Process reliability evaluation and optimization method of spiral bevel gear milling machine tools

Abstract

The present invention discloses a process reliability evaluation method for a spiral bevel gear milling machine tool, comprising the following steps: Step 1: establishing an instantaneous cutting force model and a milling dynamics model for processing spiral bevel gears based on a forming method, and calculating the cutting vibration characteristics of the spiral bevel gear milling machine tool during the milling process; Step 2: based on the cutting vibration characteristics in Step 1, evaluating the sensitivity of various influencing factor parameters to the cutting vibration; and calculating the amplitude eigenvalue distribution type; Step 3: based on the amplitude eigenvalue distribution type in Step 2, using the Bayesian formula, establishing a BP neural network model, and using the Garson algorithm to update the BP neural network model; using the updated BP neural network model to calculate the amplitude eigenvalue under extreme working conditions, and combining the vibration trajectory curve of the milling tool and the process reliability formula to complete the machine tool process reliability evaluation. The present invention also discloses an optimization method for tuning machine tool process parameters using the above evaluation method.

Description

Technical Field

[0001] The invention belongs to the field of spiral bevel gear milling machine tools and relates to a process reliability evaluation and optimization method for spiral bevel gear milling machine tools. Background Art

[0002] A machine tool's process reliability assessment is the probability that the machine tool will complete its specified function within a specified time and under specified process conditions. It is an important method for quantitatively analyzing current process reliability. It is primarily used to measure whether the machine tool meets its design and operational requirements.

[0003] Spiral bevel gears are transmission components with advantages such as high efficiency, smooth transmission, and high load transfer. They are widely used in the automotive, aerospace, and marine industries, and are in high demand. Spiral bevel gear milling machines are essential equipment for producing and processing spiral bevel gears. During the gear cutting process, the time-varying cutting forces and intermittent cutting generate significant factors that force the machine tool to vibrate, causing self-excited vibration in the cutting system (cutting vibration mainly includes free vibration, forced vibration, and self-excited vibration, of which self-excited vibration has the greatest impact because it is a strong vibration with a complex generation mechanism and is difficult to eliminate and prevent). This causes the metal to vibrate during the cutting process, which can reduce machine tool stability, affect processing quality, and even lead to premature tool failure. Therefore, the process reliability of spiral bevel gear milling machines must be evaluated.

[0004] Patent document CN101804580A discloses "a method for evaluating the process reliability of large-scale CNC machine tools". This method obtains the frequency response function curve of a large-scale CNC machine tool through a structural comprehensive dynamic stiffness experiment, uses the nonlinear least squares method to identify the dynamic parameters through curve fitting, identifies the processing parameters of the cutting force dynamic model through a cutting force experiment, establishes a nonlinear dynamic model of the CNC machine tool cutting process, and then uses a random sampling method to simulate the tool processing motion trajectory and calculate the number of failure points to solve the process reliability probability.

[0005] However, the above-mentioned “a method for evaluating the process reliability of large CNC machine tools” still has the following shortcomings:

[0006] This evaluation method only evaluates the process reliability of machine tools from the dimension of surface roughness. It does not take into account the common processing technology of spiral bevel gears and the influence of milling machine tool tools on the process reliability of machine tools. It is not accurate enough in evaluating the process reliability of spiral bevel gear milling machines.

[0007] Based on this, the applicant considered designing a more suitable evaluation and optimization method for the process reliability of spiral bevel gear milling machines. Summary of the Invention

[0008] In view of the above-mentioned deficiencies in the prior art, the technical problem to be solved by the present invention is: how to provide a method for evaluating and optimizing the process reliability of spiral bevel gear milling machines that is better suitable for the same.

[0009] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0010] The process reliability evaluation method of a spiral bevel gear milling machine tool comprises the following steps:

[0011] Step 1: Establish an instantaneous cutting force model for spiral bevel gear machining based on the forming method; establish a milling dynamics model of the bevel gear machine tool tool-workpiece system, and calculate the cutting vibration characteristics of the spiral bevel gear milling machine tool during the milling process;

[0012] Step 2: Based on the cutting vibration characteristics in step 1, evaluate the sensitivity of each influencing factor parameter to the cutting vibration; calculate the distribution type of the amplitude characteristic value;

[0013] Step 3. Based on the amplitude eigenvalue distribution type in step 2, the Bayesian formula is used to establish a BP neural network model and the Garson algorithm is used to update the BP neural network model. The amplitude eigenvalue under the extreme working conditions is calculated using the updated BP neural network model. Combined with the vibration trajectory curve of the gear milling tool and the process reliability formula, the machine tool process reliability evaluation is completed.

[0014] Compared with the prior art, the process reliability evaluation method for spiral bevel gear milling machine tools of the present invention has the following advantages:

[0015] The influence of parameters such as spindle speed, feed per tooth, tool rake angle, and cutting edge inclination angle on cutting vibration during gear milling can be calculated; the evaluation results can be used to achieve better active suppression of gear milling vibration, and can also help adjust and optimize process parameters during gear cutting, thereby helping to achieve more reliable spiral bevel gear cutting results.

[0016] Furthermore, in the process reliability evaluation method of spiral bevel gear milling machine tools, in step 1: the instantaneous cutting force model is:

[0017] At any time t, the instantaneous tangential cutting force F on blade j is Tqj The value of the tangential cutting force F of the main cutting edge and the top edge is determined by Tqm , F Tqv Composition: Instantaneous radial cutting force F on blade j Nqj The radial cutting force F of the main cutting edge and the top edge Nqm , F Nqv Composition: Instantaneous axial cutting force F on blade j ZqjThe axial cutting force F of the main cutting edge and the top cutting edge Zqm , F Zqv composition;

[0018] where b qm (t) corresponds to the cutting width of the main cutting edge of insert j, and the outer cutter is b ew (t), inner knife takes b iw (t);h qm The cutting thickness of the main cutting edge of the corresponding insert j, the outer cutter is h ew , inner knife takes h iw ; b qv The cutting width of the top edge of the corresponding blade j, the outer blade is b w , inner knife takes b i ;h qv The cutting thickness of the top edge of the corresponding blade j is h for the outer blade. w , inner knife takes h i ;but:

[0019] F Tqj =F Tqm +F Tqv F Tqm =τb qm (t)h qm F Tqv =τb qv h qv

[0020] F Nqj =F Nqm +F Nqv F Nqm =τb qm (t)h qm F Nqv =τb qv h qv

[0021] F Zqj =F Zqm +F Zqv F Zqm =τb qm (t)h qm F Zqv =τb qv h qv

[0022] Decompose the tangential, radial, and axial cutting forces of the main cutting edge and top edge of insert j into the x, y, and z directions of the cutter head coordinate system. The instantaneous cutting forces of the jth insert along the coordinate axis in the three directions are:

[0023] F xt =F Tqj sin(θ(t))-F Nqjcos(θ(t))

[0024] F yt =F Tqj cos(θ(t))+F Nqj sin(θ(t))

[0025] F zt =F Zqj .

[0026] After verification, the instantaneous cutting force model established by this technical solution shows that the relative errors of the cutting forces in all directions are within the error range of 0-14%, which proves that the instantaneous cutting force model has good accuracy and can lay a good foundation for the subsequent establishment of the milling gear dynamics model.

[0027] Furthermore, in the process reliability evaluation method of spiral bevel gear milling machine tool, in step 1: the milling dynamics model is:

[0028] In the tool-workpiece system of a bevel gear machine tool, the vibration differential equations of the tool in the X and Y directions are expressed as follows:

[0029]

[0030] In the above formula: m x 、m y represents the modal mass of the tool in the X and Y directions in the gear milling system, c x , c y Indicates the equivalent damping of the tool in the X and Y directions in the gear milling system, k x , k y Indicates the equivalent stiffness of the tool in the X and Y directions in the gear milling system; x, y represent the vibration acceleration, vibration velocity, and vibration displacement of the tool in the X and Y directions, respectively; F x (t), F y (t) represents the instantaneous dynamic milling force of the tool in the X and Y directions;

[0031] in And the natural frequency of the tool in the X direction ω x , damping ratio ξ x , stiffness coefficient k x and the natural frequency ω in the Y direction y , damping ratio ξ y , stiffness coefficient k y , the mathematical expression of the vibration differential equation is:

[0032]

[0033] After verification, the above milling dynamics model established by this technical solution can be seen: the overall change trend of the experimental results and simulation calculation results of the tool vibration in the X and Y directions is basically consistent, the amplitude error is small, and the accuracy requirements are met. It can more realistically reflect the cutting vibration characteristics of the milling process.

[0034] Further, in step three: establish a BP neural network prediction model as:

[0035] Define the function γ:

[0036]

[0037] In the above formula, n is the number of neurons in the output layer, y is the target prediction value, and y′ is the actual output value.

[0038] The connection strength correction formula between neurons is:

[0039]

[0040] In the above formula, ω i is the connection weight from input data to hidden layer; α is the learning efficiency of BP neural network model; I i is the transfer function of each neuron in the hidden layer.

[0041] The BP neural network prediction model established in this technical solution and its update can make the prediction results more accurate.

[0042] Furthermore, in step 3: the process reliability formula is:

[0043]

[0044] n f is the number of amplitude root mean square values ​​less than the threshold, n 总 is the total number of samples.

[0045] This technical solution is different from the existing technology that evaluates the process reliability of machine tools from the perspective of machining surface roughness; this technical solution calculates the process reliability of machine tools based on the cutting vibration characteristics of machine tool tools and an iterative Bayesian BP neural network model, so that the calculation results can more truly reflect the process reliability status of machine tools.

[0046] The invention relates to a method for optimizing the process reliability of a spiral bevel gear milling machine tool, which is characterized in that the process parameters of the spiral bevel gear milling machine tool are adjusted or set using the evaluation results of the process reliability evaluation method of the spiral bevel gear milling machine tool.

[0047] After adopting the above-mentioned spiral bevel gear milling machine process reliability evaluation method, the influence of parameters such as spindle speed, feed per tooth, tool rake angle, and blade inclination angle on cutting vibration can be known, which can be used to guide the setting or adjustment of machine tool process parameters, promote better suppression of cutting vibration, improve the use stability of bevel gear machine tools, and help achieve the best processing quality and efficiency of spiral bevel gears. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is the logic block diagram of the process reliability evaluation method for spiral bevel gear milling machine tools of the present invention.

[0049] Figure 2.1 Schematic diagram of the forming method gear milling processing principle

[0050] Figure 2.2 Schematic diagram of a double-sided disc milling cutter

[0051] Figure 2.3 Coordinate system for forming large wheel cutter head

[0052] Figure 2.4 Schematic diagram of the large wheel cone coordinate system and the large wheel coordinate system

[0053] Figure 2.5 Coordinate system of machine tool for forming spiral bevel gear

[0054] Figure 2.6 Schematic diagram of the relative position of the tool and gear blank

[0055] Figure 2.7 Schematic diagram of the installation position of the blade on the cutter disc

[0056] Figure 2.8 Schematic diagram of instantaneous cutting width and thickness

[0057] Figure 2.9 for Figure 2.8 Middle AA section view

[0058] Figure 2.10 Schematic diagram of bevel cutting

[0059] Figure 2.11 Schematic diagram of the instantaneous cutting area of ​​the inner and outer teeth

[0060] Figure 2.12 Instantaneous cutting force diagram of inner and outer teeth

[0061] Figure 2.13 Cutting force calculation flow chart

[0062] Figure 2.14-1 Comparison chart of experimental and simulated cutting force in X direction

[0063] Figure 2.14-2Comparison chart of experimental and simulated cutting force in the Y direction

[0064] Figure 2.14-3 Comparison chart of experimental and simulated cutting force in Z direction

[0065] Figure 3.1 Schematic diagram of the real frequency and imaginary frequency curves of the frequency response function

[0066] Figure 3.2 Schematic diagram for test point layout

[0067] Figure 3.3-1 X-direction coherence spectrum

[0068] Figure 3.3-2 Coherence spectrum in the Y direction

[0069] Figure 3.4 The dynamic simulation model diagram of the gear milling system

[0070] Figure 3.5 Matlab simulation result interface

[0071] Figure 3.6 Simulink simulation result interface

[0072] Figure 3.7 Vibration signal acquisition interface for gear cutting

[0073] Figure 3.8-1 The gear tooth shape after processing

[0074] Figure 3.8-2 A partial enlarged view of the gear tooth shape after processing

[0075] Figure 3.9-1 Trend diagram of peak-to-peak value of vibration displacement in the X direction for simulation and experiment at different speeds

[0076] Figure 3.9-2 Trend diagram of the root mean square value of vibration displacement in the X direction under different speeds of simulation and experiment

[0077] Figure 3.9-3 Trend diagram of the peak-to-peak value of vibration displacement in the Y direction under different speeds for simulation and experiment

[0078] Figure 3.9-4 Trend diagram of the root mean square value of vibration displacement in the Y direction under different speeds of simulation and experiment

[0079] Figure 4.1 Vibration waveforms in the X and Y directions with a spindle speed of 120 r / min and a feed rate of 0.2 mm per tooth.

[0080] Figure 4.2Vibration waveforms in the X and Y directions with a spindle speed of 180 r / min and a feed rate of 0.2 mm per tooth.

[0081] Figure 4.3 Vibration waveforms in the X and Y directions with a spindle speed of 240 r / min and a feed rate of 0.2 mm per tooth.

[0082] Figure 4.4 Vibration waveforms in the X and Y directions with a spindle speed of 300 r / min and a feed rate of 0.2 mm per tooth

[0083] Figure 4.5 Vibration waveforms in the X and Y directions with a spindle speed of 360 r / min and a feed rate of 0.2 mm per tooth.

[0084] Figure 4.6 Vibration waveforms in the X and Y directions with a spindle speed of 420 r / min and a feed rate of 0.2 mm per tooth.

[0085] Figure 4.7 Calculation results of the root mean square value of vibration displacement at different speeds

[0086] Figure 4.8 Calculation results of the root mean square value of vibration displacement under different feed rates

[0087] Figure 4.9 Calculation results of the root mean square value of vibration displacement at different rake angles

[0088] Figure 4.10 Calculation results of the root mean square value of vibration displacement at different blade inclination angles

[0089] Figure 5.1 BP neural network model diagram for determining the importance of influencing factors

[0090] Figure 5.2-1 Screenshot of the X-direction BP neural network model training results

[0091] Figure 5.2-2 Screenshot of the X-direction BP neural network model training results

[0092] Figure 5.2-3 Screenshot of the X-direction BP neural network model training results

[0093] Figure 5.3-1 Screenshot of the Y-direction BP neural network model training results

[0094] Figure 5.3-2 Screenshot of the Y-direction BP neural network model training results

[0095] Figure 5.3-3 Screenshot of the Y-direction BP neural network model training results

[0096] Figure 5.4 Amplitude root mean square probability density histogram and fitting curve

[0097] Figure 5.5 Distribution probability test plot

[0098] Figure 5.6 Simulate the process for Openbugs software

[0099] Figure 5.7 Iterative trajectory diagram of parameter μ

[0100] Figure 5.8 is the posterior probability distribution function of the parameter μ

[0101] Figure 5.9 is the quantile map of parameter μ

[0102] Figure 5.10 is the autocorrelation function of parameter μ

[0103] Figure 5.11 Screenshot of the neural network training results after iterative updates in the X direction

[0104] Figure 5.12 Screenshot of the neural network training results after iterative update in the Y direction

[0105] Figure 5.13 Output diagram of vibration displacement in X direction

[0106] Figure 5.14 Output diagram of vibration displacement in the Y direction

[0107] Figure 5.15 Reliability change curve in X and Y directions DETAILED DESCRIPTION

[0108] The present invention will be described in further detail below with reference to the accompanying drawings.

[0109] In specific implementation: The process reliability evaluation method of the spiral bevel gear milling machine tool includes the following steps:

[0110] Step 1: Establish an instantaneous cutting force model for spiral bevel gear machining based on the forming method; establish a milling dynamics model of the bevel gear machine tool tool-workpiece system, and calculate the cutting vibration characteristics of the spiral bevel gear milling machine tool during the milling process;

[0111] Step 2: Based on the cutting vibration characteristics in step 1, evaluate the sensitivity of each influencing factor parameter to the cutting vibration; calculate the distribution type of the amplitude characteristic value;

[0112] Step 3. Based on the amplitude eigenvalue distribution type in step 2, the BP neural network model is updated using the Bayesian formula, BP neural network model and Garson algorithm. The amplitude eigenvalue under extreme working conditions is calculated using the updated BP neural network model. Combined with the vibration trajectory curve of the gear milling tool, the machine tool process reliability assessment is completed.

[0113] A. Establishment of instantaneous cutting force model

[0114] In step 1: the instantaneous cutting force model is:

[0115] At any time t, the instantaneous tangential cutting force F on blade j is Tqj The value of the tangential cutting force F of the main cutting edge and the top edge is determined by Tqm , F Tqv Composition: Instantaneous radial cutting force F on blade j Nqj The radial cutting force F of the main cutting edge and the top edge Nqm , F Nqv Composition: Instantaneous axial cutting force F on blade j Zqj The axial cutting force F of the main cutting edge and the top cutting edge Zqm , F Zqv composition;

[0116] where b qm (t) corresponds to the cutting width of the main cutting edge of insert j, and the outer cutter is b ew (t), inner knife takes b iw (t);h qm The cutting thickness of the main cutting edge of the corresponding insert j, the outer cutter is h ew , inner knife takes h iw ; b qv The cutting width of the top edge of the corresponding blade j, the outer blade is b w , inner knife takes b i ;h qv The cutting thickness of the top edge of the corresponding blade j is h for the outer blade. w , inner knife takes h i ;but:

[0117] F Tqj =F Tqm +F Tqv F Tqm =τb qm (t)h qm F Tqv =τb qv h qv

[0118] F Nqj =F Nqm +F Nqv F Nqm =τb qm(t)h qm F Nqv =τb qv h qv

[0119] F Zqj =F Zqm +F Zqv F Zqm =τb qm (t)h qm F Zqv =τb qv h qv

[0120] Decompose the tangential, radial, and axial cutting forces of the main cutting edge and top edge of insert j into the x, y, and z directions of the cutter head coordinate system. The instantaneous cutting forces of the jth insert along the coordinate axis in the three directions are:

[0121] F xt =F Tqj sin(θ(t))-F Nqj cos(θ(t))

[0122] F yt =F Tqj cos(θ(t))+F Nqj sin(θ(t))

[0123] F zt =F Zqj .

[0124] A1. Regarding "forming method" and "forming tool":

[0125] The "forming method" is a method of processing a workpiece using a forming tool. This means that a forming tool replaces an ordinary tool, and the cutting edge of the forming tool is the shape of the workpiece. When processing spiral bevel gears using the forming method, the installation angle of the tooth blank and the position of the cutter head must be adjusted first to maintain the correct relative position. During the gear milling process, the relative position of the tooth blank and the cutter head remains unchanged, the tooth blank remains stationary, and the cutter head rotates and feeds along the axis. The gear tooth shape depends on the shape of the tool. Figure 2.1 shown.

[0126] When processing the instantaneous cutting force model of the spiral bevel gear wheel in this technical solution, the tool used is a double-sided disc milling cutter (the processing efficiency is higher, such as Figure 2.2 (As shown in Figure 1), the milling cutter disc has two types of blades, inner and outer, alternating across the disc. The inner blades primarily machine the convex surface of the gear tooth groove, while the outer blades primarily machine the concave surface. The bottom of the gear tooth groove is formed by the top cutting edges of the inner and outer blades. Existing literature does not consider the inner and outer blades separately, resulting in significant modeling errors.

[0127] In order to improve the deficiencies of existing literature, this technical solution simultaneously considers and calculates the force on the main cutting edge and the force generated by the top cutting edge when modeling the instantaneous cutting force of the spiral bevel gear wheel during the forming method processing. This can better restore and simulate the actual cutting conditions and improve the accuracy of modeling.

[0128] A2. Calculation of “Undeformed Cutting Width and Thickness”

[0129] When forming the spiral bevel gear, the inner and outer blade cutting edges are generally straight edges, sometimes arc edges. The inner and outer blade cutting edges rotate around the center of the cutter head to form two conical surfaces, and the cutter head coordinate system is established, such as Figure 2.3 shown.

[0130] According to the cutter head coordinate system of the large wheel processed by the forming method, the equations of the inner and outer blades’ production surfaces can be obtained as follows:

[0131]

[0132] Where (μ,θ) is the moving point on the blade's surface; r c is the radius of the inner and outer blade tip, where r c =r0±0.5W, r0 is the nominal radius of the cutter head, W represents the cutter offset, when the blade is an outer blade, take "+", when the blade is an inner blade, take "-". α m is the tooth profile angle of the inner and outer blades, m = (e, i), where e represents the outer blade taking "+" and i represents the inner blade taking "-".

[0133] A3. About the equation of the large wheel surface of spiral bevel gears

[0134] During the cutting process of spiral bevel gears, the outer and inner blades on the cutter head first contact the large wheel cone, so the large wheel cone coordinate system S is first established. a , and establish the large wheel coordinate system S2 at the axis intersection point O2 (such as Figure 2.4 After the gear blank is designed, all parameters of the large gear blank are known.

[0135] According to the large wheel cone coordinate system S a , the equation of the large wheel cone can be obtained as:

[0136]

[0137] Where:

[0138] (p,β) represents the parameters of the moving point on the large wheel cone;

[0139] B represents the width of the large gear tooth surface, in mm;

[0140] δa Indicates the large wheel cone angle;

[0141] M is the distance between the vertex of the face cone and the intersection point of the axis;

[0142] A4. About the "Coordinate System of Gear Milling Machines Using the Forming Method"

[0143] Figure 2.5 The figure shows the machine tool coordinate system for forming the spiral bevel gear wheel. The bevel gear machine tool adjustment parameters included are: bed position z j , horizontal tool position H, vertical tool position V, horizontal wheel position X2 and bevel gear machine installation root cone angle δ M2 .

[0144] Therefore, the blade surface equation can be transformed into the machine tool coordinate system through coordinate transformation, and its equation can be expressed as:

[0145] r tm (μ,θ)=M mt r t (μ,θ) (2.3)

[0146] Among them, M mt is the cutterhead coordinate system S t The transformation matrix to the machine tool coordinate system is based on Figure 2.5 We can get:

[0147]

[0148] The large wheel cone equation can be expressed in the machine tool coordinate system through coordinate transformation, and its equation is:

[0149] r am (p,β,z j )=M mf M f2 M a2 r a (p,β) (2.5)

[0150] Where:

[0151]

[0152] In the above matrix, δ M2 is the root cone angle of the machine tool installation, M is the distance from the vertex of the cone to the axis intersection point, z j For beds.

[0153] By combining equations (2.3) and (2.5), we can obtain the intersection equation of the large wheel cone equation and the blade production surface equation in the machine tool coordinate system:

[0154] L M (μ,θ,p,β,z j)=r am (p,β,z j )-r tm (μ,θ)=0 (2.7)

[0155] In order to obtain the cutting-in and cutting-out angles of the inner and outer blades on the cutter head, as well as when the blades participate in cutting and when they exit cutting, the inner and outer blades cut the gear blank within the cutting-in and cutting-out angle range. Therefore, the cutting-in and cutting-out angles of the inner and outer blades need to be calculated. In the process of forming gear milling, the relative positions of the blades entering and cutting out of the gear blank are as follows: Figure 2.6 shown.

[0156] according to Figure 2.6 The cutting angle θ can be obtained st , cutting angle θ ex As shown in Equations (2.8) and (2.9) respectively, k is the number of revolutions of the cutter head.

[0157]

[0158]

[0159] A5. About the calculation of "instantaneous undeformed cutting width and thickness"

[0160] This technical solution: During the forming method gear milling process, only a single tooth is in contact with the gear blank at any time, that is, the tooth line length is less than the distance between adjacent cutting edges. Therefore, only the single tooth cutting at any time is selectively considered. This condition is met and expressed in the mathematical formula as follows:

[0161]

[0162] Where r0 is the nominal radius of the cutter head, Z H is the number of teeth on the cutter head, B is the tooth surface width, β M is the helix angle at the midpoint of the large wheel.

[0163] During the milling process of spiral bevel gears: the cutter head rotates at a speed n, the cutting direction of the tool is the cutter head tangential direction, and the tool feeds along its own axis. When the tool is at the full tooth height Hg position of the large wheel, the tool contacts the gear blank and the cutting begins. When it moves to the bed position z j =0, the blade tip plane is tangent to the bottom plane of the gear tooth groove, completing the processing of one tooth, the tool retracts and the gear blank is indexed to cut the next tooth, and the cycle continues until all teeth are processed.

[0164] The distribution of the teeth on the cutter head is as follows Figure 2.7 shown.

[0165] Among them, the angle between adjacent blades, that is, the pitch angle φ1 = 2π / Z H , feed per tooth fc =f / (nZ H ), bed j (t) = Hg - f c t; then the rotation angle of blade j at any time is:

[0166] θ(t)=2πnt-(j-1)φ1 (2.11)

[0167] In the formula, j takes an odd number to represent an outer blade, j takes an even number to represent an inner blade, j=1,2…Z H .

[0168] For the outer blade, when the axial feed motion bed position is kept at 0≤z j (t)≤Hg, and the blade angle at any time is maintained at 2kπ+θ st ≤θ(t)≤2kπ+θ ex When (i.e. within the range of cutting in and out angles), k is the number of revolutions of the cutter head, (θ(t), z j Substituting (t)) into the intersection equation established in the machine tool coordinate system, we can obtain u ej (θ(t),z j (t));

[0169] Therefore, the instantaneous undeformed cutting width and thickness of the main cutting edge of the outer insert are:

[0170] b ew (t) = u ej (θ(t),z j (t)) (2.12)

[0171] h ew =2f z sinα e (2.13)

[0172] Since the gear tooth groove is formed by the top cutting edge of the tool during the actual processing of spiral bevel gears, the influence of the top cutting edge needs to be considered in the calculation. The instantaneous undeformed cutting width and thickness of the outer insert when cutting with the top cutting edge are:

[0173] b w =S b (2.14)

[0174] h w =2f z (2.15)

[0175] Where S b is the blade top width, S b =(0.5-0.75)W, W is the tool offset.

[0176] Similarly, for the inner blade, when the axial feed motion bed position is kept at 0≤z j (t)≤Hg, and the blade angle at any time is maintained at 2kπ+θ st ≤θ(t)≤2kπ+θ ex When k is the number of revolutions of the cutter head, (θ(t), z j Substitute (t)) into the intersection equation established in the machine tool coordinate system, and we can get u ij (θ(t),z j (t));

[0177] Therefore, the instantaneous undeformed cutting width and thickness of the main cutting edge of the inner insert are:

[0178] b iw (t) = u ij (θ(t),z j ) (2.16)

[0179] h iw =2f z sinα i (2.17)

[0180] The instantaneous undeformed cutting width and thickness of the inner insert top edge are:

[0181] b i =S b (2.18)

[0182] h i =2f z (2.19)

[0183] A6. About “Material Shear Zone Stress Calculation”

[0184] This technical solution adopts the JC constitutive model (i.e., the "Johnson-Cook model") as the constitutive model of the gear blank material 42CrMo structural steel to calculate the stress value in its shear zone.

[0185] The JC constitutive model is a type of function that describes the relationship between strain, strain rate, and temperature. Based on the oblique cutting theory and the JC constitutive model of the material, the shear zone stress τ of the material, i.e., the cutting force per unit cross section, can be calculated. The specific formula is as follows:

[0186]

[0187] where ξ is the shear strain, is the shear strain rate, Reference shear strain rate, T is the temperature at which the workpiece deforms (usually 25°C), T r is the initial temperature of the workpiece, T mis the melting temperature of the material, and A, B, C, m, and n are all material-related constants. The gear blank material used in this technical solution is 42CrMo. The constitutive model parameters of the gear blank material can be obtained by referring to the Metal Materials Handbook. The model parameter values ​​are shown in Table 2.1 below:

[0188] Table 2.1 42CrMo material constitutive model parameters

[0189]

[0190] Applying the non-uniform shear zone model on the equivalent plane can obtain the corresponding material's thermal control equation, that is, the material shear zone stress equation. In this model, the shear strain ξ and shear strain rate in the shear zone are The calculation formula is:

[0191]

[0192]

[0193] In the above calculation formulas for shear strain and shear strain rate, is the maximum shear strain rate; k is the unequal division coefficient, which means the ratio of the distance from the lower boundary to the width of the main shear surface of the shear zone to the distance from the lower boundary to the thickness of the main shear surface of the shear zone; the specific calculation formula is as follows:

[0194]

[0195]

[0196] Because in the process of forming gear milling, the cutting edge direction of the tool and the cutting speed direction are not perpendicular, but form an angle, such as Figures 2.8 to 2.10 As shown, the bevel cutting theory is satisfied.

[0197] Therefore, the shear flow angle η is calculated according to the oblique cutting theory. s , equivalent plane angle η e The calculation formula is:

[0198]

[0199]

[0200] Similarly, the normal shear angle φ n , normal to front angle α n , chip angle η c The value of is calculated.

[0201] According to the bevel cutting theory, the calculation formula of the normal rake angle is as follows:

[0202] αn =tan -1 (tanα0cosλ s ) (2.27)

[0203] In bevel cutting, the normal rake angle α n , normal shear angle φ n , the friction angle β satisfies the Merchant formula.

[0204]

[0205] Similarly, the relationship between the average friction coefficient and friction angle on the chip surface satisfies:

[0206]

[0207] Where f is the average friction coefficient, f0 and p are constant values, and their typical values ​​are f0 = 0.704, p = -0.2048, and chip velocity V C It can be calculated according to the theoretical formula of bevel cutting:

[0208]

[0209] The chip angle η in the formula c According to Stabler's law, when the blade inclination angle is small (λ s ≤15°), the chip flow angle and the blade inclination angle are approximately equal. The blade inclination angle of the tool used in this technical solution is 5°, which meets the conditions, so:

[0210] η c =λ s (2.31)

[0211] By taking special values ​​(0,kh,h) for y, the shear strains at the initial shear line, main shear surface and final shear line can be calculated.

[0212] When y = 0, ξ = 0;

[0213] When y = kh,

[0214] When y=h,

[0215] Taking special values ​​of y (0,kh,h), the shear strain rates at the initial shear line, main shear surface and final shear line can be calculated.

[0216] When y=0,

[0217] When y = kh,

[0218] When y=h,

[0219] In the above formula, q is the velocity distribution characteristic parameter of the shear zone, and the empirical value q=7 is taken in this technical solution;

[0220] A7. About “Calculation of Cutting Force of Cutting Teeth”

[0221] During the forming method gear milling process, the instantaneous cutting force on the inner and outer teeth is determined by the unit cross-sectional cutting force and the instantaneous cutting area of ​​the gear blank material. The instantaneous cutting area is determined by the instantaneous undeformed cutting width and thickness. After each feed of the tool, the instantaneous cutting area of ​​the inner and outer teeth is as follows: Figure 2.11 shown.

[0222] At any time t, the instantaneous tangential cutting force F on blade j is Tqj The value of the tangential cutting force F of the main cutting edge and the top edge is determined by Tqm , F Tqv Composition: Instantaneous radial cutting force F on blade j Nqj The radial cutting force F of the main cutting edge and the top edge Nqm , F Nqv composition( Figure 2.12 As shown); instantaneous axial cutting force F on blade j Zqj The axial cutting force F of the main cutting edge and the top cutting edge Zqm , F Zqv composition( Figure 2.12 where b qm (t) corresponds to the cutting width of the main cutting edge of insert j, and the outer cutter is b ew (t), inner knife takes b iw (t);h qm The cutting thickness of the main cutting edge of the corresponding insert j, the outer cutter is h ew , inner knife takes h iw ; b qv The cutting width of the top edge of the corresponding blade j, the outer blade is b w , inner knife takes b i ;h qv The cutting thickness of the top edge of the corresponding blade j is h for the outer blade. w , inner knife takes h i .

[0223] The calculation results are:

[0224] F Tqj =F Tqm +F Tqv F Tqm =τb qm (t)h qm F Tqv =τb qv h qv(2.34)

[0225] F Nqj =F Nqm +F Nqv F Nqm =τb qm (t)h qm F Nqv =τb qv h qv (2.35)

[0226] F Zqj =F Zqm +F Zqv F Zqm =τb qm (t)h qm F Zqv =τb qv h qv (2.36)

[0227] Decompose the tangential, radial, and axial cutting forces of the main cutting edge and top edge of insert j into the x, y, and z directions of the cutter head coordinate system. The instantaneous cutting forces of the jth insert along the coordinate axis in the three directions are:

[0228]

[0229] A8. Verification of the accuracy of the above “instantaneous cutting force model”

[0230] (1) Cutting force measurement equipment

[0231] Note: Due to the machine tool limitations caused by the installation of the dynamometer, this verification experiment was unable to cut the standard large gear blank. Therefore, a single cut was performed on a small gear blank. Cutting with the small gear blank only altered the geometric parameters of the large gear blank and the machine tool adjustment parameters, but the parameters and machining principles required for the forming method remained unchanged. Therefore, this method can be used to verify the theoretical cutting force model for forming large spiral bevel gears. According to the forming method machining principle, the tool was adjusted to the tooth cutting position, maintaining the relative position of the gear blank and the tool unchanged, and a single cut was performed.

[0232] The machine tool used in this verification experiment is a YKH2235 CNC spiral bevel gear milling machine. The dynamometer is installed on the spindle, the cutterhead is connected to the dynamometer, and the rotor is installed on the dynamometer (the rotor rotates with the dynamometer). The stator is installed on the fixture outside the dynamometer. When cutting, due to the cutting force acting on the dynamometer, the quartz crystal inside it generates an electrical signal. The electrical signal is transmitted to the stator through magnetic induction between the stator and the rotor. The stator is connected to a charge amplifier, which amplifies the received charge signal and transmits the amplified charge signal to the data acquisition system. The data acquisition system finally transmits the signal to the computer, and the measured cutting force is displayed in real time on the DynoWare software interface. The model and specifications of the cutting force measurement equipment are shown in Table 2.2.

[0233] Table 2.2 Cutting force measuring instruments

[0234]

[0235] (2) Experimental verification process

[0236] In order to ensure the accuracy of the experimental results, after installing the dynamometer on the cutter head, it is necessary to use a dial indicator to check whether the coaxiality between the machine tool spindle, dynamometer and milling cutter head meets the experimental requirements, so as to ensure that the runout error value does not exceed 0.01mm. The stator on the external tooling of the dynamometer is connected to the charge amplifier through a signal transmission line, the charge amplifier is connected to the data acquisition system, and finally the data acquisition system is connected to the computer via a USB cable. After the connection is completed, the relevant parameters of the data acquisition process need to be set in the DynoWare acquisition software before measurement. After the settings are completed, the milling force acquisition range in the three directions is 1500N; the acquisition frequency is 1000HZ; when the machine tool spindle starts to rotate, click to start recording, and click to end after the cutting is completed, thereby realizing the collection of data for the entire cutting process.

[0237] (3) Experimental results

[0238] In this experiment, the parameters of the tooth blank and the main parameters of the milling cutter disc used in the experiment are shown in Table 2.3:

[0239] Table 2.3 Geometric parameters of gear blanks and main parameters of milling cutter discs processed by forming method

[0240]

[0241]

[0242] The cutting force of gear milling is measured under the working conditions of spindle speed n=120r / min and feed speed 20mm / min. The measurement results can be displayed in real time in DynoWare cutting force acquisition software.

[0243] From the measurement result graph, it can be found that the cutting force changes smoothly at the beginning. At this time, the main spindle is idling, and its cutting force value is still fluctuating. The reason is caused by the deadweight of the dynamometer and the cutter disc. At this time, the cutter teeth have not cut into the workpiece. When the cutting force has a trend of increasing, it means that the cutter teeth begin to cut into the tooth blank. When the experimental cutting force data is processed later, the cutting force generated by the deadweight of the dynamometer and the cutter disc will be subtracted accordingly. In order to further analyze the cutting force data, the cutting force data in the three directions of X, Y, and Z are exported respectively, and the cutting force data within the stable cutting time (22.16-22.43 seconds) are intercepted. The measured data of the cutting force in the three directions and the theoretical calculation results are plotted in the same graph, as shown below. Figures 2.14-1 to 2.14-3 shown.

[0244] It can be seen from the figure that the overall trend of the theoretical calculation results of the milling cutting force is basically consistent with the experimental results. The changes in the cutting force of the teeth in the three directions of X, Y, and Z are first increased and then decreased, that is, when each tooth cuts into the tooth blank, the cutting width first increases and then decreases; the Y-direction cutting force changes with the direction; in the Z-direction cutting force, the force amplitude is the smallest. By calculating the absolute average value of the difference between the experimental and theoretical calculation maximum values ​​of the cutting force of each peak, it can be concluded that the relative error of the cutting force in the X direction is 9.24%, the relative error of the cutting force in the Y direction is 13.18%, and the relative error of the cutting force in the Z direction is 13.25%. The relative errors of the cutting forces in each direction are all within the error range of 0-14%. Therefore, it can be seen that the instantaneous cutting force model for processing spiral bevel gears based on the forming method established by this technical solution has a high accuracy.

[0245] A9. Summary of instantaneous cutting force model and its verification

[0246] like Figure 2.13 As shown, this technical solution uses the forming method to process the spiral bevel gear wheel, and derives the calculation formula for the instantaneous undeformed cutting area during the gear milling process. The Johnson-Cook model of the material and the bevel cutting theory are used to calculate the shear strain and shear strain rate of the shear zone, and the shear stress of the shear zone is obtained. The instantaneous cutting force model of the spiral bevel gear wheel processed by the forming method is constructed, and the corresponding simulation program is compiled to solve the theoretical model. The theoretical model is verified by gear milling experiments. After analysis, it is found that the relative errors of the cutting forces in all directions are within the error range of 0-14%, which proves that the instantaneous cutting force model has a certain degree of accuracy and prepares for the subsequent establishment of the gear milling dynamics model.

[0247] B. Gear milling dynamics model

[0248] In step 1: the dynamic model of gear milling is:

[0249] In the tool-workpiece system of a bevel gear machine tool, the vibration differential equations of the tool in the X and Y directions are expressed as follows:

[0250]

[0251] In the above formula: m x 、m y represents the modal mass of the tool in the X and Y directions in the gear milling system, c x , c y Indicates the equivalent damping of the tool in the X and Y directions in the gear milling system, k x , k y Indicates the equivalent stiffness of the tool in the X and Y directions in the gear milling system; x, y represent the vibration acceleration, vibration velocity, and vibration displacement of the tool in the X and Y directions, respectively; F x (t), F y (t) represents the instantaneous dynamic milling force of the tool in the X and Y directions;

[0252] in And the natural frequency of the tool in the X direction ω x , damping ratio ξ x , stiffness coefficient k x and the natural frequency ω in the Y direction y , damping ratio ξ y , stiffness coefficient k y , the mathematical expression of the vibration differential equation is:

[0253]

[0254] Since the axial vibration mode is small during the gear milling process and has little effect on the surface processing quality of the workpiece, this technical solution does not consider the vibration in the Z direction, but only considers the vibration in the X and Y directions. While ensuring better modeling to simulate the actual processing process, it can also reduce the amount of data calculation for modeling and improve computing efficiency.

[0255] After verification, the above milling dynamics model established by this technical solution can be seen that the overall change trend of the experimental results and simulation calculation results of the tool vibration in the X and Y directions is basically consistent, the amplitude error is small, and the accuracy requirements are met. It can more realistically reflect the cutting vibration characteristics of the milling process.

[0256] B1. Modal Analysis

[0257] Modal analysis is a method for studying the dynamic characteristics of product structures. Modes reflect the inherent vibration characteristics of mechanical structures, and different structures correspond to different modes. Each mode includes parameters such as the corresponding natural frequency, damping ratio, stiffness coefficient, and mode shape. Therefore, the essence of modal analysis is the process of solving the modal parameters of the product structure through theoretical or experimental methods. Modal analysis includes theoretical modal analysis and experimental modal analysis. This technical solution selects the experimental modal method to identify the modal parameters of the gear milling system.

[0258] B2. Incentive Methods

[0259] This technical solution selects a hammer as the excitation source.

[0260] B3. Modal parameter calculation method

[0261] For a vibration system, most of the energy that causes vibration is concentrated in the low-order vibration system, and high-order flutter is difficult to excite. Therefore, in the selection of characteristic frequency, this technical solution selects the first-order natural frequency as the characteristic frequency. Looking at each direction separately, X and Y are both single-degree-of-freedom viscous damping systems, and their frequency response function expressions are as follows:

[0262]

[0263] In formula (3.3), k is the system stiffness, ξ is the damping ratio of the system, and λ is the characteristic value of the test system.

[0264] The frequency response function can also be expressed in the form of imaginary part and real part, as shown in formula (3.4).

[0265]

[0266]

[0267] Once the real and imaginary parts of the frequency response function are determined, the real frequency curve and imaginary frequency curve can be drawn. Take the real frequency curve and imaginary frequency curve of a certain order mode as an example. Figure 3.1 shown.

[0268] right Figure 3.1 The analysis can obtain the system's modal parameters such as the natural frequency, damping ratio, and stiffness coefficient. In the solution process, the solution idea is to first analyze the natural frequency of the vibration system, then solve the damping ratio of the vibration system, and finally calculate the stiffness coefficient of the system. The specific solution steps for each parameter are as follows:

[0269] First, solve the natural frequency. There are differences between single-degree-of-freedom systems and multi-degree-of-freedom systems when calculating the natural frequency. The natural frequency value of a single-degree-of-freedom system is the intersection value of the real frequency curve and the horizontal axis. The natural frequency of a multi-degree-of-freedom system is the horizontal axis corresponding to the peak value of the imaginary frequency curve, that is, the corresponding Figure 3.1 The horizontal coordinate value of point C is:

[0270] ω n =ω C (3.5)

[0271] Secondly, the damping ratio is solved, and the calculation formula is:

[0272]

[0273] Finally, the stiffness coefficient is solved and the calculation formula is:

[0274]

[0275] In formula (3.7), I C is the ordinate of the peak point of the imaginary frequency curve.

[0276] B4. Modal test process

[0277] (1) Excitation point and acceleration sensor location layout

[0278] Before conducting the vibration experiment, it is necessary to determine in advance the location of the hammer striking point and the location of the response point for installing the acceleration sensor in the test system. The following principles are generally followed for the arrangement of measurement points: it can better reflect the dynamic characteristics of the system; the locations of the excitation point and the response point avoid the mechanical structure nodes; it is conducive to the installation and measurement of the sensor. This technical solution adopts the single-point excitation-multi-point response test method, establishes the geometric model of the spindle-tool system in the PULSE Reflex software, and divides it into grids, selects point 1 on the tool disc as the hammer excitation point, and selects 8 points opposite the excitation point as response points, such as Figure 3.2 As shown, the three-axis acceleration sensors are moved separately for measurement.

[0279] (2) Experimental equipment

[0280] This technical solution utilizes a YKH2235 CNC spiral bevel gear milling machine to conduct a corresponding modal hammer test on the machine tool milling cutter disc, thereby obtaining the tool's frequency response curve and identifying the tool's modal parameters. Before conducting the modal hammer test, a preliminary experiment was conducted. The preliminary experimental results showed that the time domain waveforms generated by hammer excitations of different materials were different. After repeated comparisons, it was found that plastic hammer excitation had the best effect. Therefore, the hammer used in this experiment was a plastic hammer. The sensor for collecting vibration signals was a PCB three-axis sensor, and the acquisition and measurement software used was PULSE Reflex software. The specific experimental equipment parameters are shown in Table 3.1 below.

[0281] Table 3.1 Main test equipment parameters

[0282]

[0283]

[0284] (3) Experimental process

[0285] A hammer was used to excite the cutterhead excitation point, and a PCB three-axis accelerometer was used to collect the response point signal. To eliminate the influence of the external environment during the acquisition process, the average of five measurements was taken for each response point.

[0286] B5. Modal test results and analysis

[0287] When conducting modal hammer tests, the influence of noise signals is unavoidable. If the influence of noise signals is too great, the frequency response function (FRF) obtained by the hammer test system will be inaccurate, causing the identified machine tool modal parameters to differ from the actual situation. Therefore, before calculating the modal parameters, it is necessary to perform a coherence test on the FRF.

[0288] In practical engineering applications, it is necessary to detect the reliability of the acquired frequency response function. The commonly used detection method is the coherence function test, which uses the coherence function to determine the correlation between two arbitrary signals within the frequency range. The specific function expression is:

[0289]

[0290] Where S xy (w) is the cross power spectral density function of the excitation signal and the response signal, S x (w), S y (w) are the auto-power spectral density functions of the excitation signal and the response signal, respectively. It represents the closeness between the stimulus signal and the response signal, and the causal relationship between the two signals. The value range is [0,1]. When using coherence functions in engineering, it is usually required At this point, it can be considered that other factors have little influence on the experimental results, and the obtained frequency response function is reliable. The frequency response function obtained from the experiment is considered unreliable. The coherent spectrum in the X and Y directions and the acquisition interface are obtained from this modal hammer test. Figure 3.3-1 and 3.3-2 shown.

[0291] according to Figure 3.3-1 and 3.3-2 It can be seen that the coherence spectrum values ​​in the X and Y directions of this modal experiment are mostly above 0.8. Therefore, it is believed that the results of this modal experiment are less affected by other factors and the test results are true and reliable. The frequency response function data obtained from the modal hammer test is exported and expressed in the form of real frequency and imaginary frequency. Then, the modal parameters of the tool are calculated according to the calculation methods of equations (3.5) to (3.7). Since most of the energy of the vibration system is concentrated in the low order, the natural frequency of the milling system is taken as its first-order natural frequency as its characteristic frequency. The modal parameter calculation results are shown in Table 3.2.

[0292] Table 3.2 Tool modal parameters of gear milling system

[0293]

[0294] B6. Computer simulation verification of cutting vibration (milling dynamics model)

[0295] The computer simulation of cutting vibration is to establish the established mathematical model on the computer through programming, and substitute the initial condition value into the model, advance it according to the time point, and calculate the instantaneous dynamic cutting force and the relative vibration displacement F on the tool at each time point. x 、F y The calculation results at each time point are displayed graphically on the computer. This intuitive simulation method facilitates analysis of cutting frequency, cutting vibration displacement, and other changes during the gear milling process. Because cutting vibration simulation is digital, it offers flexibility and repeatability, making it easy to update the model simply by changing certain parameters.

[0296] The cutting vibration simulation software is Matlab / Simulink. The dynamic model you need is established in Matlab / Simulink software to realize dynamic monitoring of the entire simulation process and analysis of simulation results.

[0297] In Matlab / Simulink environment, a dynamic simulation model of the gear milling system is established. Figure 3.4 As shown, the numerical solution of the simulation model is calculated using the numerical integration method.

[0298] exist Figure 3.4 In the dynamic simulation model of the milling gear system shown, it is necessary to set the integration start time and integration end time before solving, and select the corresponding solution method. The solution method selected by this technical solution is the fixed-step 4th-order Runge-Kutta method. For the selection of the integration step, in order to ensure the convergence of the integration, 1 / n of the external exciting force period is often used as the set step. Taking the working condition of spindle speed of 120r / min and feed per tooth of 0.2mm as an example, the simulation solution is carried out. The simulation result interface in the X and Y directions is as follows Figure 3.5 and 3.6 shown.

[0299] B7. Experimental verification of the dynamic model of the gear milling system

[0300] (1) The experimental object of the milling vibration measurement experiment is the YKH2235 CNC spiral bevel gear milling machine. This experiment is the forming method for processing spiral bevel gear large wheels. The main tool parameters and gear blank parameters for the milling experiment are shown in Table 3.3. After the tool and the designed gear blank are installed on the bevel gear machine tool, the tool and gear blank need to be adjusted to the correct cutting position according to the machine tool adjustment parameters. The machine tool adjustment parameters are shown in Table 3.4.

[0301] Table 3.3 Main gear blank parameters and tool parameters of large wheel

[0302]

[0303] Table 3.4 Machine tool adjustment parameters during processing

[0304]

[0305]

[0306] (2) Experimental process

[0307] To validate the milling dynamics model, a vibration test experiment was conducted on a YKH223 CNC spiral bevel gear milling machine. A PCB three-axis accelerometer was used to collect vibration signals. The Reflex Pulse data acquisition system processed the vibration signals and transmitted them to the computer. The LabShop module within the Reflex software completed the vibration signal acquisition process. To minimize the impact of different acquisition positions on the vibration signal, two three-axis accelerometers were placed at the spindle end. The average of the two locations was used as the calculation result for the subsequent vibration characteristic value calculation. The operating conditions for this milling experiment are shown in Table 3.5.

[0308] Table 3.5 Experimental working conditions

[0309]

[0310] (3) Experimental results and analysis

[0311] The gear is cut under five working conditions and the vibration signal is collected during the gear cutting process. The collection interface is as follows: Figure 3.7 shown.

[0312] After the processing, the gear teeth of the large wheel are as follows Figure 3.8-1 and 3.8-2 shown.

[0313] To further validate the dynamic model, we extracted and analyzed certain characteristic indicators of the vibration signal. Among signal statistical indicators, time-domain statistical parameters are widely used in signal analysis as indicators of vibration conditions. The root mean square (RMS) value performs well in signal analysis, characterizing the level of vibration, while the peak-to-peak value measures the range of signal fluctuation. Both indicators are highly representative of vibration analysis. Their calculation formulas are shown below.

[0314]

[0315] peak-peak=|max(x)-min(x)| (3.10)

[0316] Therefore, this technical solution uses two parameters, peak-to-peak value and root mean square value (RMS), to statistically analyze the vibration of the tool at different speeds. The vibration signal collected in the experiment is an acceleration signal, but the displacement signal obtained through Matlab\simulink software simulation analysis. In order to make the two signals correspond, the collected vibration acceleration signal is quadratically integrated to obtain the corresponding displacement signal. According to the experimental working condition table,

[0317] The peak-to-peak value and root mean square (RMS) of the vibration displacement in the X and Y directions of the dynamic model results and the experimental results at different speeds are calculated. The experimental results remove the interference value of idling. The comparison of the changes in the simulation and experimental characteristic values ​​is shown as follows: Figures 3.9-1 to 3.9-4 shown.

[0318] From the analysis results, it can be seen that the RMS (root mean square) and peak-to-peak value of the tool vibration in the X and Y directions tend to increase with the increase of the rotational speed. The overall change trend of the experimental results and the simulation calculation results is basically consistent, and there is a certain gap in the amplitude. The main reason for the gap between the theoretical amplitude and the experimental amplitude is that in the actual cutting process, the collected vibration signal is affected by factors such as the surrounding environment and certain errors in the instrument itself. However, the overall gap is small and can meet the accuracy requirements, which proves the correctness of the established gear milling dynamics model.

[0319] B8. Overview of the dynamic model of the gear milling system and its verification

[0320] Part B above: A dynamic model of a gear milling system was established for the machine tool tool-workpiece system. Modal parameters of the dynamic model, such as the damping ratio, natural frequency, and stiffness coefficient, were first obtained through modal hammer testing. A simulation program for the gear milling system dynamic model was developed using Matlab\Simulink software, and a gear cutting experiment was designed to verify the simulation model. Analysis of experimental and simulation results at different speeds revealed that the RMS and peak-to-peak values ​​of the tool's vibration displacement in the X and Y directions showed similar trends between the experimental and simulation results, with minimal amplitude errors, meeting accuracy requirements. This validates the established dynamic model of the gear milling system.

[0321] C. Analysis of the sensitivity of factors affecting cutting vibration characteristics to vibration

[0322] Milling is a common machining method that generates vibrations whenever it is performed. The machine tool used in this technical solution is a YKH2235 CNC spiral bevel gear milling machine, which is also accompanied by vibrations during its cutting process. The causes of vibrations during machining can be roughly divided into two categories:

[0323] The first type is caused by the degradation of machine tool performance due to continuous service, and this type of vibration is unavoidable.

[0324] The second type is the self-excited vibration during the processing and the vibration caused by external excitation. This type of vibration can be controlled and its impact can be reduced. In the second type of vibration, the impact of external excitation can be controlled by maintaining a good processing environment. The impact of self-excited vibration is due to the change of instantaneous cutting force, discontinuous cutting of the tool, regeneration effect and the influence of the inherent characteristics of the machine tool itself, which causes the machine tool to generate vibration. Specifically, in the forming method of processing spiral bevel gears, the relative motion between the tool and the tooth blank is the rotation motion and feed motion of the tool. Under these two motions, the tool can cut off the excess material on the tooth blank to form the required tooth surface. After completing the processing of a gear tooth shape, the gear tooth blank will index and rotate to the next cutting position. Cutting vibration will exist during the entire processing process. For this type of vibration, the technical solution establishes a dynamic model of the cutting process, analyzes the dynamic model, and obtains the corresponding rules, so as to help optimize the process reliability of the machine tool by controlling the adverse effects of this type of vibration.

[0325] C1. Influence of spindle speed on cutting vibration

[0326] Set the corresponding simulation working condition table as shown in Table 4.1. The spindle speed range is 120r / min-420r / min. Substitute the parameters into the simulation model and use Matlab / Simulink software to simulate and solve it. The same time period of the simulation displacement curve obtained at each speed is intercepted, and the results are as follows: Figure 4.1-Figure 4.6 According to the indicators reflecting the vibration level introduced in the previous chapter, the root mean square value is selected as the characteristic indicator to draw the changes in cutting vibration at different speeds, as shown in the figure. Figure 4.7 shown.

[0327] Table 4.1 Simulation working condition table 1

[0328]

[0329] from Figure 4.7 It can be seen from the figure that when the speed is within the range of 120-420r / min, as the speed increases, the cutting vibration in the X direction increases to a peak value and then decreases within the range of 120-240r / min, while the cutting vibration in the Y direction increases continuously.

[0330] C2. Influence of feed per tooth on cutting vibration

[0331] Similarly, the corresponding simulation working condition table is set as shown in Table 4.2. The feed rate per tooth varies in the range of 0.2-0.7. The vibration displacement curve is obtained by simulation analysis respectively, and the same time period under each working condition is intercepted to calculate its root mean square value, so as to draw the curve of the vibration displacement root mean square value changing with the feed rate per tooth, as shown in Figure 4. Figure 4.8 shown.

[0332] Table 4.2 Simulation working condition table 2

[0333]

[0334] As the feed rate increases, cutting vibration in both the X and Y directions increases. The X-direction feed rate and the RMS value of the vibration displacement generally follow a linear increasing relationship. This is because as the feed rate increases, the area of ​​the material cutting layer increases, which increases deformation resistance and friction, further leading to an increase in cutting vibration.

[0335] C3. Influence of tool rake angle on cutting vibration

[0336] Set the simulation working condition table as shown in Table 4.3, calculate the root mean square value of vibration displacement under different tool rake angles, and draw its change law curve as shown in Figure 4.9 shown.

[0337] Table 4.3 Simulation working condition table 3

[0338]

[0339] from Figure 4.9 As can be seen from the figure, as the tool rake angle increases from 5° to 30°, the cutting vibration in the X and Y directions decreases. This change occurs because as the tool rake angle increases, the cutting edge becomes sharper, reducing chip deformation and, consequently, the cutting vibration.

[0340] C4. Effect of cutting edge inclination angle on cutting vibration

[0341] Set the simulation working condition table as shown in Table 4.4, calculate the root mean square value of vibration displacement under different blade inclination angles, and draw its change law curve as shown in Figure 4.10 shown.

[0342] Table 4.4 Simulation working conditions Table 4

[0343]

[0344] from Figure 4.10 It can be seen from the figure that when the cutting edge angle changes in the range of 5°-30°, as the cutting edge angle of the tool increases, the cutting vibration in the X and Y directions tends to increase.

[0345] D. Use Bayesian formula to build BP neural network model and use Garson algorithm to update prediction model

[0346] D1. BP neural network model

[0347] Analyzing from the perspective of neural network structure, the structure can be divided into three parts: input layer, hidden layer and output layer. Figure 5.1 As shown in the figure, the input layer is primarily responsible for transmitting external information into the network. The hidden layer processes the data transmitted from the input layer and transmits it to the output layer. The output layer finally transmits the processed data to the actuator or display device. One of the key features of the BP neural network is its ability to learn and train. The learning process involves the continuous adjustment of its weights.

[0348] The essence of the weights of each neuron is that they reveal certain patterns in the data through neural network training. The weights are its external mathematical representation. Once the weights are determined, the neural network model is also determined. The learning process of a neural network can be roughly summarized into the following four steps:

[0349] (1) External data is input through the input layer, the input data is processed in the hidden layer, and then transmitted to the output layer. This process is called the "forward propagation of the signal".

[0350] (2) If the error between the neural network prediction result of the output layer and the actual value exceeds the target value set by the model, the signal will be back-propagated from the output layer to the hidden layer. After receiving the returned signal, the hidden layer will correct the connection weights of each layer so that the model error meets the set value. This process is called the "error back propagation" process.

[0351] (3) The training process of a neural network is a process of repeated "forward propagation of signals" and "backward propagation of errors".

[0352] (4) After continuous training, the overall error of the neural network continues to shrink and approaches the target value.

[0353] The learning process of a neural network can be expressed by a mathematical formula. The calculation process is as follows. First, define the function γ:

[0354]

[0355] In formula (4.1), n ​​is the number of neurons in the output layer, y is the target prediction value, and y′ is the actual output value.

[0356] The connection strength correction formula between neurons is:

[0357]

[0358] In formula (4.2), ω i is the connection weight from input data to hidden layer; α is the learning efficiency of BP neural network model; I i is the transfer function of each neuron in the hidden layer. In the BP neural network model established in this technical solution, the transfer function selected in the hidden layer is the tansig function, the transfer function selected in the output layer is the Purelin function, and the training function selected in the reverse transfer process is the traingdm function. In order to obtain the input and output of the neural network model, and thus establish a BP neural network prediction model, the orthogonal experiment method is used in this technical solution to determine the input and output of the neural network model. The orthogonal experiment design method is a mathematical statistics method for arranging and analyzing multi-factor experiments based on the orthogonal experiment table. This method has many advantages, such as high efficiency, small number of experiments, and easy use. An orthogonal experiment table with 4 factors and 5 levels was designed according to the minitab software, and the data was substituted into the kinetic model for calculation. The results are shown in Table 4.5.

[0359] Table 4.5 Orthogonal test results

[0360]

[0361]

[0362] The first 21 rows of spindle speed, feed per tooth, rake angle, and blade inclination angle are used as the input of the neural network model training set, the first 21 rows of the root mean square value of the vibration displacement in the X and Y directions are used as the output of the neural network model training set, and the last 22-25 rows of data are used as the input and output of the test set respectively. The target error of the training model is set to 0.0001, the maximum number of training times is 300,000 times, the learning efficiency is 0.01, and the number of hidden layer neurons is 9. The BP neural network model training results in the X and Y directions are shown in Figure 2. Figures 5.2-1 to 5.2-3 , as shown in 5.3-1 to 5.3-3.

[0363] From the training results of the BP neural network model, it can be seen that the target error of the training model is slightly higher than the set value, but the model accuracy is high and can meet the prediction requirements.

[0364] Parameter sensitivity analysis of D2 and Garson algorithm

[0365] The Garson algorithm is a method for analyzing the sensitivity of neural network connection weights. It is a typical sensitivity analysis method based on connection weights. During the neural network training process, the connection weights between the input layer, hidden layer, and output layer determine the degree of influence of the input unit on the output result, that is, the sensitivity of the input parameter to the output result. In the Garson algorithm, the degree of influence of the input variable on the output variable can be expressed as follows:

[0366]

[0367] Where N is the number of neurons in the input layer, and L is the number of neurons in the output layer. W represents the connection weight between the input layer neurons and the hidden layer neurons, and V represents the connection weight between the hidden layer neurons and the output layer neurons. The number of neurons in the hidden layer is determined by the number of neurons in the input and output layers, and is generally 2N + L.

[0368] For a trained BP neural network model, the connection weights of each neuron can be derived and processed using the Garson algorithm to determine the contribution of each input neuron to the output. The calculation results in the X and Y directions are shown in Tables 4.6 and 4.7.

[0369] Table 4.6 Relative contribution of various influencing factors in the X direction

[0370]

[0371]

[0372] Table 4.7 Relative contribution of each influencing factor in the Y direction

[0373]

[0374] From the calculation results of Table 4.6 and Table 4.7, we can know that:

[0375] The weight order of each parameter on cutting vibration in the X direction is: spindle speed, feed rate, cutting edge inclination angle, and rake angle;

[0376] The weight order of each parameter on cutting vibration in the Y direction is: spindle speed, feed rate, rake angle, and cutting edge inclination angle.

[0377] This technical solution shows that during the cutting process, the spindle speed and feed rate in the X and Y directions are the main factors affecting cutting vibration. When controlling cutting vibration by varying parameters, prioritizing the spindle speed and feed rate to appropriate values ​​can better achieve effective control of cutting vibration.

[0378] D3. Evaluate the process reliability of the YKH2235 CNC spiral bevel gear milling machine.

[0379] Taking the X direction under the working conditions of spindle speed of 300r / min and feed per tooth of 0.2mm as an example, the simulation results of the amplitude root mean square value are shown in Table 5.1.

[0380] Table 5.1 Amplitude RMS simulation results

[0381]

[0382]

[0383] D4. Drawing of empirical distribution scatter plot

[0384] In order to preliminarily determine the distribution of the RMS amplitude, its probability density function is plotted. The specific steps are as follows:

[0385] (1) Determine the maximum and minimum values ​​of the RMS amplitude. Sorting the n=41 feature data, we can get the maximum value x max =0.01375, minimum value x min =0.00981.

[0386] (2) Calculate the number of groups k. Group the simulation data according to the method of equal interval frequency.

[0387] k=1+3.3lg n (5.4)

[0388] Where n is the total number of simulation data, and it can be calculated that k≈7.

[0389] (3) Calculate the interval ΔP

[0390] ΔP=(x max -xmin ) / k (5.5)

[0391] x max , x min , k is substituted into Equation 5.5, and we can calculate ΔP≈0.000563

[0392] (4) Determine the starting point of each interval. Once the interval interval is determined, the value of each interval starting point can be calculated, and the midpoint value of each interval is x j , the calculation formula is as follows:

[0393] x j =(x jmin +x jmax ) / 2 (5.6)

[0394] In formula (5.6), j is the serial number of each interval.

[0395] (5) Determine the number of samples that fall into each interval and calculate the empirical distribution function of the population. j is the number of samples in each interval, and n is the total number of sample points.

[0396]

[0397] Through the above steps, the probability density of the root mean square value of the amplitude can be calculated, as shown in Table 5.2.

[0398] Table 5.2 Probability density calculation table of amplitude root mean square value

[0399]

[0400]

[0401] (6) With amplitude x as the horizontal coordinate and sample probability density f(x) as the vertical coordinate, draw the probability density histogram and its fitting curve.

[0402] from Figure 5.4 It can be seen that the amplitude root mean square probability density curve is not a monotonic trend. It first increases to a peak, then decreases, and finally tends to be stable.

[0403] D5. Identification of the distribution type of amplitude root mean square data

[0404] The Anderson-Darling statistical method in the probability diagram of Minitab software was used to evaluate the distribution type of the amplitude root mean square data. The analysis results are as follows: Figure 5.5 shown.

[0405] According to the test results of the probability graph, the p-value of the exponential distribution test is less than 0.05, and the data obviously does not conform to the exponential distribution. The p-values ​​of the normal distribution, Weibull distribution, and Gamma distribution tests are all greater than 0.05, but from the results of the p-value size, it is obvious that the p-value of the normal distribution is the largest, which is 0.524, indicating that the normal distribution fits the data best. In this technical solution, the maximum likelihood estimation method is used to estimate the distribution model parameters. This method has a high fitting accuracy and is closer to the true value. The mean calculation results are shown below:

[0406]

[0407] Among them, x i (i=1, 2, 3, ... 41) is the value of the characteristic quantity, and n is the total number of simulation data. The standard deviation calculation results are shown below:

[0408]

[0409] D6, KS goodness of fit test

[0410] The data samples fitted in this technical solution are 41, and the KS test method is obviously more consistent. Assuming that the theoretical distribution model and the empirical distribution model follow the same distribution, the test formula is as follows.

[0411]

[0412] In formula (5.10), F n (t) is the empirical distribution, F0(t) is the theoretical distribution, and D n Indicates F n The difference between F0(t) and F0(t), d i is the maximum order statistic of the test results, D n,α is the test critical value.

[0413]

[0414] Calculate the normal fitting table according to the above formula:

[0415] Table 5.3 Normal fitting calculation table

[0416]

[0417] According to the data in column e of Table 5.3, take the maximum absolute difference value D n =0.0528. Taking the significance level factor α = 0.1, the threshold value can be calculated according to the empirical formula Obviously D n <D nα, so the assumption is reasonable, accept the assumption made, the amplitude root mean square value obeys the normal distribution.

[0418] D7. Compatibility test of prior information and posterior information

[0419] This technical solution adopts the rank sum test method, and the specific steps of the rank sum test are as follows:

[0420] Assume that the prior information is the population X and the field test data is the population Y. Sample (X1, X2, X3…X m ) belongs to the population X, the sample (Y1, Y2, Y3…Y m ) belongs to the population Y. Make the corresponding test hypothesis, H0 when X and Y follow the same distribution, and H1 when X and Y do not follow the same distribution. Combine the two samples into a whole and arrange them in order from small to large to form a new population Z, where Z j The subscript j is the rank. Assume that the kth sample in the population Y is Y k , Y k In the new statistical population Z, if it is in the jth position, then Y k =Z j , j represents Y k When the same sample appears in Y, the sample observation results are equal in the new statistical population Z, that is, Y k =Z j =Z j+1 , the rank at this time is the average value of the adjacent subscripts, that is, j+0.5. Then the test data (Y1, Y2, Y3…Y m ) in the statistical population Z is:

[0421]

[0422] Where T is the rank sum of the statistical parameters. When X and Y come from the same distribution, the significance level is clear, and the T value should meet the following test criteria:

[0423] P(T1<T<T2|H0)=1-α (5.13)

[0424] When the T-value test result meets the criteria, the hypothesis H0 is accepted and X and Y follow the same distribution. Otherwise, the hypothesis H1 is accepted and X and Y do not follow the same distribution.

[0425] The rank sum test function in MATLAB is used for this test. The calling format for the rank sum test function is [p,h] = ranksum(x,y), where x and y are the two vectors to be tested. The lengths of the two vectors can be unequal. If the test result p is greater than 0.05 and the returned h is equal to 0, the hypothesis is considered to be true, and the data sets x and y generally follow the same distribution. Otherwise, the hypothesis is false, and the data sets x and y generally do not follow the same distribution.

[0426] According to the field test, multiple groups of vibration signals were collected when processing different teeth of the same gear under the same working conditions, and the amplitude root mean square value of the vibration displacement signal was calculated. The field test data sample composed of them is y = [0.01184, 0.0131, 0.0124, 0.0128, 0.0119]. The simulation data and field test data y were imported into the software and tested using the ranksum function. The test results are shown in Table 5.4.

[0427] Table 5.4 Compatibility test results

[0428]

[0429] The compatibility test results show that p = 0.5025 > 0.05, returning the hypothesis value h = 0, indicating that the hypothesis is established. Overall, there is no significant difference between the simulated data samples and the field test samples, and they approximately follow the same distribution. Therefore, the simulated data can be used as prior information for Bayesian evaluation.

[0430] D8. Derivation of posterior distribution and parameter estimation

[0431] Through data fitting and goodness of fit tests, we know that the most suitable distribution type for the root mean square amplitude is the normal distribution. Therefore, the prior distribution function can be determined as follows, and the probability density function of the normal distribution is:

[0432]

[0433] When the parameters of the normal distribution are known, the probability density function of the normal distribution can be treated as a conditional distribution, and its expression is as follows:

[0434]

[0435] The likelihood function can also be obtained as:

[0436]

[0437] In formula (5.16), r is the number of samples.

[0438] According to the Bayesian formula, the posterior distribution of the data can be calculated by combining the prior information and the likelihood function. The Bayesian posterior probability density formula for the parameters μ and θ can be calculated as follows:

[0439]

[0440] In formula (5.17), i,j are numbers 1, 2…, M.

[0441] D9. Calculation of posterior distribution

[0442] Through Gibbs sampling and Markov chain Monte Carlo methods, we can calculate the 95% confidence interval, mean, standard deviation and median of the posterior distribution of model parameters, as well as the iterative trajectory, kernel density function, autocorrelation function, etc. during the sampling process.

[64] The sampling process can be expressed as follows:

[0443] (1) Initial value setting process:

[0444] (2) In distribution Randomly select

[0445] (3) In distribution Randomly select

[0446] (4) In distribution Randomly select

[0447] Repeating the above sampling process continuously can generate a Markov chain (θ (1) ,θ (2) ,...,θ (k) ), when the number of sampling tends to infinity, the Markov chain is considered to converge, and the parameter estimates of the posterior samples can be solved.

[0448] D10, posterior parameter simulation

[0449] Using Openbugs software, the simulation process of Openbugs software is as follows Figure 5.6 As shown:

[0450] The prior distribution is a normal distribution with mean μ = 0.01211 and standard deviation σ = 0.0009. A program is developed to establish an estimation model for the prior distribution and likelihood function, and a program is developed to estimate the posterior distribution. Field test data is loaded into the program, and the model is compiled. After the model is compiled, initial values ​​are preset to complete model initialization. The root mean square value μ of the amplitude is used as the monitored parameter in the simulation, and the number of iterations must be set before the simulation. After the iterations are completed, the statistical estimation results of the monitored parameters are output in the parameter monitoring module.

[0451] Once the number of iterations reaches the preset value, the iteration is complete and the estimated results of the monitoring parameter μ need to be analyzed. Based on the output results, it is determined whether the iteration process has converged and whether the simulation estimation results are accurate. The results of iterations of 1000, 2000, 3000, 4000, and 5000 are shown in Table 5.5 below. The MC error calculation formula in Table 5.5 is MC = σ / N 0.5 , σ is the standard deviation, and N is the number of random samples.

[0452] Table 5.5 Estimation results of monitoring parameter μ in posterior distribution

[0453]

[0454] According to the simulation estimation results in Table 5.5, as the number of iterations increases, the MC error decreases. When the number of iterations is less than 3000, the mean and variance are changing. When the number of iterations is greater than 3000, the mean and variance remain basically unchanged, indicating that the Markov chain has converged to a stable state. After 5000 iterations, the iterative trajectory of the parameter μ is as follows: Figure 5.7 shown.

[0455] From the iterative trajectory of the parameter μ, we can see that the Markov chain converges within a certain range without obvious volatility and periodicity. This state indicates that the Markov chain is in a stable state. The sampling results obtained at this time can be considered as estimates under the posterior distribution. Using the output module of openbugs, we can also obtain the posterior probability function and quantile diagram of the parameter μ, as shown in the following example: Figure 5.8 、 Figure 5.9 shown.

[0456] It is very useful to monitor the convergence speed of the parameter μ during the iteration process based on the autocorrelation function. The autocorrelation function can indicate the correlation between the current moment and the previous moment, that is, the correlation between the current iteration result and the previous iteration result. If the autocorrelation is lower, the convergence speed is faster. The autocorrelation function of the parameter μ is as follows: Figure 5.8 shown.

[0457] from Figure 5.10It can be seen that the autocorrelation function of the parameter μ approaches 0 when the number of iterations is small, indicating that the parameter μ converges quickly. Observing the three statistical parameters of the iteration trajectory plot, quantile plot, and autocorrelation function plot of the parameter μ, we can see that the iteration process of the parameter μ has converged, and the estimated value of the posterior parameter μ is 0.0125mm.

[0458] Similarly, according to the same method, the updated posterior parameter values ​​using the Bayesian method under various working conditions are obtained, as shown in Table 5.11.

[0459] Table 5.6 Posterior parameter values ​​obtained after Bayesian method update

[0460]

[0461] D11. Reliability index calculation and machine tool process reliability evaluation

[0462] After updating according to the Bayesian method, new posterior parameter values ​​are obtained. The updated posterior parameters are substituted into the established BP neural network prediction model as training data, thereby realizing the iterative update of the neural network prediction model. The training results of the updated BP neural network prediction model are as follows: Figure 5.11 and 5.12 shown.

[0463] The trained BP neural network model has higher prediction accuracy than before and is more consistent with the actual machining process. After consulting the relevant information of the machine tool, the spindle speed n = 200 and the feed per tooth f z =1.2mm is the critical working condition of unstable cutting state. Substituting the process parameters into the neural network prediction model, it can be calculated that the critical amplitude root mean square of the X and Y directions under the extreme working condition is μ x =0.0284, μ y =0.0138.

[0464] During the cutting process, tool vibration varies depending on the process parameter combination. Therefore, it's unreasonable to evaluate machine tool reliability without considering changes in the machine tool's dynamic characteristic parameters. A conservative process parameter combination, such as low speed and slow feed, can ensure smooth machining and high reliability. However, in actual machining, overly conservative process parameters can lead to low machining efficiency. Therefore, while ensuring machining quality, efficiency is generally maximized by increasing feed and speed. Overly aggressive process parameters can easily cause chatter, resulting in substandard part quality. Therefore, when selecting process parameters for bevel gear machines, it's important to evaluate the process parameter combination to provide guidance for process parameter selection from a reliability perspective.

[0465] Since the vibration of the tool is directly related to the surface machining accuracy of the workpiece, it is believed that the ratio of the number of multiple root mean square values ​​of the vibration signal on the tool less than the threshold over a period of time to the total number of samples is the process reliability of the machine tool. The calculation formula is:

[0466]

[0467] n f is the number of amplitude root mean square values ​​less than the threshold, n 总 is the total number of samples.

[0468] Take a set of processing technology combinations (n,f z )=(300,0.2) as an example, the vibration displacement signals of the tool in two directions under this working condition are obtained through dynamic model simulation, such as Figure 5.13 、 5.14 shown.

[0469] The reliability of the data in the figure is calculated using Matlab as the platform. 65,000 points in the figure are taken as the sample set. The cutter head rotates one circle and calculates an amplitude root mean square value. A total of 319 amplitude root mean square values ​​can be obtained. x =0.0284, μ y =0.0138 is the failure threshold, and the processing parameters are calculated by the above reliability calculation method as (n,f z )=(300,0.2), the reliability value of the vibration level in the X direction can be obtained as R x =0.945, the reliability value of the vibration level in the Y direction is R y =0.948. Using the same method, we can calculate the reliability in the X and Y directions when the spindle speed is 120r / min, 180r / min, 240r / min, 300r / min, 360r / min, 420r / min and the feed per tooth is 0.2mm, as shown in Table 5.7, and the corresponding change curves are plotted, as shown in Table 5.7. Figure 5.15 shown.

[0470] Table 5.7 Reliability calculation results at different speeds

[0471]

[0472] from Figure 5.15As can be seen from the figure, when the spindle speed varies between 120 r / min and 420 r / min, the reliability in the X direction decreases first and then increases with increasing speed; the reliability curve in the Y direction decreases with increasing speed. In actual production, while ensuring machining efficiency, process parameters with high reliability in both the X and Y directions can be selected. Combining Table 5.7, we can see that a spindle speed of 300 r / min (with a feed per tooth of 0.2 mm) is the process parameter that ensures both machining efficiency and high reliability.

[0473] The above are only preferred embodiments of the present invention. It should be pointed out that various modifications and improvements made by those skilled in the art without departing from the present technical solution should also be deemed to fall within the scope of protection required by the claims.

Claims

1. A method for evaluating the process reliability of a spiral bevel gear milling machine tool, comprising the following steps: Step 1: Establish an instantaneous cutting force model for spiral bevel gear machining based on the forming method; establish a milling dynamics model of the bevel gear machine tool tool-workpiece system, and calculate the cutting vibration characteristics of the spiral bevel gear milling machine tool during the milling process and the vibration trajectory curve of the milling tool; Step 2: Based on the cutting vibration characteristics in step 1, evaluate the sensitivity of each influencing factor parameter to the cutting vibration; Step 3: Use the Bayesian formula to establish a BP neural network model and use the Garson algorithm to update the BP neural network model; use the updated BP neural network model to calculate the amplitude characteristic value under the extreme working condition, and combine the vibration trajectory curve of the gear milling tool and the process reliability formula to complete the machine tool process reliability assessment; In step 1: the instantaneous cutting force model is: At any time t, the instantaneous tangential cutting force F on blade j is Tqj The value of the tangential cutting force F of the main cutting edge and the top edge is determined by Tqm , F Tqv Composition: Instantaneous radial cutting force F on blade j Nqj The radial cutting force F of the main cutting edge and the top edge Nqm , F Nqv Composition: Instantaneous axial cutting force F on blade j Zqj The axial cutting force F of the main cutting edge and the top edge Zqm , F Zqv composition; where b qm (t) corresponds to the cutting width of the main cutting edge of insert j, and the outer cutter is b ew (t), inner knife takes b iw (t);h qm The cutting thickness of the main cutting edge of the corresponding insert j, the outer cutter is h ew , inner knife takes h iw ; b qv The cutting width of the top edge of the corresponding blade j, the outer blade is b w , inner knife takes b i ;h qv The cutting thickness of the top edge of the corresponding blade j is h for the outer blade. w , inner knife takes h i ;but: F Tqj =F Tqm +F Tqv F Tqm =τb qm (t)h qm F Tqv =τb qv h qv F Nqj =F Nqm +F Nqv F Nqm =τb qm (t)h qm F Nqv =τb qv h qv F Zqj =F Zqm +F Zqv F Zqm =τb qm (t)h qm F Zqv =τb qv h qv Where τ is the shear zone stress, i.e., the cutting force per unit cross section. The tangential, radial, and axial cutting forces of the main cutting edge and top edge of insert j are decomposed into the x, y, and z directions in the cutterhead coordinate system. The instantaneous cutting forces of the jth insert along the coordinate axis in the three directions are: F xt =F Tqj sin(θ(t))-F Nqj cos(θ(t)) F yt =F Tqj cos(θ(t))+F Nqj sin(θ(t)) F zt =F Zqj Where θ(t) is the rotation angle of the blade at any time.

2. The process reliability evaluation method for spiral bevel gear milling machine tools according to claim 1, characterized in that: In step 1: the dynamic model of gear milling is: In the tool-workpiece system of a bevel gear machine tool, the vibration differential equations of the tool in the X and Y directions are expressed as follows: In the above formula: m x 、m y represents the modal mass of the tool in the X and Y directions in the gear milling system, c x , c y Indicates the equivalent damping of the tool in the X and Y directions in the gear milling system, k x , k y Indicates the equivalent stiffness of the tool in the X and Y directions in the gear milling system; x, y represent the vibration acceleration, vibration velocity, and vibration displacement of the tool in the X and Y directions, respectively; F x (t), F y (t) represents the instantaneous dynamic milling force of the tool in the X and Y directions; in And the natural frequency of the tool in the X direction ω x , damping ratio ξ x , stiffness coefficient k x and the natural frequency ω in the Y direction y , damping ratio ξ y , stiffness coefficient k y , the mathematical expression of the vibration differential equation is:

3. The process reliability evaluation method for spiral bevel gear milling machine tools according to claim 1, characterized in that: In step three: establish the BP neural network prediction model as follows: Define the function γ: In the above formula, n is the number of neurons in the output layer, y is the target prediction value, and y′ is the actual output value; The connection strength correction formula between neurons is: In the above formula, ω i is the connection weight from input data to hidden layer; α is the learning efficiency of BP neural network model; I i is the transfer function of each neuron in the hidden layer.

4. The process reliability evaluation method for spiral bevel gear milling machine tools according to claim 1, characterized in that: In step 3: the process reliability formula is: n f is the number of amplitude root mean square values ​​less than the threshold, n 总 is the total number of samples.

5. A process reliability optimization method for spiral bevel gear milling machine tools, characterized by: The process parameters of the spiral bevel gear milling machine tool are adjusted or set using the evaluation result of the process reliability evaluation method of the spiral bevel gear milling machine tool according to any one of claims 1 to 4.

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