Cutter flank width wear rate calculation method

Abstract

The invention discloses a cutter flank width wear rate calculation method, which comprises the following steps of: firstly, describing a thermal-viscoplastic relationship of a material by adopting a Johnson-Cook constitutive model, calculating heat generated in processing and a cutter surface temperature, and then calculating a cutter surface contact stress; and finally, substituting the obtained surface temperature and surface contact stress of the tool into a tool wear rate calculation formula, obtaining a tool wear rate calculation formula by combining a hard point wear rate calculation formula, a bonding wear rate calculation formula and a hardness calculation formula, and calculating the tool wear volume according to the initial wear width of the tool. And finally obtaining the tool flank width wear rate of the tool. By using the wear rate calculation method provided by the invention, the wear rate of the cutter during milling of the aluminum-based silicon carbide can be accurately calculated.

Description

Technical Field

[0001] The invention belongs to the field of cutting of difficult-to-cut materials and relates to a method for calculating the wear rate of the flank width of a tool. Background Art

[0002] Aluminum-based silicon carbide composite materials (hereinafter referred to as "aluminum-based silicon carbide") have the characteristics of high specific strength, good dimensional stability, not easy to deform, non-hygroscopic, non-aging, stable chemical properties, etc., so they have been widely used in the fields of inertial navigation platform structural parts manufacturing, optical components, etc. Especially used in some high-precision occasions, such as reflector brackets, sensor brackets, azimuth and pitch axis systems, etc. The above occasions require that the structural parts remain unchanged under frequent alternating hot and cold conditions, and aluminum-based silicon carbide with excellent performance can meet the above stringent requirements.

[0003] Although aluminum-based silicon carbide has many excellent properties, this type of material is hard and brittle, and its reinforcing phase particle hardness is second only to diamond. It is a typical difficult-to-process material. When using PCD insert cutters during production, tool wear is still very serious. Therefore, effectively suppressing the wear of PCD milling cutters when processing aluminum-based silicon carbide is the key to achieving high-quality and economical processing of aluminum-based silicon carbide. In order to effectively control the wear of PCD milling cutters, the wear rate of the tool during the processing process must first be obtained, of which theoretical calculation is an accurate expression.

[0004] Wear rate calculation methods are usually divided into two types: analytical calculation and numerical simulation. For the former, French scholar Iliescu published a paper titled "Modeling and tool wear in drilling of CFRP" in the International Journal of Machine Tools and Manufacture journal to predict tool wear in drilling by establishing an empirical model. This model better predicts the wear of uncoated and coated tools during the drilling of carbon fiber composite materials. However, due to the uneven manufacturing process of tools and different on-site processing conditions, the empirical model has great limitations, and the workload is large and the cost is high.

[0005] Deng Ben from Huazhong University of Science and Technology published a paper titled "Research on the Mechanism and Machinability Enhancement Process of Micro-milling of SiC / Al Composite Materials", which proposed an analytical model for the tool flank wear rate that includes abrasive wear and adhesive wear, and realized the prediction of the flank wear width of PCD micro-diameter tools. This method does not consider the influence of cutting temperature on tool wear, and the calculation accuracy is limited.

[0006] For the latter, Mu Han et al. proposed a wear calculation method that considers the effect of temperature on hard point wear in a paper titled "An anti-wear tool structure within integrated-micro hybrid cutting edges for milling of Carbon Fiber Reinforced Plastics composites" published in the International Journal of Advanced Manufacturing Tecnology in 2023, and designed a special milling cutter for milling thermosetting carbon fiber composites based on this method. Since almost no adhesive wear occurs when processing thermosetting carbon fiber, this method only considers hard point wear and is not suitable for predicting the wear rate of the back face of aluminum-based silicon carbide tools.

[0007] In summary, if a wear rate calculation method that takes into account the influence of temperature on hard point wear and adhesive wear can be developed for aluminum-based silicon carbide, and the wear width of the flank of the PCD tool can be predicted, the aluminum-based silicon carbide cutting theory will be further improved, providing technical support for the high-quality and high-economic processing of aluminum-based silicon carbide. Summary of the invention

[0008] In order to overcome the shortcomings of the prior art, the present invention invents a wear rate calculation method which takes into account the influence of temperature on hard point wear and adhesive wear.

[0009] The technical solution adopted by the present invention to solve its technical problems is: a method for calculating the wear rate of the back face width of a tool, using the Johnson-Cook constitutive model to describe the thermal-viscoplastic relationship of the material, and based on the assumption that all the heat comes from the friction and sliding between the tool and the workpiece, calculating the heat generated during processing and the surface temperature of the tool, and then calculating the surface contact stress of the tool by the Hertz contact theory, and finally substituting the obtained surface temperature and surface contact stress of the tool into the tool wear rate calculation formula; combining the hard point wear rate calculation formula, the bonding wear rate calculation formula and the hardness calculation formula, the tool wear rate calculation formula considering the dynamic influence of temperature on the tool surface hardness is: Assuming the initial wear width of the tool is VB, the tool wear volume Where Δl1, Δl2, Δh are the lengths of the geometric line segments divided for the convenience of calculation. Substituting Δl1 = Δhcotα and Δl2 = Δhcotγ into the above formula and ignoring the highest order terms, the above formula can be further written as follows: Where γ is the tool rake angle, α is the tool back angle, and the tool back face width wear rate ΔVB can be expressed as

[0010] Furthermore, the tool surface temperature calculation steps are as follows: First, the heat generation and transfer during the workpiece material removal process are modeled: Considering strain, strain rate, temperature and pressure, the chip separation criterion is defined using the Johnson-Cook damage law, and the formula is derived through the damage accumulation law and Where d1~d5 are constants of the workpiece material, D is the damage parameter, is the equivalent plastic strain increment for one time step, is the equivalent plastic strain, ε f is the strain at failure, σ * is the stress triaxiality, is the reference strain rate, T is the instantaneous temperature, T0 is the reference temperature, T melt is the melting temperature, m is a temperature-related parameter; assuming that all the heat comes from the friction and sliding between the tool and the workpiece, the unit volume heat generation rate is as shown in the formula: q = λμpv, where μ is the friction coefficient, q is the unit volume heat generation rate, λ is the proportion of friction work converted into heat, p is the contact pressure between the tool surface and the workpiece, and v is the relative sliding speed between the tool surface and the workpiece surface; the generated heat will be transferred in the contact area between the workpiece material and the tool and in the interior of the two, and the heat transfer process in the contact area is described by the following formula: Where q workpiece and q tool represents the total heat flowing into the workpiece material, h p represents the contact thermal conductivity, r is the ratio of the generated heat distributed to the workpiece material, T tool is the instantaneous temperature of the tool side, T workpiece is the instantaneous temperature of the workpiece side; update T tool and T workpiece Values: Where k is the thermal diffusivity, ρ and C are the density and specific heat capacity of the material, respectively.

[0011] Further, the tool surface contact stress calculation steps are as follows:

[0012] The maximum contact stress calculation formula obtained from Hertz theory is: Where ρ1 and ρ2 are the different contact radii of the two contact surfaces, σ Hmax is the maximum contact stress, F is the contact load, the elastic modulus and Poisson's ratio of the two objects are E1, E2, μ1, μ2 respectively, and b is the contact length; the calculation formula for the half-width of the contact surface is

[0013] Furthermore, the calculation steps of the tool back face width wear rate are as follows: Based on Archard wear theory, the formula Calculate the hard particle wear, where dW is the wear volume with a sliding distance of dL, σ t is the contact stress on the tool surface, which changes with time during milling; k1 is the wear coefficient determined by the material properties of the mating surface and the actual lubrication conditions; H is the Vickers hardness of the softer side of the mating surface, which is related to temperature; Based on Archard wear theory, the calculation formula for adhesive wear is Where k2 is the adhesive wear coefficient, w is the cutting width, V c is the cutting speed; in the contact process between the tool and the workpiece material, the binder metal cobalt on the tool side is considered to be the softer side, and its hardness calculation formula is H = A1 exp(-A2T tool ), where A1 and A2 are constants, A1 is the basic hardness, that is, the hardness of the material at a temperature of 0K, and A2 is the thermal coefficient.

[0014] The beneficial effects of the present invention are:

[0015] The present invention first analyzes the heat generation, heat transfer in the contact area, and heat transfer behavior inside the material and the tool during milling to obtain the tool surface temperature value; at the same time, the contact stress between the tool and the material surface is calculated according to the Hertz contact theory; then, based on the obtained tool surface temperature and contact stress, the dynamic influence of temperature on the tool surface hardness is considered to construct a complete tool wear rate calculation method.

[0016] The calculation method of the present invention takes into account the dynamic influence of temperature on hard point wear and adhesive wear for the first time, thereby realizing the accurate prediction of tool wear rate when PCD milling cutter mills aluminum-based silicon carbide.

[0017] The method involved in the present invention is realized by finite element simulation software. The finite element method can accurately describe the complex cutting process and can also effectively reduce the test cost. Its application is helpful to further clarify the cutting mechanism of aluminum-based silicon carbide. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flow chart of the calculation method of the present invention;

[0019] Figure 2 It is a schematic diagram for calculating the geometric loss of the tool back face;

[0020] Figure 3 It is a three-dimensional milling simulation model of aluminum-based silicon carbide;

[0021] Figure 4 It is the comparison result of model calculation accuracy. DETAILED DESCRIPTION

[0022] The tool wear rate calculation method of the present invention is described below in conjunction with the accompanying drawings and specific embodiments.

[0023] Reference Figure 1 As shown, the present invention discloses a method for calculating tool wear rate that takes into account the influence of temperature on hard point wear and adhesive wear, and the steps are as follows.

[0024] Firstly, the Johnson-Cook constitutive model is used to describe the thermal-elastic (visco)-plastic relationship of the material. Based on the assumption that all the heat comes from the friction and sliding between the tool and the workpiece, the heat generated during processing and the tool surface temperature are calculated. Then, the tool surface contact stress is calculated by the Hertz contact theory. Finally, the obtained tool surface temperature and surface contact stress are substituted into the tool wear rate calculation formula.

[0025] The first step is to calculate the tool surface temperature.

[0026] First, the heat generation and transfer during the workpiece material removal process are modeled: the chip separation criterion is defined using the Johnson-Cook damage law considering strain, strain rate, temperature and pressure, and the following formula is derived through the damage accumulation law:

[0027]

[0028] Where d1~d5 are constants of the workpiece material, D is the damage parameter, is the equivalent plastic strain increment for one time step, is the equivalent plastic strain, ε f is the strain at failure, σ * is the stress triaxiality, is the reference strain rate, T is the instantaneous temperature, T0 is the reference temperature, T melt is the melting temperature and m is a temperature related parameter.

[0029] In this process, as the workpiece material is continuously removed, heat is continuously generated and transferred. Since the plastic deformation of aluminum-based silicon carbide is small, it is assumed that all the heat comes from the friction and sliding between the tool and the workpiece. The unit volume heat generation rate is shown as follows: q = λμpv, where μ is the friction coefficient, q is the unit volume heat generation rate, λ is the proportion of friction work converted into heat, p is the contact pressure between the tool surface and the workpiece, and v is the relative sliding speed between the tool surface and the workpiece surface.

[0030] The generated heat will be transferred in the contact area between the workpiece material and the tool and inside both. The heat transfer process in the contact area is described by the following formula: Where q workpiece and q tool represents the total heat flowing into the workpiece material, h p represents the contact thermal conductivity, r is the ratio of the generated heat distributed to the workpiece material, T tool is the instantaneous temperature of the tool side, Tworkpiece is the instantaneous temperature of the workpiece side.

[0031] Update T according to the above formula tool and T workpiece Values: Where k is the thermal diffusivity, ρ and C are the density and specific heat capacity of the material, respectively.

[0032] The second step is to calculate the contact stress on the tool surface.

[0033] The maximum contact stress calculation formula obtained from Hertz theory is: Where ρ1 and ρ2 are the different contact radii of the two contact surfaces, σ Hmax is the maximum contact stress, F is the contact load, the elastic modulus and Poisson's ratio of the two objects are E1, E2, μ1, μ2 respectively, and b is the contact length; the calculation formula for the half-width of the contact surface is

[0034] The third step is to calculate the wear rate of the tool flank width.

[0035] After calculating the contact stress and temperature state of the tool surface through the above steps, the next step is to calculate the tool wear amount and distribution state under this state. According to existing research, aluminum-based silicon carbide mainly suffers from hard point wear and adhesive wear during processing. During the processing, the surface hardness of the tool has a significant effect on the wear process. Therefore, this patent adopts a wear calculation method that takes into account the dynamic effect of temperature on the surface hardness of the tool.

[0036] This calculation method is based on Archard wear theory, and the calculation formula for hard point wear is:

[0037] Where dW is the wear volume with a sliding distance of dL; σ t is the contact stress on the tool surface, which changes with time during milling; k1 is the wear coefficient determined by the material properties of the mating surface and the actual lubrication conditions; H is the Vickers hardness of the softer side of the mating surface, which is related to temperature.

[0038] Based on Archard wear theory, the calculation formula for adhesive wear is: Where k2 is the adhesive wear coefficient, w is the cutting width, V c is the cutting speed.

[0039] The hardness of the diamond particles in the PCD blade is higher than that of the SiC particles, while the hardness of the binder metal cobalt is lower than that of the SiC particles. During the processing, the metal cobalt is removed by the sliding and bonding of the SiC particles, and the diamond particles also fall off after losing the binder. Therefore, during the contact between the tool and the workpiece material, the binder metal cobalt on the tool side is considered to be the softer side, and its hardness calculation formula is H = A1 exp(-A2T tool ) In the formula, A1 and A2 are constants, A1 is the basic hardness, that is, the hardness of the material when the temperature meets the requirements, and A2 is the thermal coefficient.

[0040] The calculation formulas for hard point wear rate, bonding wear rate and hardness can be obtained by combining the calculation formulas. The calculation formula for tool wear rate considering the dynamic effect of temperature on tool surface hardness is:

[0041] like Figure 2 As shown in the figure, assuming that the initial wear width of the tool is VB, the tool wear volume ΔV wear It can be calculated by the following formula: Wherein Δl1, Δl2, Δh are the lengths of geometric line segments divided for the convenience of calculation, and are not specifically defined. Their specific meanings are shown in the figure. From the geometric relationship in the figure, it can be seen that by substituting Δl1=Δhcotα and Δl2=Δhcotγ into the above formula and ignoring the highest order terms, the above formula can be further written as follows: Where γ is the tool rake angle, α is the tool back angle, and the tool back face width wear rate ΔVB can be expressed as

[0042] The following is a description of an implementation of a method for calculating tool wear rate that takes into account the effect of temperature on hard point wear and adhesive wear according to the present invention.

[0043] Taking the commonly used commercial analysis software ABAQUS (2016 version) as an example, the following is established: Figure 3 The aluminum-based silicon carbide three-dimensional milling simulation model shown is calculated using the method proposed in the present invention. The calculation results of the tool surface temperature and surface contact stress are output by the simulation software, and the tool wear rate is obtained by calculating through Python secondary development. The calculation results are compared with the experimental results to verify the calculation accuracy. The model settings are shown in the following table (representative example simulation model settings).

[0044] parameter value <![CDATA[Density ρ (kg / m 3 )]]> 14600 Elastic modulus E(Gpa) 840 <![CDATA[Thermal conductivity (W·m -1 ·K -1 )]]> 700 Thermal expansion coefficient (1 / ℃) <![CDATA[9×10 -7 ]]> <![CDATA[Rake angle γ0 (°)]]> 0° and 5° <![CDATA[Back angle α0 (°)]]> 3°, 7° and 15° <![CDATA[Axial inclination β0 (°)]]> 0°, 5° and 10° .

[0045] The material properties are shown in the following table (Representative example simulation model material properties).

[0046] Material Aluminum-based silicon carbide <![CDATA[Density ρ (kg / m 3 )]]> 2900 Elastic modulus E(Gpa) 145 Poisson's ratio 0.24 <![CDATA[Thermal conductivity (W·m -1 ·K -1 )]]> 130 Thermal expansion coefficient (1 / ℃) <![CDATA[12×10 -6 ]]> .

[0047] The accuracy comparison results are as follows Figure 4 As shown in the figure, the tool structure 0-3-5 indicates a PCD end mill with a tool rake angle of 0°, a back angle of 3°, and an axial inclination angle of 5°.

[0048] The wear rate calculation method proposed in the present invention can be used to accurately calculate the wear rate of the tool during aluminum-based silicon carbide milling.

[0049] The above embodiments are only illustrative of the principles and effects of the present invention, as well as some embodiments of its application. A person skilled in the art may make several modifications and improvements without departing from the inventive concept of the present invention, and all of these belong to the protection scope of the present invention.

Claims

1. A method for calculating the wear rate of the tool flank width for PCD inserts, characterized in that: Firstly, the Johnson-Cook constitutive model is used to describe the material thermo-viscoplastic relationship, calculate the heat generated during processing and the tool surface temperature, then calculate the tool surface contact stress, and finally substitute the obtained tool surface temperature and surface contact stress into the tool wear rate calculation formula; The tool wear rate calculation formula is obtained by combining the hard point wear rate calculation formula, the bonding wear rate calculation formula and the hardness calculation formula. The tool wear volume is calculated from the initial wear width VB of the tool. Where Δl1, Δl2, Δh are the lengths of the geometric line segments for the convenience of calculation. Substituting Δl1 = Δhcotα and Δl2 = Δhcotγ into the above formula and ignoring the highest order terms, we get Where γ is the tool rake angle, α is the tool back angle, and the tool back face width wear rate is finally obtained:

2. The method for calculating the wear rate of the tool flank width according to claim 1, characterized in that: The calculation steps of tool surface temperature are as follows: First, the Johnson-Cook damage law is used to define the chip separation criterion, and the formula is derived through the damage accumulation law: and Where d1~d5 are constants of the workpiece material, D is the damage parameter, is the equivalent plastic strain increment for one time step, is the equivalent plastic strain, ε f is the strain at failure, σ * is the stress triaxiality, is the reference strain rate, T is the instantaneous temperature, T0 is the reference temperature, T melt is the melting temperature, m is a temperature-related parameter; the heat comes entirely from the unit volume heat generation rate q=λμpv during the friction sliding between the tool and the workpiece, where μ is the friction coefficient λ is the proportion of friction work converted into heat, p is the contact pressure between the tool surface and the workpiece, and v is the relative sliding speed between the tool surface and the workpiece surface; the generated heat is transferred in the contact area between the workpiece material and the tool and inside the two, and the description formula is Where q workpiece and q tool represents the total heat flowing into the workpiece material, h p represents the contact thermal conductivity, r is the ratio of the generated heat distributed to the workpiece material, T tool is the instantaneous temperature of the tool side, T workpiece is the instantaneous temperature of the workpiece side; finally, through the formula Update T tool and T workpiece where k is the thermal diffusivity, ρ and C are the density and specific heat capacity of the material, respectively.

3. The method for calculating the wear rate of the tool flank width according to claim 2, characterized in that: The calculation steps of the tool surface contact stress are as follows: The maximum contact stress calculation formula of the tool surface is: Where ρ1 and ρ2 are the different contact radii of the two contact surfaces, σ Hmax is the maximum contact stress, F is the contact load, the elastic modulus and Poisson's ratio of the two objects are E1, E2, μ1, μ2 respectively, and b is the contact length; the calculation formula for the half-width of the contact surface is 4. The method for calculating the wear rate of the tool flank width according to claim 3, characterized in that: The calculation steps of the tool back face width wear rate are as follows: Calculate the hard particle wear, where dW is the wear volume with a sliding distance of dL, σ t is the contact stress on the tool surface, k1 is the wear coefficient, and H is the Vickers hardness of the softer side of the mating surface; the calculation formula for adhesive wear is Where k2 is the adhesive wear coefficient, w is the cutting width, V c is the cutting speed; the hardness calculation formula of the softer side of the tool is H = A1exp(-A2T tool ), where A1 and A2 are constants, A1 is the basic hardness, and A2 is the thermal coefficient.

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