CN106777773B - Diamond circular saw blade design and sawing process parameter making method - Google Patents
Diamond circular saw blade design and sawing process parameter making method Download PDFInfo
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Abstract
the invention relates to a method for designing a diamond circular saw blade and formulating sawing technological parameters, which is characterized in that firstly, a modal experiment is used for verifying the reliability of a modal simulation analysis method; selecting diamond circular saw blades of different models to perform constraint modal analysis by taking the diameter and the thickness of the diamond circular saw blades as independent variables to obtain the functional relation between the front 6-order resonance frequency of the diamond circular saw blades and the diameter and the thickness; determining the diameter, linear cutting speed and processing rotating speed of the diamond circular saw blade and the relation between each order of resonance frequency and the diameter and thickness of the diamond circular saw blade according to the size and hardness of the processed material, obtaining the relation between the excitation frequency generated during processing and the rotating speed and the number of teeth of the diamond circular saw blade, finally formulating the proper thickness and the number of teeth of the diamond circular saw blade under the condition that the resonance is avoided and the working rotating speed is less than the critical rotating speed, and establishing a constraint model of the design of the diamond circular saw blade and the sawing process parameters. The method has strong universality and is suitable for the design of various diamond circular saw blades and the optimization of saw cutting process parameters.
Description
Technical Field
The invention belongs to the technical field of engineering, and particularly relates to a method for designing a diamond circular saw blade and making sawing technological parameters.
background
diamond circular saw blades have been widely used in the processing of stone, glass, ceramics, crystals, gems and other materials and in the construction of buildings, roads, bridges and other projects. The diamond circular saw blade is of a circular thin plate structure, has low transverse rigidity and is easy to bend and deform. Modal analysis is the study of the natural vibration characteristics of a mechanical structure, with the modal frequencies of the various orders of the structure corresponding to their natural frequencies (i.e., resonant frequencies). According to the critical rotation speed theory, the working rotation speed of the circular saw blade must be far less than the critical rotation speed to ensure the stability of the rotation state of the circular saw blade, and the critical rotation speed refers to the rotation speed corresponding to the 3 rd order (0,2) order modal frequency of the diamond circular saw blade, wherein (m, n) refers to the mode with the pitch circle number of m and the pitch diameter number of n. And if the external excitation frequency is close to or equal to the natural frequency of each step of the circular saw blade, the circular saw blade can generate resonance, and the saw slot deflection, the saw blade abrasion, the surface processing quality reduction, the stone material cracking and even the damage of the diamond circular saw blade are caused. At present, the design of the circular saw blade and the formulation of the sawing process parameters are designed according to experience, and relevant theoretical researches are not converted into a basis and a guidance method which can be actually operated.
disclosure of Invention
the invention aims to provide a technical basis for the design and optimization of a circular saw blade structure and a method for making sawing process parameters, and provides a method for designing a diamond circular saw blade and making sawing process parameters.
in order to achieve the purpose, the invention adopts the technical scheme that: firstly, verifying the reliability of a modal simulation analysis method by using a modal experiment, carrying out the modal experiment by using a common diamond circular saw blade as a test piece, carrying out a constrained modal experiment on the test piece, and further analyzing modal experiment data to obtain the modal frequency of the test piece; carrying out three-dimensional solid modeling on the test piece by using three-dimensional modeling software, then importing the test piece into modal analysis software, adding corresponding material attributes, setting constraint conditions identical to those of a modal experiment, and then carrying out modal simulation analysis to obtain modal frequency of a simulation structure; performing error analysis on the results of the first 7-order modal frequency obtained by the modal experiment and the modal simulation, and verifying that the results of the modal experiment and the modal simulation are correct and reliable if the errors of the results of the two modal analysis are within 10%; the method comprises the following steps:
Step one, selecting different types of diamond circular saw blades to perform constraint modal analysis, taking the diameter D and the thickness H of the diamond circular saw blades as independent variables, and obtaining the functional relation between the first 6-order resonance frequency of the diamond circular saw blades and the diameter and the thickness of the diamond circular saw blades through data analysis:
Uniformly selecting N diamond circular saw blades with different specifications and thicknesses according to the national standard GB11270-1989 and the foreign standard ISO-6105-1988 of the diamond circular saw blade, establishing a model of the selected diamond circular saw blade by using three-dimensional modeling software, and respectively carrying out constrained mode simulation analysis to obtain the mode frequency of the N-type diamond circular saw blade;
Secondly, the first 6 orders of modal frequency, namely the first 6 orders of resonant frequency, is taken, and the function with the diameter D and the thickness H of the diamond circular saw blade as independent variables is used for fitting to obtain the function relation between each order of resonant frequency of the diamond circular saw blade and the diameter and the thickness of the diamond circular saw blade;
Step two, providing a constraint model of diamond circular saw blade design and sawing technological parameters:
i. Determining the diameter and linear cutting speed of the diamond circular saw blade according to the size and hardness of the processed material, and further obtaining the processing rotating speed of the diamond circular saw blade;
ii. Providing the functional relation among the excitation frequency, the rotating speed and the number of teeth of the diamond circular saw blade when the diamond circular saw blade works; obtaining the relation between the critical rotating speed frequency of the diamond circular saw blade and the thickness of the diamond circular saw blade;
iii, under the condition of avoiding resonance, combining the obtained relational expression, and providing a constraint model of the diamond circular saw blade and the sawing process parameters;
And iv, according to the constraint model, making the thickness, the tooth number and the processing rotating speed of the diamond circular saw blade.
The functional relationship between the first 6-order modal frequency of the diamond circular saw blade and the diameter and the thickness of the diamond circular saw blade in the first step of the invention is as follows:
Expression of 1 st order (1,0) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f1(D,H)＝－64.52+88.5×D－0.85+4.178×103×H
expression of 2 nd order (0,1) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f2(D,H)＝－60+84.91×D－0.85+4×103×H
expression of 3 rd order (0,2) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f3(D,H)＝－70.23+98.24×D－0.85+4.732×103×H
expression of 4 th order (0,3) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f4(D,H)＝－98.8+139.4×D－0.85+6.635×103×H
expression of 5 th order (0,4) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f5(D,H)＝－148.3+211.9×D－0.85+9.9×103×H
expression of 6 th order (0,5) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f6(D,H)＝－218.1+312.7×D－0.85+14.54×103×H
wherein: d is the diameter of the diamond circular saw blade, and H is the thickness of the diamond circular saw blade.
The diamond circular saw blade design and sawing technological parameter constraint model in the second step of the invention is as follows:
wherein: n is the processing speed of the diamond circular saw blade, n0Is the critical rotating speed of the diamond circular saw blade, m is the number of teeth of the diamond circular saw blade, v is the cutting linear velocity, f0The resonant frequency is f, the excitation frequency is D, the diameter of the diamond circular saw blade is D, and the thickness of the diamond circular saw blade is H.
the invention relates to a method for designing a diamond circular saw blade and making sawing process parameters, which firstly verifies the reliability of a modal simulation analysis method by using a modal experiment; carrying out a large number of modal analyses and data analyses on the diameters and thicknesses of different circular saw blades to obtain the functional relation between the modal frequency of the diamond circular saw blade and the diameters and thicknesses of the diamond circular saw blade; secondly, a relational expression of the excitation frequency, the diameter and the number of sawteeth of the diamond circular saw blade is provided, then a constraint model of the design of the diamond circular saw blade and the sawing process parameters is established by taking the condition that the resonance of the circular saw blade is avoided and the working rotating speed of the circular saw blade is less than the critical rotating speed as a constraint condition, a theoretical basis is provided for the design and optimization of the structure of the circular saw blade, and a technical guide is provided for the sawing process.
the method for designing the diamond circular saw blade and making the sawing technological parameters has the following advantages:
The method clarifies the essential characteristics of the first 6-order resonance frequency and the diameter and the thickness of the diamond circular saw blade, can directly, quickly and accurately calculate the first 6-order resonance frequency of the diamond circular saw blade, does not need to carry out field modal experiments and modal simulation analysis on the diamond circular saw blade, and is simple in analysis process and high in universality.
The method can optimize the structural size and the processing technological parameters of the diamond circular saw blade, avoid the diamond circular saw blade from resonance, reduce vibration and improve the sawing efficiency.
The method can provide a theoretical basis for the design and optimization of the diamond circular saw blade under the condition of given stone processing and size. The invention is suitable for the design of various diamond circular saw blades and the optimization of sawing process parameters.
Drawings
FIG. 1 is a schematic diagram of the principle of the modal experiment performed in the present invention.
Fig. 2 is a graph of an error analysis of a modal simulation analysis and a modal experiment analysis.
FIG. 3 is a graph of the 3 rd order (0,2) mode frequency of a diamond circular saw blade with different diameters and thicknesses.
In the above figures: 1-diamond circular saw blade; 2-a chuck; 3-a sensor; 4-a charge adjuster; 5-Signal test analysis System.
Detailed Description
The diamond circular saw blade design and the sawing process parameter setting method of the present invention will be described in further detail with reference to the accompanying drawings and examples, but the present invention is not limited thereto.
Example 1: the invention provides a method for designing a diamond circular saw blade and formulating sawing technological parameters, which firstly verifies the reliability of a modal simulation analysis method by using a modal experiment:
The method includes the steps that a common diamond circular saw blade 1 with the diameter phi of 400mm is used as a test piece, and constraint modal experimental analysis is carried out on the test piece, the test schematic diagram is shown in fig. 1, a chuck plate 2 with the diameter phi of 100mm is used for clamping and constraining, various sensors 3 for measurement are arranged on the diamond circular saw blade 1 and comprise force sensors and a plurality of acceleration sensors, signals received by the sensors are respectively conveyed to a signal testing and analyzing system 5 through a charge adjuster 4, experimental data are analyzed, and after an experiment is finished, various modal frequencies of the diamond circular saw blade 1 can be obtained.
and secondly, performing three-dimensional solid modeling on the diamond circular saw blade by using three-dimensional modeling software, then importing the three-dimensional solid modeling into ANSYS software, adding corresponding material attributes, performing grid division, then setting chuck constraint conditions, performing constraint modal simulation analysis, and obtaining modal frequencies of each order of the diamond circular saw blade 1.
thirdly, performing error analysis on the first 7-order modal frequency obtained by the obtained modal simulation analysis and modal experiment analysis respectively, and obtaining error results of the two analysis methods as shown in fig. 2.
As can be seen from fig. 2, the error percentage is substantially within 5%, which mutually proves the correctness and reliability of the two modal analysis methods.
at this time, the following steps are carried out:
Step one, carrying out constraint modal analysis on diamond circular saw blades of different models, and obtaining the functional relation between the first 6-order resonance frequency of the diamond circular saw blade and the diameter and the thickness of the diamond circular saw blade by taking the diameter and the thickness of the diamond circular saw blade as independent variables:
Firstly, according to the national standard GB11270-1989 and the foreign standard ISO-6105-1988 of the diamond circular saw blade, N diamond circular saw blades with different specifications and thicknesses are uniformly selected, in the embodiment, N is 37, namely, 37 diamond circular saw blades with different diameters and thicknesses are selected for analysis, the specific models are shown in Table 1, and the clamping diameter ratio (the ratio of the diameter of the chuck to the diameter of the diamond circular saw blade) is 0.4. And respectively carrying out constraint modal analysis on the selected diamond circular saw blade of each model to obtain the first 6-order modal frequency of the diamond circular saw blade of each model.
and secondly, sorting the analysis data, for example, sorting 3 rd order (0,2) modal frequency (critical rotating speed frequency) of each type of diamond circular saw blade to obtain a table 1.
TABLE 1 summary of 3 rd order (0,2) modal frequencies for various types of diamond circular saw blades
Combining the data of the table 1, applying numerical analysis software, respectively using the diameter D and the thickness H of the diamond circular saw blade as independent variables, using the corresponding 3 rd order modal frequency value as dependent variables, and applying the diameter D and the thickness H of the diamond circular saw blade as functions of the independent variables to carry out fitting so as to obtain a fitting curve graph 3 and a functional relation formula as follows:
the function relation of the 3 rd order (0,2) modal frequency of the diamond circular saw blade and the diameter and the thickness is
f3(D,H)＝－70.23+98.24×D－0.85+4.732×103×H (1)
Similarly, other 5 th order modal frequencies of a diamond circular saw blade are as follows as a function of diameter and thickness:
Expression of 1 st order (1,0) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f1(D,H)＝－64.52+88.5×D－0.85+4.178×103×H (2)
Expression of 2 nd order (0,1) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f2(D,H)＝－60+84.91×D－0.85+4×103×H (3)
Expression of 4 th order (0,3) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f4(D,H)＝－98.8+139.4×D－0.85+6.635×103×H (4)
Expression of 5 th order (0,4) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f5(D,H)＝－148.3+211.9×D－0.85+9.9×103×H (5)
Expression of 6 th order (0,5) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f6(D,H)＝－218.1+312.7×D－0.85+14.54×103×H (6)
Wherein: d is the diameter of the diamond circular saw blade in m (meter), and H is the thickness of the diamond circular saw blade in m.
Therefore, for any given type of diamond circular saw blade, the first 6 natural frequencies of the diamond circular saw blade can be directly calculated by applying the formulas (1) to (6) according to the diameter and the thickness of the diamond circular saw blade.
step two, providing a constraint model of diamond circular saw blade design and sawing process parameters:
Determining the diameter D and the linear cutting speed v of the diamond circular saw blade according to the size and the hardness of the processed stone, and selecting the cutting linear speed to be lower for the stone which has higher quartz content and is difficult to saw; for free-cutting stone materials, the selected cutting line speed should be relatively high, and is usually selected according to empirical data, and table 2 is only used for reference. And then the processing rotating speed n of the diamond circular saw blade is obtained.
TABLE 2 Linear cutting speed of diamond circular saw blade of different working materials
The relation between the cutting linear velocity and the rotating speed is as follows:
Wherein: n is the rotation speed of the diamond circular saw blade, D is the diameter of the circular saw blade, and v is the linear cutting speed of the circular saw blade.
Ii, when the diamond circular saw blade is cut and processed, the excitation frequency f is mainly determined by the processing rotating speed n and the number of teeth m of the circular saw blade together, and the calculation formula of the excitation frequency is as follows:
Wherein: f is the exciting frequency, n is the rotating speed of the diamond circular saw blade, and m is the number of teeth of the circular saw blade.
iii, engineering, the empirical formula for calculating the resonance range is
0.85fi≤fs≤1.15fi (9)
In the formula: f. ofiis a resonance frequency of a certain order of the circular saw blade, fsIs the order resonance frequency range.
In order to avoid the resonance of the diamond circular saw blade, the excitation frequency of the circular saw blade is required to be kept away from the resonance frequency range. Therefore, the excitation frequency of the circular saw blade should be satisfied
f＜0.85fiOr f > 1.15fi i＝1,2,3,4,5,6 (10)
and i is the order of the diamond circular saw blade.
The working speed n of the diamond circular saw blade is far less than the critical speed n0Then there is
n＜＜n0＝60×f3(D,H) (11)
iv, combining the analysis results, providing a constraint model of the size and the working parameters of the diamond circular saw blade as follows:
Example 2: the method for designing the diamond circular saw blade and formulating the sawing technological parameters is applied to actual production, and the diamond circular saw blade is selected and formulated, and the method is specifically operated according to the following steps:
if the stone needing to be processed in actual production is granite, if the linear cutting speed of the pre-selected diamond circular saw blade is 25m/s, the depth of the cut stone is 120mm, the clamping ratio is 0.4, and the cutting depth of the circular saw blade is more than 120mm in consideration of the size of the chuck, the calculation formula of the maximum cutting depth of the circular saw blade is shown as follows: 0.5 × (D-0.4D) > 120; the diameter of the diamond circular saw blade is larger than 400 mm.
according to the specification standard of the diamond circular saw blade, the specification of the circular saw blade with the diameter being slightly larger than 400mm comprises the following components:
| Diameter D | Thickness H | Number of teeth m |
| 450mm | 2.8mm | 26 |
| 500mm | 2.8mm | 30 |
| 550mm | 3.0mm | 32 |
| 600mm | 3.5mm | 36 |
the parameters of the specifications and the models of the four diamond circular saw blades are respectively substituted into a constraint model, and the first model in the table is taken as an example for explanation:
Mixing (D is 0.45m, H is 2.8X 10)-3m, m ═ 26) into the constraint model, the results obtained are given in the table below
From the above calculation results, it can be seen that: the working rotating speed of the diamond circular saw blade is far less than the critical rotating speed, the requirement is met, but the excitation frequency of the diamond circular saw blade is just in the range of the 6 th order resonance frequency, and the requirement is not met.
At the moment, the linear cutting speed of the diamond circular saw blade is adjusted from 25m/s to 20m/s through adjusting parameters, the working rotating speed is far less than the critical rotating speed according to the calculation result, the excitation frequency is between the 5 th order and the 6 th order resonance frequency range, the resonance frequency range is accurately avoided, and the requirements are met.
If another type D is 500mm diamond circular saw blade, the thickness of (D is 0.5m, H is 2.8X 10)-3m, m is 30) is substituted into the constraint model, and the working rotating speed is far less than the critical rotating speed according to the calculation result, and the excitation frequency is greater than the 6 th order resonance frequency range, which also meets the requirement.
The invention provides a method for designing a diamond circular saw blade and formulating sawing technological parameters, the method can be used for directly, quickly and accurately calculating the first 6-order resonance frequency of the diamond circular saw blade, the analysis process is simple, and the universality is strong. The method is suitable for the design of various diamond circular saw blades and the optimization of sawing process parameters.
Claims (3)
1. A method for designing a diamond circular saw blade and formulating sawing technological parameters comprises the steps of firstly verifying the reliability of a modal simulation analysis method by using a modal experiment, carrying out the modal experiment by using a common diamond circular saw blade as a test piece, carrying out a constrained modal experiment on the test piece, and further analyzing modal experiment data to obtain the modal frequency of the test piece; carrying out three-dimensional solid modeling on the test piece by using three-dimensional modeling software, then importing the test piece into modal analysis software, adding corresponding material attributes, setting constraint conditions identical to those of a modal experiment, and then carrying out modal simulation analysis to obtain modal frequency of a simulation structure; performing error analysis on the results of the first 7-order modal frequency obtained by the modal experiment and the modal simulation, and verifying that the results of the modal experiment and the modal simulation are correct and reliable if the errors of the results of the two modal analysis are within 10%; the method is characterized by comprising the following steps:
Step one, selecting different types of diamond circular saw blades to perform constraint modal analysis, taking the diameter D and the thickness H of the diamond circular saw blades as independent variables, and obtaining the functional relation between the first 6-order resonance frequency of the diamond circular saw blades and the diameter and the thickness of the diamond circular saw blades through data analysis:
Uniformly selecting N diamond circular saw blades with different specifications and thicknesses according to the national standard GB11270-1989 and the foreign standard ISO-6105-1988 of the diamond circular saw blade, establishing a model of the selected diamond circular saw blade by using three-dimensional modeling software, and respectively carrying out constrained mode simulation analysis to obtain the mode frequency of the N-type diamond circular saw blade;
Secondly, the first 6 orders of modal frequency, namely the first 6 orders of resonant frequency, is taken, and the function with the diameter D and the thickness H of the diamond circular saw blade as independent variables is used for fitting to obtain the function relation between each order of resonant frequency of the diamond circular saw blade and the diameter and the thickness of the diamond circular saw blade;
Step two, providing a constraint model of diamond circular saw blade design and sawing technological parameters:
i. determining the diameter and linear cutting speed of the diamond circular saw blade according to the size and hardness of the processed material, and further obtaining the processing rotating speed of the diamond circular saw blade;
ii. Providing the functional relation among the excitation frequency, the rotating speed and the number of teeth of the diamond circular saw blade when the diamond circular saw blade works; obtaining the relation between the critical rotating speed frequency of the diamond circular saw blade and the thickness of the diamond circular saw blade;
iii, under the condition of avoiding resonance, combining the obtained relational expression, and providing a constraint model of the diamond circular saw blade and the sawing process parameters;
and iv, according to the constraint model, making the thickness, the tooth number and the processing rotating speed of the diamond circular saw blade.
2. The method of claim 1, wherein the diamond circular saw blade is designed and the sawing process parameters are established by: the function relation of the first 6 th order modal frequency of the diamond circular saw blade and the diameter and the thickness thereof in the first step is as follows:
Expression of 1 st order (1,0) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f1(D,H)＝－64.52+88.5×D－0.85+4.178×103×H
expression of 2 nd order (0,1) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f2(D,H)＝－60+84.91×D－0.85+4×103×H
Expression of 3 rd order (0,2) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f3(D,H)＝－70.23+98.24×D－0.85+4.732×103×H
Expression of 4 th order (0,3) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f4(D,H)＝－98.8+139.4×D－0.85+6.635×103×H
Expression of 5 th order (0,4) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f5(D,H)＝－148.3+211.9×D－0.85+9.9×103×H
Expression of 6 th order (0,5) modal frequency of diamond circular saw blade as function of diameter and thickness thereof
f6(D,H)＝－218.1+312.7×D－0.85+14.54×103×H
Wherein: d is the diameter of the diamond circular saw blade, and H is the thickness of the diamond circular saw blade.
3. The method of claim 1, wherein the diamond circular saw blade is designed and the sawing process parameters are established by: the design of the diamond circular saw blade and the constraint model of the sawing technological parameters in the step two are as follows:
wherein: n is the processing speed of the diamond circular saw blade, n0is the critical rotating speed of the diamond circular saw blade, m is the number of teeth of the diamond circular saw blade, v is the cutting linear velocity, f0the resonant frequency is f, the excitation frequency is D, the diameter of the diamond circular saw blade is D, and the thickness of the diamond circular saw blade is H.
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