Structural optimization design and application of variable helix angle end mill based on improved genetic algorithm

With the continuous improvement of the comprehensive national power, China’s rapid development in the ship, automobile and aerospace and other national key industries, the performance of related products is gradually improved, and new materials with excellent performance are continuously developed and applied in these fields. Milling as one of the main ways of parts machining, in these important areas are also widely used [1–3]. Due to the difference in the stiffness of the milling cutter and the workpiece, vibration is easily generated in milling machining, especially in the face of complex structural parts and difficult-to-machine materials, and this problem has become one of the key factors affecting the efficiency of machine tool machining and the quality of product machining [4–6]. The study of vibration in milling mainly has two directions: vibration triggered by the system itself (self-excited vibration) and vibration triggered by the external excitation of the system (forced vibration). The regenerative chattering vibration is the most common in engineering, and it is also a kind of self-excited vibration with the most research and concentration [7–9]. Chattering phenomenon originates from the cutting regeneration effect in the milling process, which will leave vibration lines on the surface of the workpiece, and these vibration lines seriously affect the use of high-precision products, and sometimes they have to reduce the machining parameters to inhibit the occurrence of chattering, but this practice restricts the performance of the machine tool and cutting tool, and seriously reduces the machining efficiency [10–12]. Researchers have conducted a lot of meaningful research on this problem, and have achieved some results, and proposed a variety of chatter suppression strategies. The use of variable helix angle end mills is one of the chatter suppression strategies. This kind of milling cutter changes the time lag of adjacent cutting edges into cutting by changing the helix angle of the cutting edge, which effectively disturbs the regeneration effect and improves the vibration situation during machining [13–15]. Common variable helix angle end mills have two structures, namely, different helix angles for each cutting edge, constant helix angle for the same cutting edge, and gradually changing helix angle on the same cutting edge with the height of the cutting edge [16–17]. In order to maximize the chatter stability of variable helix angle end mill, it is necessary to analyze the dynamic milling model and stability of variable helix angle end mill. The optimal design of the milling cutter with unequal tooth pitch and helix angle variation is combined with the improved genetic algorithm to maximize the stability limit corresponding to the optimal variable helix angle and variable tooth pitch angle, which can improve the stability limit of the variable helix angle end mill and provide guidance and support for practical machining [18–21].

In this paper, a penalty function is proposed to optimize the unconstrained problem in traditional genetic algorithms to achieve two-way evolution of the genetic algorithm population. The value of the degree of constraint violation and the improved tournament selection method are used to optimize the hierarchical ranking and selection operator of the genetic algorithm. At the same time, dynamic crossover and mutation probability are used to improve the ability of the improved genetic algorithm to search for the optimal solution. The objective function and constraints of the optimal design of variable helix angle end mill structure are proposed according to the demands in industrial production, and the best solution of the optimal design of end mill structure is sought based on the improved genetic algorithm. Subsequently, a finite element simulation model of the variable helix angle end mill structure is established in Abaqus software to carry out the simulation analysis. In this study, the validity of the finite element model is verified, and then the application effect of the optimized variable helix angle end mill is investigated through simulation experiments and example analysis.

2

Improved genetic algorithm based end mill structure optimization method

2.1

Improved penalty function hierarchical genetic algorithm design

2.1.1

Treatment of constraints

The basic genetic algorithm can be better applied in unconstrained problem optimization. This paper proposes a penalty function [22] better to achieve the two-way evolution of the population, improve the performance of the genetic algorithm, especially for the variable helix angle end mill structure optimization problems need to consume time to carry out finite element analysis its effect is significant. The penalty function is realized in the form of: 1 $F (x_{i}) = {\begin{array}{l} f_{\max}^{p} - (f (x_{i}) + P (x_{i})) & x_{i} i s a n o n - v i a b l e s o l u t i o n \\ f_{\max}^{p} - f (x_{i}) & O t h e r c a s e s \end{array}$

Among them: 2 $f_{\max}^{p} = \max_{i = 1, \dots, n} {f (x_{i}) + P (x_{i})}$ 3 $f (x_{i}) = {\begin{array}{l} f (x_{i}) & f (x_{i}) > \bar{f} (x_{i}) \\ \bar{f} (x_{i}) & O t h e r c a s e s \end{array}$ 4 $P (x_{i}) = \bar{f} (x) [{(1 + V (i))}^{α} - 1]$ 5 $V_{i} = \frac{1}{m} \sum_{j = 1}^{m} ζ_{j} v_{j} (x_{i})$ 6 $\bar{f} (x) = \frac{1}{n} \sum_{i = 1}^{n} f (x_{i})$ 7 $v_{j} (x_{i}) = \max {0, | g_{j} (x_{i}) |}$

F(x_i) is the fitness value of the ind individual in the population, f(x_i) denotes the objective value corresponding to the i th individual, and P(x_i) is the value of the penalty function corresponding to the ith individual. $\bar{f} (x)$ is the average value of the objective function of the current population individuals, v_j (x_i) is the degree of deviation from the constraints of the ith individual of the current population. m is the number of constraints, ζ_j is the adjustment coefficient, and α is the constant for controlling the penalty, which is 4 here.

2.1.2

Hierarchical Sorting and Selection Operators

In this paper, the population is categorized and graded according to the fitness value of the current population individuals. In order to avoid the elimination of potential non-feasible solutions due to grading too far back, an individual attribute label one violates the constraint degree value V [23] is introduced here, and label V is assigned to the current population individuals according to the degree of their deviation from the constraint limit value at the same time when they are penalized. When a selection operation is performed, the probability of an individual being selected is determined based on the individual’s grading and V value, e.g., for individual x_i, both its grading R_i and deviation from constraint value V_i will determine the probability that this individual will be selected as a parent.

The traditional roulette selection method has a relatively large error, which may lead to the omission of individuals with high fitness values, ultimately making the evolutionary direction biased and thus making it difficult to obtain an optimal solution. In this paper, we adopt an improved tournament selection method [24], which selects the selected individuals according to their population level R and deviation from constraints V labels, and its specific operation procedure is as follows. 1)

Select two individuals x_i and x_j at random.

2)

First compare the population level R of the two individuals, and if R_i ≠ R_j, select the individual with the higher level as the parent.

3)

If R_i= R_j, compare their deviation from the constraint level V, and select the individual with the larger value of V as the parent.

4)

Repeat 1)-3) until all parent individuals are selected.

2.1.3

Crossing and variation

The crossover and mutation probabilities are generally constant in the basic genetic algorithm, which leads to iterative agitation in the later stages of the optimization, and the results tend to converge near the global optimal solution instead of the optimal solution. In this paper, we adopt a dynamic crossover and mutation probability. A larger crossover and mutation probability in the pre-evolutionary stage can produce new individuals with a larger probability and maintain the diversity of the population, and the crossover and mutation probability is smoothly reduced in the late evolutionary stage to protect the excellent individuals from destruction. The expression is shown in Eq: 8 $P_{X} (i) = {\begin{array}{l} \frac{P_{X \max}}{1 + g e n (i) / m g e n} & I f P_{X} > P_{X \min} \\ P_{X \min} & O t h e r s i t u a t i o n s \end{array}$ 9 $P_{M S} (i) = {\begin{array}{l} P_{M \max} * \exp (\frac{- 2.5 * g e n (i)}{m g e n}) & I f P_{M} > P_{M \min} \\ P_{M \min} & O t h e r s i t u a t i o n s \end{array}$ where P_X(i) denotes the crossover probability of the i nd generation population, P_Xmax and P_Xmin denote the upper and lower values of the crossover probability, respectively, P_M(i) denotes the mutation probability of the ith generation population, P_Mmax and P_Mmin denote the upper and lower values of the mutation probability, respectively, gen(i) denotes the number of evolutionary generations of the current population, and mgen the maximum number of evolutionary generations.

2.1.4

Algorithm flow

The improved penalty function hierarchical genetic algorithm proposed in this paper can be used for the optimization design of variable helix angle end mill structure, and the overall flow of the program is shown in Fig. 1. The selection of the best solution for the optimal design of variable helix angle end mill structure is realized through the process of determining the operation parameters, initial population assignment and finite element analysis.

2.2

Structure optimization model construction of end milling cutter

2.2.1

Objective function

The standard deviation of the spectral distribution of the milling force of a variable helix angle end mill was used to evaluate the distribution of the frequency domain energy of the milling force: 10 $S D = \sqrt{\lim_{x \to \infty} (\frac{1}{N} \sum_{i = 1}^{N} {(A (w) - \bar{A})}^{2})}$

Where N is the number of each harmonic, A(w) is the amplitude of each harmonic in the spectrum, and $\bar{A}$ is the average value of the corresponding amplitude of each harmonic. The smaller SD is, the more frequency components of milling force are indicated, the flatter the distribution is, and the more uniform the frequency domain energy distribution is. Therefore, SD can be minimized as the optimization objective function of the intertooth angle.

This thesis focuses on the side milling process of variable helix angle end mill, with Y direction milling force as the main research object. So the objective function can be set as: 11 $\min (S D) = \min (\sqrt{\lim_{x \to \infty} (\frac{1}{N} \sum_{i = 1}^{N} {(A_{y} (w) - \bar{A_{y}})}^{2})})$ where A_y(w) and $\bar{A_{y}}$ are the frequency amplitude and mean value of each harmonic of the Y - way milling force, respectively.

2.2.2

Constraints

The design of the inter-tooth angle of the variable helix angle end mill needs to consider the strength of the cutter teeth, enough chip space and the dynamic balance of the tool, so the minimum pitch of the tool is generally selected to be not less than 2/3 of the maximum pitch.In order to reduce the dynamic balance of the variable pitch end mill, the tool is designed as a symmetric structure.

Therefore, the range of inter-tooth angle can be obtained by the following formula: 12 ${\begin{array}{l} ϕ_{p \min} + ϕ_{p \max} = π \\ ϕ_{p \min} \geq \frac{2}{3} ϕ_{p \max} \end{array}$

The helix angle affects the actual cutting front angle of the cutting process and the direction of chip removal, which in turn affects the magnitude of the cutting force and the magnitude of the cutting heat. In the cutting process, the helix angle should be selected to a reasonable range, which can reduce the cutting force and produce a smaller cutting heat. Cutting heat is mainly related to the friction of the cutting process, by analyzing the relationship between the milling cutter geometry angle and the cutting friction energy can be obtained and its relationship with the cutting heat. As the helix angle increases, the average friction power in the milling process increases. In addition, the helix angle is also related to the tool edge strength and chip removal. The larger the helix angle, the larger the corresponding tool rake angle, so the edge strength is smaller. Within a certain range, the increase of the helix angle is beneficial to chip removal, but if the helix angle is too large, chip removal becomes difficult. After the helix angle is greater than 50 degrees, the average friction power increases greatly, the friction increases, and the chip removal is more difficult accordingly. Therefore, the selection of helix angle needs to take into account the cutting force, cutting heat, chip removal, edge strength, etc. For the variable helix angle end mill in this paper, the range of helix angle can be set at 41~47 degrees.

3

Three-dimensional finite element simulation modeling of iron cutting process

3.1

Material principal modeling

When solving a specific mechanical problem using the finite element method [25], it is necessary to introduce a relation that can reflect the intrinsic properties of the material of the deformable body, which is known as the intrinsic relationship. The constitutive model is the basis of finite element analysis and its accuracy will affect the correctness of the simulation results. In this paper, a modified form of the J-C model [26] is used: 13 $σ = [A + B ε^{n}] [1 + C \ln (\frac{\dot{ε}}{{\dot{ε}}_{0}})] [1 - {(\frac{T - T_{r}}{T_{m} - T_{r}})}^{m}]$ where A is the quasi-static material yield strength, B is the material hardening coefficient, C is the strain rate sensitivity parameter, n is the strain hardening index, m is the temperature softening coefficient, ${\dot{ε}}_{0}$ is the reference strain rate, ε is the equivalent plastic strain, T is the room temperature, T_r is the transition temperature, and T_m is the melting point temperature of the material.

3.2

Material damage modeling

In the end mill cutting process accompanied by the separation of chips and workpiece matrix, the external force on the material exceeds its own yield limit making part of the material detached from the matrix, so it is more suitable to separate the chips by defining the material failure method when simulating the end mill cutting process. In this paper, the physical separation criterion is used, and the Johnson Cook failure model is used in Abaqus software, which can take the strain, strain rate, and temperature into account in the damage criterion. The failure parameters can be defined as: 14 $ω = Σ (\frac{Δ {\bar{ε}}_{f}^{p l}}{{\bar{ε}}_{f}^{p l}})$ where $Δ {\bar{ε}}_{f}^{p l}$ is the equivalent plastic strain increment and ${\bar{ε}}_{f}^{p l}$ is the failure strain.

The expression for the failure strain is: 15 ${\bar{ε}}_{f}^{p l} = [d_{1} + d_{2} \exp (d_{3} \frac{σ_{m}}{σ})] [1 + d_{4} \ln (\frac{{\dot{\bar{ε}}}^{p l}}{{\dot{\bar{ε}}}_{0}})] [1 + d_{5} (\frac{T - T_{r}}{T_{m} - T_{r}})]$

Where ${\dot{\bar{ε}}}^{p l}$ is the equivalent plastic strain rate, ${\dot{\bar{ε}}}_{0}$ is the reference strain rate, σ_m is the average value of positive stress, σ is the equivalent plastic stress, and d₁~ d₅ is the material failure coefficient, which can be measured by the cylinder explosion test.

J-C damage model in ABAQUS can be defined by defining the failure displacement or fracture energy to define the damage evolution. The use of energy evolution can effectively reduce the dependence on the mesh in the simulation process, is currently the most used evolution, usually defined as the fracture energy of the fracture material unit area of the energy, fracture energy formula is as follows: 16 $D = \frac{\int \bar{σ} d {\bar{u}}^{p l}}{G f}$ 17 $G f = \frac{1 - v^{2}}{E} K I C^{2}$ where KIC is the fracture toughness of the material in units of MPa·m^1/2, v is the Poisson's ratio, E is the modulus of elasticity, and Gf is the fracture energy in units of J/m² or mJ/mm².

3.3

Friction models

The friction between the tool and the chip needs to be described when modeling the milling simulation, and the friction stress is the product of the friction coefficient and the positive stress, as shown in Eq: 18 $τ_{f} = {\begin{array}{l} τ_{\max} & τ \geq τ_{\max} (b o n d e d a r e a) \\ μ σ_{n} & τ < τ_{\max} (s l i d i n g z o n e) \end{array}$

Where τ_f is the friction stress, τ_max is the shear stress, σ_n is the positive stress, and μ is the friction coefficient.

Due to the relatively small range of the bonding zone and not easy to measure, the influence of the bonding zone on the cutting process is usually not considered in the finite element analysis, but the friction between the tool and the chip is regarded as a single sliding friction. Therefore, it is necessary to set the friction coefficient of the workpiece and the tool in ABAQUS simulation software. In this paper, the friction coefficient μ is set to 0.3 when the finite element model is established, and the contact mode is chosen as a penalty function to increase the convergence.

3.4

Finite element meshing

Compared with the two-dimensional milling model three-dimensional model in the grid size increases greatly, the increase in grid size often means that the cost of computation increases, so it is necessary to control the size of the number of grids in the mesh division, through a reasonable set of mesh size in the simulation results without affecting the accuracy of the case can effectively improve the efficiency of the calculation. In the use of finite element model to study the formation of chips in the cutting process can be determined by the thickness of the cutting layer size to set the mesh size of the workpiece.

The principle of area equivalence can be utilized to simplify a continuously varying thickness cutting layer into an equivalent cutting layer of uniform thickness. Kc is the envelope angle of the milling cutter from cut-in to cut-out is: 19 $K c = \arccos \frac{r - a_{e}}{r} + \arctan \frac{f_{z}}{2 r}$

Where Ac is the cutting layer area and f_z is the feed per tooth.

Ac can be expressed as: 20 $A c = \frac{1}{2} r^{2} [π - 2 \arccos (\frac{f_{z}}{2 r}) + \sin (2 \arccos (\frac{f_{z}}{2 r}))] - f_{z} (r - a_{ε})$

The equivalent cutting layer area is: 21 $A c = [r^{2} - {(r - h_{e})}^{2}] \cdot K c / 2$

Where h_e is the equivalent cutting layer thickness, the equivalent thickness h_e can be found by combining Eq. (20) with Eq. (21).

4

Analysis of the optimization effect of the structure of variable helix angle end milling cutter

4.1

Finite element simulation model validation results

4.1.1

Purpose of the experiment and program

The main purpose of the experiments in this section is to verify the validity of the three-dimensional finite element simulation model of the iron cutting process of variable helix angle end mills, and to explore the feasibility of the simulation model through finite element simulation based on the error between the milling experiments and the simulation results, so the specific experimental program is the same as the simulation program.

4.1.2

Experimental equipment

The main machine tool equipment used for the experiment is the VDL-1000E vertical machining CNC machine tool produced by Dalian Machine Tool Works. The milling force measurement equipment used in the experiment is a Kistler three-way piezoelectric force gauge. The tools used in the experiment are the two most commonly used materials in the current industrial production of variable helix angle end mills, respectively, Al7075-T6 and TC4 material variable helix angle end mills.

4.1.3

Analysis of experimental results

The milling force data of the tool in the stable milling stage within 0.5s were selected to calculate the three-way average milling force of the two materials and the simulation results respectively (for the convenience of comparative calculations, the average milling force is taken as the absolute value).The simulation and experimental comparison results of the milling force of the variable helix angle end mill for the Al7075-T6 material are shown in Table 1, and the comparison results of the simulation and experimental comparison results of the milling force of the variable helix angle end mill for the TC4 material are shown in Table 2. Since the material intrinsic model and damage model used in the simulation process of this paper are generalized models, they may be slightly different from the materials used in this experiment. At the same time, consider the friction coefficient of the cutter, mesh division and the deformation and wear of the tool in the experiment, so there is a certain gap between the simulation value and the experimental value. Among them, most of the simulation values are higher than the experimental values, and the errors of both (1.87%-14.57%) are below 15%, which belong to the reasonable range that can be accepted, and the lowest error value is only 1.87%. It shows that the simulation model established in this paper is effective, and the three-way milling force of the variable helix angle end milling cutter obtained by finite element simulation method has high reliability.

Table 1.

Simulation and experimental results of Al7075-T6

Program number	1	2	3	4	5
$\bar{F_{x}}$ experimental (N)	43.99	62.15	85.01	86.59	107.6
$\bar{F_{x}}$ simulation (N)	50.14	68.73	95.84	98.30	119.89
Error value (%)	13.97%	10.59%	12.74%	13.52%	11.42%
$\bar{F_{y}}$ experimental (N)	140.29	159.3	219.99	221.34	274.1
$\bar{F_{y}}$ simulation (N)	152.33	165.08	238.43	242.41	295.95
Error value (%)	8.58%	3.63%	8.38%	9.52%	7.97%
$\bar{F_{z}}$ experimental (N)	28.92	41.97	68.64	80.83	81.85
$\bar{F_{z}}$ simulation (N)	32.68	42.75	75.86	84.75	93.78
Error value (%)	13.01%	1.87%	10.52%	4.85%	14.57%

Table 2.

Simulation and experimental results of TC4

Program number	1	2	3	4	5
$\bar{F_{x}}$ experimental (N)	145.72	222.33	247.37	273.62	277.67
$\bar{F_{x}}$ simulation (N)	153.53	228.18	259.94	285.71	284.36
Error value (%)	5.36%	2.63%	5.08%	4.42%	2.41%
$\bar{F_{y}}$ experimental (N)	295.26	336.6	348.53	356.75	387.65
$\bar{F_{y}}$ simulation (N)	313.03	362.92	357.91	367.49	397.38
Error value (%)	6.02%	7.82%	2.69%	3.01%	2.51%
$\bar{F_{z}}$ experimental (N)	75.13	117.36	130.47	150.76	172.02
$\bar{F_{z}}$ simulation (N)	85.82	134.30	142.41	169.03	196.57
Error value (%)	14.23%	14.43%	9.15%	12.12%	14.27%

4.2

Structure optimization simulation results and analysis

According to the objective function as well as the constraints proposed in the previous section, the corresponding program is written in Matlab to optimize the design of the structure of the variable helix angle end mill using the improved genetic algorithm. Set the crossover probability of the improved genetic algorithm as 0.75, the variance probability as 0.05, the step size of the change of inter-tooth angle as 0.5°, and the step size of the change of helix angle as 0.25°. Considering more variable factors, a larger population number can be set. The population number set in this paper is 300, and the number of iterations is 35. 1)

Analysis results of structural optimization design scheme

In the actual milling process of variable helix angle end mill, for different processing conditions and processing requirements, the weight degree of the two objectives of reducing the vibration between cutters and improving the material processing efficiency will be different. In this paper, considering the weight of the two is the same, using the improved genetic algorithm can be derived from the structure optimization of the end milling cutter Al7075-T6 material optimal solution focused on the best solution as shown in Table 3. The solution with serial number 1 is taken as the best solution for the structure optimization design of variable helix angle end mill, and the SD and material removal rate under this solution are 12.94 and -69.72, respectively, which are the lowest. The spindle speed of the variable helix angle end mill for Al7075-T6 material under the optimal structure optimization design solution is 4600 r/min, the axial and radial depths of cut are 7.41 mm and 0.58 mm, respectively, and the inter-tooth angle and helix angles β₁ and β₂ are set to 97.5°, 45° and 46.5°, respectively.

The best solution in the set of optimal solutions for structural optimization of end mill for TC4 material is shown in Table 4. From the simulation results, it is found that Solution 3 has the lowest SD value of 26.02, and the material removal rate (-20.94) is ranked second among the five optimization solutions, so Solution 3 is taken as the best solution for the optimal design of the structure optimization of the end mill with variable helix angle for TC4 material. The spindle speed in the best structural optimization scheme for TC4 material end mills is set at 3300 r/min, and the inter-tooth angle as well as helix angles β₁ and β₂ are set at 97.5°, 36.5° and 35°, respectively.

2)

Simulation analysis of the effect of structure optimization design scheme

Taking the optimal solution for the structure optimization of the variable helix angle end mill obtained by the improved genetic algorithm in this paper and comparing it with the structural design scheme used in the current production, the simulation comparison results of the two materials end mills are shown in Table 5. Compared with the control scheme used in current production, the optimal scheme proposed in this paper results in a reduction of 17.21% and 19.09% in the SD values of the end mills in Al7075-T6 and TC4 materials, respectively. This indicates that the feasibility and effectiveness of the structural optimization design scheme obtained in this paper using the improved genetic algorithm for optimization were verified in simulation experiments.

Table 3.

Side milling top 5 solutions in A17075-T6

Number	1	2	3	4	5
Spindle speed (r/min)	4600	4600	4600	4600	4600
Axial depth (mm)	7.41	7.41	7.1	6.57	6.82
Radial depth (mm)	0.58	0.58	0.58	0.58	0.58
Average amount per tooth (mm)	0.04	0.04	0.04	0.06	0.06
Intertooth Angle (φ_p1)	97.5°	97.5°	97.5°	97.5°	97.5°
Spiral Angle (β₁)	45°	45°	45°	45°	45°
Spiral Angle (β₂)	46.5°	46.5°	46.5°	46.5°	46.5°
SD	12.94	13.01	13.31	13.56	13.91
Material removal rate	-69.72	-67.2	-66.83	-66.53	-66.48

Table 4.

Side milling top 5 solutions in TC4

Number	1	2	3	4	5
Spindle speed (r/min)	3300	3300	3300	3300	3300
Axial depth (mm)	5.9	5.95	6.05	6.88	5.95
Radial depth (mm)	0.35	0.35	0.35	0.35	0.35
Average amount per tooth (mm)	0.03	0.03	0.06	0.03	0.06
Intertooth Angle (φ_p1)	97.5°	97.5°	97.5°	97.5°	97.5°
Spiral Angle (β₁)	36.5°	36.5°	36.5°	36.5°	36.5°
Spiral Angle (β2)	35°	35°	35°	35°	35°
SD	26.55	26.08	26.02	27.07	27.8
Material removal rate	-19.56	-19.99	-20.94	-19.69	-20.28

Table 5.

Comparison results of the best scheme and control scheme

Milling structure	Al7075-T6		TC4
Milling structure	This article	Control	This article	Control
Spindle speed (r/min)	4600	4500	3300	3300
Axial depth (mm)	7.41	7.35	6.05	5.82
Radial depth (mm)	0.58	0.52	0.35	0.31
Average amount per tooth (mm)	0.04	0.07	0.06	0.07
Intertooth Angle (φ_p1)	97.5°	95°	97.5°	95°
Spiral Angle (β₁)	45°	45°	36.5°	35°
Spiral Angle (β₂)	46.5°	45°	35°	35°
SD	12.94	15.63	26.02	32.16
Material removal rate	-69.72	-64.52	-20.94	-18.52

4.3

Practical application analysis of end mill cutting performance

In order to further investigate the application effect of the variable helix angle end mill structure optimization scheme based on the improved genetic algorithm, this section applies the structurally optimized variable helix angle end mill to the actual industrial production and compares the cutting performance with the variable helix angle end mill that is actually applied in this factory.

4.3.1

Rear face wear and tool life

Using C1 and C2 to represent the variable helix angle end mills of Al7075-T6 material and TC4 material used in this industrial production, E1 and E2 represent the variable helix angle end mills obtained after optimizing the design structure using the scheme of this paper, respectively. The variation curves of the back face wear with cutting length for the four variable helix angle end mills are shown in Fig. 2. Taking the average wear of the tool back face of 1mm as the tool dulling standard, the tool life of the original structure variable helix angle end mill C1 and C2 is 4.51m and 5.50m, and the tool life of the optimized structure variable helix angle end mill E1 and E2 is increased to 6.52m and 6.92mm, which is an increase in life of 44.56% and 25.82%, respectively, which proves that the optimized structure of the variable helix angle end mill based on the improved genetic algorithm can effectively improve the cutting length of the variable helix angle end mills. The optimized structure of an end mill can effectively improve the tool life of a variable helix angle end mill. It can be seen that the C1 tool did not enter the normal wear stage after the end of the initial wear stage (0-0.51 mm), but directly entered the intense wear stage. Combined with the performance of the tool cutting process, it can be seen that when the cutting length reaches about 1.5m, the chipping phenomenon occurs at the tip of the two teeth with small inter-tooth angle. As the cutting continues, the chipping phenomenon is aggravated, and at the same time, the tips of the two teeth with larger inter-tooth angles also follow the chipping phenomenon, which leads to an increase in the wear rate of the back face of the tool. In summary, when the difference between the teeth of the variable helix angle end mill is too large, the strength of the teeth with smaller inter-tooth angle is insufficient, resulting in chipping of the tip of the cutter during the cutting process, which is the main reason for the decline in the life of the original tool in the industrial production.

4.3.2

Cutting forces and quality of the machined surface of the workpiece

The variation curves of cutting force with cutting length for four variable helix angle end mills are shown in Fig. 3. After the end of initial wear, the cutting forces of all the tools fluctuated smoothly between 927N and 1116N without drastic changes. The average cutting forces of tools C1 and C2 during the cutting process were 790.05N and 806.53N, and the average cutting forces of tools E1 and E2 were 1002.41N and 983.41N, which were 26.88% and 21.94% higher compared to the original tools C1 and C2 cutting forces, respectively.

The variation curves of the machined surface roughness with cutting length of the workpieces machined by the four variable helix angle end mills are shown in Fig. 4. Compared with the workpieces machined by the original structure variable helix angle end mills C1 and C2, the surface roughness of the workpieces machined by the optimized structure variable helix angle end mills E1 and E2 is significantly reduced. In more precise numerical representation, the average surface roughness of the workpieces machined by the original tools C1 and C2 in the whole cutting process is 3.57 microns and 3.31 microns, and the average surface roughness of the workpieces machined by the optimized tools E1 and E2 is 2.38 microns and 2.40 microns. In summary, the variable-helix angle end mill has good performance after optimizing the structure design based on an improved genetic algorithm.

5

Conclusion

In this paper, an improved penalty function hierarchical genetic algorithm is proposed to determine the best optimization scheme by combining the objective function and constraints of the structural optimization of variable helix angle end mill and carry out simulation experiments by constructing a finite element analysis model. It is verified that the error (1.87%-14.57%) between the simulated and experimental values of the model is less than 15%, which is within the acceptable reasonable range, indicating that the simulation model established in this paper is effective. The simulation experiments found that compared with the control scheme used in the current production, the optimal scheme proposed in this paper reduces the standard deviation values of the spectral distribution of the milling force of end milling cutters with Al7075-T6 and TC4 materials by 17.21% and 19.09%, respectively. The empirical results show that the tool life of the original structure variable helix angle end mills C1 and C2 is 4.51m and 5.50m, and the tool life of the optimized structure variable helix angle end mills E1 and E2 is increased to 6.52m and 6.92mm, which is an increase in life by 44.56% and 25.82%, respectively. In addition, the average surface roughness of the workpiece after machining of the original tools C1 and C2 is 3.57 microns and 3.31 microns, and the average surface roughness of the workpiece after machining of the structure-optimized tools E1 and E2 is 2.38 microns and 2.40 microns. This proves that variable-helix angle end mills with optimized structure design based on an improved genetic algorithm have good performance and can provide a reference for further development of milling machining technology.

Langue:: Anglais

Périodicité:: 1 fois par an
Sujets de la revue:: Sciences de la vie, Sciences de la vie, autres, Mathématiques, Mathématiques appliquées, Mathématiques générales, Physique, Physique, autres

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Structural optimization design and application of variable helix angle end mill based on improved genetic algorithm

Tao Chen

Publié en ligne: 19 mars 2025

Reçu: 08 oct. 2024

Accepté: 02 févr. 2025

DOI: https://doi.org/10.2478/amns-2025-0490

Mots clésGenetic algorithm, Penalty function, Finite element model, Objective function, End milling tool

© 2025 Tao Chen, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Genetic algorithm, Penalty function, Finite element model, Objective function, End milling tool