Three-order vibration reduction boring bar optimization method

Abstract

The invention discloses a three-order vibration reduction boring bar optimization method, and belongs to the field of machining. The implementation method comprises the following steps: solving a series of response displacements of a main system of a corresponding boring bar body based on an original point frequency response function of an undamped second-order system, and taking the mass of a first additional system corresponding to the minimum mean value of the system response displacements as an optimization result of the mass of the first additional system; according to the mass, the density and the length of the first additional system, a first additional system damping coefficient is obtained based on a first additional system damping coefficient model; the dynamic equation set of the third-order vibration reduction boring rod is solved, and the displacement response of the third-order vibration reduction boring rod under the unit stable acting force is obtained; obtaining a mean value of the displacement response of the main system based on the displacement response of the third-order vibration reduction boring rod under different second additional system masses; and the minimum value is obtained based on the average value of the displacement response of the main system, the second additional mass corresponding to the minimum average value serves as the mass optimization result of the second additional system, and mass distribution of the third-order vibration reduction boring rod is achieved.

Description

Technical Field

[0001] The invention relates to a three-order vibration-damping boring bar optimization method and belongs to the field of mechanical processing. Background Art

[0002] In the process of metal cutting, the processing of hole features is particularly important, especially in the current stage of rapid development of my country's equipment technology, the demand for deep hole and large hole processing is increasing. However, due to the chatter problem in the large overhang boring process of deep holes and large holes, which can cause severe wear of the machining tool and deterioration of the machining quality of the machined surface, it is particularly important to control the vibration during the deep hole and large hole processing.

[0003] At present, the commonly used method to reduce vibration in industrial production is to use a boring bar with a damping vibration absorber. This type of boring bar has a pre-adjusted carbide mass block placed inside, so that the vibration absorber can be regarded as an additional system of the boring bar, thereby interacting with the main system (bar body) during the cutting process to reduce the cutting amplitude and improve the processing quality of the processed surface.

[0004] At present, most of the vibration-damping boring bars that have been commercialized in the market are second-order systems, that is, the vibration-damping boring bar as a whole is composed of a tool bar body and a vibration damper. The structure and manufacturing process of this type of vibration-damping boring bar are now mature and have been applied in various parts processing, with extremely high economic benefits. However, the vibration resistance of the second-order system vibration-damping boring bar is still limited. When the boring bar overhang exceeds 7 times the diameter, its vibration-damping effect will be limited, and for small-diameter (less than 40 in diameter) deep holes, its vibration-damping effect will also be greatly reduced. Therefore, it is necessary to conduct further analysis and design on the basis of the traditional second-order system vibration-damping boring bar to solve the current problems.

[0005] Based on the above discussion, the three-order vibration-damping boring bar is an option. Its overall structure consists of a boring bar body (main system) and two vibration dampers (additional system) of unequal mass. It is worth noting that if the mass distribution of the additional system is unreasonable during the design process of the three-order vibration-damping boring bar, the vibration reduction effect may deteriorate and the two vibration dampers may not work together. Therefore, a systematic calculation method is needed to actively design the three-order vibration-damping boring bar system. Summary of the invention

[0006] The purpose of the present invention is to provide a third-order vibration damping boring bar optimization method, in which the mass of the first additional system corresponding to the modulus of the minimum mean value obtained by the undamped second-order system is taken as the optimization result of the mass of the first additional system, and the dynamic equations of the third-order vibration damping boring bar are solved, and the minimum value of the average value is obtained based on the displacement response of the third-order vibration damping boring bar within a predetermined time as the mass optimization result of the second additional system, so as to realize the active optimization of the third-order vibration damping boring bar, improve the processing quality of the third-order vibration damping boring bar processing parts, and reduce the surface roughness.

[0007] The objectives of the present invention are achieved through the following technical solutions.

[0008] The invention discloses a third-order vibration-damping boring bar optimization method. The method comprises the following steps: obtaining a series of response displacements of a corresponding boring bar body main system based on an origin frequency response function of an undamped second-order system, and taking a first additional system mass corresponding to a minimum mean value of the system response displacement as an optimization result of the mass of the first additional system; obtaining a first additional system damping coefficient based on a first additional system damping coefficient model according to the mass, density and length of the first additional system; solving a group of dynamic equations of the third-order vibration-damping boring bar to obtain a displacement response of the third-order vibration-damping boring bar under a unit stabilizing force; obtaining a mean value of the displacement response of the main system based on the displacement response of the third-order vibration-damping boring bar under different second additional system masses; obtaining a minimum value based on the mean value of the displacement response of the main system, and taking a second additional mass corresponding to the minimum mean value as a mass optimization result of the second additional system, thereby realizing mass distribution of the third-order vibration-damping boring bar.

[0009] The present invention discloses a method for optimizing a three-order vibration-damping boring bar. The optimization object is a three-order vibration-damping boring bar, which includes a boring head, a boring bar body main system, a main vibration damper of a first auxiliary system and a boring bar tail end cover, and also includes a secondary vibration damper of a second auxiliary system. The present invention discloses a method for optimizing a three-order vibration-damping boring bar, which includes the following steps:

[0010] Step 1: The boring bar body of the main system and the main shock absorber of the first additional system form an undamped second-order system. The origin frequency response function of the undamped second-order system is established. According to the added mass of the first additional system and the input signal frequency, the series response displacement of the corresponding boring bar body main system is obtained based on the origin frequency response function of the undamped second-order system. The response displacement of the boring bar body main system corresponds to the modulus of the origin frequency response function of the undamped second-order system.

[0011] The model of the origin frequency response function of the undamped second-order system is shown in formula (1):

[0012]

[0013] In formula (1), |H 11 | represents the modulus of the frequency response function of the origin of the system, that is, the response displacement amplitude of the main system of the boring bar body; k1, k2 are the equivalent stiffness of the main system of the boring bar body and the first additional system, m1, m2 are the masses of the main system of the boring bar body and the first additional system, ω is the frequency of the input signal of the system; introduce Variable, simplify the modular formula of the origin frequency response function of the undamped second-order system.

[0014] Step 2: According to different additional masses and different input signal frequencies of the first additional system, the series response displacements of the corresponding boring bar body main system are obtained based on the origin frequency response function of the undamped second-order system, and the series modulus of the origin frequency response function of the undamped second-order system is obtained accordingly.

[0015] Step 3: Take the average of the series modes of the origin frequency response function in step 2 under different additional masses, and the mode with the minimum average corresponds to the first additional system mass m 2t As the first additional system mass m 2t Optimization results.

[0016] Step 4: Based on the first additional system mass m obtained in step 3 2t As well as the density and length of the first additional system, the damping coefficient c2 of the first additional system is obtained based on the damping coefficient model of the first additional system.

[0017] The damping coefficient c2 model of the first additional system is shown in formula (2):

[0018] c2=4lru (2)

[0019] In formula (2), l is the actual length of the first additional system, r is the density of the damping fluid used, and u is the kinematic viscosity of the damping fluid.

[0020] Step 5: Based on the first additional system mass m in step 3 2t Together with the damping coefficient c2 of the first additional system obtained in step 4, a group of dynamic equations of the third-order vibration-damping boring bar is established, in which the mass m3 of the second additional system is the optimization target, and the stiffness k3 and damping c3 of the second additional system are known quantities.

[0021] The dynamic equations of the third-order vibration-damped boring bar are shown in formula (3):

[0022]

[0023] Among them, m3 is the mass of the second additional system, k3 is the stiffness of the second additional system, c3 is the damping of the second additional system, x1, x2, x3 represent the displacements of the main system, the first additional system, and the second additional system respectively. Represent the first and second order derivatives of displacement, namely velocity and acceleration respectively; Denoted as M, Denoted as K, Denoted as C.

[0024] Step 6: Based on the dynamic equation group of the third-order vibration-damping boring bar established in step 5, the dynamic equation group of the third-order vibration-damping boring bar is solved to obtain the displacement response of the third-order vibration-damping boring bar under a unit stabilizing force.

[0025] The methods for solving the dynamic equations of the third-order vibration-damping boring bar include the linear acceleration method, the Runge-Kutta method, and the Wilson-θ method. Preferably, the linear acceleration method is used to solve the dynamic equations of the third-order vibration-damping boring bar.

[0026] The specific implementation method of step 6 is:

[0027] Step 6.1, determine the initial conditions of the dynamic equations (3) of the third-order damping boring bar, that is, determine the initial displacement conditions u of the dynamic equations (3) ini With the initial velocity condition v ini .

[0028] Step 6.2: Calculate the initial acceleration condition according to formula (4):

[0029] a ini =M -1 ×(fC×v ini -K×u ini ) (4)

[0030] Where f is the time-varying function of the external force on the main system of the boring bar body, that is, the unit stabilizing force.

[0031] Step 6.3: Calculate the displacement response of the boring bar main system, the first additional system, and the second additional system at the next moment according to formula (5):

[0032]

[0033] Where Δt is the time step, and a2 and a1 are functions of known quantities:

[0034]

[0035] Step 6.4: Based on the calculation result of the displacement response of the second additional system in step 6.3, obtain the velocity v at the next moment xia and the acceleration a at the next moment xia :

[0036]

[0037] According to equations (5), (6), and (7), the initial condition u of the third-order vibration-damping boring bar is: ini ,v ini The response for the next time interval in the case.

[0038] Step 6.5: Solve u obtained in step 6.4 xia ,v xia ,a xia As the new initial condition, the displacement response of the third-order damped boring bar in the next time interval is solved.

[0039] Step 6.6, repeat steps 6.2 to 6.5 until the response of the third-order vibration-damped boring bar within a predetermined time is solved, and the displacement response of the third-order vibration-damped boring bar under a unit stabilizing force is obtained.

[0040] Step 7, adjust the second additional system mass m3, repeat steps 5 and 6, and obtain the response of the system within a predetermined time under different second additional system masses m3, that is, obtain the main system displacement response of the third-order vibration-damping boring bar under different second additional system masses per unit stabilizing force.

[0041] Step 8: Based on Step 5, Step 6, and Step 7, the displacement response u of the third-order vibration-damping boring bar within a predetermined time under different second additional system masses m3 is obtained. xia The average value of .

[0042] Step 9: The displacement response u of the third-order vibration-damping boring bar obtained in step 8 within a predetermined time xia The average value of obtains the minimum value, and the second additional system mass m3 corresponding to the minimum value is the mass optimization result of the second additional system.

[0043] The method further comprises step 10, according to which the first additional system mass m obtained in step 3 is 2t The optimization result of and the optimization result of the second additional system mass m3 obtained in step 9 are used to counterweight the third-order vibration-damping boring bar. The third-order vibration-damping boring bar after active counterweighting can suppress the vibration caused by insufficient stiffness of the boring bar when processing the workpiece, thereby suppressing the generation of vibration marks on the machined surface and reducing the surface roughness of the workpiece.

[0044] Beneficial effects:

[0045] 1. The present invention discloses a method for optimizing a third-order vibration-damped boring bar. The method obtains a series of response displacements of a corresponding boring bar body main system based on an origin frequency response function of an undamped second-order system, and uses the mass of a first additional system corresponding to the minimum mean value of the system response displacement as an optimization result of the mass of the first additional system. The damping coefficient of the first additional system is obtained based on a damping coefficient model of the first additional system according to the mass, density and length of the first additional system. The mass distribution of the third-order vibration-damped boring bar system is optimized by solving the origin frequency response function of the undamped second-order system and the dynamic equations of the third-order vibration-damped boring bar, and the surface roughness of the workpiece is reduced by actively suppressing the generation of vibration marks on the machined surface.

[0046] 2. The present invention discloses a third-order vibration-damped boring bar optimization method, which obtains the displacement response of the third-order vibration-damped boring bar under a unit stabilizing force by solving the dynamic equations of the third-order vibration-damped boring bar. Compared with the traditional frequency response function method, the method is closer to the stress condition of the boring bar in the actual boring process, reduces the vibration of the boring bar during machining, and thus improves the machining quality of the workpiece. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 The present invention discloses a flow chart of a three-order vibration-damping boring bar optimization method.

[0048] Figure 2 The calculation results of the origin frequency response function of the undamped second-order system under different input frequencies and different additional masses are shown in the figure.

[0049] Figure 3 This is a comparison chart of the mean value of the modulus of the origin frequency response function of the undamped second-order system.

[0050] Figure 4 This is the partial displacement response curve within 200s based on the linear acceleration algorithm when the additional mass m3 = 0.001kg.

[0051] Figure 5 This is the design drawing of the three-order vibration-damped boring bar. DETAILED DESCRIPTION

[0052] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0053] Embodiment 1:

[0054] The method of the present invention is used to calculate the mass distribution of the first and second additional systems of a third-order vibration-damping boring bar with a main system mass of 3kg and a design length of 380mm, and obtain the optimized mass of the additional system.

[0055] like Figure 1 As shown, the invention disclosed in the present invention discloses a flow chart of a three-order vibration-damping boring bar optimization method, and its specific implementation process is as follows:

[0056] Step 1: The boring bar body of the main system and the main shock absorber of the first additional system form an undamped second-order system. The origin frequency response function of the undamped second-order system is established. According to the added mass of the first additional system and the input signal frequency, the series response displacement of the corresponding boring bar body main system is obtained based on the origin frequency response function of the undamped second-order system. The response displacement of the boring bar body main system corresponds to the modulus of the origin frequency response function of the undamped second-order system.

[0057] like Figure 2 Shown are the calculation results of the origin frequency response function of the undamped second-order system under different input frequencies and different additional masses.

[0058] Step 2: According to different additional masses and different input signal frequencies of the first additional system, the series response displacements of the corresponding boring bar body main system are obtained based on the origin frequency response function of the undamped second-order system, and the series modulus of the origin frequency response function of the undamped second-order system is obtained accordingly.

[0059] Step 3: Take the average of the series modes of the origin frequency response function in step 2 under different additional masses, and the mode with the minimum average corresponds to the first additional system mass m 2t As the first additional system mass m 2t The optimization results.

[0060] Based on the known condition that the mass of the main system = 3kg, the mean value of the modulus of the origin frequency response function of the undamped second-order system is Figure 3 As shown in the figure, according to the results in the figure, we can know that the system m 2t =0.08kg.

[0061] Step 4: Based on the first additional system mass m obtained in step 3 2t As well as the density and length of the first additional system, the damping coefficient c2 of the first additional system is obtained based on the damping coefficient model of the first additional system.

[0062] Based on m 2t =0.08kg, the density of cemented carbide is about 13′10 3 kg / m 3 The hollow diameter of the third-order vibration damping tool bar is 14 mm, so l = 93 mm in formula (2). In the design, 46# anti-wear hydraulic oil is used as the damping fluid, and its density is about 0.9′10 3 kg / m 3 , kinematic viscosity is about 45.6mm 2 / s, after calculation we can get c2=0.015.

[0063] Step 5: Based on the first additional system mass m in step 3 2t Together with the damping coefficient c2 of the first additional system obtained in step 4, a group of dynamic equations of the third-order vibration-damping boring bar is established, in which the mass m3 of the second additional system is the optimization target, and the stiffness k3 and damping c3 of the second additional system are known quantities.

[0064] Based on literature and actual tests, it is known that steel boring bar body k1 = 1.3′10 6 N / m, k2=k3=1.1′10 for two additional systems with exactly the same design 5 N / m, and the damping fluid is no longer injected into the second additional system, then c3=0 can be taken. Therefore, the established third-order vibration-damping boring bar dynamic equations can be written as:

[0065]

[0066] Step 6: Based on the dynamic equation group of the third-order vibration-damping boring bar established in step 5, the dynamic equation group of the third-order vibration-damping boring bar is solved to obtain the displacement response of the third-order vibration-damping boring bar under a unit stabilizing force.

[0067] Based on the linear acceleration algorithm, when the additional mass m3 = 0.001 kg, the partial displacement response curve within 200 seconds is as follows: Figure 4 shown.

[0068] Step 7, adjust the second additional system mass m3, repeat steps 5 and 6, and obtain the response of the system within a predetermined time under different second additional system masses m3, that is, obtain the main system displacement response of the third-order vibration-damping boring bar under different second additional system masses per unit stabilizing force.

[0069] Step 8: Based on Step 5, Step 6, and Step 7, the displacement response u of the third-order vibration-damping boring bar within a predetermined time under different second additional system masses m3 is obtained. xia The average value of .

[0070] Step 9: The displacement response u of the third-order vibration-damping boring bar obtained in step 8 within a predetermined time xia The average value of obtains the minimum value, and the second additional system mass m3 corresponding to the minimum value is the mass optimization result of the second additional system.

[0071] Based on the calculation results, m3 is 0.154 kg. The boring bar designed based on the above calculation results is as follows Figure 5 shown.

[0072] Step 10: Based on the first additional system mass m obtained in step 3 2t The optimization result of and the optimization result of the second additional system mass m3 obtained in step 9 are used to counterweight the third-order vibration-damping boring bar. The third-order vibration-damping boring bar after active counterweighting can suppress the vibration caused by insufficient stiffness of the boring bar when processing the workpiece, thereby suppressing the generation of vibration marks on the machined surface and reducing the surface roughness of the workpiece.

[0073] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing a three-order vibration-damped boring bar, wherein the optimization object is a three-order vibration-damped boring bar, comprising a boring head, a boring bar body main system, a main vibration damper of a first additional system, and a boring bar tail end cover, and wherein: The optimized object three-order vibration-damping boring bar also includes a secondary vibration damper of a second additional system; a three-order vibration-damping boring bar optimization method includes the following steps: Step 1, the boring bar body of the main system and the main shock absorber of the first additional system form an undamped second-order system; establish an origin frequency response function of the undamped second-order system, and obtain a series of response displacements of the corresponding boring bar body main system based on the origin frequency response function of the undamped second-order system according to the added mass of the first additional system and the input signal frequency. The response displacement of the boring bar body main system corresponds to the modulus of the origin frequency response function of the undamped second-order system; Step 2, according to different additional masses and different input signal frequencies of the first additional system, the series response displacements of the corresponding boring bar body main system are obtained based on the origin frequency response function of the undamped second-order system, and the series modulus of the origin frequency response function of the undamped second-order system is obtained accordingly; Step 3: Take the average of the series modes of the origin frequency response function in step 2 under different additional masses, and the mode with the minimum average corresponds to the first additional system mass m 2t As the first additional system mass m 2t The optimization results of Step 4: Based on the first additional system mass m obtained in step 3 2t and the density and length of the first additional system, and obtaining the damping coefficient c2 of the first additional system based on the damping coefficient model of the first additional system; Step 5: Based on the first additional system mass m in step 3 2t With the damping coefficient c2 of the first additional system obtained in step 4, a group of dynamic equations of the third-order vibration-damping boring bar is established, wherein the mass m3 of the second additional system is the optimization target, and the stiffness k3 of the second additional system and the damping c3 of the second additional system are known quantities; Step 6: Based on the dynamic equation group of the third-order vibration-damping boring bar established in step 5, the dynamic equation group of the third-order vibration-damping boring bar is solved to obtain the displacement response of the third-order vibration-damping boring bar under a unit stabilizing force; Step 7, adjust the mass m3 of the second additional system, repeat steps 5 and 6, and obtain the response of the system within a predetermined time under different masses m3 of the second additional system, that is, obtain the main system displacement response of the third-order vibration-damping boring bar under different masses of the second additional system per unit stabilizing force; Step 8: Based on Step 5, Step 6, and Step 7, the displacement response u of the third-order vibration-damping boring bar within a predetermined time under different second additional system masses m3 is obtained. xia The average value of Step 9: The displacement response u of the third-order vibration-damping boring bar obtained in step 8 within a predetermined time xia The average value of obtains the minimum value, and the second additional system mass m3 corresponding to the minimum value is the mass optimization result of the second additional system.

2. A method for optimizing a third-order vibration-damping boring bar according to claim 1, characterized in that: The method further comprises step 10, according to which the first additional system mass m obtained in step 3 is 2t The optimization result of and the optimization result of the second additional system mass m3 obtained in step 9 are used to counterweight the third-order vibration-damping boring bar. The third-order vibration-damping boring bar after active counterweighting can suppress the vibration caused by insufficient stiffness of the boring bar when processing the workpiece, thereby suppressing the generation of vibration marks on the machined surface and reducing the surface roughness of the workpiece.

3. A method for optimizing a third-order vibration-damping boring bar according to claim 1 or 2, characterized in that: In step 1, The model of the origin frequency response function of the undamped second-order system is shown in formula (1): In formula (1), |H 11 | represents the modulus of the frequency response function of the origin of the system, that is, the response displacement amplitude of the main system of the boring bar body; k1, k2 are the equivalent stiffness of the main system of the boring bar body and the first additional system, m1, m2 are the masses of the main system of the boring bar body and the first additional system, ω is the frequency of the input signal of the system; introduce Variable, simplify the modular formula of the origin frequency response function of the undamped second-order system.

4. A method for optimizing a third-order vibration-damping boring bar as claimed in claim 3, characterized in that: In step 4, The damping coefficient c2 model of the first additional system is shown in formula (2): c2=4lru (2) In formula (2), l is the actual length of the first additional system, r is the density of the damping fluid used, and u is the kinematic viscosity of the damping fluid.

5. A method for optimizing a third-order vibration-damping boring bar as claimed in claim 4, characterized in that: In step 5, The dynamic equations of the third-order vibration-damped boring bar are shown in formula (3): Among them, m3 is the mass of the second additional system, k3 is the stiffness of the second additional system, c3 is the damping of the second additional system, x1, x2, x3 represent the displacements of the main system, the first additional system, and the second additional system respectively. Represent the first and second order derivatives of displacement, namely velocity and acceleration respectively; Denoted as M, Denoted as K, Denoted as C.

6. A method for optimizing a third-order vibration-damping boring bar according to claim 5, characterized in that: The dynamic equations for solving the third-order vibration-damped boring bar include the linear acceleration method, the Runge-Kutta method, and the Wilson-θ method.

7. A method for optimizing a third-order vibration-damping boring bar according to claim 6, characterized in that: The dynamic equations of the third-order vibration-damped boring bar are solved by the linear acceleration method.

8. A method for optimizing a third-order vibration-damping boring bar according to claim 7, characterized in that: The specific implementation method of step 6 is: Step 6.1, determine the initial conditions of the dynamic equations (3) of the third-order damping boring bar, that is, determine the initial displacement conditions u of the dynamic equations (3) ini With the initial velocity condition v ini ; Step 6.2: Calculate the initial acceleration condition according to formula (4): a ini =M -1 ×(f-C×v ini -K×u ini ) (4) Where, f is the time-varying function of the external force of the main system of the boring bar body, that is, the unit stabilizing force; Step 6.3: Calculate the displacement response of the boring bar main system, the first additional system, and the second additional system at the next moment according to formula (5): Where Δt is the time step, and a2 and a1 are functions of known quantities: Step 6.4: Based on the calculation result of the displacement response of the second additional system in step 6.3, obtain the velocity v at the next moment xia and the acceleration a at the next moment xia : According to equations (5), (6), and (7), the initial condition u of the third-order vibration-damping boring bar is: ini ,v ini The response of the next time interval under the condition; Step 6.5: Solve u obtained in step 6.4 xia ,v xia ,a xia As the new initial condition, solve the displacement response of the third-order vibration-damped boring bar in the next time interval; Step 6.6, repeat steps 6.2 to 6.5 until the response of the third-order vibration-damped boring bar within a predetermined time is solved, and the displacement response of the third-order vibration-damped boring bar under a unit stabilizing force is obtained.

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