CN112207291A

CN112207291A - Transition zone cutter path optimization ultra-precise turning method under slow cutter servo

Info

Publication number: CN112207291A
Application number: CN202010695140.0A
Authority: CN
Inventors: 陈宝华; 唐运海; 吴泉英; 张慧星
Original assignee: Suzhou University of Science and Technology
Current assignee: Suzhou University of Science and Technology
Priority date: 2020-07-19
Filing date: 2020-07-19
Publication date: 2021-01-12
Anticipated expiration: 2040-07-19
Also published as: CN112207291B

Abstract

The invention discloses a transition zone cutter track optimization ultra-precise turning method under slow cutter servo, which is realized on a three-axis ultra-precise single-point diamond lathe formed by a linear motion shaft X, Z and a turning main shaft C with angle positioning. The tool path is divided into a cutting zone and a transition zone for off-axis or multiple arrays of identical or non-identical optical surfaces. In the cutting area, the cutter moves along the rise direction of the optical surface to cut the workpiece to be processed; and in the transition area, establishing a custom tool path equation by combining the rise equation characteristics of the cutting area, so that the tool smoothly moves from the tail end of the last cutting path of the cutting area to the starting point of the next cutting path. Compared with the prior art, the tool path in the transition area designed by the invention meets the requirement of stable turning under the servo of a slow tool, the acceleration of the main shaft C is kept continuous without sudden change in the rotating process, the processing quality is higher, and the tool compensation calculation is simple.

Description

Transition zone cutter path optimization ultra-precise turning method under slow cutter servo

Technical Field

The invention relates to a transition zone cutter track optimization ultra-precision turning method under slow cutter servo, belongs to the technical field of optical ultra-precision machining, and particularly relates to a transition zone cutter track optimization calculation method.

Background

At present, the technical field of ultra-precision machining is divided into three technologies of ultra-precision turning, ultra-precision grinding and polishing. One typical ultra-precision turning technique is a single-point diamond lathe including a rotary spindle C, a guide X-axis, and a tool Z-axis. The slow-tool servo turning is to precisely control the lathe spindle and the Z axis to change the lathe spindle into the angle-controllable C axis, at the moment, X, Z, C three axes of the lathe form a cylindrical coordinate system in space, all motion axes of a lathe control system send interpolation feeding instructions to precisely coordinate the relative motion of the spindle and a cutter, and the turning processing of parts with complex surface shapes is realized.

In addition, the Z axis of the cutter and the X axis of the guide rail are usually subjected to sinusoidal reciprocating motion under the slow cutter servo, the influence of the inertia of a lathe sliding seat and the response speed of a motor is avoided, the dynamic response speed is low, and the device is suitable for processing complex optical devices with continuous and non-abrupt surface shapes. However, in the processing requirements of the actual optical surface, various problems often exist, such as a plurality of different array reflectors or aspheric surfaces with large off-axis amount (the off-axis amount exceeds the caliber of a lathe), and at the moment, the traditional processing mode generally moves the aspheric surface with large off-axis amount to the center of the lathe, and directly performs slow-tool servo turning. However, the turning mode has extremely low efficiency, and the back angle of the cutter is easy to touch the optical surface, thereby affecting the surface shape; in another mode, a plurality of large off-axis mirrors with the same optical parameters are uniformly distributed on a machined fixture, the distance between the center of the mirror and the center of a lathe is smaller than the off-axis distance, and a transition region and a cutting region exist at the moment. The cutting area is determined by the sagittal height equation of the mirror, and the transition area needs to be compensated manually. In the patent 'an ultra-precise turning method of a large off-axis aspherical mirror', the compensation mode of a transition region is directly realized by keeping the Z-direction rise of a cutter unchanged, so that the rise of the transition region and the cutting region are not smooth and continuous, the acceleration of a main shaft C in the cutting-transition region of a lathe is suddenly changed, the phenomenon of shaking and instant stopping is easy to occur, and the integral cutting speed and precision are influenced; and the patent can not solve the problem of different surface types of array optical surfaces, such as aspheric surfaces or free-form surfaces with alternate concave and convex shapes.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, and provides a slow-tool servo ultra-precision turning method by optimizing the tool path in a transition area.

The technical scheme for realizing the aim of the invention comprises the following steps:

firstly, under a slow tool servo working mode, according to the known face rise characteristic of a cutting area, establishing a tool path equation of a transition area of an nth path circle, and setting

Where ρ is_nTAs a tool path Z_nTThe distance polar diameter between the projection point and the origin o on the xy plane; a. the_niB is a coefficient to be solved; theta_TIs ρ_nTAngle with respect to the x-axis, theta_nT∈[θ₁，θ₂](ii) a For several cutting zones with equal arrays of convex or concave off-axis optical surfaces,

wherein in a cutting-transition-cutting area, the coefficient A is to be determined_niThe total number of unknown coefficients of B and B is 4, the solving of the coefficients needs to satisfy the following boundary conditions,

Z_nT(ρ₁，θ₁)＝Z_a(ρ₁，θ₁)， (2)

Z_nT(ρ₂，θ₂)＝Z_b(ρ₂，θ₂)， (3)

wherein (rho)₁，θ₁) And (rho)₂，θ₂) Is the cutting point of the edge of the cutting area-transition area, namely the projection polar coordinate of the tool path on the xy plane, and rho is in the same path circle₁And ρ₂And the two parts can be equal or gradually changed according to the Archimedes spiral. Z_a(p, theta) and Z_b(rho, theta) are surface profile height loss equations of the cutting area a and the cutting area b respectively, specific expressions of the equations are as follows,

wherein Q is 1/R, R is the radius of curvature of the cutting region; k is the conic coefficient; coefficient of performance G _mp0, the cutting surface is a normal off-axis aspheric surface, if G_mpIf not 0, the cutting surface is a W-order free-form surface. l 'and h' are actual off-axis quantities of the cutting area a and the cutting area b respectively, and l and h are distances between the center of the cutting area and an origin, namely the placement distance of the optical surface during turning, and the distances do not need to be equal to the actual off-axis quantities.

When the transition zone cutter track provided by the invention runs, the movement mode of the Z axis and the C axis of the lathe has the following characteristics that the C axis rotation angular velocity of the lathe is omega, and the feeding velocity v of the Z axis of the lathe is set_zCan be expressed as a number of times,

wherein τ is time, and θ is ω · τ because θ is continuously conductable at the edges of the constrained transition region and the cutting region in equations (3) and (4), when the angular velocity ω is constant, the feed velocity ν of the Z axis of the lathe is constant_zIs a continuous sinusoid-like curve and vice versa.

Similarly, let us say the feed acceleration α of the Z-axis of the lathe_zIn order to realize the purpose,

the second derivatives at the edges of the constraint transition area and the cutting area in the formula (5) and the formula (6) are equal, and v is the feed speed of the Z axis of the lathe_zIs a continuous quasi-sinusoidal curve, so its acceleration a_zA continuous curve is also formed in the whole path circle.

The invention has the advantages that the invention is suitable for turning most optical surfaces with transition regions, the number of the off-axis arrays is not limited, the transition track and the cutting track are continuous, and the turning acceleration and the cutting region acceleration are continuous, thereby ensuring the stable rotation speed of the main shaft in the turning process and improving the efficiency and the cutting precision.

Drawings

FIG. 1 is a projection of an optical surface to be machined on an xy plane;

FIG. 2 is a schematic view of an off-axis array optical surface provided by an embodiment of the invention;

FIG. 3 is a three-dimensional view of the complete path of the nth turn;

FIG. 4 is a two-dimensional view of the complete path of the nth turn;

FIG. 5 is a Z-direction cutting speed diagram of the tool shaft;

FIG. 6 is a Z-direction cutting acceleration diagram of the tool shaft;

fig. 7 is a schematic diagram of the complete tool path.

Detailed Description

The technical scheme of the invention is further explained by combining the embodiment.

Taking 4 same off-axis paraboloids as the objects of the embodiment, the specific parameters are as follows with reference to the formulas (8) and (9): the caliber D is 50 mm; k is-1; curvature R is 300 mm; the off-axis amounts l 'and h' are 300 mm; the placing distances l and h during processing are both 50 mm; g _mp0; drawings1 and 2, the projection of the optical surface mounting area on the xy plane is a gray area, and the area range

The light black area is the transition area. Selecting rho_nThe edge cutting point coordinate Z of the cutting zone-transition zone can be obtained by (8) and (9) with reference to a path circle of 50mm_a(ρ_n，θ₁) And Z_b(ρ_n，θ₁) Written in the form of cylindrical coordinates (ρ, θ, Z), specifically (50, 21.6 °, 156.9) and (50, 68.4 °, 156.9), θ ∈ [0, 360 ° [ ]]。

Similarly, equation (4) the equation for the optical surface loss height in equation (7) and the first derivative Z of the angle of the principal axis C at the two edge cutting points_a′、Z_b' and second derivative Z_a″、Z_b"can be obtained. With a particular coordinate of Z_a′(50，21.6°，-0.3003)、Z_a' (50, 68.4 °, 0.3003) and Z_a″＝(50，21.6°，0.01324)、Z_b″＝(50，68.4°，0.01324)。

As shown in FIG. 3, the route ρ can be obtained from the equations (1) and (7) based on the known boundary conditions_nEquation of tool path in the transition zone at 50mm_nT. Fig. 4 shows that the transition zone and the cutting zone are relatively completely combined together, and the transition curve and the cutting curve are similar to sine within the range of 0-360 degrees, so that the whole body is relatively smooth and smooth without break points. Fig. 5 shows the cutting speed v of the tool axis in the Z direction, and it can be clearly seen that the speed curve shows a trend of descending first and then ascending in a cutting-transition region period, the maximum and minimum cutting speeds are located at two edge cutting points, and the speed change in the middle process is continuous and stable. Similarly, the main cause of the instant stop of the shaking of the lathe spindle C is the cutting acceleration jump, and fig. 6 shows that the acceleration α in the whole path circle has no obvious abrupt change, and the acceleration curve is relatively continuous. Fig. 7 is a schematic diagram of the complete tool path.

According to the embodiment of the invention, the tool path in the transition area designed by the invention meets the requirement of stable turning under the slow tool servo, the spindle C does not stop in the rotating process, the processing quality is higher, and the tool compensation calculation is simple.

Claims

1. A transition zone cutter track optimization ultra-precise turning method under slow cutter servo is characterized in that: the technical scheme comprises the following steps:

Z_nT(ρ₁，θ₁)＝Z_a(ρ₁，θ₁)， (2)

Z_nT(ρ₂，θ₂)＝Z_b(ρ₂，θ₂)， (3)

wherein (rho)₁，θ₁) And (rho)₂，θ₂) Is the cutting point of the edge of the cutting area-transition area, namely the projection polar coordinate of the tool path on the xy plane, and rho is in the same path circle₁And ρ₂Can be equal or gradually changed according to the Archimedes spiral; z_a(p, theta) and Z_b(rho, theta) are surface profile height loss equations of the cutting area a and the cutting area b respectively, specific expressions of the equations are as follows,

wherein Q is 1/R, R is the radius of curvature of the cutting region; k is the conic coefficient; coefficient of performance G_mp0, the cutting surface is a normal off-axis aspheric surface, if G_mpIf not 0, the cutting surface is a W-order free curved surface; l 'and h' are actual off-axis quantities of the cutting area a and the cutting area b respectively, and l and h are distances between the center of the cutting area and an origin, namely the placement distance of the optical surface during turning, and the distances do not need to be equal to the actual off-axis quantities;

where τ is time, since θ is ω · τ, which is continuously derivable at the edges of the constrained transition zone and the cutting zone in equations (3) and (4), the feed speed v of the Z axis of the lathe is constant when the angular velocity ω is constant_zIs a continuous sine-like curve and vice versa;

the second derivatives at the edges of the constraint transition zone and the cutting zone in the formula (5) and the formula (6) are equal, and the feeding speed v of the Z axis of the lathe is also caused_zIs a continuous quasi-sinusoidal curve, so its acceleration a_zA continuous curve is also formed in the whole path circle.