Double-tool parallel turning non-vibration machining method based on process parameter optimization

Abstract

The application belongs to the technical field of turning, and discloses a double-tool parallel turning non-vibration machining method based on process parameter optimization. The double-tool parallel turning non-vibration machining method constructs a double-tool parallel turning machining dynamic equation considering tool wear, carries out high-precision machining stability analysis, accurately determines non-vibration process parameters, determines optimal non-vibration process parameters with the highest machining efficiency as the target, carries out machining path planning, obtains a non-vibration machining numerical control program, realizes double-tool parallel turning non-vibration machining, and achieves the purposes of improving machining efficiency and reducing production cost.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of turning, and relates to turning machining, in particular double-tool parallel turning machining. BACKGROUND

[0002] As a typical mechanical machining method, turning machining is widely used in the machining of key components of major equipment such as aero-engines and compressors, and it is of great significance to realize high-performance turning.

[0003] An important prerequisite for realizing high-performance turning is to solve the vibration problem in machining, and among the many cutting vibrations, chatter has the greatest harmfulness to the machining system. It not only aggravates the wear and damage of the tool, but also easily induces tool tooth chipping, which endangers the personal safety of the operator. Therefore, it is of great significance to realize chatter-free turning.

[0004] Double-tool parallel turning is a high-performance turning method developed in recent years. Compared with single-tool turning, double-tool parallel turning can have two turning tools participate in cutting at the same time, and has the advantage of high machining efficiency. However, due to the lack of effective means to avoid the occurrence of machining chatter in double-tool parallel turning, there are currently problems such as large machining chatter and unguaranteed machining quality in double-tool parallel turning. Therefore, it is of great significance to realize chatter-free machining in double-tool parallel turning.

[0005] The main method to realize chatter-free machining in double-tool parallel turning is to analyze the machining stability of the double-tool parallel turning system, optimize the chatter-free process parameters, and plan the double-tool parallel turning machining path based on the optimization results. The detailed steps mainly include: using time-delay differential equation to describe the dynamic characteristics of the double-tool parallel turning system, expanding the machining stability analysis, and constructing the machining stability domain lobe diagram. The critical machining stability curve in the lobe diagram divides the plane composed of the cutting depth of No. 1 turning tool and the cutting depth of No. 2 turning tool into a chatter-free machining area and a chatter machining area. In the chatter-free machining area, appropriate process parameters are selected, the turning machining path is planned, and chatter-free machining in double-tool parallel turning is realized.

[0006] Traditional turning chatter-free process parameter optimization method is mainly aimed at single turning tool machining. Since in double-tool parallel turning, the machining system dynamics equation has changed from single time-lag dynamics system to multi-time-lag dynamics system, the traditional chatter-free process parameter optimization method for single turning tool cannot be applied to double-tool parallel turning. Some scholars have proposed a multi-turning tool parallel turning stability determination method based on differential quadrature method, but this method does not consider tool wear efficiency. In turning tool machining, tool wear is an inevitable phenomenon, and tool wear plays an important role in machining stability analysis. Without considering tool wear, the prediction accuracy of machining stability domain lobe diagram will be reduced, and the accuracy and reliability of the obtained chatter-free process parameters cannot be guaranteed. In addition, the multi-turning tool parallel turning stability determination method based on differential quadrature method uses too many fitting or interpolation methods in the calculation process, which inevitably causes overfitting, Long effect and other phenomena, resulting in large numerical calculation error and seriously affecting the prediction accuracy of the critical machining stability curve. Therefore, how to consider tool wear to carry out double-tool parallel turning machining stability analysis, reduce numerical error in the calculation process, and obtain high-precision chatter-free process parameters is a key problem to realize double-tool parallel turning chatter-free machining.

[0007] The present application provides a double-tool parallel turning chatter-free machining method based on process parameter optimization, constructs a double-tool parallel turning machining dynamics equation considering tool wear, carries out high-precision machining stability analysis, accurately determines the chatter-free process parameters, and then selects appropriate chatter-free process parameters for machining path planning to realize double-tool parallel turning chatter-free machining. Compared with the traditional double-tool parallel turning machining stability analysis method, the provided method considers the double-tool wear condition in the dynamics model, improving the accuracy of the model. Secondly, compared with the traditional double-tool turning machining stability analysis method which uses too many fitting or interpolation methods in the calculation process, causing large numerical calculation error, the provided method uses one-time discretization to obtain high-precision machining system discrete output, constructs a state transition matrix with the smallest dimension, and constructs a machining stability domain lobe diagram with high precision to accurately determine the chatter-free process parameters. On this basis, the optimal chatter-free process parameters are determined with the highest machining efficiency as the target, the machining path is planned, the chatter-free machining numerical control program is obtained, the double-tool parallel turning chatter-free machining is realized, the machining efficiency is improved, and the production cost is reduced. SUMMARY

[0008] The present application provides a double-tool parallel turning chatter-free machining method based on process parameter optimization, and the specific steps are as follows:

[0009] 1. Double-tool parallel turning machining dynamics equation considering tool wear

[0010] As shown in the accompanying drawings Figure 1 An x-coordinate system is established along the axial direction of the workpiece, with the x-positive direction being away from the machining direction; the cutting depth of the No. 1 turning tool is a1, and the cutting depth of the No. 2 turning tool is a2; the vibration displacements of the No. 1 turning tool and the No. 2 turning tool in the x direction are represented by x1(t) and x2(t) respectively.

[0011] Considering the tool wear effect, the double-tool parallel turning machining system is described as follows:

[0012] (1)

[0013] wherein, f1 and f2 are the cutting forces caused by the wear of the No. 1 turning tool and the No. 2 turning tool respectively; M, C, K, and F(t) are specifically represented as follows

[0014] , , , ,

[0015]

[0016] m1, , are the modal mass, the damping coefficient and the natural circular frequency of the No. 1 turning tool in the x direction respectively; m2, , are the modal mass, the damping coefficient and the natural circular frequency of the No. 2 turning tool in the x direction respectively; K f is the cutting force coefficient; T is the workpiece rotation period, which is equal to 60 / Ω, and Ω is the workpiece rotation speed.

[0017] In the turning machining, the tool wear inevitably exists, and the tool wear plays an important role in the machining stability analysis, directly affecting the accuracy of the process parameter optimization result. In the following, the tool wear is considered in the dynamic model.

[0018] The tool wear changes the contact state between the cutting edge and the workpiece in the cutting process, and thus causes the change of the force condition of the tool. The cutting force f1 of the No. 1 turning tool and the cutting force f2 of the No. 2 turning tool caused by the tool wear are

[0019] (2)

[0020] (3)

[0021] wherein, K sp1 and K sp2 are the specific indentation force coefficients of the No. 1 turning tool and the No. 2 turning tool respectively; C d1= 0.25W1 2 , W1 is the length of the wear zone of the No. 1 turning tool d2 = 0.25W2 2 , W2 is the length of the wear zone of the No. 2 turning tool.

[0022] Equations (2) and (3) are combined as follows

[0023] (4)

[0024] wherein, .

[0025] Equation (4) is brought into equation (1) as follows

[0026] (5)

[0027] wherein, .

[0028] 2. High-precision discrete output expression of the double-tool parallel turning system

[0029] Equation (5) is expressed in the state space format as

[0030] (6)

[0031] wherein, , , ,

[0032] , ,

[0033] ,

[0034] Definition , the output of the double-tool parallel turning system is obtained as

[0035] } (7)

[0036] wherein, is a variable, t is time, t p is the moment when t = t p . In order to establish the discrete output of the double-tool parallel turning system, a numerical algorithm is introduced for discretization. First, the workpiece rotation period is divided into m parts, each part having a length of τ, and then, the interval [t p , t p+1 ] is divided into

[0037] = r0+ r1(δ-tp+1 ) (8)

[0038] t p+1 = t p+1 = t p = t p+1 = t

[0039] r0and r1are expressed as

[0040] r0= (t p+1 ), r1=[ (t p+1 )- (t p )] / τ

[0041] r0and r1are simplified as

[0042] r0= p+1 , r1=( p+1 - p ) / τ (9)

[0043] Based on equations (7) and (8), v(t p+1 ) is expressed as

[0044] v(t p+1 )=T1v(t p )+M0r0+M1r1(10)

[0045] wherein, , , , l is a variable.

[0046] r i in equation (10) (i = 0, 1) is replaced by equation (9):

[0047] v(t p+1 )= v(t p )+G0 p+1 +G1 p (11)

[0048] wherein, G0 = M0 + M1 / τ, G1 = -M1 / τ.

[0049] v(t p+1 ) is simplified as v p+1 , v(t p ) is simplified as v p .

[0050] Since , formula (11) is converted to

[0051] (12)

[0052] Formula (12) is converted to

[0053] (13)

[0054] wherein, , and respectively represent , and , k1 = fix( )+1, k2 = fix( )+1, fix is a function capable of determining the integer part of a number. Formula (13) is converted to

[0055] (14)

[0056] Further simplified to

[0057] (15)

[0058] Formula (15) establishes the discrete output recursive relationship at t p , t p+1 , t , t , t and t , and by changing the value of t p , the discrete output recursive relationship at different times can be obtained.

[0059] 3. State transition matrix construction method with minimum dimension

[0060] Divide the workpiece rotation period into m parts, and the discrete time in one period is {t1, t2, t3, …., t m}, and the corresponding discrete output is { , , ,…., }, and by using the recursive relationship between , and , , , in formula (15), the discrete sequence { , , ,…., , } and discrete sequences { , , ,…., , } and discrete sequences { , , ,…., , } and discrete sequences { , , ,…., , } are contained in { , , ,…., , } and { , , ,…., , }, the relationship between discrete sequences { , , ,…., , } and discrete sequences { , , ,…., , } and discrete sequences { , , ,…., , } is shown in equation (16):

[0061] ( ) (16)

[0062] , , and as follows

[0063]

[0064]

[0065]

[0066] Wherein, U1, U2 and U3 are (4m+4) x (4m+4) matrix, I is 4 x 4 unit matrix.

[0067] In order to determine the stability of the machining system, the transition matrix is defined as follows If is reversible, the state transition matrix is defined as follows

[0068] (17)

[0069] On the basis of the direct integral format shown in formula (7), only through the one-time discretization shown in formula (8), the discrete output expression of the double-tool parallel turning machining system is obtained, the state transition matrix with the minimum dimension is constructed, the error loss in the discretization process is greatly reduced, and the accuracy and reliability of the calculation result are guaranteed.

[0070] According to the Floquet theorem, when the maximum value of the eigenvalue modulus of the state transition matrix is greater than 1, the machining state corresponding to the process parameters, that is, the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is chatter machining; when the maximum value of the eigenvalue modulus of the state transition matrix is less than 1, the machining state corresponding to the process parameters, that is, the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is non-chatter machining; when the maximum value of the eigenvalue modulus of the state transition matrix is equal to 1, the machining state corresponding to the process parameters, that is, the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is the critical machining state.

[0071] If is irreversible, the extended Moore-Penrose matrix can be used as a substitute.

[0072] 4. According to the tool wear condition, the process parameter non-chatter optimization is carried out

[0073] The wear band length W1 of the No. 1 turning tool and the wear band length W2 of the No. 2 turning tool are measured; the specific indentation force coefficient K sp1 of the No. 1 turning tool and the specific indentation force coefficient K sp2 of the No. 2 turning tool are determined; the modal mass m1 corresponding to the No. 1 turning tool in the x direction, the damping coefficient , and the modal mass m2 corresponding to the No. 2 turning tool in the x direction, the damping coefficient , are measured; the cutting force coefficient K is determinedf ; determine the workpiece rotation speed Ω.

[0074] determine the cutting depth range of the first turning tool , is the lower limit of the range, is the upper limit of the range; determine the cutting depth range of the second turning tool , is the lower limit of the range, is the upper limit of the range; discretize the cutting depth range of the first turning tool and the cutting depth range of the second turning tool, obtain the cutting depth of the first tool at a certain discrete position and the cutting depth of the second tool , construct the corresponding state transition matrix , by comparing the maximum value of the eigenvalue modulus of the state transition matrix with 1, determine that the machining state corresponding to the cutting depth of the first tool and the cutting depth of the second tool is non-vibration machining or vibration machining;

[0075] By this method, the machining state corresponding to the cutting depth of the first tool and the cutting depth of the second tool at different discrete positions is determined, and the machining stability domain lobe diagram is constructed. The curve in the lobe diagram is the critical machining stability curve, which divides the plane composed of the cutting depth range of the first tool and the cutting depth range of the second tool into non-vibration machining region and vibration machining region.

[0076] 5. Double-tool parallel turning non-vibration machining method based on process parameter optimization

[0077] From the non-vibration machining region, obtain several combinations of the cutting depth of the first turning tool and the cutting depth of the second turning tool, on this basis, add the cutting depth of the first tool and the cutting depth of the second tool in each obtained combination, determine that when the addition result is the maximum, the combination of the cutting depth of the first turning tool and the cutting depth of the second turning tool is the optimal combination, through numerical control machining programming software, according to the optimal combination of the cutting depth of the first tool and the cutting depth of the second tool, plan the machining path of turning, obtain the numerical control program after machining path planning, carry out double-tool parallel turning, realize double-tool parallel turning non-vibration machining.

[0078] Compared with the traditional double-tool parallel turning non-vibration process parameter optimization method, the provided method considers the double-tool wear condition into the dynamic model, improves the accuracy of the model; secondly, compared with the traditional double-tool parallel turning non-vibration process parameter optimization method, too many fitting or interpolation methods are used in the calculation process, which causes a large numerical calculation error, the provided method obtains high-precision machining system discrete output by using one-time discretization under the direct integration framework, constructs the state transition matrix with the minimum dimension, and accurately determines the non-vibration process parameters, determines the optimal combination of the cutting depth of the first tool and the cutting depth of the second tool according to the maximum machining efficiency as the target, plans the machining path for turning, obtains the numerical control program after the machining path planning, carries out double-tool parallel turning machining, realizes double-tool parallel turning non-vibration machining, improves the machining efficiency, and reduces the generation cost. BRIEF DESCRIPTION OF DRAWINGS

[0079] Figure 1 is a double-tool parallel turning machining dynamics simplified model. DETAILED DESCRIPTION

[0080] The specific embodiments of the application will be described in detail below in combination with the technical solutions and drawings, and the implementation process is as follows:

[0081] Step 1, establishing a double-tool parallel turning machining dynamics equation considering tool wear effect

[0082] As shown in the accompanying Figure 1 , an x coordinate system is established along the axial direction of the workpiece, and the x positive direction is away from the machining direction; the cutting depth of the first turning tool is a1, and the cutting depth of the second turning tool is a2; the vibration displacement of the first turning tool and the second turning tool in the x direction is represented by x1(t) and x2(t) respectively.

[0083] Considering the tool wear effect, the double-tool parallel turning machining system is described as follows:

[0084] (18)

[0085] wherein, , f1 and f2 are the cutting forces caused by the wear of the first turning tool and the second turning tool respectively; M, C, K, and F(t) are specifically represented as follows

[0086] , , , ,

[0087]

[0088] m1, , These represent the modal mass, damping coefficient, and natural circular frequency of tool number 1 in the x-direction; m2, , These represent the modal mass, damping coefficient, and natural circular frequency of cutting tool No. 2 in the x-direction; K f Ω is the cutting force coefficient; T is the workpiece rotation period, which is equal to 60 / Ω, and Ω is the workpiece rotation speed.

[0089] In turning, tool wear is inevitable. Tool wear plays an important role in machining stability analysis and directly affects the accuracy of process parameter optimization results. The tool wear will be considered in the dynamic model below.

[0090] Tool wear alters the contact state between the cutting edge and the workpiece during cutting, thus changing the stress state on the tool. The forces f1 on tool 1 and f2 on tool 2 caused by tool wear are:

[0091] (19)

[0092] (20)

[0093] Among them, K sp1 and K sp2 These are the specific indentation force coefficients for cutting tools No. 1 and No. 2, respectively; C d1 = 0.25W1 2 W1 is the length of the wear band of tool #1; C d2 = 0.25W2 2 W2 represents the length of the wear band of tool #2.

[0094] Equations (19) and (20) combined are as follows:

[0095] (twenty one)

[0096] in, .

[0097] Substituting equation (21) into equation (18):

[0098] (twenty two)

[0099] in, .

[0100] Step 2: Establish a high-precision discrete output expression for the dual-tool parallel turning system.

[0101] Equation (22) is expressed in the state-space format as follows:

[0102] (twenty three)

[0103] in, , , ,

[0104] , ,

[0105] ,

[0106] definition To obtain the output of the dual-tool parallel turning system for

[0107] } (twenty four)

[0108] in, Let t be a variable, and t be time. p For t=t p To establish the discrete output of the dual-tool parallel turning system, a numerical algorithm is introduced for discretization. First, the workpiece rotation cycle is divided into m parts, each with a length of τ. Then... At the spacing [t] p , t p+1 Decomposed into

[0109] =r0+r1(δ-t p+1 (25)

[0110] t p+1 For t=t p+1 At that moment, [t] p , t p+1 The length is τ.

[0111] r0 and r1 are represented as

[0112] r0= (t p+1 ), r1=[ (t p+1 )- (t p )] / τ

[0113] r0 and r1 are simplified to

[0114] r0= p+1 r1=( p+1 - p ) / τ (26)

[0115] Based on equations (24) and (25), v(t) p+1 ) represents

[0116] v(t p+1 )=T1v(t p )+M0r0+M1r1(27)

[0117] wherein, , , and l is a variable.

[0118] r i in equation (27) is replaced by equation (26):

[0119] v(t p+1 )=T1v(t p )+G0 p+1 +G1 p (28)

[0120] wherein G0=M0+M1 / τ and G1=-M1 / τ.

[0121] v(t p+1 ) is simplified to v p+1 and v(t p ) is simplified to v p . Since , equation (28) is converted to

[0122] (29)

[0123] Equation (29) is converted to

[0124] (30)

[0125] wherein, , and represent , and respectively, k1 = fix( )+1, k2 = fix( )+1, fix being a function capable of determining the integer part of a number.

[0126] Equation (30) is converted to

[0127] (31)

[0128] and further simplified to

[0129] (32)

[0130] Equation (32) establishes t p At time t p+1 time, time, time, Time and The time-discrete output recursive relationship is obtained by changing t. p The value can be used to obtain the discrete output recursive relationship at different times.

[0131] Step 3: Construct the state transition matrix with minimum dimension

[0132] The workpiece rotation period is divided into m parts, and the discrete time of one period is {t1, t2, t3, ..., t}. m The corresponding discrete output is { , , ,…., }, using equation (32) , and , , , The recursive relationship between them is used to establish a discrete sequence { , , ,…., , } and discrete sequence { , , ,…., , } and discrete sequences { , , ,…., , The relationship between}, due to the discrete sequence { , , ,…., , } contained in { , , ,…., , }and{ , , ,…., , In}, therefore the discrete sequence { , , ,…., ,} and discrete sequence , , ,…., , } and discrete sequence , , ,…., , The relationship between the above two is shown in equation (33):

[0133] ( ) (33)

[0134] U1, U2, and U3 are shown below

[0135]

[0136]

[0137]

[0138] wherein U1, U2 and U3 are (4m+4) x (4m+4) matrices, and I is a 4 x 4 unit matrix.

[0139] In order to determine the stability of the machining system, the transition matrix is defined.

[0140] If is invertible, the state transition matrix is defined as follows

[0141] (34)

[0142] According to the Floquet theorem, when the maximum value of the modulus of the eigenvalues of the state transition matrix is greater than 1, the machining state corresponding to the process parameters, i.e. the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is a chatter machining state; when the maximum value of the modulus of the eigenvalues of the state transition matrix is less than 1, the machining state corresponding to the process parameters, i.e. the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is a non-chatter machining state; when the maximum value of the modulus of the eigenvalues of the state transition matrix is equal to 1, the machining state corresponding to the process parameters, i.e. the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is a critical machining state.

[0143] If Irreversible, the extended Moore-Penrose matrix can be used as an alternative.

[0144] Step 4, process parameter chatter-free optimization according to tool wear condition

[0145] Measure the length of the wear zone of the No. 1 turning tool and the length of the wear zone of the No. 2 turning tool ; Determine the specific indentation force coefficient of the No. 1 turning tool and the specific indentation force coefficient of the No. 2 turning tool ; Measure the modal mass , damping coefficient , natural circular frequency of the No. 1 turning tool in the x direction , damping coefficient , natural circular frequency of the No. 2 turning tool in the x direction

[0146] Determine the cutting depth range of the No. 1 turning tool , as the lower limit of the range, as the upper limit of the range; Determine the cutting depth range of the No. 2 turning tool , as the lower limit of the range, as the upper limit of the range; Discretize the cutting depth range of the No. 1 turning tool and the cutting depth range of the No. 2 turning tool, obtain the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool at a certain discrete position, and construct the corresponding state transition matrix ; By comparing the maximum value of the eigenvalue modulus of the state transition matrix with 1, determine whether the machining state corresponding to the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool is chatter-free machining or chatter machining;

[0147] By this method, the machining state corresponding to the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool at different discrete positions is determined, and the machining stability domain lobe diagram is constructed. The curve in the lobe diagram is the critical machining stability curve, which divides the plane composed of the cutting depth range of the No. 1 tool and the cutting depth range of the No. 2 tool into a chatter-free machining region and a chatter machining region.

[0148] Step 5, double-tool parallel turning chatter-free machining method based on process parameter optimization

[0149] Several groups are combined by the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool obtained from the chatter-free machining area, on the basis of which, the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool in each obtained combination are added, and the combination corresponding to the maximum addition result is determined as the optimal combination, the turning machining path is planned according to the optimal combination of the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool through numerical control machining programming software, the numerical control program after machining path planning is obtained, and double-tool parallel turning is carried out, so that double-tool parallel turning chatter-free machining is realized.

[0150] The application provides a double-tool parallel turning chatter-free machining method based on process parameter optimization, constructs a double-tool parallel turning dynamics equation considering tool wear, carries out high-precision machining stability analysis, accurately determines chatter-free process parameters, selects appropriate chatter-free process parameters, plans machining path, and realizes double-tool parallel turning chatter-free machining. Compared with the traditional double-tool parallel turning machining stability analysis method, the provided method considers the double-tool wear condition in the dynamics model, improves the accuracy of the model, and directly integrates the high-precision machining system discrete output obtained by one-time discretization in the framework, constructs the state transition matrix with the minimum dimension, constructs the machining stability domain lobe diagram with high precision, accurately determines the chatter-free process parameters, and then determines the optimal chatter-free process parameters with the highest machining efficiency as the target, plans the machining path, realizes double-tool parallel turning chatter-free machining, improves the machining efficiency, and reduces the production cost.

Claims

1. A dual tool parallel turning chatter-free machining method based on process parameter optimization, characterized by, Comprising the following steps: Step 1, obtaining the length of the tool wear zone and the double-tool parallel turning parameters, and substituting into the double-tool parallel turning machining dynamics equation considering tool wear; Obtaining the length of the wear zone of the turning tool and the parameters of double-tool parallel turning includes: establishing an x-coordinate system along the axial direction of the workpiece, with the x-positive direction being away from the machining direction; measuring the length of the wear zone W1 of the No. 1 turning tool and the length of the wear zone W2 of the No. 2 turning tool; determining the specific indentation force coefficient K sp1 of the No. 1 turning tool and the specific indentation force coefficient K sp2 of the No. 2 turning tool; measuring the modal mass m1 and the damping coefficient 、 of the No. 1 turning tool in the x direction and the modal mass m2 and the damping coefficient 、 of the No. 2 turning tool in the x direction; determining the cutting force coefficient K f ; and determining the workpiece rotation speed Ω; The construction of the double-tool parallel turning machining dynamics equation considering tool wear comprises the following steps: The cutting depth of the No. 1 turning tool is a1, and the cutting depth of the No. 2 turning tool is a2; the vibration displacements of the No. 1 turning tool and the No. 2 turning tool in the x direction are represented by x1(t) and x2(t) respectively; The double-tool parallel turning machining system considering the tool wear effect is described as follows: (1) ， wherein, f1and f2are cutting forces due to the wear of the No. 1 and No. 2 tools, respectively; M, C, K, and F(t) are specifically expressed as follows: ， ， ， ， ， Wherein, T is the workpiece rotation period, T = 60 / Ω; The cutting force f1 of the No. 1 turning tool and the cutting force f2 of the No. 2 turning tool caused by tool wear are (2) ， (3) ， where C d1 = 0.25W1 2 ; C d2 = 0.25W2 2 ; Equations (2) and (3) are combined as follows: (4) ， wherein ; Equation (4) is brought into equation (1) as follows: (5) ， wherein ; Step 2, obtaining the discrete output expression of the double-tool parallel turning machining system according to the double-tool parallel turning machining dynamics equation, comprising the following steps: Equation (5) is expressed in state space format as follows: (6) ， wherein , , , ， ， ， Definitions , obtaining an output of the dual-tool parallel turning machining system is: } (7) ， wherein is a variable, t is time, t p is t = t p moment; The workpiece rotation period is divided into m parts, each part having a length of τ, then, At intervals [t p , t p+1 ] are resolved: = r0+ r1(δ-t p+1 ) (8), t p+1 For t = t p+1 , the length of [t p , t p+1 ] is τ; r0 and r1 are expressed as follows: r0= (t p+1 ), r1=[ (t p+1 )- (t p )] / τ, r0 and r1 are simplified as follows: r0= p+1 , r1( p+1 - p ) / τ (9), Based on equations (7) and (8), v(t p+1 ) is expressed as: v(t p+1 )=T1v(t p )+M0r0+M1r1(10) , wherein , , , l is a variable; r in formula (10) i , i = 0, 1, is replaced by formula (9): v(t p+1 )=T1v(t p )+G0 p+1 +G1 p (11), Wherein, G0 = M0 + M1 / τ, G1 = -M1 / τ; v(t) p+1 Simplify to v p+1 ,v(t p Simplify to v p ; Due to , the formula is converted to (12) ， Equation (12) is converted as follows: (13) ， wherein , and represent , and , k1 = fix( )+1, k2 = fix( )+1, fix being a function determining the integer part of a number; Equation (13) is converted as follows: (14) ， Further simplified as (15) Equation (15) establishes t p time, t p+1 time, time, time, time, and time discrete output recursive relationship, by changing t p value, the discrete output recursive relationship at different times is obtained; Step 3, obtaining the state transition matrix with the minimum dimension according to the discrete output expression, comprising the following steps: The workpiece rotation period is divided into m parts, and a cycle discrete moment is {t1, t2, t3, …., t m} and the corresponding discrete output is { , , ,…., } and the recursive relationship between 、 and , , 、 is used to establish the relationship between the discrete sequence { , , ,…., , }, the discrete sequence { , , ,…., , } and the discrete sequence { , , ,…., , }. Since the discrete sequence { , , ,…., , } is contained in { , , ,…., , } and { , , ,…., , }, the relationship between the discrete sequence { , , ,…., , }, the discrete sequence { , , ,…., , } and the discrete sequence { , , ,…., , } is shown in equation (16). =( ) (16) ， U1, U2, and U3 are as follows: ， ， ， Wherein, U1, U2 and U3 are (4m+4) × (4m+4) matrices, and I is a 4 × 4 unit matrix; State transition matrix for determining stability of a machining system, If Reversible, state transition matrix As follows: (17) ， When the maximum value of the eigenvalue modulus of the state transition matrix is greater than 1, the machining state corresponding to the process parameters, i.e. the cutting depth a1 of the No. 1 turning tool and the cutting depth a2 of the No. 2 turning tool, is chatter machining. When the maximum value of the eigenvalue modulus of the state transition matrix is greater than 1, the machining state corresponding to the process parameters, i.e. the cutting depth a1 of the No. 1 turning tool and the cutting depth a2 of the No. 2 turning tool, is chatter machining. When the maximum value of the eigenvalue modulus of the state transition matrix is less than 1, the machining state corresponding to the process parameters, i.e. the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is chatter-free machining. When the transition matrix When the maximum value of the eigenvalue modulus is equal to 1, the process parameter at this time is the cutting depth of tool No.

1. and the cutting depth of tool No. 2 The corresponding processing state is the critical processing state; If Irreversible, extended Moore-Penrose matrix as The processing state is determined by equation (17) instead of Step 4, determining the machining state corresponding to the double-tool parallel turning cutting depth according to the state transition matrix, whether it is chatter-free machining or chatter machining, and further obtaining the machining lobe diagram; Specifically as follows: By comparing the maximum value of the eigenvalue module of the state transition matrix with 1, it is obtained that the machining state corresponding to the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is chatter-free machining or chatter machining; further, the machining state corresponding to the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool at different discrete positions is obtained, and a machining lobe diagram is constructed; a critical machining stability curve divides the plane composed of the cutting depth range of the No. 1 turning tool and the cutting depth range of the No. 2 turning tool into a chatter-free machining region and a chatter machining region. Step 5, obtaining the double-tool parallel turning tool cutting depth combination from the chatter-free machining area in the machining lobe diagram, and selecting the optimal combination for double-tool parallel turning chatter-free machining; Specifically as follows: From the chatter-free machining area, a plurality of combinations of the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool are obtained, the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool in each combination obtained are added, and when the addition result is the maximum, the combination of the cutting depth of the No. 1 turning tool and the cutting depth of the No. 2 turning tool is the optimal combination. According to the optimal combination of the cutting depth of the No. 1 tool and the cutting depth of the No. 2 tool, the turning machining path is planned, and the double-tool parallel turning is carried out, so as to realize the double-tool parallel turning chatter-free machining.

2. A system for use in the method of double tool parallel turning without chatter based on optimization of process parameters as claimed in claim 1, characterized in that, The double-tool parallel turning chatter-free machining system based on process parameter optimization comprises: A turning parameter acquisition and dynamics equation construction module is used to obtain the length of the tool wear zone and the double-tool parallel turning parameters, and substitute into the double-tool parallel turning machining dynamics equation considering tool wear; A discretization module is used to obtain the discrete output expression of the double-tool parallel turning machining system according to the double-tool parallel turning machining dynamics equation; A state transition matrix acquisition module is used to obtain the state transition matrix with the minimum dimension according to the discrete output expression; A machining state determination module is used to determine the machining state corresponding to the double-tool parallel turning cutting depth according to the state transition matrix, whether it is chatter-free machining or chatter machining, and further obtain the machining lobe diagram; The parameter optimization processing module is used for obtaining a double-tool parallel turning tool cutting depth combination according to the chatter-free processing area in the processing vane petal diagram, and selecting an optimal combination to control double-tool parallel turning chatter-free processing.

Images