Ultrasonic elliptical vibration turning surface residual height prediction method

Abstract

The invention belongs to the field of ultrasonic elliptical vibration assisted ultra-precision cutting machining, and discloses a method for predicting the residual height of an ultrasonic elliptical vibration turning surface. According to the method, a numerical method for solving the residual height introduced in the cutting direction by ultrasonic elliptical vibration turning is established on the basis of a simple harmonic vibration time reversal symmetry principle according to the principle that ultrasonic simple harmonic vibration has motion displacement symmetry and time reversal symmetry about a balance position in a complete period. The method can be suitable for calculating the theoretical residual height of common plane cutting and slope cutting in the cutting direction. According to the method, a new thought is provided for calculation of the theoretical residual height of the ultrasonic elliptical vibration cutting surface, and the reasonability of ultrasonic elliptical vibration auxiliary ultra-precision cutting process parameter selection can be judged in an auxiliary mode in actual production.

Description

Technical Field

[0001] The present invention belongs to the field of ultrasonic elliptical vibration assisted ultra-precision cutting processing, and more specifically, relates to a method for predicting the residual height of a surface cut by ultrasonic elliptical vibration. Background Art

[0002] Ultrasonic elliptical vibration turning technology is widely used in the ultra-precision machining of difficult-to-machine materials such as ferrous metals and brittle materials. Due to its tool-work separation, this technology effectively reduces cutting forces, facilitates the entry of cutting fluid into the cutting zone, and further enhances cooling and lubrication. These significant advantages extend the application range of conventional single-point diamond turning, particularly for suppressing the severe chemical wear of diamond tools during ferrous metal cutting.

[0003] In ordinary arc blade single-point diamond turning, the feed rate, spindle speed and tool nose radius determine the theoretical residual height of the machined surface in the feed direction (radial direction). In ultrasonic elliptical vibration-assisted single-point diamond turning, in addition to the feed direction, due to the influence of the tool elliptical vibration and cutting speed, under the combined action of ultrasonic vibration frequency, vibration amplitude and cutting speed, periodic machining textures will also be introduced in the cutting direction (circumferential direction), which is called the theoretical residual height in the cutting direction. Therefore, the micromorphology and surface roughness of the final machined surface are the superposition of the theoretical residual height in the feed direction and the theoretical residual height in the cutting direction. However, in actual production, the surface roughness requirements for ultra-precision machined workpieces are extremely high, generally required to reach the nanometer level. The influence of the additional machining texture introduced in the cutting direction by ultrasonic elliptical vibration turning on the surface roughness of ultra-precision machined surfaces cannot be ignored. If it is impossible to quickly determine the influence of the process parameter selection on the residual height in the cutting direction, more time and cost of process parameter debugging and optimization will be required in actual processing, which is not conducive to improving processing efficiency.

[0004] CN113042823A discloses a method for predicting the residual height of straight-line cutting under multi-process parameter conditions. The method comprises the following steps: step 1: inputting the tool parameters and ultrasonic elliptical vibration cutting parameters of the workpiece processing, obtaining the vibration processing parameters, and judging the surface processing condition of the part based on the tool parameters and ultrasonic elliptical vibration cutting parameters; step 2: measuring the semi-finished product or finished product after processing, obtaining the measurement model through surface reconstruction, and analyzing and obtaining the residual height Rth1 after the actual processing considering the blunt radius; step 3: obtaining the vibration parameter equation of the processing trajectory and the tool front and back face parameter equations based on the processing parameters, and then analyzing and obtaining the residual height Rth2 when the blunt radius is not considered. This invention takes into account the influence of the blunt radius on the tool. When the tool used for processing is a tool with a circular front face and a conical back face, the method explores the influence of the composite cutting process parameters, ultrasonic vibration parameters, and tool geometry parameters on the residual height in ultrasonic-assisted vibration cutting technology.

[0005] CN113901388A discloses a method for predicting the residual height of cutting along a curve under variable parameter conditions. The method obtains the curve equation based on the processed surface; establishes a variable parameter elliptical vibration equation to obtain the elliptical trajectory equation of ultrasonic elliptical vibration processing, and combines the elliptical trajectory equation with the curve equation obtained in step 1 to determine the coordinates of the intersection of the curve and the elliptical trajectory; calculates the elliptical vibration trajectory equation of the nth tool contact point during the cutting process, and then calculates the intersection of the elliptical vibration trajectories of two adjacent tool contact points, and finally calculates the residual height between adjacent elliptical vibration trajectories.

[0006] The ultrasonic elliptical vibration cutting surface residual height prediction method mentioned in CN113042823A focuses on the study of ordinary planes and only considers the effect of tool motion speed along the cutting direction on the residual height when the machining tool moves along a single axis. It does not address the problem of calculating the surface residual height when cutting inclined surfaces in the case of multi-axis linkage. The residual height prediction method for cutting along a curve under variable parameter conditions proposed in CN113901388A does not consider the effect of tool cutting speed on the intersection position calculation result when determining the intersection point between the elliptical vibration trajectory and the curve. However, tool cutting speed actually affects the shape of the continuous tool relative motion trajectory, thereby affecting the intersection point between the tool vibration trajectory and the curve.

[0007] Therefore, a new theoretical residual height prediction method for the cutting direction needs to be developed for ultrasonic elliptical vibration turning to solve the problem of surface residual height calculation when multi-axis linkage ultrasonic elliptical vibration cutting bevels. Summary of the Invention

[0008] The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a method for obtaining the numerical solution of the residual height in the cutting direction of ultrasonic elliptical vibration turning, so as to make a preliminary judgment on the rationality of the selection of process parameters in ultrasonic elliptical vibration-assisted ultra-precision cutting under multi-axis linkage using ordinary arc-edged diamond tools, help operators quickly determine the appropriate process parameter range, thereby reducing the time cost of process parameter debugging and optimization and improving processing efficiency.

[0009] To achieve the above objectives, the present invention provides a method for predicting the residual height of a surface during ultrasonic elliptical vibration turning. Based on the principle that ultrasonic simple harmonic vibration exhibits motion displacement symmetry and time reversal symmetry about the equilibrium position within a complete cycle, this method establishes a numerical method for calculating the residual height introduced in the cutting direction by ultrasonic elliptical vibration turning. This method is applicable to calculating the residual height of a surface during both conventional plane cutting and multi-axis coordinated inclined surface cutting. The specific steps of this method are as follows:

[0010] Step 1: Obtain the corresponding surface equation z for the target surface to be processed s =f(y);

[0011] Step 2: Based on the surface equation to be machined and combined with the tool vibration form, establish the cutting trajectory expression of the tool relative to the workpiece in ultrasonic elliptical vibration cutting for:

[0012]

[0013] Among them, A y 、A z They represent the unilateral amplitude of the tool along the y and z directions of the machine tool coordinate system during the ultrasonic elliptical vibration-assisted cutting process, f is the vibration frequency of the ultrasonic elliptical vibration, and v c represents the cutting speed in the y direction, k is the proportional coefficient of the machine tool z-direction guide rail moving speed and the y-direction cutting speed, and its specific value depends on the angle α between the target surface to be processed and the positive direction of the y axis, z d To ensure the cutting path The offset in the z-axis direction added at a certain distance above the target surface to be processed;

[0014] Step 3: Starting from t=0, according to the tool relative cutting trajectory expression The cutting trajectory is solved using the Newton-Raphson iteration method in the first vibration cycle. From the point on the target surface to be processed z s = f(y) The cutting time t1 corresponding to the shortest straight line distance along the z-axis direction, and the corresponding shortest straight line distance along the z-axis direction at this time is z d1 ;

[0015] Step 4: Cutting the tool path Translate z downward along the z axis d1 Get tool cutting trajectory

[0016]

[0017] The cutting trajectory corresponding to time t1 The point on the cutting path The tangent point A0 of the target surface to be machined is recorded as the cutting time corresponding to point A0 According to the periodic characteristics of the tool's ultrasonic elliptical vibration, along the cutting trajectory The time direction of the second tangent point can be determined as point D0 in the next adjacent cycle. The time corresponding to point D0 can be expressed as:

[0018]

[0019] Wherein, T is the period of ultrasonic elliptical vibration of the tool;

[0020] Step 5: Define the moment when the tool cuts into the material again in the first vibration cycle as t c , set its corresponding cutting trajectory Point C0 on

[0021] Step 6: At the same time, let point A0 and point D0 start moving from the initial position, where point A0 is on the cutting trajectory. The upper edge moves gradually in the direction of time with a change of Δt (t increases by Δt), and point D0 is on the cutting trajectory. The upper edge moves in the reverse direction of time by a change of Δt (t minus Δt). Once the magnitude relationship of the y-axis coordinates of the two moving points reverses, it means that the two have reached the overlapping point C0. At this time, the time corresponding to point C0 can be expressed as:

[0022]

[0023] Where n is the point D0 with a change of Δt on the cutting trajectory. The number of steps required for the upper edge to move in the time-reverse direction to the coincidence point C0;

[0024] Step 7: Time t corresponding to the coincidence point C0 obtained in step 6 c And the tool cutting trajectory expression obtained in step 4 The position coordinates of point C0 in the YOZ plane are (y'(t c ),z'(t c ));

[0025] Step 8. Use the point-to-line distance formula to calculate the distance from point C0 to the ideal target surface z s =f(y) The distance result is the theoretical residual height Rz in the cutting direction v .

[0026] Moreover, the distance from a point to a line is calculated as follows:

[0027]

[0028] Among them, k and b are called the directional coefficients of the straight line equation, and c is a constant term representing the spatial position offset.

[0029] As a further preference of the present invention, the parameter k related to the type of surface to be processed in step 2 is taken as k=0 when the surface is an end plane; when the surface is an inclined surface, k depends on the angle α between the target inclined surface to be processed and the horizontal plane in the clockwise direction, specifically k=tanα.

[0030] As a further preferred embodiment of the present invention, the time variation Δt in step 6 is preferably set to Where T is the period of ultrasonic elliptical vibration of the tool, m represents the number of time segments, and it is preferably set to be greater than or equal to 10 5 natural number.

[0031] Advantages and beneficial effects of the present invention:

[0032] 1. The method of the present invention takes into account the influence of the synthetic cutting speed of the tool end generated by the multi-axis linkage of the machine tool on the relative motion trajectory of the tool elliptical vibration, and is also applicable to the calculation of the residual height of the cutting surface of an ordinary horizontal plane, and has a certain universality.

[0033] 2. This method is based on the characteristics of motion displacement symmetry and time reversal symmetry of ultrasonic simple harmonic oscillation. Through the established numerical calculation method, the residual height introduced in the cutting direction when ultrasonic elliptical vibration turning planes and inclined surfaces can be easily calculated. It can assist relevant operators in preliminarily judging the rationality of process parameter selection in actual processing, and make up for the shortcomings of traditional trial cutting steps with long time cycle and cumbersome process adjustment and optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is the principle diagram of ultrasonic elliptical vibration assisted cutting;

[0035] Figure 2 This is the principle diagram of ultrasonic elliptical vibration cutting bevel;

[0036] ( Figure 2 Middle: 1 is the initial cutting trajectory 2 is the cutting trajectory after translation

[0037] Figure 3 This is an enlarged view of the local details of the ultrasonic elliptical vibration cutting bevel;

[0038] Figure 4 This is the principle diagram of ultrasonic elliptical vibration cutting plane. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not restrictive, and should not be used to limit the scope of protection of the present invention.

[0040] The schematic diagram of ultrasonic elliptical vibration assisted cutting is as follows Figure 1 As shown in Figure 1, this method applies ultrasonic simple harmonic vibration to the diamond tool along the cutting direction and the cutting normal, resulting in the tool removing material in the form of elliptical vibration. Because ultrasonic elliptical vibration cutting has the periodic cutting characteristics of tool-work separation, it introduces a periodic texture in the cutting direction, which is called the residual height in the cutting direction.

[0041] Figure 2 The diagram below shows the principle of ultrasonic elliptical vibration cutting of bevel. Figure 2 After analyzing several cycles, we can get the enlarged schematic diagram of the local details of the residual height in the cutting direction. Figure 3 As shown. Figure 3 When the angle between the inclined surface to be machined and the positive direction of the y-axis is 0° (i.e. Figure 3 The circumferential inclination angle α=0°), the whole cutting process will become the process of ultrasonic elliptical vibration cutting plane, such as Figure 4 As shown in the figure, the ultrasonic elliptical vibration cutting process is included in the special case when the inclined plane angle α is 0°, so the following will refer to Figure 3 The principle diagram shown in FIG. 1 is used to explain in more detail the method for obtaining the numerical solution of the theoretical residual height in the cutting direction of ultrasonic elliptical vibration cutting in the present invention from a general perspective:

[0042] The first step is to obtain the corresponding surface equation z for the target surface to be processed s =f(y), that is, Figure 3 The surface is indicated by the black dashed line;

[0043] The second step is to establish the cutting trajectory expression of the tool relative to the workpiece in ultrasonic elliptical vibration cutting based on the surface equation to be machined and combined with the tool vibration form.

[0044]

[0045] Where A y 、A zare the unilateral amplitudes of the tool along the y and z directions of the machine tool coordinate system during ultrasonic elliptical vibration-assisted cutting, f is the vibration frequency of ultrasonic elliptical vibration, and v c Represents the cutting speed along the y direction, k is the proportional coefficient of the machine tool z-direction guide rail moving speed and the y-direction cutting speed, which depends on the angle α between the target surface to be machined and the positive direction of the y axis. Therefore, when the machined surface is an end plane, k = 0, and the cutting trajectory is as follows: Figure 2 As shown; when the machined surface is an inclined surface, k = tanα, and the cutting trajectory is as follows Figure 1 As shown, z d To ensure the cutting path An offset in the z-axis direction added at a certain distance above the surface to be machined;

[0046] Furthermore, the relative motion speed v of the tool along the cutting direction and the cutting normal is y (t), v z (t) can be expressed by the cutting trajectory The derivation yields:

[0047]

[0048] Step 3: Starting from t=0, according to the relative cutting trajectory expression of the tool The tool path is solved using the Newton-Raphson iteration method in the first vibration cycle. From the point on the target surface to be processed z s = f(y) The cutting time t1 corresponding to the shortest straight-line distance along the z-axis direction, and the straight-line distance along the z-axis direction corresponding to this moment is set as z d1 .

[0049] Step 4: Figure 2 As shown, the tool cutting path Translate z downward along the z axis d1 Get tool cutting trajectory

[0050]

[0051] The cutting trajectory corresponding to time t1 The point on the cutting path The point of tangency with the target surface to be processed. Figure 3 As shown, the tangent point is marked as point A0, and the cutting time is also recorded as According to the periodic characteristics of the tool's ultrasonic vibration, along the cutting path The time direction of the second tangent point can be determined as point D0 in the next adjacent cycle, and the corresponding moment can be expressed as:

[0052]

[0053] Wherein, T is the period of ultrasonic elliptical vibration of the tool;

[0054] Step 5: Define the moment when the tool cuts into the material again in the first vibration cycle as t c , set its corresponding cutting trajectory Point C0 on

[0055] Step 6: At the same time, let point A0 and point D0 start moving from the initial position, where point A0 is on the cutting trajectory. The upper edge moves gradually in the direction of time with a change of Δt (t increases by Δt), and point D0 is on the cutting trajectory. The upper edge moves in the reverse direction of time by a change of Δt (t minus Δt). Once the magnitude relationship of the y-axis coordinates of the two moving points reverses, it means that the two have reached the overlapping point C0. At this time, the time corresponding to point C0 can be expressed as:

[0056]

[0057] Where n is the point D0 with a change of Δt on the cutting trajectory. The number of steps required to move in the time reverse direction to the coincidence point C0, and the time change Δt is preferably set to m represents the number of time segments, and it is preferably set to be greater than or equal to 10 5 natural numbers;

[0058] More specifically, the following will deduce and explain in detail why points A0 and D0 can simultaneously reach the trajectory overlap point C0 (B0) according to the movement method of step 6:

[0059] from Figure 3 The distance from point A0 to point D0 along the cutting trajectory is one vibration cycle. A0 and D0 are both tangent points between the elliptical trajectory envelope and the ideal target surface. The initial position coordinates of points A0 and D0 in the YOZ plane of the Cartesian coordinate system can be expressed as According to the cutting trajectory expression It can be seen that:

[0060]

[0061] in, Respectively represent the cutting trajectory The cutting moment corresponding to the initial position of A0 and D0;

[0062] exist Figure 3 From point B0(y'(t b ),z'(t b )) moves along the cutting trajectory to point B1(y'(tb1 ),z'(t b1 )) is also a vibration cycle, according to the cutting trajectory expression Similarly, we can get:

[0063]

[0064] Among them, t b , t b1 Respectively represent the cutting trajectory The moments corresponding to B0 and B1;

[0065] like Figure 3 As shown, point B0 and point C0 coincide in the cutting trajectory, so it can be seen that:

[0066]

[0067] where t c Indicates the cutting path The moment corresponding to the upper point C0;

[0068] Next, Figure 3 Point D0 on the tool path is the starting point, and the time corresponding to this point at the initial position is The cutting time corresponding to points C0 and B1 is used And the time intervals Δt1 and Δt2 are expressed as:

[0069]

[0070] Where Δt1 and Δt2 represent the cutting trajectory The time interval required to move from C0 to D0 and from D0 to B1;

[0071] Next, we will t represented by Δt1 and Δt2 c and t b1 Substitute into the relation In combination with the cutting trajectory expression The following relationship R1 can be obtained:

[0072]

[0073] Since the direction of the resultant velocity of the tool relative motion at the cutting moment corresponding to point D0 is parallel to the target surface to be machined, it can be obtained:

[0074]

[0075] On this basis, combined with the relative motion speed expression v of the tool along the cutting direction and the cutting normal, y (t) and v z(t) can further obtain the relationship R2:

[0076]

[0077] Combining the relationships R1 and R2, we can obtain the following equation R3:

[0078]

[0079] Analysis shows that in equation R3 It is not always 0, so to satisfy the equality relationship in R3, the following additional conditions must be met:

[0080] Δt1-Δt2=0;

[0081] Therefore, we know that the time Δt1 required to move from C0 to D0 is equal to the time Δt2 required to move from D0 to B1. Furthermore, according to the periodic law of ultrasonic vibration, the time required to move from A0 to B0 is equal to the time Δt2 required to move from D0 to B1, so the time required to move from C0 to D0 is equal to the time required to move from A0 to B0. Therefore, according to the movement method in step 4, points A0 and D0 can simultaneously reach the trajectory overlap point C0;

[0082] Step 7: Cutting time t corresponding to the coincidence point C0 obtained in step 6 C And the cutting trajectory expression obtained in the fourth step The position coordinates of point C0 in the YOZ plane are (y'(t c ),z'(t c ));

[0083] Step 8. Use the point-to-line distance formula to calculate the distance from point C0 to the target surface to be processed, which is the theoretical residual height Rz in the cutting direction. v More specifically, the target surface to be processed is set at Figure 3 The YOZ coordinate plane shown can be expressed in the form of a straight line equation:

[0084] ky+bz+c=0

[0085] Among them, k and b are called the directional coefficients of the straight line equation, and c is the constant term representing the spatial position offset;

[0086] Furthermore, Rz v It can be calculated as:

[0087]

[0088] Application Example 1:

[0089] The numerical solution method for the theoretical residual height in the cutting direction of ultrasonic elliptical vibration turning in the present invention is applicable to plane and inclined surface processing. In this embodiment, plane cutting processing is taken as an example, and the vibration frequency is f = 40kHz (corresponding to the vibration period T = 1 / 40000s), and the cutting direction amplitude is A y =2μm, cutting normal amplitude is A z =1μm ultrasonic vibration parameter, select cutting speed as v c =10m / min, using a circular arc diamond turning tool with a rake angle of 0° and a clearance angle of 15°. The specific implementation method for obtaining the numerical solution of the theoretical residual height in the cutting direction for plane cutting is as follows:

[0090] First, for example, setting the plane to be processed in the YOZ coordinate plane can be expressed by the equation z=0.

[0091] Next, the cutting trajectory expression of the tool relative to the workpiece is obtained based on the ultrasonic vibration parameters and cutting process parameters.

[0092] When cutting a plane, k = 0. In addition, set z d =2mm, ensuring that the envelope line of the lower half of the cutting trajectory has a certain distance from the surface to be machined.

[0093] Next, starting from time t=0, solve the tool path in the first vibration cycle The cutting time t1 corresponding to the shortest straight-line distance from the point on the surface to be machined along the z-axis is obtained by the Newton-Raphson iteration method as t1 = 1.25 × 10 -5 s, the corresponding shortest straight line distance along the z axis is z d1 =1.999mm.

[0094] Next, the tool path Translate z downward along the z axis d1 Get tool path

[0095]

[0096] Then the cutting trajectory corresponding to time t1 The point on the cutting path The point of tangency with the inclined surface to be machined.

[0097] Then, on the cutting path At time t1 and t1+T, the corresponding points are point A0 and point D0 respectively. Let them start moving simultaneously. Among them, point A0 moves step by step along the direction of time advancement on the cutting trajectory with a change amount of Δt (t increases by Δt), and point D0 moves step by step along the direction of time regression on the cutting trajectory with a change amount of Δt (t increases by Δt). Take Then the y coordinate values corresponding to the two moving points A0 and D0 on the cutting trajectory can be dynamically expressed as y'(t1+nΔt) and y'(t1+T-nΔt) respectively.

[0098] At first, y'(t1)<y'(t1+T). Next, let n = 1, and calculate the corresponding y coordinate values at this time as y'(t1+Δt) and y'(t1+T-Δt) respectively. If y'(t1+Δt)<y'(t1+T-Δt), then let n = n+1, and repeat the above operation until the condition y'(t1+nΔt)≥y'(t1+T-nΔt) is satisfied. At this time, the cutting time corresponding to the coincidence point C0 can be expressed as t c =t1+T-nΔt, and the corresponding coordinates on the cutting trajectory are (y'(t c ),z'(t c )).

[0099] Finally, through iterative calculation, when n = 136659, it just satisfies y'(t1+nΔt)≥y'(t1+T-nΔt). At this time, the cutting time t c =3.40835×10 -5 s, and the theoretical residual height along the cutting direction can be calculated by the distance formula from a point to a line as

[0100] Application Example 2 <00​​​​​​​​​​​​​​​

[0103] Next, the cutting trajectory expression of the tool relative to the workpiece is obtained based on the ultrasonic vibration parameters, cutting process parameters and the inclination angle of the bevel to be machined.

[0104]

[0105] When cutting the set bevel, In addition, set z d =2mm, to ensure that the envelope line of the lower half of the cutting trajectory is at a certain distance from the inclined surface to be machined.

[0106] Next, starting from time t=0, solve the tool path in the first vibration cycle The cutting time t1 corresponding to the shortest straight-line distance from the point on the surface to be machined along the z-axis is obtained by the Newton-Raphson iteration method as t1=1.500364×10 -5 s, the corresponding shortest straight line distance along the z axis is z d1 =1.9987631mm.

[0107] Next, the tool path Translate z downward along the z axis d1 Get tool path

[0108]

[0109] Then the cutting trajectory corresponding to time t1 The point on the cutting path The point of tangency with the inclined surface to be machined.

[0110] Then, on the cutting path Take the points A0 and D0 corresponding to time t1 and time t1+T, respectively, and let them start moving at the same time. Point A0 moves gradually along the cutting trajectory in the direction of time advancement with a change of Δt (t increases by Δt), and point D0 moves gradually along the cutting trajectory in the direction of time regression with a change of Δt (t increases by Δt). Then the two moving points A0 and D0 are on the cutting trajectory. The corresponding y-coordinate values ​​can be expressed as and y'(t1+t-nΔt).

[0111] At first, y'(t1) < y'(t1 + T). Next, let n = 1, and calculate the corresponding y coordinate values at this time as y'(t1 + Δt) and y'(t1 + T - Δt) respectively. If y'(t1 + Δt) < y'(t1 + T - Δt), then let n = n + 1, and repeat the above operation until the condition y'(t1 + nΔt) ≥ y'(t1 + T - nΔt) is satisfied. At this time, the cutting time corresponding to the coincidence point C0 can be expressed as t c = t1 + T - nΔt, and the corresponding coordinate on the cutting trajectory is (y'(t c ), z'(t c )).

[0112] Finally, through iterative calculation, when n = 165435, it just satisfies y'(t1 + nΔt) ≥ y'(t1 + T - nΔt). At this time, the cutting time t c = 3.586779×10 -5 s, and the theoretical remaining height along the cutting direction can be calculated by the distance formula from a point to a line as

[0113] The above are only the preferred embodiments of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the inventive concept, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention.

Claims

1. A method for predicting residual height of a surface during ultrasonic elliptical vibration turning, characterized in that: The specific steps of this method are as follows: Step 1: Obtain the corresponding surface equation z for the target surface to be processed s =f(y); Step 2: Based on the surface equation to be machined and combined with the tool vibration form, establish the cutting trajectory expression of the tool relative to the workpiece in ultrasonic elliptical vibration cutting Among them, A y 、A z are the unilateral amplitudes of the tool along the y and z directions of the machine tool coordinate system during the ultrasonic elliptical vibration assisted cutting process, f is the vibration frequency during the ultrasonic elliptical vibration cutting process, and v c represents the cutting speed in the y direction, k is the proportional coefficient of the machine tool z-direction guide rail moving speed and the y-direction cutting speed, which depends on the angle α between the target surface to be machined and the positive direction of the y axis. d To ensure the cutting path An offset in the z-axis direction added at a certain distance above the surface to be machined; Step 3: Starting from t=0, according to the tool relative cutting trajectory expression Solve the cutting trajectory within the first tool vibration cycle From the point on the target surface to be processed z s = f(y) The cutting time t1 corresponding to the shortest straight line distance along the z-axis direction, and the corresponding shortest straight line distance along the z-axis direction at this time is z d1 ; Step 4: Set the tool path Translate z downward along the z axis d1 Get tool path Set the cutting trajectory corresponding to time t1 The point on the cutting path The tangent point A0 of the inclined surface to be machined is recorded as the cutting time corresponding to point A0 According to the periodic characteristics of the tool's ultrasonic elliptical vibration, along the cutting trajectory The time direction of the second tangent point can be determined as point D0 in the next adjacent cycle, and the corresponding moment is expressed as: Wherein, T is the period of ultrasonic elliptical vibration of the tool; Step 5: Define the moment when the tool cuts into the material again during the first vibration cycle of the tool as t c , set its corresponding cutting trajectory Point C0 on Step 6: At the same time, let point A0 and point D0 start moving from the initial position, where point A0 is on the cutting trajectory. The upper edge moves gradually in the direction of time with a change of Δt (t increases by Δt), and point D0 is on the cutting trajectory. The upper edge moves in the time-reversed direction by a change of Δt (t decreases by Δt). Once the magnitude relationship of the y-axis coordinates of the two moving points reverses, it means that the two have reached the point C0 where the trajectories overlap. The time corresponding to point C0 can be expressed as: Where n is the point D0 with a change of Δt on the cutting trajectory. The number of steps required for the upper edge to move in the time-reverse direction to the coincidence point C0; Step 7: Time t corresponding to the coincidence point C0 obtained in step 6 c And the tool cutting trajectory expression obtained in step 4 The position coordinates of point C0 in the YOZ plane are (y'(t c ),z'(t c )); Step 8. Use the point-to-line distance formula to calculate the distance from point C0 to the ideal target surface z s =f(y) The distance result is the theoretical residual height Rz in the cutting direction v .

2. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: The y-axis and the z-axis in step 2 correspond to the y-direction and the z-direction of the multi-axis ultra-precision machining tool coordinate system.

3. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: The tool is a diamond turning tool with an arc edge and a zero-degree rake angle.

4. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: When the tool performs ultrasonic elliptical vibration, the starting point along the y direction is the equilibrium position of simple harmonic vibration, and the phase difference between the vibration along the y direction and the vibration along the z direction is That is, the major axis and minor axis of the elliptical vibration mode of the tool vibration are parallel to the y-axis and z-axis respectively.

5. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: The proportional coefficient k between the z-direction guide rail movement speed and the y-direction cutting speed of the machine tool in step 1 is k=0 when the surface is an end plane; when the surface is an inclined surface, k depends on the angle α between the target inclined surface to be processed and the positive direction of the y-axis, k=tanα.

6. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: The time variation Δt is set to Where T is the period of ultrasonic elliptical vibration of the tool, m represents the number of time segments, and m is greater than or equal to 10 5 natural number.

7. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: Solve the tool path line in step 3 From the point on the target surface to be processed z s =f(y) The cutting moment corresponding to the shortest straight-line distance along the z-axis direction is obtained by the Newton-Raphson iterative method.

8. The method for predicting residual height of a surface during ultrasonic elliptical vibration turning according to claim 1, wherein: The distance calculation formula from the point to the straight line in step 8 is as follows: Among them, k and b are called the directional coefficients of the straight line equation, and c is a constant term representing the spatial position offset.

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