Computing method for radius of cylindrical ball-end cutter for rough milling of complex channel

Abstract

The invention discloses a method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel, and the method comprises the steps: generating a cutter center drive surface SB, 1; the method comprises the following steps: offsetting a cutter center driving surface SB, 1 to obtain a cutter center driving surface SB, 2, and discretizing the SB, 2 to obtain a plurality of straight generatrix lines; taking any point on any straight generatrix as a sphere center, and calculating a parameter interval in which the sphere center passes through the current straight generatrix and is internally tangent to the radius of an internally tangent sphere of S1 and S2; obtaining an iterative equation of the sphere center; the SB, 2 is biased with the minimum value of the radius parameter set of the SB, 2 as the offset distance to obtain the cutter center driving faces SB, 3, and the steps 2-5 are repeated till the radius parameter set of all the cutter center driving faces SB, k in the machining area is obtained through calculation; in each machining area, the minimum value in the corresponding radius parameter set serves as the radius of the cylindrical ball-end cutter in the machining area; according to the method, the maximum radius of the cylindrical ball-end cutter for multi-axis point milling rough machining of the complex channel parts can be solved while interference of the cutter is avoided.

Description

Technical Field

[0001] The invention belongs to the field of milling tool size optimization, and in particular relates to a method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel. Background Art

[0002] In order to reduce the weight of aircraft engines and improve their operating efficiency, complex channel parts, as core components of the new generation of aircraft engines, adopt the manufacturing process of integral cutting and forming, such as supercharger impellers, integral blade disks, etc. From the perspective of geometric structure and manufacturing materials, complex channel parts have the same characteristics, that is, such parts can be regarded as thin-walled parts with deep narrow grooves formed by sweeping irregular cross-section lines with a shape similar to "U" along the direction of the part channel, which results in the parts having geometric structural characteristics of narrow channel area and high degree of surface distortion, and the parts are mostly made of high-strength, difficult-to-mill titanium alloys or high-temperature alloys.

[0003] CNC multi-axis point milling with ball-end cutters has the advantages of good process adaptability, high machining accuracy and short production preparation cycle, and is one of the commonly used key technologies for manufacturing complex channel parts. However, the common geometric characteristics of such parts make them less efficient when rough milling. The main reason is that in order to avoid global and local interference of the tool, cylindrical ball-end cutters with smaller radius are often used for milling, which makes the material removal efficiency of the same tool path low when machining such parts, which leads to more cutting layers and cutting lines when rough milling the channel area. Moreover, under the condition of a certain tool length, when machining the same cutting line, the cylindrical ball-end cutter with smaller radius has a larger length-to-diameter ratio, which makes the tool rigidity weaker, thereby increasing the risk of tool breakage. In order to prevent tool breakage, only lower cutting depth and lower feed speed can be used, which greatly reduces cutting efficiency. Summary of the invention

[0004] The purpose of the present invention is to provide a method for calculating the radius of a cylindrical ball-end cutter for rough milling a complex channel, so as to solve the problem that the size of the cylindrical ball-end cutter for rough milling without interference multi-axis is small in the existing method.

[0005] The present invention adopts the following technical solution: a method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel, comprising:

[0006] Step 1: The adjacent blades in the same channel are the first blade and the second blade. The upper boundary line of the blade base surface S1 of the first blade and the upper boundary line of the blade back surface S2 of the second blade are used as the guide to generate the blade core driving surface S B,1 ;

[0007] Step 2: Drive the knife center to the surface S B,1 Offset to obtain the tool center driving surface S B,2 , and S B,2Discretize to get several straight buses;

[0008] Step 3: Take any point on any straight generatrix as the sphere center, and calculate the parameter interval where the solution of the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 exists;

[0009] Step 4: Based on the chord-intercept iteration method, the iterative equation of the sphere center is obtained according to the parameter interval; then the sphere center and radius on the straight generatrix are solved, and S is traversed. B,2 All straight busbars on the B,2 The radius parameter set;

[0010] Step 5: S B,2 The minimum value of the radius parameter set is the offset distance S B,2 Offset to obtain the tool center driving surface S B,3 Repeat steps 2-5 until all tool center drive surfaces S in the processing area are calculated. B,k The radius parameter set;

[0011] Step 6: Divide all tool center drive surfaces into multiple adjacent processing areas, and then in each processing area, use the minimum value in the corresponding radius parameter set as the radius of the cylindrical ball-end tool in the processing area.

[0012] Furthermore, the calculation formula for the parameter interval of the solution for calculating the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 in step 2 is:

[0013] D(t)=|O B,ki (t)-S1| min -|O B,ki (t)-S2| min =0

[0014] Where D(t) is the difference in distance from the center of the sphere to S1 and S2; B,ki S is the blade driving surface B,k The sphere center point on the i-th straight generatrix; S1 is the blade basin surface of the first blade; S2 is the blade back surface of the second blade;

[0015] The boundary values ​​of the parameter interval meet the following conditions:

[0016] D(t a )·D(t a+1 )<0;

[0017] In the formula, D(t a ) is the straight busbar L B,k (t,w i ) is the difference in distance from the point with parameter a to S1 and S2, D(t a+1 ) is the straight busbar L B,k(t,w i ) is the difference in distance from the point with parameter a+1 to S1 and S2.

[0018] Furthermore, the iterative equation of the sphere center in step 4 is:

[0019]

[0020] The termination condition of the iterative equation of the sphere center is:

[0021] 0≤|O B,ki (t)-S1| min -|O B,ki (t)-S2| min ≤ε;

[0022] Where t* is the straight busbar L B,k (t,w i ) is the spherical center parameter after iterative calculation; t a+1 For straight busbar L B,k (t,w i ) The parameter of the point with parameter a+1; t a For straight busbar L B,k (t,w i ) with parameter a as the point on the B,ki S is the blade driving surface B,k The center point of the sphere on the i-th generatrix; S1 is the blade basin surface of the first blade; S2 is the blade back surface of the second blade; ε is a positive number ≥0.

[0023] Furthermore, the algorithm for solving the center and radius of the sphere in step 4 is:

[0024]

[0025] In the formula, R B,ki (t*) is the parameter t* the radius of the center of the sphere; B,ki (t*) is the center point of the sphere with parameter t*.

[0026] Furthermore, the specific method of step 6 is:

[0027] Divide the n tool center driving surfaces into c adjacent processing areas;

[0028] The first c-1 processing areas contain b tool center drive surfaces, and in the first c-1 processing areas, the minimum value of the radius parameter set corresponding to the b tool center drive surfaces of each processing area is used as the cylindrical ball head tool radius of the processing area;

[0029] Among them, in the cth processing area, the minimum value in the radius parameter set corresponding to the remaining tool center driving surface is used as the radius of the cylindrical ball-end cutter in the processing area.

[0030] The beneficial effects of the present invention are:

[0031] The present invention can solve the maximum radius of a cylindrical ball-end cutter for multi-axis point milling rough machining of complex channel parts while avoiding tool interference, thereby improving tool rigidity to increase the available cutting depth and feed speed of milling, and reducing the number of tool cutting rows under the same material removal amount, while reducing the risk of tool breakage, and ultimately improving the machining efficiency of multi-axis point milling;

[0032] The present invention can quickly and accurately calculate the maximum value of the radius of the available non-interference cylindrical ball-end cutter in different processing areas during the high-efficiency spot milling roughing process, thereby reducing the tool aspect ratio in the rough processing of complex channels to improve the rigidity of the tool, and increasing the available cutting depth and tool feed speed of the cylindrical ball-end cutter, ultimately achieving the material removal efficiency and shortening the overall processing time during the multi-axis rough processing of complex channel parts. DETAILED DESCRIPTION

[0033] The present invention is described in detail below in conjunction with specific implementation modes.

[0034] The invention discloses a method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel, comprising:

[0035] Step 1: The adjacent blades in the same channel are the first blade and the second blade. The upper boundary line of the blade base surface S1 of the first blade and the upper boundary line of the blade back surface S2 of the second blade are used as the guide to generate the blade core driving surface S B,1 .

[0036] Taking the metal reinforcement edge of a complex channel part as an example, the inner cavity rough machining area of ​​the reinforcement edge is selected, and the two side surfaces of the inner cavity of the reinforcement edge part are set to S1 and S2, and its bottom surface is S bot The upper boundary of S1 is C S1,1 , the upper boundary line of S2 is C S2,1 , the lower boundary line of S1 is C S1,e , the lower boundary line of S2 is C S2,e .

[0037] C S1,1 and C S2,1 Generate the tool center driving surface S as two wires B,1 , with C S1,e and C S2,e Generate the tool center driving surface S as two wires B,e , S B,1 With S B,e The area in between is the processing area.

[0038] Determine the blade drive surface S B,e With Sbot Whether they intersect, if they do, the radius R of the cylindrical ball end cutter is obtained B,e , which is calculated as follows: R B,e =1 / max{k bot ,k1,k2}, where k bot For S bot If they do not intersect, the upper boundary line of the blade base surface S1 of the first blade and the upper boundary line of the blade back surface S2 of the second blade are used as the guide line to generate the blade core driving surface S B,1 , and perform steps 2-6 until the radius of the cylindrical ball-end cutter in each processing area is obtained.

[0039] Step 2: Drive the knife center to the surface S B,1 Offset a certain distance to get the tool center driving surface S B,2 , and S B,2 Discretization is performed to obtain several straight busbars.

[0040] Tool center driving surface S B,2 Perform equal parameter discretization to obtain S B,2 The direct generatrix sequence L B,2 (t,w i ), where w i Indicates the blade center driving surface S B,2 The i-th busbar on the upper line, where i = 1, 2…, m, and t is the parameter on the i-th straight busbar.

[0041] Step 3: Take any point on any straight generatrix as the center of the sphere, and calculate the parameter interval in which the solution of the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 exists.

[0042] Select S B,2 On one of the straight busbars L B,2 (t,w i ), based on the parameter point t on the straight generatrix, calculate the parameter interval where the solution of the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 exists.

[0043] Step 4: Based on the chord-intercept iteration method, the iterative equation of the sphere center is obtained according to the parameter interval; then the center and radius of the sphere on the straight generatrix are obtained by solving, and S is traversed. B,2 All straight busbars on the B,2 The radius parameter set.

[0044] Step 5: S B,2 The minimum value of the radius parameter set is the offset distance S B,2 Offset to obtain the tool center driving surface S B,3 Repeat steps 2-5 until all tool center drive surfaces S in the processing area are calculated. B,kThe radius parameter set.

[0045] Among them, let {|O B,ki (t)-S1| min} is the ball point O B,ki The minimum distance to the constraint surface S1, let {|O B,ki (t)-S2| min} is the center of the sphere O B,ki The minimum distance to the constraint surface S2, the formula for the parameter interval of the solution for calculating the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 in step 3 is:

[0046] D(t)=|O B,ki (t)-S1| min -|O B,ki (t)-S2| min =0

[0047] Where D(t) is the difference between the distances from the center of the sphere to S1 and S2; B,ki S is the blade driving surface B,k The center point of the sphere on the i-th straight generatrix; S1 is the blade basin surface of the first blade; S2 is the blade back surface of the second blade.

[0048] Among them, the center of the ball O in step 3 B,ki On the straight busbar L B,k (t,w i ) The parameter interval t where the solution exists * ∈[t a ,t a+1 ], the boundary value of the parameter interval should satisfy the following formula:

[0049] D(t a )·D(t a+1 )<0

[0050] In the formula, D(t a ) is the straight busbar L B,k (t,w i ) is the difference in distance from the point with parameter a to S1 and S2, D(t a+1 ) is the straight busbar L B,k (t,w i ) is the difference in distance from the point with parameter a+1 to S1 and S2.

[0051] Among them, the iterative equation of the center of the sphere in step 4 is:

[0052]

[0053] The termination condition of the iterative equation of the sphere center is:

[0054] 0≤|O B,ki(t)-S1| min -|O B,ki (t)-S2| min ≤ε;

[0055] Where t* is the straight busbar L B,k (t,w i ) is the spherical center parameter after iterative calculation; t a+1 For straight busbar L B,k (t,w i ) The parameter of the point with parameter a+1; t a For straight busbar L B,k (t,w i ) with parameter a as the point on the B,ki S is the blade driving surface B,k The center point of the sphere on the i-th generatrix; S1 is the blade basin surface of the first blade; S2 is the blade back surface of the second blade; ε is a positive number ≥0.

[0056] Among them, the solution algorithm for the center and radius in step 4 is:

[0057]

[0058] In the formula, R B,ki (t*) is the parameter t* the radius of the center of the sphere; B,ki (t*) is the center point of the sphere with parameter t*.

[0059] In step 5, S B,k The minimum value of the radius parameter set is the offset distance S B,k Offset to obtain the tool center driving surface S B,k+1 , at this time S B,k+1 is the lower boundary of the k-th layer processing area, and determines S B,k+1 With S B,e Whether they intersect. If they do, the radius R of the cylindrical ball-end cutter in the processing area can be directly obtained. B,ks =R B,e If they do not intersect, the radius of the cylindrical ball-end cutter in the processing area is calculated according to the following formula, which is the same as the solution algorithm in step 4.

[0060] Step 6: Divide all tool center drive surfaces into multiple adjacent processing areas, and then in each processing area, use the minimum value in the corresponding radius parameter set as the radius of the cylindrical ball-end tool in the processing area.

[0061] Since all tool center driving surfaces have the corresponding tool radius R B,k, which means that n tools will be provided to process complex channel parts, which increases the processing cost and tool change time. In order to reduce the number of tools, the n tool core drive surfaces can be divided into c adjacent processing areas, each processing area has b tool core drive surfaces, and then each processing area is processed with one tool. The final number of tools used should be: c = n / b. If n / b is an integer, the integer is directly taken as the number of tools. If n / b is not an integer, the integer part plus 1 is taken as the number of tools.

[0062] The specific method of step 6 is:

[0063] Divide the n tool center driving surfaces into c adjacent processing areas;

[0064] The first c-1 processing areas contain b tool center drive surfaces, and in the first c-1 processing areas, the minimum value of the radius parameter set corresponding to the b tool center drive surfaces of each processing area is used as the radius of the cylindrical ball head tool in the processing area;

[0065] Among them, in the cth processing area, the minimum value in the radius parameter set corresponding to the remaining tool center driving surface is used as the radius of the cylindrical ball-end tool in this area.

[0066] After obtaining the radius of the cylindrical ball end cutter in each processing area, adjust the radius of the cylindrical ball end cutter. The adjustment method is:

[0067] R B,k =R B,ks -μ

[0068] In the formula, R B,ks S is the blade driving surface B,k The radius parameter set {R B,ki}; μ is the rough machining allowance.

[0069] If the tool center driving surface of the upper processing area is narrow, the tool under the calculated tool radius in the lower processing area will interfere with the inner cavity of the part. In order to avoid the concave surface on the inner cavity side of the part, which may cause global interference of the generated cylindrical ball-end tool, it is necessary to check the tools under all diameters.

[0070] The specific inspection methods are:

[0071] According to the distance R B,k The part channel side surfaces S1 and S2 are offset to generate offset surfaces S1' and S2', and the offset direction is the direction that can intersect with the inner cavity blank of the part. B,k As the interface, if the blade driving surface S B,k In the above space, the offset surfaces S1' and S2' do not intersect, so the radius R of the cylindrical ball end cutter is output.B,k ; If the blade driving surface S B,k In the above space, the offset surfaces S1' and S2' intersect, and then use R B,k -ΔR is the radius of the cylindrical ball end cutter until the offset surfaces S1' and S2' do not intersect. Repeat the above steps until the R of the n-layer processing area is checked. B,k .

[0072] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel, characterized in that: include: Step 1: The adjacent blades in the same channel are the first blade and the second blade. The upper boundary line of the blade base surface S1 of the first blade and the upper boundary line of the blade back surface S2 of the second blade are used as the guide to generate the blade core driving surface S B,1 ; Step 2: Drive the knife center to the surface S B,1 Offset to obtain the tool center driving surface S B,2 , and S B,2 Discretize to get several straight buses; Step 3: Take any point on any straight generatrix as the sphere center, and calculate the parameter interval where the solution of the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 exists; Step 4: Based on the chord-intercept iteration method, the iterative equation of the sphere center is obtained according to the parameter interval; then the sphere center and radius on the straight generatrix are solved, and S is traversed. B,2 All straight busbars on the B,2 The radius parameter set; Step 5: S B,2 The minimum value of the radius parameter set is the offset distance S B,2 Offset to obtain the tool center driving surface S B,3 Repeat steps 2-5 until all tool center drive surfaces S in the processing area are calculated. B,k The radius parameter set; Step 6: Divide all tool center drive surfaces into multiple adjacent processing areas, and then in each processing area, use the minimum value in the corresponding radius parameter set as the radius of the cylindrical ball-end tool in the processing area.

2. The method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel according to claim 1 is characterized in that: The calculation formula for the parameter interval of the solution for calculating the radius of the inscribed sphere whose center passes through the current straight generatrix and is inscribed in S1 and S2 in step 2 is: D(t)=|O B ,ki(t)-S1|min-|O B ,ki(t)-S2|min=0 Where D(t) is the difference in distance from the center of the sphere to S1 and S2; B,ki S is the blade driving surface B,k The sphere center point on the i-th straight generatrix; S1 is the blade basin surface of the first blade; S2 is the blade back surface of the second blade; The boundary values ​​of the parameter interval meet the following conditions: D(t a )·D(t a+1 )<0; In the formula, D(t a ) is the straight busbar L B,k (t,w i ) is the difference in distance from the point with parameter a to S1 and S2, D(t a+1 ) is the straight busbar L B,k (t,w i ) is the difference in distance from the point with parameter a+1 to S1 and S2.

3. The method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel according to claim 1 is characterized in that: The iterative equation for the center of the sphere in step 4 is: The termination condition of the iterative equation of the sphere center is: 0≤|O B,ki (t)-S1| min -|O B,ki (t)-S2| min ≤ε; Where t* is the straight busbar L B,k (t,w i ) is the spherical center parameter after iterative calculation; t a+1 For straight busbar L B,k (t,w i ) The parameter of the point with parameter a+1; t a For straight busbar L B,k (t,w i ) with parameter a as the point on the B,ki S is the blade driving surface B,k The center point of the sphere on the i-th generatrix; S1 is the blade basin surface of the first blade; S2 is the blade back surface of the second blade; ε is a positive number ≥0.

4. The method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel according to claim 3 is characterized in that: The algorithm for finding the center and radius of the sphere in step 4 is: In the formula, R B,ki (t*) is the parameter t* the radius of the center of the sphere; B,ki (t*) is the center point of the sphere with parameter t*.

5. The method for calculating the radius of a cylindrical ball-end cutter for rough milling of a complex channel according to claim 1, characterized in that: The specific method of step 6 is: Divide the n tool center driving surfaces into c adjacent processing areas; The first c-1 processing areas contain b tool center drive surfaces, and in the first c-1 processing areas, the minimum value of the radius parameter set corresponding to the b tool center drive surfaces of each processing area is used as the cylindrical ball head tool radius of the processing area; Among them, in the cth processing area, the minimum value in the radius parameter set corresponding to the remaining tool center driving surface is used as the radius of the cylindrical ball-end tool in the processing area.

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