A Stability Analysis Method for Mirror Image Machining of Thin-walled Cylinders

Abstract

The present invention provides an analysis method for the stability of the mirror image processing process of a thin-walled cylinder, comprising the following steps: simplifying the thin-walled cylinder mirror image cutting process system; applying shell theory to establish the forced vibration equation of the rotating thin-walled cylinder; establishing the vibration dynamics equation of the boring bar; establishing a dynamic cutting thickness model; combining the above equations to establish a thin-walled cylinder mirror image cutting dynamics model, using the full discrete method to solve and calculate the stability of the model, and studying the influence of various processing parameters on the stability of the cutting process. The present invention takes into account the modal vibration shape of the thin-walled cylinder in the circumferential and axial directions and the rotation of the workpiece, converts the turning / boring of the thin-walled cylinder into the vibration response of the cylindrical shell under the rotating load, and solves the stability of the cutting process by the full discrete method. The calculation accuracy is high, and the influence of various processing parameters and the modal parameters of the cutting system components on the stability of the cutting process can be analyzed, and the optimization of the cutting process parameters and the system structure can be guided accordingly.

Description

Technical Field

[0001] The invention belongs to the field of metal material cutting and processing, and in particular relates to a method for analyzing the stability of a thin-walled tube mirror processing process. Background Art

[0002] At present, thin-walled parts represented by engine blades and thin-walled cylinders are widely used in aerospace, nuclear industry and other fields due to their light weight, compact structure and superior comprehensive performance. In general, thin-walled parts often require high processing accuracy and surface quality, while the stiffness of thin-walled structures is poor, resulting in large deformation and vibration during processing. In addition, the processing system will vibrate under certain working conditions, which will have a devastating impact on the processing surface quality, tool life and even machine tool accuracy. Therefore, it is very necessary to study the stability of thin-walled parts during processing. By dynamic modeling of the cutting process system and stability calculation and analysis of the cutting process, the cutting state under various working conditions can be analyzed and predicted, providing a theoretical basis for the implementation of vibration suppression schemes. At present, the prediction of the stability of the cutting process is mainly concentrated in traditional turning and milling processing, and there is less prediction and analysis of the mirror processing of thin-walled parts, and there are more processing parameters and complex models during the mirror processing. Therefore, a stability analysis method for the mirror cutting process of thin-walled parts is needed to guide the process optimization and improvement work. Summary of the invention

[0003] In view of this, the present invention aims to propose an analysis method for the stability of the thin-walled cylinder mirror machining process, so as to provide a thin-walled cylinder mirror cutting modeling method based on shell theory. This modeling method can well represent the vibration characteristics of the thin-walled cylinder, breaking through the limitations of traditional mass-damping-stiffness unit and beam theory modeling.

[0004] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0005] A method for analyzing the stability of a thin-walled cylinder mirror machining process, a mechanical modeling of a workpiece power system, and the workpiece power system includes a machine tool spindle, a machine tool tail top, a turning tool and a boring bar, the workpiece is a thin-walled cylindrical part, the two ends of the workpiece are respectively fixedly sleeved to the machine tool spindle and the machine tool tail top, the turning tool is located outside the workpiece, and one end of the turning tool is fixedly connected to a fixed position, and the other end of the turning tool is contacted and connected to the periphery of the workpiece, a boring bar is arranged inside the workpiece, and one end of the boring bar is fixedly connected to the machine tool, and a boring tool is arranged at the other end of the boring bar, and the boring tool and the turning tool are arranged correspondingly, and the method for mechanical modeling of the workpiece power system is S1, to carry out dynamic theoretical modeling of the workpiece; S2, to carry out dynamic theoretical modeling of the boring bar; S3, to model the dynamic cutting force of the turning tool on the workpiece; S4, to model the cutting system of the modeling machine tool.

[0006] Furthermore, the method of performing theoretical dynamic modeling on the workpiece in step S1 can be to perform theoretical modeling using the plate and shell vibration theory. The part processing process is a forced vibration of a rotating cylindrical shell. Here, the workpiece is fixed, and the centripetal force and Coriolis force when the part rotates are ignored, and the processing process is simplified to the forced vibration of a stationary cylindrical shell under the excitation of the rotating force. The cutting force is regarded as a continuous impact load acting on the surface of the workpiece.

[0007] The force on the workpiece in the radial direction is expressed as:

[0008] p z (z,θ,t)=f(t)δ(zz*)δ(θ-θ*)

[0009] δ is the Dirac function:

[0010]

[0011] z* and θ* represent the position of the cutting point on the workpiece;

[0012] Combining the above formula, we can get the second-order differential equation under the main resonance state:

[0013]

[0014] Among them, ω wmn is the natural frequency of this mode, ξ w is the modal damping ratio, F wmn (t) is the external force, expressed as:

[0015]

[0016] M wmn is the modal mass of the workpiece, expressed as:

[0017]

[0018] Rewrite the equation in the form of MCK equation:

[0019]

[0020] Among them, C wmn =2ξ wmn ω wmn M wmn ,

[0021] The final vibration of the workpiece at the cutting point can be expressed as:

[0022] w w =Σ m Σ n T wmn (t)Wmn (z*,θ*)

[0023] Furthermore, the method of performing a dynamic theoretical model on the boring bar in step S2 is to simplify the boring bar into a mass, damping, and stiffness model, and each modal parameter is obtained by a frequency response test:

[0024]

[0025] Furthermore, in step S3, the method for modeling the dynamic cutting force of the turning tool on the workpiece is that the turning tool and the boring tool simultaneously process the inner and outer surfaces of the thin-walled tube, and the two tools maintain the same feed rate f c , where a pt Cutting depth of turning tool, a pb is the cutting depth of the boring bar, κ is the main deflection angle of the turning tool and the boring bar, and the dynamic cutting thickness on both sides of the workpiece can be expressed as:

[0026] Turning:

[0027]

[0028] Boring:

[0029]

[0030] Δa pw is the change in radial cutting depth caused by workpiece vibration, Δa pb is the change in back cutting depth caused by boring bar vibration, h t 、h b is the dynamic cutting thickness of turning and boring, h t0 、h b0 is the nominal cutting thickness for turning and boring, b t , b b is the dynamic cutting width for turning and boring, b t0 , b b0 is the dynamic cutting width for turning and boring,

[0031] Substituting into the phenomenal cutting force formula, we get the dynamic cutting force:

[0032]

[0033] Kct and Kcb are the dynamic radial cutting force coefficients during turning and boring, respectively;

[0034] Taking into account the time lag effect of cutting chatter marks, the change in back cutting depth can be expressed as follows:

[0035]

[0036] Among them, w w(t) and w b (t) are the real-time vibrations of the workpiece and boring tool, w w (tT) and w b (tT) is the vibration of the workpiece and the boring tool in the previous revolution, that is, the vibration mark left on the workpiece surface, T is the time required for the machine tool spindle to rotate one circle, and μ is the overlap coefficient of tool cutting between two revolutions, which is 0 to 1.

[0037] Furthermore, the method of modeling the cutting system of the machine tool in step S4 is that during the cutting process, the feed rate and the spindle speed remain unchanged, so the position of the cutting point on the workpiece surface can be expressed as:

[0038]

[0039]

[0040] W w (t) is the vibration mode function of the workpiece at the cutting point, expressed as:

[0041]

[0042] By coupling the above workpiece, boring bar, and cutting force equations, the dynamic equation of the mirror machining process system is obtained:

[0043]

[0044] Taking the nominal cutting depth as input and the vibration of the workpiece and the boring bar as output, the following form is obtained:

[0045]

[0046] in,

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] Rewrite the second-order differential equation into C:

[0054]

[0055] in,

[0056] Furthermore, the stability analysis of the model is solved by the full discrete method. In the full discrete method, the dynamic equation of the system needs to be transformed. remember Convert the C formula into the following state space form:

[0057]

[0058] In the above formula, A 0 is the constant matrix of the system’s time-invariant properties, A 0 (t) and A T (t) is the periodic variation matrix of the dynamic cutting force considering the regenerative chatter, satisfying A 0 (t+T)=A 0 (t), A T (t+T)=A T (t), T is the main axis rotation period and also the time lag.

[0059] The three coefficient matrix expressions are:

[0060]

[0061]

[0062]

[0063] The non-homogeneous solution of can be expressed as:

[0064]

[0065] The full discrete method discretizes the time in a cycle T into i small time periods of length τ, that is, T = iτ. In the time period k in the time period segment, that is, the segment, that is, the week, (k = 0, that is, the segment, i), the above formula can be rewritten as:

[0066]

[0067] This formula can be equivalent to:

[0068]

[0069] Among them, 0 is equivalent to: the above formula.

[0070] Note that Y at each time step node k =Y(at point k, when t = k, that is, the next time step node, there is Y k =Y(k steps, the above formula can be expressed as:

[0071]

[0072] For the time-delay term Y(k) in the above formula, the time-delay term node is expressed by linear approximation:

[0073]

[0074] Among them, Y k-i With Y k+1-i are the time interval [(ki))ki) where the time lag term is located and the value points on both sides of the time interval.

[0075] for

[0076] The state term Y(k-state term) in the equation is:

[0077]

[0078] Among them, Y k With Y k+1 are the value points on both sides of the time interval where the state item is located [k.

[0079] For the periodic coefficient matrix A 1 (k-periodic coefficient matrix and A T (The k-period coefficient matrix is ​​also approximated by linear approximation in the time interval [k:

[0080]

[0081] in, A 1,k It means that at time point t = k, A 1 The value of (t).

[0082]

[0083] in, A T,k It means that at time point t = k, A T The value of (t).

[0084] After sorting, we can get:

[0085] Y k+1 =(F 0 +F 0,k )Y k +F k+1 Y k+1 +F i-1 Y k+1-i +F i Y k-i

[0086] in,

[0087]

[0088]

[0089] In the above formula, φ 1 ,φ 2 ,φ 3 Both can be obtained by φ 0 and express:

[0090]

[0091] By transforming the above formula, we can get an explicit expression for Yk+1. k+1 ] is a non-singular matrix, it can be expressed as:

[0092] Y k+1 =[IF k+1 ] -1 (F 0 +F 0,k )Y k +[IF k+1 ] -1 F i-1 Y k+1-i +[IF k+1 ] -1 F i Y k-i

[0093] For the above formula, [I in F k+1 ] is a singular matrix, the generalized inverse matrix of the matrix can be used instead of its inverse matrix for calculation.

[0094] Constructing discrete mappings: Z k+1 =D k Z k , where Z k+1 n Y (i+1)-dimensional column vector, n Y is the dimension of vector Y. Z k+1 Expressed as:

[0095] Z k =col(Y k ,Y k-1 ,…,Y k+1-i ,Y k-i )

[0096] Among them, the coefficient matrix D k It is expressed as:

[0097]

[0098] From this, we can construct the transfer matrix Φ in one cycle, Z k =ΦZ 0 Where Φ = D i-1 D i-2 …D 1 D 0 , according to Floquet theory, the stability of the system is judged. If all the eigenvalues ​​of the transfer matrix Φ are less than 1, the system is in a stable state; otherwise, the system is in an unstable state or close to a stable state.

[0099] Compared with the prior art, the analysis method of the stability of the thin-walled cylinder mirror processing process described in the present invention has the following beneficial effects: it provides a thin-walled cylinder mirror cutting modeling method based on shell theory, which can well represent the vibration characteristics of thin-walled cylinders and break through the limitations of traditional mass, damping, stiffness unit and beam theory modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0100] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0101] Figure 1 It is a schematic diagram of the composition of the thin-walled tube mirror cutting process system of the present invention;

[0102] Figure 2 It is a schematic diagram of the cross-sectional structure of the thin-walled tube mirror cutting process system in the present invention;

[0103] Figure 3 It is a schematic structural diagram of a thin-walled cylindrical member in the present invention;

[0104] Figure 4 is the stability lobe diagram calculated in the present invention;

[0105] Figure 5 It is a workpiece cutting vibration signal diagram obtained through cutting processing test in the present invention.

[0106] Description of reference numerals:

[0107] 1-workpiece; 2-boring bar; 3-turning tool; 4-machine tool spindle; 5-machine tool tailstock; 6-external surface; 7-inner surface; 8-boring tool; 9-mid-plane. DETAILED DESCRIPTION

[0108] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0109] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and the like are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0110] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood by specific circumstances.

[0111] The present invention will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments.

[0112] like Figure 1-5 As shown, a method for analyzing the stability of a thin-walled cylinder mirror machining process is provided, and a mechanical modeling is performed on a workpiece power system, and the workpiece 1 power system includes a machine tool spindle 4, a machine tool tail top 5, a turning tool 3 and a boring bar 2. The workpiece 1 is a thin-walled cylindrical part, and the two ends of the workpiece 1 are respectively fixedly sleeved to the machine tool spindle 4 and the machine tool tail top 5. The turning tool is located outside the workpiece 1, and one end of the turning tool 3 is fixedly connected to a fixed position, and the other end of the turning tool 3 is contacted and connected to the periphery of the workpiece. A boring bar 2 is arranged inside the workpiece 1, and one end of the boring bar 2 is fixedly connected to the machine tool, and a boring tool 8 is arranged at the other end of the boring bar 2, and the boring tool 8 is arranged corresponding to the turning tool 3. The method for mechanical modeling of the workpiece 1 power system is S1, performing dynamic theoretical modeling on the workpiece 1; S2, performing dynamic theoretical modeling on the boring bar; S3, modeling the dynamic cutting force of the turning tool 3 on the workpiece 1; S4, modeling the cutting system of the modeling machine tool.

[0113] The method of performing a dynamic theoretical modeling of the workpiece in step S1 is to perform a theoretical modeling using the plate and shell vibration theory. The part processing process is a forced vibration of a rotating cylindrical shell. Here, the workpiece 1 is fixed, and the centripetal force and Coriolis force during the rotation of the part are ignored, and the processing process is simplified to the forced vibration of a stationary cylindrical shell under the excitation of the rotating force. The cutting force is regarded as a continuous impact load acting on the surface of the workpiece.

[0114] The force on workpiece 1 in the radial direction is expressed as:

[0115] p z (z,θ,t)=f(t)δ(zz*)δ(θ-θ*) (1)

[0116] δ is the Dirac function:

[0117]

[0118] z* and θ* represent the positions of the cutting points on the workpiece 1;

[0119] Substituting equations (2-3)-(2-6) into equation (2-1), we obtain the second-order differential equation under the main resonance state:

[0120]

[0121] Among them, ω wmn is the natural frequency of this mode, ξ w is the modal damping ratio, F wmn (t) is the external force, expressed as:

[0122]

[0123] M wmn is the modal mass of workpiece 1, expressed as:

[0124]

[0125] Rewrite the equation in the form of MCK equation:

[0126]

[0127] Among them, C wmn =2ξ wmn ω wmn M wmn ,

[0128] The final vibration of workpiece 1 at the cutting point can be expressed as:

[0129] w w =Σ m ∑ n Twmn (t)W mn (z*,θ*) (7)

[0130] Step 2: Dynamic model of boring bar 2

[0131] The structure of the boring bar 2 is relatively complex, and the beam theory cannot accurately describe the boring bar 2. Therefore, the boring bar 2 is simplified into a mass-damping-stiffness model, and each modal parameter is obtained by a frequency response test.

[0132]

[0133] Step 3: Modeling dynamic cutting forces

[0134] The turning tool 3 and the boring tool 8 process the inner and outer surfaces 6 of the thin-walled tube at the same time, and the two tools maintain the same feed rate f c In the figure, a pt with a pb are the cutting depths of turning tool 3 and boring tool 8, respectively, and κ is the main rake angle of the two tools. The dynamic cutting thickness on both sides of the workpiece 1 can be expressed as:

[0135] Turning

[0136]

[0137] Boring

[0138]

[0139] Δa pw is the change in radial back cutting depth caused by the vibration of workpiece 1, Δa pb is the change in back cutting depth caused by the vibration of boring bar 2, h t 、h b is the dynamic cutting thickness of turning and boring, h t0 、h b0 is the nominal cutting thickness for turning and boring, b t , b b is the dynamic cutting width for turning and boring, b t0 , b b0 It is the dynamic cutting width for turning and boring.

[0140] Substituting into the phenomenal cutting force formula, we get the dynamic cutting force:

[0141]

[0142] K ct , K cb are the dynamic radial cutting force coefficients during turning and boring, respectively.

[0143] Taking into account the time lag effect of cutting chatter marks, the change in back cutting depth can be expressed as follows:

[0144]

[0145] Among them, w w (t) and w b (t) are the real-time vibrations of the workpiece 1 and the boring tool 8, respectively, and w w (tT) and w b (tT) is the vibration of the workpiece 1 and the boring tool 8 in the previous revolution, that is, the chatter mark left on the surface of the workpiece 1, T is the time required for the machine tool spindle to rotate one circle, and μ is the overlap coefficient of tool cutting between two revolutions, which is 0~1.

[0146] Step 4: Model the cutting process system:

[0147] During the cutting process, the feed rate and the spindle speed remain unchanged, so the position of the cutting point on the surface of the workpiece 1 can be expressed as:

[0148]

[0149] W w (t) is the vibration mode function of workpiece 1 at the cutting point, expressed as:

[0150]

[0151] By coupling the above workpiece 1, boring bar 2, and cutting force equation, the dynamic equation of the mirror machining process system is obtained:

[0152]

[0153] Taking the nominal cutting depth as input and the vibration of workpiece 1 and boring bar 2 as output, the following form is obtained:

[0154]

[0155] in,

[0156]

[0157]

[0158]

[0159]

[0160]

[0161]

[0162] Rewrite the second-order differential equation into C:

[0163]

[0164] in,

[0165] The method for analyzing the stability of the thin-walled tube mirror processing process according to claim 2 is characterized in that the stability analysis of the above-mentioned model is solved by a full discrete method.

[0166] In the full discrete method, the dynamic equation of the system needs to be transformed. remember Convert equation (18) into the following state space form:

[0167]

[0168] In the above formula, A 0 is the constant matrix of the system’s time-invariant properties, A 0 (t) and A T (t) is the periodic variation matrix of the dynamic cutting force considering the regenerative chatter, satisfying A 0 (t+T)=A 0 (t), A T (t+T)=A T (t), T is the main axis rotation period and also the time lag.

[0169] The three coefficient matrix expressions are:

[0170]

[0171]

[0172]

[0173] The non-homogeneous solution of formula (19) can be expressed as:

[0174]

[0175] The full discrete method discretizes the time within a period T into i small time periods of length τ, that is, T = iτ. In the time period kτ≤t≤(k+1)τ, (k=0,…,i), formula (23) can be rewritten as:

[0176]

[0177] This formula can be equivalent to:

[0178]

[0179] Among them, 0≤t≤τ.

[0180] Note that Y at each time step node k =Y(kτ), when t = τ, that is, the time step is the next node, there is Y k =Y(kτ+1), formula (25) can be expressed as:

[0181]

[0182] For the time lag term Y(kτ+t-ξ-T) in equation (26), it is expressed by linear approximation:

[0183]

[0184] Among them, Y k-i With Y k+1-i are the value points on both sides of the time interval [(ki)τ, (k+1-i)τ] where the time lag term is located.

[0185] For the state term Y(kτ+t-ξ) in equation (26), it is also expressed using linear approximation:

[0186]

[0187] Among them, Y k With Y k+1 are the value points on both sides of the time interval [kτ, (k+1)τ] where the state item is located.

[0188] For the periodic coefficient matrix A 1 (kτ+t-ξ) and A T (kτ+t-ξ) is also approximated by linear approximation on the time interval [kτ, (k+1)τ]:

[0189]

[0190] in, A 1,k It means that at time t = kτ, A 1 The value of (t).

[0191]

[0192] in, A T,k It means that at time t = kτ, A T The value of (t).

[0193] After sorting, we can get:

[0194] Y k+1 =(F 0 +F0,k )Y k +F k+1 Y k+1 +F i-1 Y k+1-i +F i Y k-i (31)

[0195] in,

[0196]

[0197]

[0198] In formula (32), φ 1 ,φ 2 ,φ 3 Both can be obtained by φ 0 and express:

[0199]

[0200] By transforming formula (31), we can get Y k+1 Explicit expression, when [IF k+1 ] is a non-singular matrix, it can be expressed as:

[0201] Y k+1 =[IF k+1 ] -1 (F 0 +F 0,k )Y k +[IF k+1 ] -1 F i-1 Y k+1-i +[IF k+1 ] -1 F i Y k-i (33)

[0202] For the above formula, [IF k+1 ] is a singular matrix, the generalized inverse matrix of the matrix can be used instead of its inverse matrix for calculation.

[0203] For formula (33), a discrete mapping can be constructed:

[0204] Z k+1 =D k Z k (34)

[0205] Among them, Z k+1 n Y (i+1)-dimensional column vector, n Y is the dimension of vector Y. Zk+1 Expressed as:

[0206] Z k =col(Y k ,Y k-1 ,…,Y k+1-i ,Y k-i ) (35)

[0207] Among them, the coefficient matrix D k It is expressed as:

[0208]

[0209] In this way, the transfer matrix Φ within one period can be constructed.

[0210] Z k =ΦZ 0 (37)

[0211] in,

[0212] Φ=D i-1 D i-2 …D 1 D 0 (38)

[0213] The stability of the system is judged according to the Floquet theory. If all the eigenvalues ​​of the transfer matrix Φ are less than 1, the system is in a stable state; otherwise, the system is in an unstable state or close to a stable state.

[0214] To ensure the accuracy of calculation, the time step τ of each calculation cycle should be a constant and less than 1 / 3 times the natural frequency vibration period of workpiece 1, and the time period number i changes with the cutting speed.

[0215] According to the above model, each working condition is calculated to obtain the stability lobe diagram between different processing parameters (turning, boring back cutting amount, feed rate, etc.) and spindle speed, such as Figure 4 As shown, the cutting depth of the boring tool 8 is 0.4mm and the feed rate is 0.33mm / rev. The relationship between the limiting cutting depth of the external turning tool 3 and the spindle speed is studied, and its critical cutting depth is 0.65mm. Figure 5 The figure shows the vibration of workpiece 1 during the cutting experiment under the same working conditions, when the critical cutting depth increases from 0.3 mm to 0.9 mm. The cutting process becomes unstable at about 13 s (cutting depth 0.67 mm), which indicates the accuracy of the model.

[0216] The present invention provides a thin-walled cylinder mirror cutting modeling method based on shell theory. The processing object of this process system is a thin-walled cylinder with a relatively simple structure. The plate-shell vibration theory can be used for theoretical modeling. The modal vibration modes of the thin-walled cylinder in the circumferential and axial directions and the rotation of the workpiece 1 are considered, and the turning / boring of the thin-walled cylinder is converted into the vibration response of the cylindrical shell under the rotating load. The stability of the cutting process is solved by the full discrete method with high calculation accuracy. The influence of various processing parameters (such as feed rate, spindle speed, internal and external tool cutting depth, tool main deflection angle, etc.) and cutting system component modal parameters (such as fixture, boring bar 2, auxiliary support device stiffness, etc.) on the stability of the cutting process can be analyzed, and the optimization of cutting process parameters and system structure can be guided accordingly.

[0217] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An analysis method for the stability of the thin-walled tube mirror processing process, Features: The workpiece power system is mechanically modeled, and the workpiece power system includes a machine tool spindle, a machine tool tail top, a turning tool and a boring bar. The workpiece is a thin-walled cylindrical part. The two ends of the workpiece are respectively fixedly sleeved to the machine tool spindle and the machine tool tail top. The turning tool is located outside the workpiece, and one end of the turning tool is fixedly connected to a fixed position, and the other end of the turning tool is contacted and connected to the periphery of the workpiece. A boring bar is arranged inside the workpiece, and one end of the boring bar is fixedly connected to the machine tool. A boring tool is arranged at the other end of the boring bar, and the boring tool and the turning tool are arranged correspondingly. The method for mechanical modeling of the workpiece power system is S1, and dynamic theoretical modeling of the workpiece is performed; S2, dynamic theoretical model of boring bar; S3, modeling of dynamic cutting force of turning tool on workpiece; S4, modeling the cutting system of the machine tool; The method for modeling the dynamic cutting force of the turning tool on the workpiece in step S3 is that the turning tool and the boring tool simultaneously process the inner and outer surfaces of the thin-walled tube, and the two tools maintain the same feed rate f c , where a pb is the cutting depth of the boring bar, κ is the main deflection angle of the turning tool and the boring bar, and the dynamic cutting thickness on both sides of the workpiece can be expressed as: Turning: Boring: Δa pw is the change in radial cutting depth caused by workpiece vibration, Δa pb is the change in back cutting depth caused by boring bar vibration, h t 、h b is the dynamic cutting thickness of turning and boring, h t0 、h b0 is the nominal cutting thickness for turning and boring, b t , b b is the dynamic cutting width for turning and boring, b t0 、b b0 It is the dynamic cutting width for turning and boring; Substituting into the phenomenal cutting force formula, we get the dynamic cutting force: K tc , K bc are the dynamic radial cutting force coefficients during turning and boring, respectively; Taking into account the time lag effect of cutting chatter marks, the change in back cutting depth can be expressed as follows: Among them, w w (t) and w b (t) are the real-time vibrations of the workpiece and boring tool, w w (tT) and w b (tT) is the vibration of the workpiece and the boring tool in the previous revolution, that is, the chatter mark left on the workpiece surface, T is the time required for the machine tool spindle to rotate one circle, μ is the overlap coefficient of tool cutting between two revolutions, which is 0~1; The method of modeling the cutting system of the machine tool in step S4 is that during the cutting process, the feed rate and the spindle speed remain unchanged, so the position of the cutting point on the workpiece surface can be expressed as: W w (t) is the vibration mode function of the workpiece at the cutting point, expressed as: By coupling the above workpiece, boring bar, and cutting force equations, the dynamic equation of the mirror machining process system is obtained: Taking the nominal cutting depth as input and the vibration of the workpiece and the boring bar as output, the following form is obtained: Among them, MW, Mb, CW, Cb Rewrite the second-order differential equation into C: in, 2. According to the method for analyzing the stability of the thin-walled tube mirror processing process according to claim 1, Features: The method of performing dynamic theoretical modeling on the workpiece in step S1 is to use the plate and shell vibration theory for theoretical modeling; the part processing process is a forced vibration of a rotating cylindrical shell. Here, the workpiece is fixed, the centripetal force and Coriolis force when the part rotates are ignored, and the processing process is simplified to the forced vibration of a stationary cylindrical shell under the excitation of the rotating force; the cutting force is regarded as a continuous impact load acting on the surface of the workpiece; The force on the workpiece in the radial direction is expressed as: p z (z,θ,t)=f(t)δ(z-z*)δ(θ-θ*) δ is the Dirac function: z* and θ* represent the position of the cutting point on the workpiece; Combining the above formula, we can get the second-order differential equation under the main resonance state: Among them, ω wmn is the natural frequency of this mode, ξ w is the modal damping ratio, F wmn (t) is the external force, expressed as: M wmn is the modal mass of the workpiece, expressed as: Rewrite the equation in the form of MCK equation: Among them, C wmn =2ξ wmn ω wmn M wmn , The final vibration of the workpiece at the cutting point can be expressed as: w w =∑ m ∑ n T wmn (t)W mn (z*,θ*)。 3. According to the method for analyzing the stability of the thin-walled tube mirror processing process according to claim 2, Features: The method of conducting a dynamic theoretical model of the boring bar in step S2 is to simplify the boring bar into a mass, damping, and stiffness model, and each modal parameter is obtained from a frequency response test:

4. According to the method for analyzing the stability of the thin-walled tube mirror processing process as described in claim 1, Features: The stability analysis of the model is solved by the full discrete method. In the full discrete method, the dynamic equation of the system needs to be transformed. remember Convert the C formula into the following state space form: In the above formula, A 0 is the constant matrix of the system’s time-invariant properties, A 0 (t) and A T (t) is the periodic variation matrix of the dynamic cutting force considering the regenerative chatter, satisfying A 0 (t+T)=A 0 (t), A T (t+T)=A T (t), T is the main axis rotation period and also the time lag; The three coefficient matrix expressions are: The full discrete method discretizes the time within a period T into i small time periods of length τ, that is, T = iτ; in the time period kτ≤t≤(k+1)τ, (k=0,…,i), the above formula can be rewritten as: This formula can be equivalent to: Among them, 0≤t≤τ; Note that Y at each time step node k =Y(at point k, when t = k, that is, the next time step node, there is Y k =Y(k steps, the above formula can be expressed as: For the time-delay term Y(k) in the above formula, the time-delay term node is expressed by linear approximation: Among them, Y k-i With Y k-+1-i are the time interval [(ki))ki) where the time lag term is located and the value points on both sides of the time interval; for The state term Y (k-state term; at time, it is also represented by linear approximation: Among them, Y k With Y k+1 is the time interval where the state item is located [k is the value point on both sides of the time interval where the state item is located; For the periodic coefficient matrix A 1 (k-periodic coefficient matrix and A T (The k-period coefficient matrix is ​​also approximated by linear approximation in the time interval [k: in, A 1,k It means that at time point t = k, A 1 The value of (t); Among them, A T,k represents the value of A at time point t = k T (t); After sorting, we can get: Y k+1 = (F 0 + F 0,k )Y k + F k+1 Y k+1 + F i-1 Y k+1-i + F i Y k-i in, In the above formula, φ 1 ,φ 2 ,φ 3 Both can be obtained by φ 0 and express: By transforming the above formula, we can get an explicit expression for Yk+1. k+1 ] is a non-singular matrix, it can be expressed as: Y k+1 =[I-F k+1 ] -1 (F 0 +F 0,k )Y k +[I-F k+1 ] -1 F i-1 Y k+1-i +[I-F k+1 ] -1 F i Y k-i For the above formula, [I in F k+1 ] is a singular matrix, the generalized inverse matrix of the matrix can be used instead of its inverse matrix for calculation; Constructing discrete mappings: Z k+1 =D k Z k , where Zk +1 n Y (i+1)-dimensional column vector, nY is the dimension of vector Y; Z k+1 Expressed as: Z k =col(Y k ,AND k-1 ,L,Y k+1-i ,AND k-i ) Among them, the coefficient matrix D k It is expressed as: From this, we can construct the transfer matrix Φ in one cycle, Z k =ΦZ 0 where Φ = D i-1 D i-2 LD 1 D 0 , the stability of the system is judged according to the Floquet theory. If all the eigenvalues of the transfer matrix Φ are less than 1, the system is in a stable state; otherwise, the system is in an unstable state or near a stable state.

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