A method for calculating the radius of a cylindrical ball end mill in rough milling of complex channels.

Abstract

This invention discloses a method for calculating the radius of a cylindrical ball end mill used for rough milling of complex channels, including: generating the tool center driving surface S. B,1 ; Drive the blade core surface S B,1 Obtain the tool center driving surface S by biasing. B,2 and S B,2 Discretize to obtain several straight generatrices; taking any point on any straight generatrice as the center of a sphere, calculate the parameter interval for the existence of solutions for the radius of the inscribed sphere whose center passes through the current straight generatrice and is internally tangent to S1 and S2; obtain the iterative equation for the center of the sphere; with S... B,2 The minimum value of the radius parameter set is the offset distance to S. B,2 Obtain the tool center driving surface S by biasing. B,3 Repeat steps 2-5 until all tool center driving surfaces S within the machining area are calculated. B,k The radius parameter set; within each machining area, the minimum value in the corresponding radius parameter set is taken as the radius of the cylindrical ball end mill for that machining area; while avoiding tool interference, this invention can solve for the maximum radius of the cylindrical ball end mill for multi-axis point milling rough machining of complex channel-type parts.

Description

Technical Field

[0001] This invention belongs to the field of milling tool size optimization, and particularly relates to a method for calculating the radius of a cylindrical ball end mill for rough milling of complex channels. Background Technology

[0002] To reduce the weight of aero engines and improve their operating efficiency, complex channel-type parts, as core components of the next-generation aero engines, are manufactured using integral cutting processes, such as turbocharger impellers and integral bladed disks. From a geometric and material perspective, complex channel-type parts share common characteristics: they can all be considered as thin-walled, deep-slotted parts formed by sweeping irregular cross-sectional lines with an approximate "U-shape" along the part's channel direction. This results in geometric features such as narrow channel areas and high degree of surface distortion. Furthermore, the materials used in their manufacture are mostly high-strength, difficult-to-mill titanium alloys or high-temperature alloys.

[0003] CNC multi-axis point milling using ball end mills offers advantages such as good process adaptability, high machining accuracy, and short production preparation cycle, making it a commonly used key technology for manufacturing complex channel-type parts. However, the common geometric characteristics of these parts result in low efficiency during rough milling. This is mainly because, to avoid global and local tool interference, smaller-radius cylindrical ball end mills are often used. This leads to lower material removal efficiency along the same toolpath when machining these parts, resulting in more cutting layers and cutting passes during rough milling of the channel area. Furthermore, given a fixed tool length, the smaller-radius cylindrical ball end mill has a larger length-to-diameter ratio when machining the same cutting pass, resulting in weaker tool rigidity and an increased risk of tool breakage. To prevent tool breakage, lower depth of cut and lower feed rates are often required, significantly reducing cutting efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the radius of a cylindrical ball end mill for rough milling of complex channels, in order to solve the problem that existing methods have small dimensions of cylindrical ball end mills for non-interference multi-axis rough milling.

[0005] This invention adopts the following technical solution: a method for calculating the radius of a cylindrical ball end mill used for rough milling of complex channels, comprising:

[0006] Step 1: Adjacent blades within the same channel are designated as the first blade and the second blade, respectively. 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 guides to generate the blade core driving surface S. B,1 ;

[0007] Step 2: Drive the tool core S B,1 Obtain the tool center driving surface S by biasing. B,2 and S B,2Discretization yields several straight busbars;

[0008] Step 3: Using any point on any straight generatrix as the center of the sphere, calculate the parameter interval for the existence of the solution for the radius of the inscribed sphere whose center passes through the current straight generatrix and is internally tangent to S1 and S2;

[0009] Step 4: Based on the secant iteration method, obtain the iterative equation for the sphere center according to the parameter interval; then solve for the sphere center and radius on the straight generatrix, and traverse S. B,2 S is obtained from all straight busbars. B,2 The set of radius parameters;

[0010] Step 5: With S B,2 The minimum value of the radius parameter set is the offset distance to S. B,2 Obtain the tool center driving surface S by biasing. B,3 Repeat steps 2-5 until all tool center driving surfaces S within the machining area are calculated. B,k The set of radius parameters;

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

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

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

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

[0015] The boundary values ​​of the parameter range satisfy the following conditions:

[0016] D(t a )·D(t a+1 ) < 0;

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

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

[0019]

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

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

[0022] In the formula, t* represents the straight bus L. B,k (t,w i The sphere center parameters calculated by iterative calculation on 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 The parameter on the top is the parameter of the point 'a'; O B,ki S is the driving surface of the cutting core. B,k S1 is the center point of the sphere on the i-th generatrix; S2 is the leaf basin surface of the first leaf; S3 is the leaf back surface of the second leaf; ε is a positive number ≥ 0.

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

[0024]

[0025] In the formula, R B,ki (t*) represents the radius of the sphere's center, which is t*. B,ki (t*) is the center point of the sphere with parameter t*.

[0026] Furthermore, the specific method for step 6 is as follows:

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

[0028] Among them, the first c-1 machining areas contain b tool center driving surfaces, and in the first c-1 machining areas, the minimum value of the radius parameter set corresponding to the b tool center driving surfaces of each machining area is taken as the radius of the cylindrical ball end mill in the machining area.

[0029] In the c-th machining region, the minimum value of the radius parameter set corresponding to the remaining tool center driving surface is taken as the radius of the cylindrical ball end mill in that machining region.

[0030] The beneficial effects of this invention are:

[0031] This invention, while avoiding tool interference, can solve for the maximum radius of the cylindrical ball end mill for roughing of complex channel-type parts in multi-axis point milling, thereby improving tool rigidity to increase the usable depth of cut and feed rate in milling, and reducing the number of cutting passes under the same material removal conditions, while reducing the risk of tool breakage, and ultimately improving the machining efficiency of multi-axis point milling.

[0032] This invention can quickly and accurately calculate the maximum radius of the non-interference cylindrical ball end mill available in different machining areas during efficient spot milling roughing, thereby reducing the tool length-to-diameter ratio in the roughing of complex channels to improve tool rigidity, increasing the available depth of cut and tool feed rate of the cylindrical ball end mill, and ultimately improving the material removal efficiency and shortening the overall machining time in the multi-axis roughing of complex channel-type parts. Detailed Implementation

[0033] The present invention will now be described in detail with reference to specific embodiments.

[0034] This invention discloses a method for calculating the radius of a cylindrical ball end mill used for rough milling complex channels, comprising:

[0035] Step 1: Adjacent blades within the same channel are designated as the first blade and the second blade, respectively. 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 guides to generate the blade core driving surface S. B,1 .

[0036] Taking a complex channel-type metal reinforcing edge as an example, the rough machining area of ​​the inner cavity of the reinforcing edge is selected, and the two side curved surfaces of the inner cavity of the reinforcing edge are set as S1 and S2, respectively, and its bottom surface is S. bot The upper boundary line 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] With C S1,1 and C S2,1 The two wires generate the core driving surface S. B,1 , with C S1,e and C S2,e The two wires generate the core driving surface S. B,e S B,1 With S B,e The area between them is the processing area.

[0038] Determine the driving surface S of the tool core B,e With Sbot If they intersect, then the radius R of the cylindrical ball end mill is obtained. B,e The calculation method is as follows: R B,e =1 / max{k bot In the formula, k1, k2}, k bot For S bot The maximum curvature of S1 is given by k1, and the maximum curvature of S2 is given by k2. If they do not intersect, the upper boundary line of the blade basin surface S1 of the first blade and the upper boundary line of the blade back surface S2 of the second blade are used as guides to generate the blade core driving surface S. B,1 Then proceed with steps 2-6 until the radius of the cylindrical ball end mill for each machining area is obtained.

[0039] Step 2: Drive the tool core S B,1 The tool center driving surface S is obtained by offsetting it by a certain distance. B,2 and S B,2 Discretize to obtain several straight busbars.

[0040] For the driving surface S of the tool center B,2 Perform isoparametric discretization to obtain S B,2 Straight bus sequence L B,2 (t,w i ), where w i S represents the driving surface of the cutting core. B,2 Let i be the i-th busbar, where i = 1, 2, ..., m, and t be the parameter on the i-th straight busbar.

[0041] Step 3: Using any point on any straight generatrix as the center of the sphere, calculate the parameter interval of the solution for the radius of the inscribed sphere whose center passes through the current straight generatrix and is internally tangent to S1 and S2.

[0042] Select S B,2 One of the straight busbars L B,2 (t,w i The parameter interval for calculating the radius of the inscribed sphere whose center passes through the current straight generatrix and is internally tangent to S1 and S2, based on the parameter point t on the straight generatrix.

[0043] Step 4: Based on the secant iteration method, obtain the iterative equation for the sphere center according to the parameter interval; then solve for the sphere center and radius on the straight generatrix, and traverse S. B,2 S is obtained from all straight busbars. B,2 The set of radius parameters.

[0044] Step 5: With S B,2 The minimum value of the radius parameter set is the offset distance to S. B,2 Obtain the tool center driving surface S by biasing. B,3 Repeat steps 2-5 until all tool center driving surfaces S within the machining area are calculated. B,kThe set of radius parameters.

[0045] Among them, let {|O B,ki (t)-S1| min} is the point O of the sphere B,ki The minimum distance to the constrained surface S1 is given by {|O B,ki (t)-S2| min} is the center of the ball O B,ki The formula for calculating the minimum distance to the constrained surface S2 in step 3, and the formula for the range of parameters for the solution of the radius of the inscribed sphere whose center passes through the current generatrix and is internally tangent to S1 and S2, is as follows:

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

[0047] In the formula, D(t) is the difference in distance from the center of the sphere to S1 and S2; O B,ki S is the driving surface of the cutting core. B,k S1 is the center point of the sphere on the i-th straight generatrix; S2 is the leaf basin surface of the first leaf; S3 is the leaf back surface of the second leaf.

[0048] In step 3, the center O of the ball B,ki On the straight bus L B,k (t,w i The parameter interval t where the solution exists. * ∈[t a ,t a+1 The boundary values ​​of this parameter range should satisfy the following formula:

[0049] D(t a )·D(t a+1 ) < 0

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

[0051] The iterative equation for the center of the sphere in step 4 is:

[0052]

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

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

[0055] In the formula, t* represents the straight bus L. B,k (t,w i The sphere center parameters calculated by iterative calculation on 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 The parameter on the top is the parameter of the point 'a'; O B,ki S is the driving surface of the cutting core. B,k S1 is the center point of the sphere on the i-th generatrix; S2 is the leaf basin surface of the first leaf; S3 is the leaf back surface of the second leaf; ε is a positive number ≥ 0.

[0056] The algorithm for solving for the center and radius of the sphere in step 4 is as follows:

[0057]

[0058] In the formula, R B,ki (t*) represents the radius of the sphere's center, which is t*. 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 to S. B,k Obtain the tool center driving surface S by biasing. B,k+1 At this time S B,k+1 Let S be the lower boundary of the k-th layer processing region, and determine S. B,k+1 With S B,e If the axes intersect, the radius R of the cylindrical ball end mill in that machining area can be directly obtained. B,ks =R B,e If they do not intersect, the radius of the cylindrical ball end mill in the machining area is calculated according to the following formula, which is the same as the solution algorithm in step 4.

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

[0061] Since the corresponding tool radius R is calculated for all tool center driving surfaces. B,kThis means that n cutting tools will be needed to machine complex channel-type parts, which increases machining costs and tool change time. To reduce the number of cutting tools, the n tool center driving surfaces can be divided into c adjacent machining areas, each machining area has b tool center driving surfaces, and each machining area uses one cutting tool. The final number of cutting tools used should be: c = n / b. If n / b is an integer, then the integer part is taken directly as the number of cutting tools. If n / b is not an integer, then the integer part is taken plus 1 as the number of cutting tools.

[0062] The specific method for step 6 is as follows:

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

[0064] Among them, the first c-1 machining areas contain b tool center driving surfaces, and in the first c-1 machining areas, the minimum value of the radius parameter set corresponding to the b tool center driving surfaces in each machining area is taken as the radius of the cylindrical ball end mill in the machining area.

[0065] In the c-th machining region, the minimum value of the radius parameter set corresponding to the remaining tool center driving surface is taken as the radius of the cylindrical ball end mill in that region.

[0066] After obtaining the radius of the cylindrical ball end mill for each machining area, adjust the radius of the cylindrical ball end mill. The adjustment method is as follows:

[0067] R B,k =R B,ks -μ

[0068] In the formula, R B,ks S is the driving surface of the cutting core. B,k The radius parameter set {R B,ki The minimum value of}; μ is the roughing allowance.

[0069] If the tool drive surface of the upper machining area is narrow, the tool with the calculated tool radius in the lower machining area will interfere with the inner cavity of the part. In order to avoid the appearance of concave surfaces on the inner surface of the part, which would cause global interference of the generated cylindrical ball end mill, it is necessary to check the tools of all diameters.

[0070] The specific inspection method is as follows:

[0071] According to distance R B,k Offset surfaces S1 and S2 on the side surfaces of the part's channel are generated as offset surfaces S1' and S2', with the offset direction being the direction that intersects with the blank inside the part's cavity. The tool center drives surface S... B,k For the interface, if the core driving surface S B,k If the offset surfaces S1' and S2' in the above space do not intersect, then the radius R of the cylindrical ball end mill will be output.B,k If the core driving surface S B,k The offset surfaces S1' and S2' intersect in the above space, then using R... B,k -ΔR is the radius of the cylindrical ball end mill, until the condition that the offset surfaces S1' and S2' do not intersect is met. Repeat the above steps until R of the n-layer machining area has been checked. B,k .

[0072] The above are merely 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 within the protection scope of the present invention.

Claims

1. A method for calculating the radius of a cylindrical ball end mill used for rough milling complex channels, characterized in that, include: Step 1: Adjacent blades within the same channel are designated as the first blade and the second blade, respectively. 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 guides to generate the blade core driving surface S. B,1 ; Step 2: Drive the tool core S B,1 Obtain the tool center driving surface S by biasing. B,2 and S B,2 Discretization yields several straight busbars; Step 3: Using any point on any straight generatrix as the center of the sphere, calculate the parameter interval for the existence of the solution for the radius of the inscribed sphere whose center passes through the current straight generatrix and is internally tangent to S1 and S2; Step 4: Based on the secant iteration method, obtain the iterative equation for the sphere center according to the parameter interval; then solve for the sphere center and radius on the straight generatrix, and traverse S. B,2 S is obtained from all straight busbars. B,2 The set of radius parameters; Step 5: With S B,2 The minimum value of the radius parameter set is the offset distance to S. B,2 Obtain the tool center driving surface S by biasing. B,3 Repeat steps 2-5 until all tool center driving surfaces S within the machining area are calculated. B,k The set of radius parameters; Step 6: Divide all the cutting center driving surfaces into multiple adjacent machining areas, and then use the minimum value of the corresponding radius parameter set as the radius of the cylindrical ball end mill in each machining area; The formula for calculating the parameter interval of the solution for the radius of the inscribed sphere whose center passes through the current generatrix and is internally tangent to S1 and S2 in step 2 is as follows: D(t)=|O B,ki (t)-S1| min -|O B,ki (t)-S2| min =0 In the formula, D(t) is the difference in distance from the center of the sphere to S1 and S2; O B,ki S is the driving surface of the cutting core. B,k The center point of the sphere on the i-th straight generatrix; S1 is the leaf basin surface of the first leaf; S2 is the leaf back surface of the second leaf; The boundary values ​​of the parameter range satisfy the following conditions: D(t a )·D(t a+1 )<0; In the formula, D(t) a ) is a straight busbar L B,k (t,w i The difference in distances from a point with parameter a to S1 and S2, D(t) a+1 ) is a straight busbar L B,k (t,w i The difference in distances from the point with parameter a+1 to S1 and S2; The iterative equation for the center of the sphere in step 4 is: The termination condition for the iterative equation of the sphere center is: 0≤|O B,ki (t)-S1| min -|O B,ki (t)-S2| min ≤ε; In the formula, t* represents the straight bus L. B,k (t,w i The sphere center parameters calculated by iterative calculation on t; a+1 For straight busbar L B,k (t,w i The parameter of the point t is a+1. a For straight busbar L B,k (t,w i The parameter on the line is the parameter of the point 'a'; O B,ki S is the driving surface of the cutting core. B,k S1 is the center point of the sphere on the i-th generatrix; S2 is the leaf basin surface of the first leaf; S3 is the leaf back surface of the second leaf; ε is a positive number ≥ 0.

2. The method for calculating the radius of a cylindrical ball end mill for rough milling of complex channels according to claim 1, characterized in that, The algorithm for solving for the center and radius of the sphere in step 4 is as follows: In the formula, R B,ki (t*) represents the radius of the sphere's center, which is t*. B,ki (t*) is the center point of the sphere with parameter t*.

3. The method for calculating the radius of a cylindrical ball end mill for rough milling of complex channels according to claim 1, characterized in that, The specific method for step 6 is as follows: Divide the n tool center driving surfaces into c adjacent machining areas; Among them, the first c-1 machining areas contain b tool center driving surfaces, and in the first c-1 machining areas, the minimum value of the radius parameter set corresponding to the b tool center driving surfaces of each machining area is taken as the radius of the cylindrical ball end mill in the machining area. In the c-th machining region, the minimum value of the radius parameter set corresponding to the remaining tool center driving surface is taken as the radius of the cylindrical ball end mill in that machining region.

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