CN104318007A - Modal-analysis-based ultrasonic cutting tool design method - Google Patents

Abstract

The invention discloses a method for designing an ultrasonic cutting tool based on modal analysis, which is used to solve the technical problem of poor safety in use of the existing ultrasonic cutting tool. The technical solution is to first determine the resonant frequency of the system, and then determine the dimensional variables that can be changed during the design of the tool, and use genetic algorithm optimization, aiming at the maximum amplitude obtained through modal analysis, to obtain the optimal result of the tool size. Due to the method of changing the variable parameters of the tool to match the working frequency of the ultrasonic vibration cutting system, the maximum amplitude can be obtained during ultrasonic machining. At the same time, during the machining process, the tool selected for each tool change is the optimal tool obtained through numerical optimization calculation, and there is no need to reposition and measure the position of the top of the selected tool every time, so automatic change can be used in the machining center The knife improves the processing efficiency and ensures the safety of processing, and is suitable for large-scale promotion and use in factories.

Description

Design method of ultrasonic cutting tool based on modal analysis

technical field

The invention relates to a design method of an ultrasonic cutting tool, in particular to a design method of an ultrasonic cutting tool based on modal analysis.

Background technique

The document "Design of Ultrasonic Vibration Cutting Tool, Mechanical Design and Manufacturing, 2012, Vol02, p242-244" discloses a design method of ultrasonic cutting tool. The purpose of this method is to expand the amplitude of the tool tip. First, analyze the motion state of the cutting system, calculate the vibration wavelength, and then determine the size of the horn, and position the end point of the tool at a quarter of the entire wavelength to achieve the maximum amplitude. . According to the principle of wave synthesis, when the system is in the resonance state, only in the wave-by-wave node plane, the particle displacement caused by the incident wave in one direction and the reflected wave in the opposite direction is equal in size and opposite in direction, and the composite displacement is always zero. Therefore, the fixed point of the variable amplitude catch is selected at the wave-by-wave node, and the amplitude gradually increases from the wave-by-wave node to both ends, and the antinode point with the largest amplitude appears again at the top of the tool to achieve the purpose of expanding the amplitude. In order to make the tool reach the maximum amplitude during each processing, the author designed a positioning tool holder and adjusted the fixed size of the tool on the spring chuck so that the tip of the tool is at the maximum amplitude of the wavelength during each processing, which is a better solution. In order to achieve the purpose of designing the tool to achieve the maximum amplitude in ultrasonic vibration cutting. The practical applicability of the method described in this document is not strong, and the position of the measuring tool needs to be repositioned every time the tool is changed, which reduces the processing efficiency; at the same time, if some tools are short in length and the required positioning length is long, it may be difficult The clamping of the tool is not reliable, and the tool is easy to fall off during vibration cutting, resulting in accidents. In process design, the length of the tool clamped by the spring chuck should be at least one-third of the entire tool length.

Contents of the invention

In order to overcome the disadvantages of poor safety in use of existing ultrasonic cutting tools, the present invention provides a design method for ultrasonic cutting tools based on modal analysis. This method firstly determines the resonant frequency of the system, and then determines the dimensional variables that can be changed during the design of the tool, and uses genetic algorithm optimization, aiming at the maximum vibration amplitude obtained through modal analysis, to obtain the optimal result of the tool size, that is, The tool of this size is selected as the tool used in this processing, so that the ultrasonic vibration cutting system composed of the tool and the ultrasonic tool holder can work in a resonance state, thereby improving the performance and effect of ultrasonic vibration cutting, only need to change the tool, no need to The measurement is repositioned each time during processing, which improves the processing efficiency and the safety factor during processing.

The technical solution adopted by the present invention to solve the technical problem is: a method for designing an ultrasonic cutting tool based on modal analysis, which is characterized in that the following steps are adopted:

Step 1. According to the characteristics of the ultrasonic vibration cutting system, a modal analysis is performed before machining to determine the operating frequency f ₀ of the system.

Step 2. According to the type and structure of the tool, on the premise of ensuring the processing requirements, determine the parameter variable of the tool to be optimized, and set the initial parameter value. If the processing is to remove material, set the variable parameters as the length of the three sides and the thickness of the cutter; if the processing is a hole, the diameter of the drill bit remains unchanged, set the variable parameters to include the length of the drill bit, the length of the spiral groove and The diameter of the handle.

Step 3, using the genetic algorithm to optimize the variable parameters in the step 2, and the optimized tool variable parameter results are used in the step 4.

Step 4. According to Step 3, the optimized variable parameters of the tool are obtained, and the modal analysis is carried out on the ultrasonic vibration cutting system, that is, the first natural frequency f and amplitude of the required mode shape are obtained, and the degree of conformity of the target variable a is verified:

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; |</span>\\ \mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

In the formula, a represents the difference between the first natural frequency and the working frequency of the ultrasonic vibration cutting system; b represents the maximum value of the magnification of the tool tip displacement; M represents the magnification of the tool tip displacement.

Step 5. After repeated calculation operations in steps 3 and 4, the result that best meets the design requirements is obtained, and the optimized tool parameters are output.

The beneficial effects of the present invention are: the method firstly determines the resonance frequency of the system, and then determines the size variables that can be changed during the design of the tool, uses genetic algorithm optimization, and takes the maximum amplitude obtained through modal analysis as the goal to obtain the size of the tool For the best result, the tool of this size can be selected as the tool used in this processing, so that the ultrasonic vibration cutting system composed of the tool and the ultrasonic tool holder can work in a resonance state, thereby improving the performance and effect of ultrasonic vibration cutting . Due to the method of changing the variable parameters of the tool to match the working frequency of the ultrasonic vibration cutting system, the maximum amplitude can be obtained during ultrasonic machining. At the same time, during the machining process, the tool selected for each tool change is the optimal tool obtained through numerical optimization calculation, and there is no need to reposition and measure the position of the top of the selected tool every time, so automatic change can be used in the machining center The knife improves the processing efficiency and ensures the safety of processing, and is suitable for large-scale promotion and use in factories.

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Description of drawings

Fig. 1 is a schematic diagram of an ultrasonic cutting tool designed by the method of the present invention.

FIG. 2 is a top view of FIG. 1 .

Detailed ways

Refer to Figure 1-2. The specific steps of the ultrasonic cutting tool design method based on modal analysis of the present invention are as follows:

1. Determine the operating frequency of the system.

According to the cutting processing requirements, determine the system operating frequency f ₀ , which is the expected natural frequency of the ultrasonic vibration cutting system. Generally, the transducer and the horn in the ultrasonic vibration cutting system are taken as a whole, and the natural frequency f ₀ is obtained by using modal analysis software, and the natural frequency f ₀ can also be obtained by measuring the vibration data with an acceleration sensor. When the excitation frequency of the applied ultrasonic power supply is consistent with the natural frequency of the ultrasonic vibration cutting system, the system resonates, so that the amplitude of the tool tip reaches the maximum and the processing effect is improved.

2. Optimization of tool structure and size parameters based on genetic algorithm.

The invention adopts the non-dominated sorting genetic algorithm based on the elite strategy to optimize the tool structure and size parameters. The specific process is as follows.

1) Determine the coding of the tool optimization genetic algorithm.

① According to the type and structure of the tool, determine the parameter variable. Taking the ultrasonic cutter shown in Figure 1 as an example, set the parameter variables of cutter size as AB=l ₁ , BC=l ₂ , AD=l ₃ , and set the thickness as h.

②The value range of the given parameter. Usually, according to the processing requirements of the part, the initial design value of the tool parameter is determined, and then the specific value range of each parameter is determined based on the designed value of the tool parameter design value. For example, l ₁ ∈{5±ΔL ₁ }, l ₂ ∈{25±ΔL ₂ }, l ₃ ∈{12±ΔL ₃ }, h∈{12±ΔL } (unit: mm).

③ Determine the coding strategy. Based on binary coding, each variable can take 16 values, so each variable is a four-bit binary code. For example, the four-bit binary code of the variable l ₂ is 0000-1111, and there are 16 values between [25-ΔL ₂ , 25+ΔL ₂ ].

2) Determine the fitness function of the tool optimization genetic algorithm.

Taking the optimization objective as the fitness function, F _n =min|ff ₀ |. f ₀ is the expected system operating frequency, and f is the actual natural frequency of the ultrasonic vibration cutting system (ultrasonic tool holder and tool) after the tool size is changed, which is obtained through modal analysis.

3) Determine the selection operator of the tool optimization genetic algorithm.

Calculate the expected number N _i of each individual in the population surviving in the next generation:

${\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; avg</span>}}}$

Among them, F _avg represents the mean value of F.

If an individual is selected and required to participate in pairing and crossover, its expected number of survival in the next generation is reduced by 0.5; if it does not participate in pairing and crossover, the expected number of the individual is reduced by 1.0. As the selection process proceeds, if the expected value of an individual is less than zero, the individual will not be selected again.

4) Determine the crossover operator of the tool optimization genetic algorithm.

Swap genes between two intersections.

5) Determine the mutation operator of the tool optimization genetic algorithm.

The basic content of the mutation operator is to change the gene values at certain gene positions of the individual code strings in the population. That is to replace the gene value at the specified mutation point with another gene value different from the original value. If the 0000 parameter is mutated to the second digit, the mutated parameter is 0010.

6) The genetic algorithm is used for calculation.

3. Modal analysis.

Through the modal analysis, the first natural frequency f of the longitudinal mode of the ultrasonic vibration cutting system composed of the designed tool and the ultrasonic tool holder and the amplification factor M of the tool tip amplitude are obtained. The specific steps of modal analysis are:

①Set the 3D model of the ultrasonic handle and tool

②Set up modal analysis items and boundary conditions

③ Grid division

④ Solve the model to obtain the natural frequency and mode shape of the tool system

⑤ Compare and optimize the objective function

$\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; |</span>\\ \mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$

4. Determine the optimal parameters.

The optimized tool parameters will be obtained through genetic algorithm and modal analysis, that is, the optimized tool geometry (or tool structure) will be obtained. Tool material: Carbide. Application range: cutting of honeycomb composite materials, fibers, leather and other materials.

Claims (1)

1. A method for designing an ultrasonic cutting tool based on modal analysis, characterized in that it may further comprise the steps: Step 1. According to the characteristics of the ultrasonic vibration cutting system, a modal analysis is performed before processing to determine the system operating frequency f ₀ ; Step 2. According to the type and structure of the tool, on the premise of ensuring the processing requirements, determine the parameter variable of the tool to be optimized, and set the initial parameter value; The thickness of the knife; if the hole is processed, the diameter of the drill remains unchanged, and the variable parameters are set to include the length of the drill, the length of the spiral groove and the diameter of the shank; Step 3, using the genetic algorithm to optimize the variable parameters in the step 2, and the optimized tool variable parameter results are used in the step 4; Step 4. According to Step 3, the optimized variable parameters of the tool are obtained, and the modal analysis is carried out on the ultrasonic vibration cutting system, that is, the first natural frequency f and amplitude of the required mode shape are obtained, and the degree of conformity of the target variable a is verified: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; min</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; |</span>\\ \mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; max</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>\end{array}\right.$ In the formula, a represents the difference between the first natural frequency and the operating frequency of the ultrasonic vibration cutting system; b represents the maximum value of the magnification of the displacement of the tool tip; M represents the magnification of the displacement of the tool tip; Step 5. After repeated calculation operations in steps 3 and 4, the result that best meets the design requirements is obtained, and the optimized tool parameters are output.