, and Z in the machine tool structure are determined, and the movement of the gear cutting cutter is controlled by the CNC program to achieve equivalent gear cutting of non-orthogonal face gears.

[0036] 3. Establish a mathematical model for gear turning. Figure 4As shown in the figure, S2 is the gear turning tool coordinate system (first coordinate system), the origin of the gear turning tool coordinate system is the intersection of the gear turning tool rake face and the gear turning tool axis, and the X, Y, and Z axes of the gear turning tool coordinate system are parallel to the linear axes of the four-axis machine tool respectively; rotate S2 around the gear turning tool axis Then we get S3. is the change in the rotation angle of the gear cutting tool during rotation. S3 is the auxiliary coordinate system, whose coordinate axes are X3, Y3, and Z3 respectively. Z2 and Z3 are coincident with the axis of the gear cutting tool. Establish the S4 auxiliary coordinate system, whose coordinate axes are X4, Y4, and Z4 respectively. Y4 and Y3 are coincident. β is the helix angle of the gear cutting tool. The helix angle of the gear cutting tool is fixed during production. When the gear cutting tool rotates to the left, β takes a positive value, and when the gear cutting tool rotates to the right, β takes a negative value. Establish the S5 auxiliary coordinate system, whose coordinate axes are X5, Y5, and Z6 respectively. S5 is parallel to S4. Let O2O5=R t , used to describe the feeding position of the gear cutting cutter in the direction of tooth depth. When feeding to the theoretical depth, R t =R0, where R0 is the radius of the gear cutting cutter pitch circle. At this time, O5 is the tangent point between the gear cutting cutter pitch circle and the pitch cone surface of the face gear. Establish the S6 auxiliary coordinate system, whose coordinate axes are X6, Y6, and Z6 respectively. S6 is parallel to S5. Let O5O6=v. O6 is any point in the first set direction, which is used to describe the feed position of the gear cutting cutter along the tooth direction. Establish the S7 auxiliary coordinate system, whose coordinate axes are X7, Y7, and Z8 respectively. X7 coincides with X6, and Y7 is perpendicular to the axis of the face gear to be machined. Σ is the angle between the non-orthogonal face gear axes. This parameter is determined before machining and remains unchanged. Establish the S8 auxiliary coordinate system, whose coordinate axes are X8, Y8, and Z8 respectively. S8 is parallel to S7. Let O6O8=R s , O8 is any point on the axis of the face gear to be machined, which is used to describe the radial distance between the contact point O6 between the gear cutter and the face gear and the axis of the face gear. The S9 coordinate system is fixedly connected to the face gear to be machined, and its coordinate axis ratio is X9, Y9, Z9, It is the rotation angle of the gear to be machined around its own axis. f Indicates the vertex of the face gear cone, establish S f Coordinate system, whose coordinate axes are Xf, Yf, Zf, S f Parallel to S9, let O8O f =A s , used to describe the axial distance of the contact position relative to the face gear. The following relationship should be satisfied:

[0037]

[0038] Among them, Z1 is the number of teeth on the face gear, and Z2 is the number of teeth on the gear cutting tool.

[0039] 4. Calculate the equations for the tooth surfaces of non-orthogonal gears.

[0040] according to Figure 4 The position relationship is:

[0041] As=Rs / tan(Σ) (2)

[0042] The tooth surface equation of non-orthogonal face gear is:

[0043]

[0044] Among them, r2(u) describes the tooth profile equation when the gear cutter moves. When calculating the right tooth surface of a non-orthogonal gear, r2(u) is:

[0045]

[0046] When calculating the left tooth surface of a non-orthogonal gear, r2(u) is:

[0047]

[0048] When calculating the tooth root transition surface of non-orthogonal gears, r2(u) is:

[0049]

[0050] The left and right tooth surfaces of non-orthogonal face gears are distinguished in the same way as bevel gears. In the above formula, u is the involute parameter, r b is the base circle radius of the gear turning cutter, a is the angle of rotation of the involute around the axis of the gear turning cutter, which is used to describe the relative position of the two cutting edges of the tool; θ is the angle between any point on the top edge of the gear turning cutter and the line connecting the origin O2 and X2, r a M is the radius of the tooth tip circle of the gear cutting tool, ab For S b to S a The transformation matrices of the coordinate system are:

[0051]

[0052] According to the meshing principle, the tooth surface equation of the non-orthogonal face gear, that is, Formula 3, should satisfy the meshing equation:

[0053]

[0054] 5. Calculation of workpiece installation angle. The vertex of the face gear cone is at S f Coordinate r in the coordinate system of for:

[0055] r of =

[0001] T (12)

[0056] The vertex of the face gear cone is at S fCoordinate r in the coordinate system o2 for:

[0057] r o2 =M 23 M 34 M 45 M 56 M 67 M 78 M 89 M 9f r of (13)

[0058] Among them, M 23 、M 34 、M 45 、M 56 、M 67 、M 78 、M 89 and M 9f Corresponding to M ab The inverse transformation matrix of . For example, M 32 Represents the transformation matrix from the S3 coordinate system to the S2 coordinate system, then M 23 It corresponds to the transformation matrix from the S2 coordinate system to the S3 coordinate system.

[0059] Unit vector e of the face gear axis af In the face gear coordinate system S f It can be expressed as:

[0060] e af =

[001] T (14)

[0061] Vector e of the face gear axis a2 In the S2 coordinate system, it can be expressed as:

[0062] e a2 =T 23 T 34 T 45 T 56 T 67 T 78 T 89 T 9f e af (15)

[0063] Among them, T ab M ab Removing the matrix in the fourth row and fourth column means that only the angular transformation of the space vector is considered.

[0064] The tooth feed direction corresponding to the tangent point between the gear cutting tool and the gear to be machined is Figure 4 The Z4 direction in the gear cutting tool coordinate system S2 can be expressed as:

[0065] e l2 =[sinβ0 cosβ] T (16)

[0066] The tooth depth feed direction corresponding to the tangent point between the gear cutting tool and the gear to be machined is Figure 4 The Y4 direction in the gear cutting tool coordinate system S2 can be expressed as:

[0067] e d2 =

[010] T (17)

[0068] The vector of the gear cutting tool axis in the S2 coordinate system is:

[0069] e t2 =

[001] (18)

[0070] Then the included angle between the gear cutting tool and the axis of the face gear, also known as the workpiece installation angle, is:

[0071] δ a =arccos(e t2 e a2 ) (19)

[0072] 6. Calculation of the equivalent rotation angle of the face gear axis around the gear cutting cutter axis. That is, the rotation angle of the face gear axis around the gear cutting cutter axis is:

[0073]

[0074] in, Set the angle for the second time, -e a2 (2) is the component of the unit vector of the face gear axis in the first coordinate system in the Y-axis direction, e a2 (1) is the component of the unit vector of the face gear axis in the first coordinate system in the X-axis direction.

[0075] 7. Calculation of the feed direction of the gear cutting tool. a Under the premise that the Z-axis direction of the S2 coordinate system coincides with the Z-axis direction of the four-axis machine tool, there is a conversion angle on the XY plane The coordinate system of the four-axis machine tool is S Y , its origin coincides with the origin of the gear cutting tool cutting edge coordinate O2, S2 revolves around S Y Z-axis rotation Get the S2 coordinate system to the machine tool coordinate system S Y The transformation matrix:

[0076]

[0077] Then in S Y In the machine tool coordinate system, the coordinates of the vertex of the face gear cone rY for:

[0078] r Y =M Y2 r o2 (twenty two)

[0079] Formula (22) is input into the CNC program of the four-axis machine tool. The program automatically executes this formula to control the four-axis machine tool so that the cone vertex of the face gear and the gear cutting cutter maintain a relative motion relationship.

[0080] The tooth feed vector of the gear cutting tool is Figure 4 The Z4 direction in the machine coordinate system S Y It can be expressed as:

[0081] e lY =T Y2 e l2 (twenty three)

[0082] 8. The tooth depth feed vector of the gear cutting tool, that is Figure 4 The Y4 direction in the machine coordinate system S Y It can be expressed as:

[0083] e dY =T Y2 e d2 (twenty four)

[0084] Among them, T Y2 M Y2 The matrix after removing the fourth row and fourth column.

[0085] In each process of gear turning, Y Superposition e lY and / or e dY After that, the feed depth of the gear cutting cutter can be controlled, that is, the gear cutting cutter is controlled to cut a little more, and the other process is controlled to cut a little less, but the total depth remains unchanged.

[0086] Based on the above theory, before gear cutting, the installation angle is adjusted to the angle δ calculated by formula (19) a During machining, the auxiliary angles for rotating the X and Y axes around the axis of the gear cutting cutter are the angles obtained by formula (20). The movement of X, Y, and Z is controlled by CNC program to achieve equivalent gear skiving of non-orthogonal face gears.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A non-orthogonal face gear turning method based on a four-axis machine tool, characterized in that: The method comprises the following steps: mounting a face gear to be processed on a spindle of a workpiece box of a four-axis machine tool, wherein the workpiece box has a first degree of freedom of horizontal rotation; the four-axis machine tool comprises a tool box on which a gear cutting cutter is mounted, wherein the tool box is arranged on a Y-axis moving mechanism, wherein the Y-axis moving mechanism is arranged on an X-axis moving mechanism, and wherein the workpiece box is arranged on a Z-axis moving mechanism; adjusting the mounting angle between the spindle axis of the workpiece box and the X-axis to a first set angle by adjusting the first degree of freedom, wherein the first set angle is obtained based on a unit vector of the axis of the gear cutting cutter in a first coordinate system and a unit vector of the axis of the face gear in a face gear coordinate system transformed into a first coordinate system; establishing the first coordinate system based on the X, Y, and Z axes, wherein the origin is the intersection of the front cutting face of the gear cutting cutter and the axis of the gear cutting cutter; During a single cutting process of the face gear by the gear skiving cutter, if a termination condition is not satisfied, the following steps are repeated: the gear skiving cutter is moved so that the origin of the first coordinate system is moved to the spatial coordinates of the vertex of the face gear cone located in the machine tool coordinate system; a transformation matrix from the first coordinate system to the machine tool coordinate system is obtained according to a second set angle, wherein the second set angle is obtained according to the X-axis component and the Y-axis component of the unit vector of the axis of the face gear in the first coordinate system; The termination condition is that the radial distance between the contact point between the gear skiving cutter and the face gear and the axis of the face gear is greater than the large end pitch circle radius of the face gear.

2. The non-orthogonal face gear machining method based on a four-axis machine tool according to claim 1, characterized in that: The space coordinates are also superimposed with a tooth direction feed vector of the gear skiving cutter and / or a tooth depth feed vector of the gear skiving cutter.

3. The non-orthogonal face gear machining method based on a four-axis machine tool according to claim 1, characterized in that: The first setting angle is obtained by the following formula: δ a =arcs(e t2 and a2 ) Among them, δ a For the first setting angle, e t2 is the unit vector of the axis of the gear cutting tool in the first coordinate system, e a2 is the vector.

4. The method for machining non-orthogonal face gears based on a four-axis machine tool according to claim 1, characterized in that: The second setting angle is obtained by the following formula: in, Set the angle for the second, -e a2 (2) is the component of the unit vector of the face gear axis in the first coordinate system in the Y-axis direction of the first coordinate system, e a2 (1) is the component of the unit vector of the face gear axis in the first coordinate system in the X-axis direction of the first coordinate system.

5. The method for machining non-orthogonal face gears based on a four-axis machine tool according to claim 2, characterized in that: The tooth feed vector of the gear cutting tool is obtained by the following formula: And lY =T Y2 And l2 Among them, e lY is the tooth feed vector of the gear cutting tool, e l2 is the tooth feed direction corresponding to the tangent point between the gear cutting cutter and the face gear, T Y2 A conversion matrix is ​​obtained according to the second set angle.

6. The method for machining non-orthogonal face gears based on a four-axis machine tool according to claim 5, characterized in that: The tooth depth feed vector of the gear cutting tool is obtained by the following formula: And dY =T Y2 And d2 Among them, e dY is the tooth depth feed vector of the gear cutting tool, e d2 It is the tooth depth feed direction corresponding to the tangent point between the gear cutting cutter and the face gear.

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