A method for optimizing a three-stage damping boring bar

Abstract

The application discloses a three-order damping reduction boring bar optimization method and belongs to the field of machining.The application is realized by the following method: a series of response displacements of a corresponding boring bar body main system are obtained based on the origin frequency response function of a non-damping second-order system, and the minimum average of the system response displacement is used to obtain the first additional system mass as the optimization result of the first additional system mass; the first additional system damping coefficient is obtained based on the first additional system damping coefficient model according to the first additional system mass, density and length; the dynamic equation set of the three-order damping reduction boring bar is solved to obtain the displacement response of the three-order damping reduction boring bar under a unit stable force; the average of the main system displacement response is obtained based on the displacement response of the three-order damping reduction boring bar under different second additional system masses; the minimum value of the average of the main system displacement response is obtained, and the second additional mass corresponding to the minimum value is used as the optimization result of the second additional system mass, so that the mass distribution of the three-order damping reduction boring bar is realized.

Description

Technical Field

[0001] This invention relates to a third-order vibration-damping boring bar optimization method, belonging to the field of machining. Background Technology

[0002] In metal cutting, the machining of hole features is particularly important, especially in the current stage of rapid development of equipment technology in my country, where the demand for machining deep and large holes is increasing. However, chatter is a problem in the large overhang boring process of deep and large holes. Chatter can cause severe wear of the machining tools and deterioration of the machining surface quality. Therefore, controlling vibration during the machining of deep and large holes is of utmost importance.

[0003] Currently, the most common way to reduce chatter in industrial production is to use boring bars with damping dampers. Because these boring bars have pre-adjusted carbide mass blocks inside, the damper can be regarded as an additional system of the boring bar. Thus, it interacts with the main system (tool bar body) during the cutting process to reduce the cutting amplitude and improve the machining quality of the machined surface.

[0004] Currently, most commercially available vibration-damping boring bars are second-order systems, meaning the entire system consists of a tool holder and a vibration damper. The structure and manufacturing process of these bars are mature and widely used in various parts processing applications, offering significant economic benefits. However, the vibration resistance of second-order system vibration-damping boring bars remains limited. Their damping effect is restricted when the boring bar overhang exceeds seven times its diameter, and the damping effect is significantly reduced for small-diameter (below 40mm) deep holes. Therefore, further analysis and design are needed based on traditional second-order system vibration-damping boring bars to address these current challenges.

[0005] Based on the above discussion, the third-order damping boring bar is an option. Its overall structure consists of a boring bar body (main system) and two dampers of unequal mass (auxiliary system). It is worth noting that if the mass distribution of the auxiliary system is not reasonable during the design process of the third-order damping boring bar, it may lead to a deterioration in the damping effect and the two dampers being unable to work together. Therefore, a systematic calculation method is needed to actively design the third-order damping boring bar system. Summary of the Invention

[0006] The purpose of this invention is to provide an optimization method for a third-order vibration-damping boring bar. The method uses the mass of the first additional system corresponding to the minimum mean value of the modulus of the undamped second-order system as the optimization result of the mass of the first additional system. By solving the dynamic equations of the third-order vibration-damping boring bar and obtaining the minimum average value of the displacement response of the third-order vibration-damping boring bar within a predetermined time as the optimization result of the mass of the second additional system, the active optimization of the third-order vibration-damping boring bar is achieved, improving the machining quality of the machined parts and reducing surface roughness.

[0007] The objective of this invention is achieved through the following technical solutions.

[0008] This invention discloses a method for optimizing a third-order vibration-damping boring bar. Based on the origin frequency response function of an undamped second-order system, a series of response displacements of the main system of the boring bar are obtained. The mass of the first additional system corresponding to the minimum mean of the system response displacement is used as the optimization result of the mass of the first additional system. The damping coefficient of the first additional system is obtained based on its mass, density, and length, using a damping coefficient model. The dynamic equations of the third-order vibration-damping boring bar are solved to obtain its displacement response under a unit stable force. The mean of the main system displacement response is obtained based on the displacement response of the third-order vibration-damping boring bar under different second additional system masses. The minimum value of the mean of the main system displacement response is obtained, and the second additional mass corresponding to the minimum mean is used as the optimization result of the mass of the second additional system, thus achieving mass distribution of the third-order vibration-damping boring bar.

[0009] This invention discloses a method for optimizing a third-order vibration-damping boring bar. The optimization object is a third-order vibration-damping boring bar, including a boring head, a main system of the boring bar body, a main vibration damper of a first auxiliary system, and a boring bar tail end cap, and also includes a secondary vibration damper of a second auxiliary system. The method for optimizing a third-order vibration-damping boring bar disclosed in this invention includes the following steps:

[0010] Step 1: The boring bar of the main system and the main damper of the first auxiliary system constitute an undamped second-order system. Establish the origin frequency response function of the undamped second-order system. Based on the added mass of the first auxiliary system and the input signal frequency, obtain the series of response displacements of the corresponding boring bar main system based on the origin frequency response function of the undamped second-order system. The response displacements of the boring bar main system correspond to the modulus of the origin frequency response function of the undamped second-order system.

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

[0012]

[0013] In equation (1), |H 11 | represents the magnitude of the frequency response function at the system origin, which is also the response displacement amplitude of the main boring bar system; k1 and k2 are the equivalent stiffnesses of the main boring bar system and the first auxiliary system, respectively; m1 and m2 are the masses of the main boring bar system and the first auxiliary system, respectively; ω is the frequency of the system input signal; introducing The variable simplifies the modulus formula of the origin frequency response function of an undamped second-order system.

[0014] Step 2: Based on the different additional masses and different input signal frequencies of the first additional system, obtain the series of response displacements of the corresponding boring bar main system based on the origin frequency response function of the undamped second-order system, and obtain the series of moduli of the origin frequency response function of the undamped second-order system.

[0015] Step 3: Take the average of the series of moduli of the origin frequency response function in Step 2 under different added masses. The modulus with the smallest average corresponds to the first added system mass m. 2t As the first additional system mass m 2t The optimization results.

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

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

[0018] c2=4lru (2)

[0019] In equation (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 Using the damping coefficient c2 of the first additional system obtained in step 4, establish a set of dynamic equations for the third-order damping boring bar, where the mass m3 of the second additional system is the optimization objective, and the stiffness k3 and damping c3 of the second additional system are known quantities.

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

[0022]

[0023] Where 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, and x1, x2, and x3 represent the displacements of the main system, the first additional system, and the second additional system, respectively. These represent the first and second derivatives of displacement, i.e., velocity and acceleration, respectively; Noted as M, Let it be K. It is denoted as C.

[0024] Step 6: Based on the dynamic equations of the third-order damping boring bar established in Step 5, solve the dynamic equations of the third-order damping boring bar to obtain the displacement response of the third-order damping boring bar under a unit stable force.

[0025] Solving the dynamic equations of a third-order damping boring bar includes the linear acceleration method, the Runge-Kutta method, and the Wilson-θ method. As the preferred method, the linear acceleration method is used to solve the dynamic equations of the third-order damping boring bar.

[0026] The specific implementation method for step 6 is as follows:

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

[0028] Step 6.2: Calculate the initial acceleration conditions according to equation (4):

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

[0030] In the formula, f is a time-varying function of the external force applied to the main system of the boring bar, that is, the unit steady force.

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

[0032]

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

[0034]

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

[0036]

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

[0038] Step 6.5: Solve for u in step 6.4 xia ,v xia ,a xia As a new initial condition, solve for the third-order vibration-damping boring bar displacement response in the next time interval.

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

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

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

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

[0043] It also includes step 10, based on the first additional system mass m obtained in step 3. 2t The optimization results and the optimization results 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 counterweight can suppress the vibration caused by insufficient boring bar stiffness when machining 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. This invention discloses a method for optimizing a third-order vibration-damping boring bar. Based on the origin frequency response function of an undamped second-order system, a series of response displacements of the corresponding main system of the boring bar are obtained. The mass of the first additional system corresponding to the minimum mean of the system response displacement is used as the optimization result of the mass of the first additional system. Based on the mass, density, and length of the first additional system, the damping coefficient of the first additional system is obtained using a damping coefficient model. The mass distribution of the third-order vibration-damping 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-damping boring bar. By actively suppressing the generation of vibration marks on the machined surface, the surface roughness of the workpiece is reduced.

[0046] 2. The present invention discloses a third-order vibration-damping boring bar optimization method, which obtains the displacement response of the third-order vibration-damping boring bar under a unit stable force by solving the dynamic equations of the third-order vibration-damping boring bar. Compared with the traditional frequency response function method, it is closer to the stress situation of the boring bar in the actual boring process, reduces the vibration of the boring bar when machining the target, and thus improves the workpiece machining quality. Attached Figure Description

[0047] Figure 1 This is a flowchart of a third-order vibration-damping boring bar optimization method disclosed in this invention.

[0048] Figure 2 The graph shows the calculated origin frequency response function of an undamped second-order system under different input frequencies and added masses.

[0049] Figure 3 This is a comparison of the mean values ​​of the magnitudes of the frequency response function at the origin of an undamped second-order system.

[0050] Figure 4 The graph shows the partial displacement response curve within 200s when the added mass m3 = 0.001kg is given by the linear acceleration algorithm.

[0051] Figure 5 This is a design drawing for a third-order vibration damping boring bar. Detailed Implementation

[0052] To better illustrate the purpose and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and examples.

[0053] Example 1:

[0054] The method of this 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 to obtain the optimized mass of the additional systems.

[0055] like Figure 1 As shown in the flowchart, this invention discloses a third-order vibration damping boring bar optimization method, and its specific implementation process is as follows:

[0056] Step 1: The boring bar of the main system and the main damper of the first auxiliary system constitute an undamped second-order system. Establish the origin frequency response function of the undamped second-order system. Based on the added mass of the first auxiliary system and the input signal frequency, obtain the series of response displacements of the corresponding boring bar main system based on the origin frequency response function of the undamped second-order system. The response displacements of the boring bar main system correspond to the modulus of the origin frequency response function of the undamped second-order system.

[0057] like Figure 2 The figure shows the calculated origin frequency response function of an undamped second-order system under different input frequencies and different added masses.

[0058] Step 2: Based on the different additional masses and different input signal frequencies of the first additional system, obtain the series of response displacements of the corresponding boring bar main system based on the origin frequency response function of the undamped second-order system, and obtain the series of moduli of the origin frequency response function of the undamped second-order system.

[0059] Step 3: Take the average of the series of moduli of the origin frequency response function in Step 2 under different added masses. The modulus with the smallest average corresponds to the first added system mass m. 2t As the first additional system mass m 2t The optimization results.

[0060] Given that the main system mass is 3 kg, the mean value of the magnitude of the frequency response function at the origin of the undamped second-order system is as follows: Figure 3 As shown in the figure, the system m 2t =0.08kg.

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

[0062] Based on m 2t =0.08kg, cemented carbide density is approximately 13×10⁻⁸. 3 kg / m 3 Furthermore, the hollow diameter of the third-order vibration damping tool bar is 14mm, so l = 93mm can be determined in equation (2). In the design, 46# anti-wear hydraulic oil is used as the damping fluid, and its density is approximately 0.9′10. 3 kg / m 3 The kinematic viscosity is approximately 45.6 mm. 2 / s, and after calculation, c2 = 0.015.

[0063] Step 5: Based on the first additional system mass m in Step 3 2t Using the damping coefficient c2 of the first additional system obtained in step 4, establish a set of dynamic equations for the third-order damping boring bar, where the mass m3 of the second additional system is the optimization objective, and the stiffness k3 and damping c3 of the second additional system are known quantities.

[0064] Based on literature review and actual testing, the steel boring bar body k1 = 1.3′10 6 N / m, with the two additional systems using identical designs, k2=k3=1.1′10 5 Since the damping fluid is no longer injected into the second additional system, c3 can be taken as 0. Therefore, the established third-order dynamic equations of the damping boring bar can be written as follows:

[0065]

[0066] Step 6: Based on the dynamic equations of the third-order damping boring bar established in Step 5, solve the dynamic equations of the third-order damping boring bar to obtain the displacement response of the third-order damping boring bar under a unit stable force.

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

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

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

[0070] Step 9: Calculate the displacement response u of the third-order vibration-damping boring bar obtained in Step 8 within a predetermined time. xia The average value reaches its minimum value, and the mass m3 of the second additional system 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 As shown.

[0072] Step 10: Based on the first additional system mass m obtained in Step 3... 2t The optimization results and the optimization results 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 counterweight can suppress the vibration caused by insufficient boring bar stiffness when machining the workpiece, thereby suppressing the generation of vibration marks on the machined surface and reducing the surface roughness of the workpiece.

[0073] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description 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 within the scope of protection of the present invention.

Claims

1. A third-order vibration reduction boring bar optimization method, optimizing a third-order vibration reduction boring bar, comprising a boring head, a boring bar body main system, a main damper of a first additional system, and a boring tail end cover, characterized in that: The optimization object three-stage damping boring bar further comprises a secondary damper of a second additional system; a three-stage damping boring bar optimization method comprises the following steps, Step 1, the boring bar body of the main system and the primary damper of the first additional system form a two-stage undamped system; an origin frequency response function of the two-stage undamped system is established; a series of response displacements of the boring bar body of the main system are obtained based on the origin frequency response function of the two-stage undamped system according to the additional mass of the first additional system and the input signal frequency; and the response displacement of the boring bar body of the main system corresponds to the modulus of the origin frequency response function of the two-stage undamped system; Step 2, a series of response displacements of the boring bar body of the main system are obtained based on the origin frequency response function of the two-stage undamped system according to different additional masses of the first additional system and different input signal frequencies; and a series of moduli of the origin frequency response function of the two-stage undamped system are obtained accordingly; Step 3, take the mean of the modulus of the series of modes of the origin frequency response function in step 2 under different additional masses, the modulus of the minimum mean corresponds to the first additional system mass m 2t As the optimization result of the first additional system mass m 2t ; Step 4, obtaining the first additional system mass m 2t and the density and length of the first additional system, obtaining the first additional system damping coefficient c2 based on the first additional system damping coefficient model. Step 5, based on the first additional system mass m 2t With the first additional system damping coefficient c2 obtained in step 4, the dynamic equation set of the third-order damping boring bar is established, wherein the second additional system mass m3 is the optimization target, and the second additional system stiffness k3 and the second additional system damping c3 are known quantities; Step 6, based on the dynamic equation set of the three-stage damping boring bar established in step 5, the dynamic equation set of the three-stage damping boring bar is solved to obtain the displacement response of the three-stage damping boring bar under the unit stable action force; Step 7, the mass m3 of the second additional system is adjusted, and steps 5 and 6 are repeated to obtain the response of the system within a predetermined time under different masses m3 of the second additional system, that is, the main system displacement response of the three-stage damping boring bar under the unit stable action force of the different second additional system mass is obtained; Step 8, based on step 5, step 6, step 7, the displacement response u of the third order vibration reduction boring bar in the predetermined time under different second additional system mass m3 is obtained xia the average value of Step 9: Calculate the displacement response u of the third-order vibration-damping boring bar obtained in Step 8 within a predetermined time. xia The average value reaches its minimum value, and the mass m3 of the second additional system corresponding to the minimum value is the mass optimization result of the second additional system.

2. The method of claim 1, wherein: Also included is a step 10 of determining a first additional system mass m 2t The optimization result of the third order damping boring bar is compared with the optimization result of the second additional system mass m3 obtained in step 9, and the third order damping boring bar is actively counterweighted. The workpiece processed by the actively counterweighted third order damping boring bar can inhibit the vibration caused by insufficient boring bar stiffness, thereby inhibiting the generation of vibration marks on the processed surface and reducing the roughness of the workpiece processed surface.

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

4. The method of claim 3, wherein: 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 liquid used, and u is the kinematic viscosity of the damping liquid.

5. The method of claim 4, wherein: In step 5, The dynamic equation set of the three-stage damping boring bar is shown in formula (3): wherein m3 is the second additional system mass, k3 is the second additional system stiffness, c3 is the second additional system damping, x1, x2, x3 represent the displacement of the main system, the first additional system, and the second additional system, respectively, represent the first and second order derivatives of displacement, i.e. velocity and acceleration, respectively; and denoted by M, denoted by K, denoted by C.

6. A method of optimizing a three-stage damping boring bar as claimed in claim 5, characterized in that: Solving the dynamic equation set of the three-stage damping boring bar includes linear acceleration method, Runge-Kutta method and Wilson-θ method.

7. The method of claim 6, wherein: the third order damping boring bar optimization method further comprises: determining a first order damping boring bar optimization method; determining a second order damping boring bar optimization method; and determining a third order damping boring bar optimization method. The dynamic equation set of the three-stage damping boring bar is solved by the linear acceleration method.

8. The third-order vibration-damping boring bar optimization method as described in 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 vibration-reducing boring bar, i.e. determine the displacement initial conditions u ini and the velocity initial conditions v ini ; Step 6.2, the acceleration initial condition is calculated according to formula (4): a ini = M -1 × (f - C × v ini - K × u ini ) (4) In the formula, f is a time-varying function of the external action force of the boring bar body of the main system, that is, a unit stable action force; Step 6.3, the displacement responses of the boring bar body of the main system, the first additional system and the second additional system at the next time are calculated according to formula (5): In the formula, Δt is the time step, and a2 and a1 are functions of known quantities: Step 6.

4. Based on the second additional system displacement response calculation result of step 6.3, the velocity v of the next time is obtained xia and the acceleration a of the next time xia : The response of a third order vibration damper bar under initial conditions u ini ini for the next time interval according to equations (5) (6) (7)​ Step 6.

5. Solve for u from step 6.4 xia xia xia Solve for the third order response of the damper shaft displacement for the next time interval as the new initial conditions.​​ Step 6.6, steps 6.2 to 6.5 are repeated until the solution of the response of the three-stage damping boring bar within a predetermined time is completed, and the displacement response of the three-stage damping boring bar under the unit stable action force is obtained.

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