CN110549155B - Method for weakening vibration of machine tool and machine tool structure - Google Patents
Method for weakening vibration of machine tool and machine tool structure Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q1/00—Members which are comprised in the general build-up of a form of machine, particularly relatively large fixed members
- B23Q1/01—Frames, beds, pillars or like members; Arrangement of ways
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- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q11/00—Accessories fitted to machine tools for keeping tools or parts of the machine in good working condition or for cooling work; Safety devices specially combined with or arranged in, or specially adapted for use in connection with, machine tools
- B23Q11/0032—Arrangements for preventing or isolating vibrations in parts of the machine
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Abstract
The invention discloses a machine tool structure for weakening flutter of a machine tool. The first marble layer, the second marble layer and the third marble layer are all made of artificial marble materials. The first elastic layer and the second elastic layer are made of viscoelastic damping materials. According to the method, the mode and the thickness of the viscoelastic material implanted in the machine tool body are obtained through analysis and calculation, so that the adverse effect caused by the chattering of the machine tool body is weakened to the maximum extent.
Description
Technical Field
The invention relates to a method for weakening vibration of a machine tool and a machine tool structure, belonging to the technical field of machine tool vibration and control.
Background
In a numerical control machine tool, the bed body is generally made of cast iron with certain strength and rigidity. Such structural members are relatively weak in absorbing chatter vibrations in actual processing and are highly susceptible to thermal expansion and contraction due to environmental influences. Under the condition that the current international steel price is unstable, machine tool factories are particularly laboured in purchasing the bed body made of cast iron materials.
Along with the improvement of the requirement of people on the machining precision of machine tools, the artificial marble is more and more widely used as a lathe bed material, and the material is prepared by adding auxiliary materials such as epoxy resin and the like into granular granite. Therefore, the shape of the machine tool can be designed at will, and embedded parts such as screw holes, line rail matrixes and the like can be embedded in the machine tool. However, the bed of marble material has a limited ability to absorb vibrations, and a very weak chatter vibration may have serious consequences in high-speed and high-precision machining applications.
Disclosure of Invention
The purpose is as follows: in order to overcome the defects in the prior art, the invention provides a method for weakening the flutter of a machine tool and a machine tool structure.
The technical scheme is as follows: in order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a machine tool structure for attenuating chatter vibrations of a machine tool, comprising: the lathe bed is provided with a first marble layer, a first elastic layer, a second marble layer, a second elastic layer and a third marble layer from top to bottom in sequence.
As the preferred scheme, the bottom of the lathe bed is provided with a support leg, and the top of the lathe bed is provided with a track.
Preferably, the first marble layer, the second marble layer and the third marble layer are all made of artificial marble.
Preferably, the first elastic layer and the second elastic layer both adopt viscoelastic damping materials.
Preferably, the first marble layer and the third marble layer have the same height, d is the height, and the first elastic layer and the second elastic layer have the same height, h is the height.
Preferably, d/h is 0.05 ρ1/ρ2Where ρ is1Is the density, rho, of the artificial marble2Is the density of the viscoelastic damping material.
A method of attenuating machine tool chatter, comprising: the method comprises the following steps:
step 1: setting parameters of a machine tool body, wherein the length is a, the width is b, the thicknesses of two elastic layers are h, the thicknesses of an upper layer and a lower layer of the artificial marble machine body are d, and the thickness of a middle layer is p;
step 2: optimally designing a strain energy loss factor of the machine tool body by adopting a genetic algorithm according to the thicknesses d of the upper layer and the lower layer of the artificial marble machine body and the thicknesses h of the two elastic layers as design variables;
and step 3: each design variable adopts binary coding, the size of the defined population is M, and the probability P of crossCThe probability of mutation is PmThe number of immigration is n, the guarantee rate PeB '/M, wherein b' is the number of the most elegant individuals in the parent retained by the improved genetic algorithm, and a termination strategy for fixing evolution algebra is adopted, and the evolution algebra is taken for N times;
in the formula, Pc1、Pc2The upper limit and the lower limit of the cross probability;
Pm1、Pm2the upper limit and the lower limit of the variation probability;
and 4, step 4: solving an optimization problem by using a genetic algorithm, wherein in each evolution generation T, the probability of x mutation to y is more than or equal to P (T) through the primary action of a mutation operator on each individual and any y in a population, and T is the time for obtaining a global extreme point for the first time, if the genetic algorithm for solving the optimization problem meets the condition, and a formula is established for the genetic probability P (T):
the genetic algorithm visits a global extreme point with a probability equal to 1 after a limited number of evolutions, i.e. P { T < ∞ } -, 1; wherein P (t) is the genetic probability, x is the original individual, and y is the new individual;
and 5: when the constraint conditions are that λ max is 1, γ max is 7.85, and the variables d and h are minimum, the value of the loss factor ξ is maximum, and the solving model is as follows:
wherein ξiDenotes the ith individual loss factor, hiDenotes the thickness of the ith individual elastomeric layer, diDenotes the thickness of the ith individual upper layer, λiDenotes the ith Poisson's ratio, γiRepresents the ith loss factor, i represents the ith individual; xi is obtained to be 0.104;
step 6: weight W per unit area of damping material2And the weight W of marble per unit area1If the 1 bit after the decimal point of the loss factor is 0.1, then W2/W1Weight ratio equals 0.1 loss factor, giving d/h 0.05 ρ1/ρ2；
W2/W1＝0.1
W2＝0.1W1
W′2＝0.1W1/2＝0.05W1，W′2Represents the weight per unit area of an elastic layer;
W′2＝0.05*W1
0.05*V1*ρ1＝0.05*d*ρ1
V2*ρ2＝h*ρ2
d/h＝0.05ρ1/ρ2
wherein, V1Volume of artificial marble of unit area 1 and thickness d
ρ1Density of artificial marble
V2Volume per unit area of 1 and thickness h of a single sheet of viscoelastic damping material
ρ2-density of the single piece of viscoelastic damping material.
Has the advantages that: the method for weakening the vibration of the machine tool and the machine tool structure have the advantages that the maximum advantage is that through analyzing the transmission mode of the vibration of the machine tool body, the viscoelastic damping material is implanted into the artificial marble body, the quality of the implanted damping material depends on the density of the material of the machine tool body, and the loss factor of the strain energy of the implanted material is optimally designed through a genetic algorithm. The method and the thickness of the viscoelastic material implanted in the machine tool body are obtained through analysis and calculation, so that the adverse effect caused by the chattering of the machine tool body is weakened to the maximum extent.
Drawings
FIG. 1 is a schematic view of vibration energy transfer of a machine tool bed system;
FIG. 2 is a schematic structural view of a viscoelastic damping material implanted in a bed;
FIG. 3 is a graph of weight ratio versus loss factor.
Detailed Description
The present invention will be further described with reference to the accompanying drawings.
In order to implement the method, the vibration energy transmission process of the machine tool body is analyzed, as shown in fig. 1.
In the system of the machine tool body, vibration energy is transmitted along the direction of an arrow in fig. 1, the vibration energy is converted into heat and is transmitted out in a heating or sounding mode, so that the amplitude is gradually reduced, the energy received by the machine tool body 1 is mainly the upper surface and the support legs 2 of the machine tool body, and the machine tool body 1 is further provided with a track 3.
In order to reduce the influence of vibration on the machine tool body, a viscoelastic damping material can be implanted into the machine tool body, and the larger the loss factor of the material is, the stronger the vibration absorption capacity is. In view of the fact that the damping material is embedded inside the bed, artificial marble is used as the material of the bed of the machine tool.
The length of the machine tool body is a, the width is b, and two layers of viscoelastic damping materials are clampedThe thicknesses of the elastic layer 101 of the material are both h, the thicknesses of the upper layer 102 and the lower layer 103 of the artificial marble bed body are both d, and the thickness of the middle layer 104 is p, as shown in fig. 2. The lathe bed is divided into five layers, namely three marble material layers and two viscoelastic damping material layers. When vibration energy is transmitted, strain energy U generated by the upper and lower surface layers and the middle layer of the artificial marble1And strain energy U of two viscoelastic damping material layers2. The elastic modulus of the artificial marble is E1 ═ 55GPA, and the elastic modulus of the viscoelastic damping material is E2 ═ 7 MPA; density of the artificial marble is ρ1The density of the implanted viscoelastic damping material is rho2。
And optimally designing the strain energy loss factor of the machine tool body by adopting a genetic algorithm according to the thickness d of the upper layer and the lower layer of the artificial marble machine body and the thickness h of the two layers of the sandwiched viscoelastic damping materials as design variables. Each design variable adopts binary coding, the size of a defined population is M, and the probability P of intersection isCThe probability of mutation is PmThe number of immigrants is n, so the guarantee rate PeB '/M, where b' is the number of best shown individuals in the parents reserved for improved genetic algorithms. And adopting a termination strategy of fixed evolution algebra, wherein the evolution algebra is taken for N times.
In the formula, Pc1、Pc2The upper limit and the lower limit of the cross probability;
Pm1、Pm2the upper limit and the lower limit of the variation probability;
Solving an optimization problem by using a genetic algorithm, wherein in each evolution generation T, the probability of x mutation to y is more than or equal to P (T) through the primary action of a mutation operator on each individual and any y in a population, and T is the time for obtaining a global extreme point for the first time, if the genetic algorithm for solving the optimization problem meets the condition, and a formula is established for the genetic probability P (T):
the genetic algorithm visits a global extreme point, i.e., P { T < ∞ } ═ 1, with a probability equal to 1 after a limited number of evolutions.
P (t) is the genetic probability, x is the original individual, y is the new individual;
the solving problem is converted into the maximum loss factor xi value when the constraint conditions are that lambada max is 1, gamma max is 7.85, and the variables d and h are minimum, and the solving model of the genetic algorithm is as follows:
wherein ξiDenotes the ith individual loss factor, hiDenotes the thickness of the ith individual elastomeric layer, diDenotes the thickness of the ith individual upper layer, λiDenotes the ith Poisson's ratio, γiRepresenting the ith loss factor and i representing the ith individual.
The variable optimization design is carried out according to the model, and the variable optimization design is shown in the table 1:
the values of the optimized variables in Table 1 represent d, h, when minimum, the loss factor is maximum, and the units of d, h are mm, lambda,
ξ is dimensionless.
After genetic algorithm optimization design, as shown in table 2:
through the optimization design of a genetic algorithm, when d is 2.86mm, h is 19.7mm, the loss factor is maximum, and xi is 0.104.
Therefore, the loss factor can be increased to a certain extent by properly selecting relevant parameters of the artificial marble and the viscoelastic damping material after optimization, and the influence caused by the flutter of the machine tool can be weakened.
The machine tool is subjected to alternating internal and external loads during operation, and the excitation force causes the machine tool to vibrate forcibly. When the frequency of the exciting force is equal to the natural frequency of the machine tool, the machine tool generates resonance, which seriously affects the processing precision of the machine tool. In order to prevent the machine tool from generating resonance, the weight ratio per unit area of the implanted damping material and the artificial marble can be analyzed from an h.oberst relationship diagram, as shown in fig. 3.
Weight W per unit area of damping material2And the weight W of marble per unit area1The ratio can be obtained from the loss factor, according to the optimized design of table 2, the 1 position after the decimal point of the loss factor is taken as 0.1, and the weight ratio is equal to the loss factor of 0.1. Since the vibration is transmitted through the upper and lower surfaces, it may be possible to adopt a manner of implanting viscoelastic damping materials at a distance of 2.86mm from the upper and lower surfaces of the marble bed, respectively, as shown in fig. 2. The implanted viscoelastic damping material consists of two parts, so that the viscoelastic damping material W2The mass calculation method of (2) is as follows:
W2/W1＝0.1
W2＝0.1W1
single piece of viscoelastic damping material W'2The mass of the method is as follows:
W′2＝0.1W1/2＝0.05W1
taking the unit area of the single viscoelastic damping material layer as 1, the single viscoelastic damping material has the following characteristics:
W′2＝0.05*W1＝0.05*V1*ρ1＝0.05*d*ρ1
＝V2*ρ2＝h*ρ2
therefore, d/h is 0.05 ρ1/ρ2
Here V1Volume of artificial marble of unit area 1 and thickness d
ρ1Density of artificial marble
d-thickness of Artificial Marble
V2Volume per unit area of 1 and thickness h of a single sheet of viscoelastic damping material
ρ2Density of a single sheet of viscoelastic damping material
h-thickness of single sheet of viscoelastic damping material
Example (b):
a method of attenuating machine tool chatter, comprising the steps of:
And 2, implanting the viscoelastic damping material into the machine tool, wherein the artificial marble can be used as the machine tool body of the machine tool, and thus the linear rail, the threaded hole and the like can be conveniently pre-embedded.
And 3, determining the thickness of the implanted viscoelastic damping material according to the size of the machine tool, selecting the Poisson ratio and the elastic modulus ratio of the artificial marble bed and the viscoelastic damping material according to a genetic algorithm, and further determining the maximization of the loss factor. Through a relationship diagram of the weight ratio and the loss factor, as shown in fig. 3, the specific calculation is that h/d is 0.05 rho1/ρ2The thickness of the implanted viscoelastic damping material is determined.
Step 4, assuming that the density of the artificial marble is 2.4kg/m3The density of the implanted viscoelastic damping material is 1.2kg/m3The bed of the artificial marble has a length of 1.5 m, a width of 1 m and a height d of 1 mThe length of the implanted viscoelastic damping material is also 1.5 meters and the width is 1 meter.
h/d＝0.05ρ1/ρ2
h/1＝0.05*2.4/1.2
h is 0.1 m
And 5, obtaining a schematic diagram of the machine tool body according to the calculation result.
The machine tool designed by the method uses the marble bed, effectively solves the problem of thermal elongation and weakens the vibration of the machine tool, and further improves the machining precision of the machine tool.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (4)
1. A machine tool structure for attenuating chatter vibrations of a machine tool, comprising: lathe bed, its characterized in that: the lathe bed is sequentially provided with a first marble layer, a first elastic layer, a second marble layer, a second elastic layer and a third marble layer from top to bottom; the areas of the first marble layer, the first elastic layer, the second marble layer, the second elastic layer and the third marble layer are the same; the first elastic layer and the second elastic layer are both made of viscoelastic damping materials; the first marble layer and the third marble layer are the same in thickness, the thickness is set to be d, the first elastic layer and the second elastic layer are the same in thickness, and the thickness is set to be h; d/h is 0.05 rho1/ρ2Where ρ is1Is the density of the marble layer, ρ2The density of the individual elastic layers;
the method for weakening the flutter of the machine tool by the structure of the machine tool comprises the following steps:
step 1: setting parameters of a machine tool body, wherein the length is a, the width is b, the thicknesses of the first elastic layer and the second elastic layer are both h, the thicknesses of the first marble layer and the third marble layer of the artificial marble machine body are both d, and the second marble layer is p;
step 2: optimally designing a strain energy loss factor of the machine tool body by adopting a genetic algorithm according to the thickness d of the first marble layer and the third marble layer of the artificial marble machine body and the thickness h of the two elastic layers as design variables;
and step 3: each design variable adopts binary coding, the size of the defined population is M, and the probability P of crossCThe probability of mutation is PmThe number of immigration is n, the guarantee rate PeB '/M, wherein b' is the number of the most elegant individuals in the parent retained by the improved genetic algorithm, and a termination strategy for fixing evolution algebra is adopted, and the evolution algebra is taken for N times;
in the formula, Pc1、Pc2The upper limit and the lower limit of the cross probability;
Pm1、Pm2the upper limit and the lower limit of the variation probability;
and 4, step 4: solving an optimization problem by using a genetic algorithm, wherein in each evolution generation T, the probability of x mutation to y is more than or equal to P (T) through the primary action of a mutation operator on each individual and any y in a population, and T is the time for obtaining a global extreme point for the first time, if the genetic algorithm for solving the optimization problem meets the condition, and a formula is established for the genetic probability P (T):
the genetic algorithm visits a global extreme point with a probability equal to 1 after a limited number of evolutions, i.e. P { T < ∞ } -, 1; wherein P (t) is a genetic probability,x is the original individual and y is the new individual;
and 5: when the constraint conditions are that λ max is 1, γ max is 7.85, and the variables d and h are minimum, the value of the loss factor ξ is maximum, and the solving model is as follows:
wherein ξiDenotes the ith individual loss factor, hiDenotes the thickness of the ith individual elastomeric layer, diDenotes the thickness of the ith individual upper layer, λiDenotes the ith Poisson's ratio, γiRepresents the ith loss factor, i represents the ith individual; xi is obtained to be 0.104;
step 6: weight W per unit area of the first elastic layer and the second elastic layer2And the weight W of the marble layer per unit area1If the 1 bit after the decimal point of the loss factor is 0.1, then W2/W1Weight ratio equals 0.1 loss factor, giving d/h 0.05 ρ1/ρ2；
W2/W1＝0.1
W2＝0.1W1
W′2＝0.1W1/2＝0.05W1，W′2Represents the weight per unit area of an elastic layer;
W′2＝0.05*W1
0.05*V1*ρ1＝0.05*d*ρ1
V2*ρ2＝h*ρ2
d/h＝0.05ρ1/ρ2
wherein, V1Volume of the first marble layer, the second marble layer, the third marble layer, per unit area of 1, and thickness d
ρ1Density of the Marble layer
V2Volume of individual elastic layers per unit area of 1 and thickness h
ρ2-density of the individual elastic layers.
2. The structure of a machine tool for attenuating chattering vibration of a machine tool according to claim 1, wherein: the bottom of the lathe bed is provided with support legs, and the top of the lathe bed is provided with a track.
3. The structure of a machine tool for attenuating chattering vibration of a machine tool according to claim 1, wherein: the first marble layer, the second marble layer and the third marble layer are all made of artificial marble materials.
4. A method of attenuating machine tool chatter, comprising: the marble pressing machine comprises a machine body, wherein the machine body is sequentially provided with a first marble layer, a first elastic layer, a second marble layer, a second elastic layer and a third marble layer from top to bottom; the areas of the first marble layer, the first elastic layer, the second marble layer, the second elastic layer and the third marble layer are the same;
the method comprises the following steps:
step 1: setting parameters of a machine tool body, wherein the length is a, the width is b, the thicknesses of the first elastic layer and the second elastic layer are both h, the thicknesses of the first marble layer and the third marble layer of the artificial marble machine body are both d, and the second marble layer is p;
step 2: optimally designing a strain energy loss factor of the machine tool body by adopting a genetic algorithm according to the thickness d of the first marble layer and the third marble layer of the artificial marble machine body and the thickness h of the two elastic layers as design variables;
and step 3: each design variable adopts binary coding, the size of the defined population is M, and the probability P of crossCThe probability of mutation is PmThe number of immigration is n, the guarantee rate PeB '/M, wherein b' is the number of the most elegant individuals in the parent retained by the improved genetic algorithm, and a termination strategy for fixing evolution algebra is adopted, and the evolution algebra is taken for N times;
in the formula, Pc1、Pc2The upper limit and the lower limit of the cross probability;
Pm1、Pm2the upper limit and the lower limit of the variation probability;
and 4, step 4: solving an optimization problem by using a genetic algorithm, wherein in each evolution generation T, the probability of x mutation to y is more than or equal to P (T) through the primary action of a mutation operator on each individual and any y in a population, and T is the time for obtaining a global extreme point for the first time, if the genetic algorithm for solving the optimization problem meets the condition, and a formula is established for the genetic probability P (T):
the genetic algorithm visits a global extreme point with a probability equal to 1 after a limited number of evolutions, i.e. P { T < ∞ } -, 1; wherein P (t) is the genetic probability, x is the original individual, and y is the new individual;
and 5: when the constraint conditions are that λ max is 1, γ max is 7.85, and the variables d and h are minimum, the value of the loss factor ξ is maximum, and the solving model is as follows:
wherein ξiDenotes the ith individual loss factor, hiDenotes the thickness of the ith individual elastomeric layer, diDenotes the thickness of the ith individual upper layer, λiDenotes the ith Poisson's ratio, γiRepresents the ith loss factor, i represents the ith individual; xi is obtained to be 0.104;
step 6: weight W per unit area of the first elastic layer and the second elastic layer2And the weight W of the marble layer per unit area1If the 1 bit after the decimal point of the loss factor is 0.1, then W2/W1Weight ratio equals 0.1 loss factor, giving d/h 0.05 ρ1/ρ2；
W2/W1＝0.1
W2＝0.1W1
W′2＝0.1W1/2＝0.05W1，W′2Represents the weight per unit area of an elastic layer;
W′2＝0.05*W1
0.05*V1*ρ1＝0.05*d*ρ1
V2*ρ2＝h*ρ2
d/h＝0.05ρ1/ρ2
wherein, V1Volume of the first marble layer, the second marble layer, the third marble layer, per unit area of 1, and thickness d
ρ1Density of the Marble layer
V2Volume of individual elastic layers per unit area of 1 and thickness h
ρ2-density of the individual elastic layers.
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| US4566427A (en) * | 1982-12-15 | 1986-01-28 | Rocamat | Device for cutting blocks of granite, marble, stone and the like materials |
| CN202527935U (en) * | 2012-01-11 | 2012-11-14 | 昆山允升吉光电科技有限公司 | High-stability table |
| CN105386472A (en) * | 2015-12-10 | 2016-03-09 | 青岛理工大学 | Embedded composite damping structure and construction method thereof |
| CN206192499U (en) * | 2016-11-24 | 2017-05-24 | 河海大学 | Waterproof blasting vibration monitoring instrument guard box that shocks resistance |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US4566427A (en) * | 1982-12-15 | 1986-01-28 | Rocamat | Device for cutting blocks of granite, marble, stone and the like materials |
| CN202527935U (en) * | 2012-01-11 | 2012-11-14 | 昆山允升吉光电科技有限公司 | High-stability table |
| CN105386472A (en) * | 2015-12-10 | 2016-03-09 | 青岛理工大学 | Embedded composite damping structure and construction method thereof |
| CN206192499U (en) * | 2016-11-24 | 2017-05-24 | 河海大学 | Waterproof blasting vibration monitoring instrument guard box that shocks resistance |
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