A drilling force prediction method based on Chladni figures

Abstract

The present invention discloses a drilling force prediction method based on Chladni figures. The method uses Chladni figures to characterize the drilling vibration of a composite material with unidirectional carbon fibers, obtains the frequency of the self-excited vibration of the workpiece, and then calculates the dynamic cutting force coefficient under the influence of the drilling vibration. During the dynamic cutting process, the dynamic cutting force is predicted based on the dynamic cutting force coefficient, tool rotational speed, tool feed rate, and cutting area at the feed time. By predicting changes in cutting force, the present invention can avoid machining vibration caused by drastic fluctuations in cutting force, thereby reducing the risk of tool breakage and workpiece surface defects. It can also help adjust cutting parameters to maintain the stability of the cutting process, thereby improving machining accuracy and surface quality.

Description

Technical Field

[0001] The invention belongs to the field of automated machining, and in particular relates to a drilling force prediction method based on Chladni figures. Background Art

[0002] During the drilling process, the cutting forces between the tool and the workpiece exert periodic excitation forces on the workpiece. These forces vary periodically as the tool rotates. This variation can align with the workpiece's natural frequency, leading to resonance. This resonance can significantly impact the machining process and the final workpiece quality. When in resonance, the workpiece exhibits specific vibration modes. These modes depend on the workpiece's rigidity, mass distribution, and boundary conditions. The vibration values ​​measured by traditional vibration sensors cannot fully capture the vibration modes and drilling forces of the workpiece in this resonant state. Summary of the Invention

[0003] The purpose of the present invention is to overcome the shortcomings of the existing technology and propose a drilling force prediction method based on Chladni figures. The research on vibration characterization and drilling force prediction based on Chladni figures is of great significance for controlling drilling resonance, optimizing cutting parameters, improving machining accuracy and extending tool life.

[0004] To achieve the above object, the present invention adopts the following technical solutions:

[0005] The present invention provides a drilling force prediction method based on Chladni figures, which is specifically as follows:

[0006] Step 1: Use different tool speed n and feed speed v f Different workpiece samples are drilled in sequence. Before drilling, the workpiece samples are clamped on the fixture and sand is evenly sprinkled on the workpiece samples. During drilling, the self-excited vibration frequency of the workpiece samples is measured by a vibration sensor, and the various Chladni figures that appear and the corresponding self-excited vibration frequencies of the workpiece samples are recorded.

[0007] Step 2: According to the relationship between the self-excited vibration frequency ω of the workpiece sample and the modal numbers m and s of the Chladni figure in formula (1), the material correction parameter a is used as the parameter to be fitted, and the modal numbers m and s of the Chladni figure and the corresponding self-excited vibration frequency ω of the workpiece sample of the Chladni figure are fitted to obtain the specific value of the material correction parameter a.

[0008] The relationship between the self-excited vibration frequency ω of the workpiece sample and the Chladni figure modal numbers m and s is as follows:

[0009]

[0010] Where m and s are the modal numbers, corresponding to the number of nodes in the row and column with the largest number of nodes in the horizontal and vertical directions of the workpiece specimen within the machining surface, respectively; E is the elastic modulus of the workpiece specimen material; ρ is the density of the workpiece specimen material; L x and L y are the length and width of the workpiece specimen respectively.

[0011] Step 3: Clamp the workpiece to be processed on the fixture, sprinkle sand evenly on the workpiece to be processed, set the tool speed n and feed speed v f , drill the workpiece to be processed, record the Chladni figure of the sand grain arrangement on the workpiece to be processed, and obtain the relationship between the tool speed n and feed speed v f The corresponding Chladni figure modal numbers m and s are calculated according to formula (1) to obtain the real-time self-excited vibration frequency ω of the workpiece to be processed during drilling, and then according to the dynamic cutting force coefficient K d Calculate the dynamic cutting force coefficient K by the relationship between the self-excited vibration frequency ω d ;

[0012] Step 4: During the dynamic cutting process, according to the dynamic cutting force coefficient K d , tool speed n, tool feed speed v f and cutting area A at feed time t c (t), the predicted dynamic cutting force F(t) is as follows:

[0013] F(t)=K d *A c (t)*n p *v f q

[0014] Among them, p and q are empirical coefficients, p ranges from -0.1 to 0.2, and q ranges from 0.2 to 0.5.

[0015] Preferably, the dynamic cutting force coefficient K d The relationship with the self-excited vibration frequency ω is:

[0016]

[0017] Where b is the tool diameter, θ is the phase difference between two adjacent cutting edges of the tool, M is the mass of the workpiece before drilling, and k is the stiffness of the workpiece.

[0018] More preferably, the phase difference θ between two adjacent cutting edges of the tool is calculated as follows:

[0019]

[0020] where N w is the number of cutting edges of the tool.

[0021] Preferably, when drilling the workpiece to be processed in step three, the vibration state of each part of the workpiece to be processed is observed by observing the Chladni figures presented by the sand grains on the workpiece to be processed.

[0022] Preferably, the cutting area A at the feed time t c (t)=π*d*v f *t, d are the diameters of the drilled holes.

[0023] The beneficial effects of the present invention are as follows:

[0024] 1. The present invention uses Chladni patterns to characterize the drilling vibration of composite materials with unidirectional carbon fiber arrangements (such as CF / PEEK materials). By observing the modal numbers in the length (transverse) and width (longitudinal) directions of the Chladni pattern, the frequency of the workpiece's self-excited vibration can be determined. By observing the Chladni patterns formed by sand grains on the workpiece, the vibration state of each part of the workpiece can be intuitively observed, revealing vibration modes of the workpiece during drilling that are not detected by traditional vibration sensors, thereby controlling the resonance of the workpiece during drilling.

[0025] 2. The present invention uses Chladni figures to determine the dynamic cutting force coefficient under the influence of drilling vibration. This dynamic cutting force coefficient can help optimize cutting parameters, improve machining quality, and increase production efficiency. During the workpiece drilling process, the dynamic cutting force coefficient can help predict and control cutting force changes, effectively avoiding vibration and tool wear during the cutting process.

[0026] 3. Based on the Chladni figure, the present invention can calculate the corresponding dynamic cutting force coefficient. Combining this coefficient with the cutting area at the time of tool rotational speed, tool feed rate, and feed time, it can predict the dynamic cutting force when drilling composite materials with unidirectional carbon fiber arrangements. By predicting cutting force fluctuations, machining vibrations caused by drastic fluctuations in cutting force can be avoided, thereby reducing the risk of tool breakage and workpiece surface defects. It can also help adjust cutting parameters to maintain cutting process stability, thereby improving machining accuracy and surface quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 Schematic diagram of the Chladni figure displayed by sand grains when a composite material workpiece with unidirectionally arranged carbon fibers is drilled at a specific rotation speed and feed rate in this embodiment. DETAILED DESCRIPTION

[0028] The present invention will be further described below with reference to the embodiments.

[0029] A drilling force prediction method based on Chladni figures is as follows:

[0030] Step 1: Use different tool speed n and feed speed v f Different workpiece specimens were drilled sequentially. Before drilling, the workpiece specimens (planar workpieces, made of composite materials with unidirectional carbon fiber arrangement) were clamped in a fixture and evenly coated with sand. During drilling, a vibration sensor was used to measure the self-excited vibration frequency of the workpiece specimens. The various Chladni patterns that appeared were recorded (photographed) along with the corresponding self-excited vibration frequencies of the workpiece specimens. Drilling at different rotational speeds and feed rates produces self-excited vibrations of varying frequencies in the workpiece specimens, and the sand grains exhibit different Chladni patterns due to the vibrations. (Although the specific patterns of the Chladni patterns vary, the sand grains on the composite materials with unidirectional carbon fiber arrangement exhibit a staggered arrangement across the machined surface, with the sand grains spaced horizontally and vertically in rows.) Each Chladni pattern that appears due to vibration corresponds to the self-excited vibration frequency ω of a specific workpiece specimen.

[0031] Step 2: According to the relationship between the self-excited vibration frequency ω of the workpiece sample and the Chladni pattern modal numbers m and s in formula (1), the material correction parameter a is used as the parameter to be fitted, and the Chladni pattern modal numbers m and s and the corresponding workpiece sample self-excited vibration frequency ω data are fitted to obtain the specific value of the material correction parameter a.

[0032] The relationship between the self-excited vibration frequency ω of the workpiece sample and the Chladni figure modal numbers m and s is as follows:

[0033]

[0034] Where m and s are modal numbers, corresponding to the number of nodes in the row and column with the largest number of nodes in the horizontal and vertical directions of the workpiece specimen on the processing surface, respectively (i.e., in the layout of the sand grains on the composite material with unidirectional carbon fiber arrangement, the number of horizontal and vertical intersections in a certain row in the horizontal direction and a certain column in the vertical direction is the largest, and the number of horizontal and vertical intersections in the row in the horizontal direction and the column in the vertical direction is taken as m and s, respectively). This can be obtained by observing the Chladni figure; the specific value of the material correction parameter a should be in the range of 0.07 to 0.09; E is the elastic modulus of the workpiece specimen material; ρ is the density of the workpiece specimen material; L x and L y are the length and width of the workpiece specimen respectively.

[0035] Step 3: Clamp the workpiece to be processed on the fixture, sprinkle sand evenly on the workpiece to be processed, set the tool speed n and feed speed v f , drilling the workpiece to be processed, such as Figure 1 As shown, the Chladni pattern of the sand grains on the workpiece to be processed is recorded and obtained (manually counted or through image recognition) and the tool speed n and feed speed v fThe corresponding Chladni figure modal numbers m and s are calculated according to formula (1) to obtain the real-time self-excited vibration frequency ω of the workpiece to be processed during drilling, and then according to the dynamic cutting force coefficient K d Calculate the dynamic cutting force coefficient K by the relationship between the self-excited vibration frequency ω d ;

[0036] Dynamic cutting force coefficient K d The relationship with the self-excited vibration frequency ω is:

[0037]

[0038] Where b is the diameter of the tool (drill or milling cutter), θ is the phase difference between two adjacent cutting edges of the tool, M is the mass of the workpiece before drilling, and k is the stiffness of the workpiece.

[0039] The phase difference θ between two adjacent cutting edges of the tool is calculated as follows:

[0040]

[0041] where N w is the number of cutting edges of the tool.

[0042] Step 4: During the dynamic cutting process, the cutting force will be affected by vibration, drilling parameters (tool speed n and feed speed v f ) and the real-time cutting area. According to the dynamic cutting force coefficient K d , tool speed n, tool feed speed v f and cutting area A at feed time t c (t), the predicted dynamic cutting force F(t) is as follows:

[0043] F(t)=K d *A c (t)*n p *v f q

[0044] Among them, A c (t)=π*d*v f *t, d are the diameters of the drilled holes, p and q are empirical coefficients, p is in the range of -0.1 to 0.2, and q is in the range of 0.2 to 0.5.

Claims

1. A drilling force prediction method based on Chladni figures, characterized by: The method is as follows: Step 1: Use different tool speed n and feed speed v f Different workpiece samples were drilled in sequence. Before drilling, the workpiece samples were clamped on a fixture and sand was evenly sprinkled on the workpiece samples. During drilling, the self-excited vibration frequency of the workpiece samples was measured using a vibration sensor, and the various Chladni figures that appeared and the corresponding self-excited vibration frequencies of the workpiece samples were recorded. Step 2: According to the relationship between the self-excited vibration frequency ω of the workpiece sample and the modal numbers m and s of the Chladni figure in formula (1), the material correction parameter a is used as the parameter to be fitted, and the modal numbers m and s of the Chladni figure and the self-excited vibration frequency ω of the workpiece sample corresponding to the Chladni figure are fitted to obtain the specific value of the material correction parameter a; The relationship between the self-excited vibration frequency ω of the workpiece sample and the Chladni figure modal numbers m and s is as follows: Where m and s are the modal numbers, corresponding to the number of nodes in the row and column with the largest number of nodes in the horizontal and vertical directions of the workpiece specimen within the machining surface, respectively; E is the elastic modulus of the workpiece specimen material; ρ is the density of the workpiece sample material; L x and L y are the length and width of the workpiece specimen respectively; Step 3: Clamp the workpiece to be processed on the fixture, sprinkle sand evenly on the workpiece to be processed, set the tool speed n and feed speed v f , drill the workpiece to be processed, record the Chladni figure of the sand grain arrangement on the workpiece to be processed, and obtain the relationship between the tool speed n and feed speed v f The corresponding Chladni figure modal numbers m and s are calculated according to formula (1) to obtain the real-time self-excited vibration frequency ω of the workpiece to be processed during drilling, and then according to the dynamic cutting force coefficient K d Calculate the dynamic cutting force coefficient K by the relationship between the self-excited vibration frequency ω d ; Step 4: During the dynamic cutting process, according to the dynamic cutting force coefficient K d , tool speed n, tool feed speed v f and cutting area A at feed time t c (t), the predicted dynamic cutting force F(t) is as follows: F(t)=K d *A c (t)*n p *v f q Among them, p and q are empirical coefficients, p ranges from -0.1 to 0.2, and q ranges from 0.2 to 0.

5.

2. The drilling force prediction method based on Chladni figures according to claim 1, characterized in that: The dynamic cutting force coefficient K d The relationship with the self-excited vibration frequency ω is: Where b is the tool diameter, θ is the phase difference between two adjacent cutting edges of the tool, M is the mass of the workpiece before drilling, and k is the stiffness of the workpiece.

3. The drilling force prediction method based on Chladni figures according to claim 2, characterized in that: The phase difference θ between two adjacent cutting edges of the tool is calculated as follows: where N w is the number of cutting edges of the tool.

4. The drilling force prediction method based on Chladni figures according to claim 1, characterized in that: When drilling the workpiece in step three, the vibration state of each part of the workpiece can be observed by observing the Chladni figures presented by the sand grains on the workpiece.

5. The drilling force prediction method based on Chladni figures according to claim 1, characterized in that: The cutting area A at the feed time t c (t)=π*d*v f *t, d are the diameters of the drilled holes.

Images