Method for identifying instantaneous cutting energy efficiency evolution characteristics of efficient face milling cutter

Abstract

The invention discloses a method for identifying instant cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter. The method comprises the following steps of S1, revealing composition of cutting energy of the face milling cutter, wherein it is determined that input total energy is composed of machine tool feeding energy in the three directions of torque energy x, y and z, additional vibration energy in the three directions and machine tool additional energy; according to the method, the instantaneous cutting boundaries, instantaneous velocity vectors and force vectors of the main and auxiliary cutting edges of the cutter teeth under the action of vibration are calculated, and then the cutting force energy consumption and the shearing energy consumption of the milling cutter are calculated respectively, so that the instantaneous change condition of the cutting energy consumption of the milling cutter is revealed, and the change characteristics of the instantaneous cutting energy efficiency and the shearing energy efficiency of the milling cutter are obtained; the energy transfer efficiency in the material removal process is revealed, and the problems that an existing method cannot accurately reveal the instantaneous change characteristic of the cutting energy consumption of the milling cutter and the cutting energy consumption calculation error is too large due to the fact that influences of vibration and cutter tooth errors are ignored are solved.

Description

Technical Field

[0001] The invention belongs to the technical field of milling cutter processing, and in particular relates to a method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter. Background Art

[0002] Milling cutters are developing towards high energy utilization. High-efficiency milling cutters are widely used in parts processing due to their high energy utilization, low tool loss rate and high machining surface quality. Face milling cutters, as a type of high-efficiency milling cutter, are mainly used for high-speed milling. The milling method of face milling cutters is intermittent cutting. The cutter teeth cut in and out of the workpiece repeatedly, which continuously generates impact, making the milling cutter and the cutter teeth always under the influence of vibration. Its instantaneous cutting behavior changes dynamically, causing the instantaneous cutting energy consumption to change continuously, which directly affects the energy utilization of the milling cutter. Therefore, establishing a method to identify the instantaneous cutting energy efficiency of the milling cutter under vibration is of great significance to improving the energy utilization of the milling cutter and achieving efficient cutting of the milling cutter.

[0003] The instantaneous cutting energy efficiency of the milling cutter directly reflects the level and variation characteristics of the milling cutter's energy utilization rate. It is related to the instantaneous cutting layer parameters of the milling cutter, the instantaneous cutting force energy consumption, the instantaneous shear energy consumption and the instantaneous input energy of the milling cutter. The instantaneous cutting energy efficiency of the milling cutter includes the cutting force energy efficiency and the shear energy efficiency, which mainly reflects the relationship between the various energies in the process of the milling cutter cutting the workpiece. Among them, the cutting force energy efficiency refers to the proportion of the cutting force energy consumption in the input energy, and the shear energy efficiency refers to the proportion of the shear energy consumption in the cutting force energy consumption. The root mean square of the cutting force energy efficiency and the shear energy efficiency is used to judge the cutting energy efficiency of the milling cutter. The root mean square is the effective value. The larger the root mean square of the cutting energy efficiency, the higher the proportion of energy involved in cutting, and the higher the energy utilization rate of the milling cutter.

[0004] The existing methods for calculating instantaneous cutting energy consumption assume that the instantaneous cutting behavior of each tooth of the milling cutter has the same changing characteristics, and calculate that the changing trend of the cutting energy consumption of each tooth is the same, ignoring the influence of milling vibration and tooth error on the cutting energy consumption of the tooth, resulting in a large error between the calculated results of the cutting force energy consumption and the experimental results; or the cutting power is integrated over time to calculate the cumulative cutting energy consumption, which cannot reveal the instantaneous change of the cutting energy consumption of the milling cutter.

[0005] To this end, we introduce a method to identify the evolution characteristics of the instantaneous cutting energy efficiency of high-efficiency face milling cutters. Summary of the invention

[0006] The purpose of the present invention is to provide a method for identifying the evolution characteristics of the instantaneous cutting energy efficiency of a high-efficiency face milling cutter. To this end, the present invention conducts experiments on cutting vibration, cutting force and cutting energy consumption of the face milling cutter according to the milling process plan; based on the experimental results, the composition of the instantaneous cutting energy of the face milling cutter is revealed, and the total energy consumption of the machine tool is solved; a model of the instantaneous cutting posture and energy distribution of the milling cutter under vibration is constructed; the instantaneous cutting boundaries of the main and secondary cutting edges of the cutter teeth are constructed, and the instantaneous velocity vectors and instantaneous force vectors of the main and secondary cutting edges of the cutter teeth are solved; a method for solving the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter is constructed; a method for solving the instantaneous cutting force energy efficiency and shear energy efficiency of the milling cutter is constructed, and then the changing characteristics of the instantaneous cutting force energy efficiency and shear energy efficiency of the milling cutter are revealed to solve the problems raised in the above background technology.

[0007] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: a method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter, comprising the following steps: S1, revealing the composition of the cutting energy of the face milling cutter: determining that the total input energy is composed of the machine tool feed energy in the three directions of torque energy x, y, and z, the additional vibration energy in the three directions, and the additional energy of the machine tool, and the output energy is composed of the milling cutter internal energy and centrifugal force energy consumption caused by the deformation of the milling cutter structure, the milling cutter main cutting force energy consumption, and the additional energy consumption of the milling cutter energy consumption, and clarifying the transmission and conversion relationship between the energies;

[0008] S2. Construct the instantaneous cutting posture and energy distribution model of the face milling cutter: establish the workpiece coordinate system, cutting coordinate system, milling cutter coordinate system without vibration, milling cutter coordinate system under vibration and cutter tooth coordinate system, and determine the equation of the cutter tooth cutting edge under vibration in the workpiece coordinate system;

[0009] S3, solving the instantaneous velocity vector and force vector of the face milling cutter teeth: defining the main and auxiliary cutting edges, constructing their instantaneous cutting boundaries, solving the coordinates and equations of the upper and lower boundary points of the main and auxiliary cutting edges, determining the instantaneous cutting layer thickness and area, and then solving the instantaneous cutting velocity vector, instantaneous shear velocity vector, instantaneous friction velocity vector, instantaneous cutting force vector and instantaneous shear force vector;

[0010] S4. Construct a solution method for the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter: respectively calculate the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the main and auxiliary cutting edges of the cutter teeth, and then obtain the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the milling cutter;

[0011] S5. Construct a solution method for the instantaneous cutting force energy efficiency and shear energy efficiency of the milling cutter: calculate the efficiency of the instantaneous input energy of the milling cutter converted into the instantaneous cutting force energy and the efficiency of the instantaneous cutting force energy of the milling cutter converted into the instantaneous shear energy, and reveal their changing characteristics;

[0012] S6. Conduct experimental verification of the instantaneous cutting force energy efficiency of the face milling cutter: compare the cutting force energy consumption measured experimentally with the cutting force energy efficiency calculated by the theoretical model, and analyze the reasons for the difference.

[0013] Preferably, in the cutting force and cutting energy consumption experiment of the face milling cutter, the number of teeth of the milling cutter is 4, the blade model is SDMT1204AZN-D57WKP35G, and the experimental parameters are the speed n=2400rpm, the feed rate f=0.16mm / z, and the cutting depth a p =0.4mm, cutting width a e =25mm.

[0014] Preferably, in the cutting energy composition of the face milling cutter, the calculation formula for the total input energy P(t) is:

[0015] P(t)=P M (t)+P1(t)+P2(t)+P3(t),

[0016] Among them, P M (t) is the energy of torque input into the milling cutter, P1(t) is the energy of machine tool feed system input into the milling cutter, P2(t) is the vibration energy of the milling process system, and P3(t) is the additional energy provided by the machine tool required for the energy consumption of the milling cutter;

[0017] The energy consumed by the milling cutter during instantaneous cutting P E (t) is:

[0018] P E (t) = P ie (t)+P ce (t)+P c (t)+P d (t),

[0019] Among them, P ie (t) is the energy consumption of milling cutter deformation, P ce (t) is the vibration energy consumption of the milling cutter, P c (t) is the energy consumption of milling cutter cutting force, P d (t) is the additional energy consumption of the milling cutter.

[0020] Preferably, when constructing the instantaneous cutting posture and energy distribution model of the face milling cutter, under the action of vibration, the equation of the cutting edge of tooth i in the workpiece coordinate system at time t is determined by the translation matrices M1, M2, M3 and rotation matrices T1, T2, T3 between the tooth coordinate system and the vibration-free milling cutter coordinate system, the vibrating milling cutter coordinate system and the cutting coordinate system, and the cutting coordinate system and the workpiece coordinate system.

[0021] Preferably, when calculating the instantaneous velocity vector and force vector of the face milling cutter tooth, in the workpiece coordinate system, the instantaneous combined velocity v of the selected point m of the main cutting edge is m (t) is:

[0022]

[0023] In the formula, v x (t) is the velocity in the x direction, v y (t) is the velocity in the y direction, v z (t) is the velocity in the z direction.

[0024] Preferably, when solving the instantaneous velocity vector and force vector of the face milling cutter tooth, the instantaneous cutting force of the selected point of the main cutting edge in the tooth coordinate system is:

[0025]

[0026]

[0027] In the formula, The cutting force at the selected point of the main cutting edge, is the cutting force at the selected point of the secondary cutting edge, k is the cutting force correction coefficient; F p is the unit cutting force.

[0028] In the tooth coordinate system, the instantaneous shear force at the selected points of the main and secondary cutting edges is:

[0029]

[0030] In the formula, h Di1 (x i ,y i ,z i ) is the instantaneous cutting layer thickness of the main cutting edge, h Di2 (x i ,y i ,z i ) is the instantaneous cutting layer thickness of the secondary cutting edge, The cutting force at the selected point of the main cutting edge, is the shear force at the selected point of the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge.

[0031] Preferably, the instantaneous cutting force energy consumption of the main and secondary cutting edges of the cutter teeth are respectively:

[0032]

[0033] In the formula, is the cutting force energy consumption of the main cutting edge, is the cutting force energy consumption of the secondary cutting edge, The instantaneous cutting speed of the selected point m is the main cutting edge, Select the instantaneous cutting speed of point b for the secondary cutting edge.

[0034] Preferably, the instantaneous cutting force energy consumption of the milling cutter Pc (t) is:

[0035]

[0036] Preferably, the instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth is:

[0037]

[0038] In the formula, is the shear energy consumption of the main cutting edge, is the shear energy consumption of the secondary cutting edge, The instantaneous shear velocity of the selected point m of the main cutting edge is, is the instantaneous shear velocity of the selected point b on the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge;

[0039] Milling cutter instantaneous shear energy consumption P s (t) is:

[0040]

[0041] The efficiency of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy is η c (t) is:

[0042]

[0043] The efficiency of the milling cutter's instantaneous cutting force energy converted into instantaneous shear energy is η sc (t) is:

[0044]

[0045] Preferably, in the experimental verification of the instantaneous cutting force energy efficiency of the face milling cutter, the cutting force energy consumption measured experimentally is compared with the cutting force energy efficiency calculated by the theoretical model. In the actual cutting process, the friction force is affected by factors such as cutting speed, temperature, and workpiece surface condition, as well as tool wear, resulting in the experimentally measured cutting force energy consumption being greater than that in the theoretical calculation, and the calculated cutting force energy efficiency is higher.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] Through the milling experiment of face milling cutter, this method reveals the instantaneous cutting energy composition, transfer and conversion characteristics of face milling cutter, considers the influence of milling vibration and tooth error on the cutting energy of milling cutter, and solves the instantaneous cutting boundary, instantaneous velocity vector and force vector of the main and secondary cutting edges of the tooth under the action of vibration, and then solves the cutting force energy consumption and shear energy consumption of the milling cutter respectively, reveals the instantaneous change of the cutting energy consumption of the milling cutter, obtains the change characteristics of the instantaneous cutting energy efficiency and shear energy efficiency of the milling cutter, reveals the energy transfer efficiency in the material removal process, and solves the problem that the existing methods cannot accurately reveal the instantaneous change characteristics of the cutting energy consumption of the milling cutter and the influence of vibration and tooth error is ignored, resulting in excessive error in the calculated cutting energy consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 A flow chart of a method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter is provided for an embodiment of the present invention; Figure 2 A structural diagram of a milling cutter is provided for an embodiment of the present invention; Figure 3 A structural diagram of a face milling cutter structure and cutter tooth error is provided for an embodiment of the present invention; Figure 4 A structural diagram of the cutting trajectory and time period division of a face milling cutter is provided for an embodiment of the present invention; Figure 5 Provides a comparison chart of cutting vibration, cutting force and cutting energy consumption experimental results for the embodiments of the present invention; Figure 6 A block diagram of the energy transfer and conversion relationship during the milling process is provided for an embodiment of the present invention; Figure 7 Provide instantaneous cutting posture and energy distribution diagram of the milling cutter under vibration for the embodiment of the present invention; Figure 8 Provide a coordinate offset diagram of a milling cutter under vibration for an embodiment of the present invention; Fig. 9 Provide instantaneous cutting boundary diagrams of the main and secondary cutting edges of the cutter teeth for the embodiments of the present invention; Fig.10 Provide instantaneous cutting layer diagrams of the main and secondary cutting edges of the cutter teeth for the embodiment of the present invention; Fig.11 A diagram of a microelement interception method of a tooth cutting edge is provided for an embodiment of the present invention; Fig.12 Provide instantaneous velocity vector diagrams of primary and secondary cutting edges for embodiments of the present invention; Fig.13 Provide instantaneous force vector diagrams of the primary and secondary cutting edges for the embodiment of the present invention; Fig.14 Provided for the embodiment of the present invention is (a) a cutting force energy efficiency diagram for a period of Δt4; Fig.15 Provide (b) Δt for the embodiment of the present invention 41 Cutting force energy efficiency diagram for each time period; Fig.16 Provide (c)Δt for the embodiment of the present invention 42 Cutting force energy efficiency diagram for each time period; Fig.17 Provide (d)Δt for the embodiment of the present invention 43 Cutting force energy efficiency diagram for each time period; Fig.18 Provide (e)Δt for the embodiment of the present invention 44Cutting force energy efficiency diagram for each time period; Fig.19 Provide (f)Δt for the embodiment of the present invention 45 Cutting force energy efficiency diagram for each time period; Fig. 20 Provide (g)Δt for the embodiment of the present invention 46 Cutting force energy efficiency diagram for each time period; Fig.21 Provided for the embodiments of the present invention are (a) a shearing energy efficiency diagram for a period of Δt4; Fig. 22 Provide (b) Δt for the embodiment of the present invention 41 Time period shear energy efficiency diagram; Fig.23 Provide (c)Δt for the embodiment of the present invention 42 Time period shear energy efficiency diagram; Fig.24 Provide (d)Δt for the embodiment of the present invention 43 Time period shear energy efficiency diagram; Fig.25 Provide (e)Δt for the embodiment of the present invention 44 Time period shear energy efficiency diagram; Fig.26 Provide (f)Δt for the embodiment of the present invention 45 Time period shear energy efficiency diagram; Fig. 27 Provide (g)Δt for the embodiment of the present invention 46 Time period shear energy efficiency diagram; Fig.28 Provided for the embodiment of the present invention is (a) an experimental cutting force energy consumption diagram during the Δt4 period; Fig.29 Provide (b) Δt for the embodiment of the present invention 41 Cutting force energy consumption diagram of time period experiment; Fig.30 Provide (c)Δt for the embodiment of the present invention 42 Cutting force energy consumption diagram of time period experiment; Fig.31 Provide (d)Δt for the embodiment of the present invention 43 Cutting force energy consumption diagram of time period experiment; Fig.32 Provide (e)Δt for the embodiment of the present invention 44 Cutting force energy consumption diagram of time period experiment; Fig.33 Provide (f)Δt for the embodiment of the present invention 45 Cutting force energy consumption diagram of time period experiment; Fig.34 Provide (g)Δt for the embodiment of the present invention 46 Cutting force energy consumption diagram of time period experiment; Fig.35 Provided for the embodiment of the present invention is (a) an experimental cutting force energy efficiency diagram during the Δt4 period; Fig.36 Provide (b) Δt for the embodiment of the present invention 41 Cutting force energy efficiency diagram of time period experiment; Fig.37 Provide (c)Δt for the embodiment of the present invention 42 Cutting force energy efficiency diagram of time period experiment; Fig.38 Provide (d)Δt for the embodiment of the present invention 43 Cutting force energy efficiency diagram of time period experiment; Fig.39 Provide (e)Δt for the embodiment of the present invention44 Cutting force energy efficiency diagram of time period experiment; Fig.40 Provide (f)Δt for the embodiment of the present invention 45 Cutting force energy efficiency diagram of time period experiment; Fig.41 Provide (g)Δt for the embodiment of the present invention 46 Cutting force energy efficiency diagram of time period experiment; Fig.42 Provided for the embodiment of the present invention is (a) a total energy consumption diagram for a period of Δt4; Fig.43 Provide (b) Δt for the embodiment of the present invention 41 Total energy consumption diagram for each period; Fig.44 Provide (c)Δt for the embodiment of the present invention 42 Total energy consumption diagram for each period; Fig.45 Provide (d)Δt for the embodiment of the present invention 43 Total energy consumption diagram for each period; Fig.46 Provide (e)Δt for the embodiment of the present invention 44 Total energy consumption diagram for each period; Fig.47 Provide (f)Δt for the embodiment of the present invention 45 Total energy consumption diagram for each period; Fig.48 Provide (g)Δt for the embodiment of the present invention 46 Total energy consumption diagram for each period; Fig.49 Provided for the embodiment of the present invention is (a) a cutting force energy consumption diagram for a period of Δt4; Fig.50 Provide (b) Δt for the embodiment of the present invention 41 Cutting force energy consumption diagram for each period; Fig.51 Provide (c)Δt for the embodiment of the present invention 42 Cutting force energy consumption diagram for each period; Fig.52 Provide (d)Δt for the embodiment of the present invention 43 Cutting force energy consumption diagram for each period; Fig.53 Provide (e)Δt for the embodiment of the present invention 44 Cutting force energy consumption diagram for each period; Fig.54 Provide (f)Δt for the embodiment of the present invention 45 Cutting force energy consumption diagram for each period; Fig.55 Provide (g)Δt for the embodiment of the present invention 46 Cutting force energy consumption diagram for each period; Fig.56 Provided for the embodiment of the present invention is (a) a shear energy consumption diagram for a period of Δt4; Fig.57 Provide (b) Δt for the embodiment of the present invention 41 Time period shear energy consumption diagram; Fig.58 Provide (c)Δt for the embodiment of the present invention 42 Time period shear energy consumption diagram; Fig.59 Provide (d)Δt for the embodiment of the present invention 43 Time period shear energy consumption diagram; Fig.60 Provide (e)Δt for the embodiment of the present invention 44 Time period shear energy consumption diagram; Fig.61 Provide (f)Δt for the embodiment of the present invention 45 Time period shear energy consumption diagram; Fig.62 Provide (g)Δt for the embodiment of the present invention 46 Energy consumption diagram for different time periods. DETAILED DESCRIPTION

[0049] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] See also Figure 1-62 The present invention provides a technical solution: a method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter, comprising the following steps:

[0051] S1. Reveal the composition of face milling cutter cutting energy: Determine that the total input energy is composed of the machine tool feed energy in the three directions of torque energy x, y, and z, the additional vibration energy in the three directions, and the additional energy of the machine tool; the output energy is composed of the milling cutter internal energy and centrifugal force energy consumption caused by the milling cutter structure deformation, the milling cutter main cutting force energy consumption, and the additional energy consumption of the milling cutter energy consumption; clarify the transmission and conversion relationship between the energies;

[0052] S2. Construct the instantaneous cutting posture and energy distribution model of the face milling cutter: establish the workpiece coordinate system, cutting coordinate system, milling cutter coordinate system without vibration, milling cutter coordinate system under vibration and cutter tooth coordinate system, and determine the equation of the cutter tooth cutting edge under vibration in the workpiece coordinate system;

[0053] S3, solving the instantaneous velocity vector and force vector of the face milling cutter teeth: defining the main and auxiliary cutting edges, constructing their instantaneous cutting boundaries, solving the coordinates and equations of the upper and lower boundary points of the main and auxiliary cutting edges, determining the instantaneous cutting layer thickness and area, and then solving the instantaneous cutting velocity vector, instantaneous shear velocity vector, instantaneous friction velocity vector, instantaneous cutting force vector and instantaneous shear force vector;

[0054] S4. Construct a solution method for the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter: respectively calculate the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the main and auxiliary cutting edges of the cutter teeth, and then obtain the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the milling cutter;

[0055] S5. Construct a solution method for the instantaneous cutting force energy efficiency and shear energy efficiency of the milling cutter: calculate the efficiency of the instantaneous input energy of the milling cutter converted into the instantaneous cutting force energy and the efficiency of the instantaneous cutting force energy of the milling cutter converted into the instantaneous shear energy, and reveal their changing characteristics;

[0056] S6. Conduct experimental verification of the instantaneous cutting force energy efficiency of the face milling cutter: compare the cutting force energy consumption measured experimentally with the cutting force energy efficiency calculated by the theoretical model, and analyze the reasons for the difference.

[0057] Face milling cutter cutting experiment plan and results:

[0058] In order to obtain the instantaneous cutting energy consumption of the milling cutter under vibration, the CNC milling machine XK7124 three-axis milling machining center was used to conduct a face milling experiment on 45 steel. The milling cutter is the M4003-050-B22-04-6.5 face milling cutter produced by Walter Company, the blade is SDMT1204AZN-D57WKP35G, the number of teeth is 4, and the milling method is dry down milling. The face milling cutter structure and cutter tooth error are shown in Figure 1 and Figure 2 The experimental parameters are shown in Table 1, and the cutting trajectory of the face milling cutter is shown in Figure 4 The experimental results of cutting vibration, cutting force and cutting energy consumption are shown in Figure 5 shown.

[0059] Table 1 Milling experimental parameters

[0060]

[0061]

[0062] Figure 2 In the figure, l is the length of the cutting edge of the cutter, b is the length of the wiper edge, and r is a is the radius of the tool tip, c is the blade thickness, α is the main clearance angle, s i is the tip of any tooth, s zmax is the tip point of the lowest axial tooth, s rmax is the tip point of the largest radial tooth, Δz i is the axial error of the cutter teeth, Δr i is the radial error of the cutter teeth, θ i For x i Axis and x d The angle between the axes. max is the maximum turning radius of the cutter teeth, r i is the turning radius of tooth i.

[0063] Figure 3 In, p r is the base surface, p s is the cutting plane, p o is an orthogonal plane, p f is the feed plane, s is the main cutting edge, s' is the secondary cutting edge, λ s is the blade inclination angle, κ r is the principal deflection angle, κ r ' is the secondary deflection angle, γ o is the rake angle, αo The back angle.

[0064] Figure 4 In the figure, Δt1 to Δt7 are different time periods. Δt1 is the idle period before milling starts, Δt2 is the period when the milling cutter starts to cut in, Δt3 is the period when the milling cutter is fully cut in, Δt4 is the stable milling period, Δt5 is the period when the milling cutter starts to cut out, Δt6 is the period when the milling cutter is fully cut out, and Δt7 is the idle period after milling ends.

[0065] According to the cutting vibration, cutting force and cutting energy consumption experiment of face milling cutter, the experimental results of vibration acceleration, cutting force and cutting energy consumption are obtained, and according to Figure 4 Divide it into time periods, and the results are as follows Figure 5 shown.

[0066] The instantaneous cutting energy of face milling cutter consists of:

[0067] During the milling process, the input energy and output energy of the milling cutter exist in various forms. The energy input by the main transmission system and feed system of the machine tool is transmitted to the milling cutter and the workpiece through the milling cutter body, the functional interface of each tooth and the cutting layer. The total input energy is composed of torque energy, machine tool feed energy in the three directions of x, y and z, additional vibration energy in the three directions and additional energy of the machine tool. The output energy is composed of the internal energy and centrifugal force energy consumption of the milling cutter caused by the deformation of the milling cutter structure, the main cutting force energy consumption of the milling cutter and the additional energy consumption of the milling cutter energy consumption.

[0068] There are many transmission and conversion relationships between the instantaneous energy input and output of the milling cutter, such as Figure 6 shown.

[0069] Depend on Figure 6 It can be seen that the energy input of the milling cutter during instantaneous cutting is:

[0070] P(t)=P M (t)+P1(t)+P2(t)+P3(t) (1)

[0071] Where P(t) is the total energy input into the milling cutter, P M (t) is the energy of torque input into the milling cutter, P1(t) is the energy of machine tool feed system input into the milling cutter, P2(t) is the vibration energy of the milling process system, and P3(t) is the additional energy provided by the machine tool required for the energy consumption of the milling cutter.

[0072] Among them, P1(t) and P2(t) can be expressed by the following formulas respectively.

[0073] P1(t)=P x (t)+P y (t)+P z (t) (2)

[0074] Where P x (t) is the feeding energy in the x direction, P y (t) is the feeding energy in the y direction, P z (t) is the feed energy in z direction.

[0075] P2(t)=P vx (t)+P vy (t)+P vz (t) (3)

[0076] Where P vx (t) is the vibration energy in the x direction, P vy (t) is the vibration energy in the y direction, P vz (t) is the vibration energy in the z direction.

[0077] The energy consumed by the milling cutter during instantaneous cutting P E (t) is:

[0078] P E (t) = P ie (t)+P ce (t)+P c (t)+P d (t) (4)

[0079] Where P ie (t) is the energy consumption of milling cutter deformation, P ce (t) is the vibration energy consumption of the milling cutter, P c (t) is the energy consumption of milling cutter cutting force, P d (t) is the additional energy consumption of the milling cutter.

[0080] Among them, the instantaneous cutting force energy consumption of the main cutting edge of the milling cutter is P c (t) can be expressed by the following formula:

[0081]

[0082] In the formula, is the instantaneous cutting force energy consumption of tooth i, is the instantaneous shear energy consumption of tooth i, is the instantaneous friction energy consumption between tooth i and the workpiece.

[0083] The input energy of the cutting teeth is:

[0084]

[0085] In the formula, The energy input into the milling cutter of the machine tool feed system is transferred to the energy of the cutter tooth i. is the energy consumption of tooth i along the x direction, is the energy consumption of tooth i along the y direction, is the energy consumption of tooth i along the z direction.

[0086] The output energy of the cutting teeth is:

[0087]

[0088] In the formula, is the energy consumed by the cutting tooth in cutting volume, The heat generated by the cutting process.

[0089]

[0090] In the formula, is the energy consumption of blade wear, The heat generated by the friction and wear of the cutting teeth.

[0091] Depend on Figure 6 According to equations (1) to (8-1), the instantaneous cutting position and energy distribution of the milling cutter under vibration are as follows: Figure 7 As shown in the figure, the milling cutter offset under vibration is as follows Figure 8 shown.

[0092] Figure 7 In the figure, o-xyz is the workpiece coordinate system, o b -x b y b z b is the cutting coordinate system, o c -x c y c z c is the milling cutter coordinate system without vibration, o d -x d y d z d is the milling cutter coordinate system under vibration, o i -x i y i z i is the tooth coordinate system, n is the spindle speed, v is f is the feed speed.

[0093] Figure 8 A x (t), A y (t), A z (t) are x b Axis, y b Axis, z b The vibration displacement in the axial direction, θ(t) is the inclination angle, and θ1(t) is the inclination angle in the x direction. b -oz b The angle of the plane projection, θ2(t) is the inclination angle in y b-oz b The angle of the plane projection, θ d (t) is the direction angle of the milling cutter, φ c (t) is the position angle of the vibration-free milling cutter coordinate system, φ d (t) is the position angle of the vibration milling cutter coordinate system.

[0094] Depend on Figure 7 and Figure 8 , under the action of vibration, the equation of the cutting edge of tooth i at time t in the workpiece coordinate system is:

[0095] [x(t) y(t) z(t) 1] T =M3M2T3T2M1T1[x i y i z i 1] T (8-2)

[0096] Among them, (x i ,y i , z i ) is the coordinate of any point of the cutting edge in the cutter tooth coordinate system. M1 is the translation matrix between the cutter tooth coordinate system and the non-vibration milling cutter coordinate system, M2 is the translation matrix between the vibrating milling cutter coordinate system and the cutting coordinate system, M3 is the translation matrix between the cutting coordinate system and the workpiece coordinate system, T1 is the rotation matrix between the cutter tooth coordinate system and the non-vibration milling cutter coordinate system, T2 is the rotation matrix between the non-vibration milling cutter coordinate system and the vibrating milling cutter coordinate system, and T3 is the rotation matrix between the vibrating milling cutter coordinate system and the cutting coordinate system.

[0097] Calculation method of instantaneous velocity vector and force vector of face milling cutter teeth

[0098] Under the influence of milling vibration, the cutting edge area involved in the cutting task changes with time. The cutting edge that is mainly responsible for removing materials is defined as the main cutting edge, and the cutting edge that is responsible for improving the surface quality of the machined surface is defined as the secondary cutting edge. Figure 3 shown.

[0099] Depend on Fig. 9 It can be obtained that the machining transition surface G formed by the cutter tooth i under vibration is i (x(t),y(t),z(t)) is:

[0100]

[0101] In the formula, l i (x(t), y(t), z(t)) is the cutting edge equation of the cutter tooth in the workpiece coordinate system, t0 is the cutting-in moment when the cutter tooth i forms the machining surface, and t1 is the cutting-out moment when the cutter tooth i forms the machining surface.

[0102] The coordinates of the upper boundary point m1 of the main cutting edge in the workpiece coordinate system are:

[0103]

[0104] In the formula, z m1 (t) is the coordinate of point m1 along the z-axis.

[0105] The coordinates of the lower boundary point m0 ​​of the main cutting edge in the workpiece coordinate system are:

[0106]

[0107] In the formula, z m0 (t) is the coordinate of point m0 ​​along the z-axis.

[0108] From the above formula, we can get the main cutting edge equation l im (x(t),y(t),z(t)) is:

[0109]

[0110] In the workpiece coordinate system, the coordinates of the lower boundary point b0 of the secondary cutting edge are the same as those of the lower boundary point m0 ​​of the main cutting edge.

[0111] The coordinates b1 (x(t), y(t), z(t)) of the upper boundary point b1 of the secondary cutting edge in the workpiece coordinate system are:

[0112]

[0113] The secondary cutting edge equation is:

[0114]

[0115] In the workpiece coordinate system, the position coordinates of point m (x(t), y(t), z(t)) satisfy:

[0116]

[0117] In the tooth coordinate system, the instantaneous cutting layer thickness h of the main cutting edge is Di1 (x i ,y i ,z i )for:

[0118]

[0119] Taking the cutting layer microelement of tooth i as an example, the cutting layer area of ​​the main cutting edge is:

[0120]

[0121] In the workpiece coordinate system, the position coordinates of point b satisfy:

[0122]

[0123] In the tooth coordinate system, the instantaneous cutting layer thickness h of the secondary cutting edge is Di2 for:

[0124]

[0125] The cutting layer area of ​​the secondary cutting edge is:

[0126]

[0127] From the above formula, we can get the instantaneous cutting layer area A of the milling cutter. D (t) is:

[0128]

[0129] The relationship between the instantaneous cutting velocity vector, the instantaneous shear velocity vector and the instantaneous friction velocity vector at the selected point m of the main cutting edge of the cutter tooth and the selected point b of the secondary cutting edge is as follows: Fig.12 shown.

[0130] Fig.12 In, P rm is the base surface of point m; P om is the cutting plane of point m; P sm is the normal plane of point m; v m (t) is the instantaneous net velocity of m; is the instantaneous cutting speed at point m; is the instantaneous shear velocity at point m; is the instantaneous friction velocity at point m; is the angle between the instantaneous cutting speed and the instantaneous resultant speed at point m; is the instantaneous shear angle at point m; θ m (t) is the instantaneous friction angle at point m.

[0131] Depend on Fig.12 It can be obtained that the instantaneous total velocity v at point m in the workpiece coordinate system is m (t) is:

[0132]

[0133] In the formula, v x (t) is the velocity in the x direction, v y (t) is the velocity in the y direction, v z (t) is the velocity in the z direction.

[0134] Instantaneous cutting speed at point m in the workpiece coordinate system for:

[0135]

[0136] Instantaneous shear velocity at point m of the main cutting edge for:

[0137]

[0138] θ s (t) = π / 4 + γ o -β (25)

[0139]

[0140] Where: γ o is the blade rake angle, β is the friction coefficient, α is the lattice constant (2.9506×10 -10 m), h is Planck's constant (h = 6.62607015 × 10 -34 J·s), kB is the Boltzmann constant (kB=1.380649×10 -23 J / K), υ is the atomic forced vibration frequency, F N is the normal stress at the characteristic point of the cutting edge.

[0141] The relationship between the instantaneous cutting force vector and the instantaneous shear force vector at the selected point m of the main cutting edge of tooth i and the selected point b of the secondary cutting edge is as follows: Fig.13 shown.

[0142] In the tooth coordinate system, the instantaneous cutting force at the selected points of the main and secondary cutting edges is:

[0143]

[0144] In the formula, The cutting force at the selected point of the main cutting edge, is the cutting force at the selected point of the secondary cutting edge, k is the cutting force correction coefficient; F p is the unit cutting force.

[0145] In the tooth coordinate system, the instantaneous shear force at the selected points of the main and secondary cutting edges is:

[0146]

[0147] In the formula, h Di1 (x i ,y i ,z i ) is the instantaneous cutting layer thickness of the main cutting edge, h Di2 (x i ,y i ,z i) is the instantaneous cutting layer thickness of the secondary cutting edge, The cutting force at the selected point of the main cutting edge, is the shear force at the selected point of the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge.

[0148] Calculation method of instantaneous cutting energy efficiency of face milling cutter

[0149] The instantaneous cutting force energy consumption of the main and secondary cutting edges of the cutter teeth are:

[0150]

[0151] In the formula, is the cutting force energy consumption of the main cutting edge, is the cutting force energy consumption of the secondary cutting edge, The instantaneous cutting speed of the selected point m is the main cutting edge, Select the instantaneous cutting speed of point b for the secondary cutting edge.

[0152] Milling cutter instantaneous cutting force energy consumption P c (t) is:

[0153]

[0154] The instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth is:

[0155]

[0156] In the formula, is the shear energy consumption of the main cutting edge, is the shear energy consumption of the secondary cutting edge, The instantaneous shear velocity of the selected point m of the main cutting edge is, is the instantaneous shear velocity of the selected point b on the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge.

[0157] Milling cutter instantaneous shear energy consumption P s (t) is:

[0158]

[0159] The efficiency of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy is η c (t) is:

[0160]

[0161] The efficiency of the milling cutter's instantaneous cutting force energy converted into instantaneous shear energy is ηsc (t) is:

[0162]

[0163] Variation characteristics of instantaneous cutting force energy efficiency and shear energy efficiency of face milling cutter

[0164] The cutting force efficiency during the stable cutting period is as follows: Figure 14-20 shown.

[0165] Depend on Figure 14-20 It can be seen that the RMS value of the cutting force energy efficiency in each cutting period remains between 31.8% and 34.0%, indicating that most of the total power of the machine tool is used to support auxiliary functions such as machine tool movement, control system, cooling, lubrication, etc., and only a part is used for direct cutting operations.

[0166] Depend on Figure 21-27 It can be seen that the root mean square value of shear energy efficiency in each cutting period is maintained between 68.0% and 69.8%, and is relatively stable. This shows that the cutting energy of the milling cutter is effectively converted into the energy of shearing and removing materials, completing the plastic deformation and cutting of the material, with a high energy utilization rate, and under the current cutting parameters and workpiece material conditions, the material deformation and energy consumption in the shearing area during the stable cutting stage have reached a relatively balanced state.

[0167] Experimental verification of instantaneous cutting force energy efficiency of face milling cutter

[0168] According to the cutting force and cutting energy consumption experiment of face milling cutter, the cutting force and energy consumption during the stable cutting period are measured as follows: Figure 28-34 shown.

[0169] The cutting force energy efficiency is calculated using the cutting force energy consumption measured in the above experiment. The results are as follows: Figure 35-41 shown.

[0170] Depend on Figure 21-41 It can be seen that the cutting force energy consumption measured experimentally is slightly larger than the cutting force energy efficiency calculated according to the theoretical model. This is because the friction force in the actual cutting process will be affected by multiple factors such as cutting speed, temperature and workpiece surface state, resulting in nonlinear changes, which will increase the friction energy consumption. In addition, the wear of the tool will further increase the friction energy consumption. The cutting force energy consumption includes shear energy consumption and friction energy consumption. Therefore, the cutting force energy consumption in the actual cutting process is greater than that in the theoretical calculation, resulting in a higher cutting force energy efficiency.

[0171] Implementation Example 1: Face milling cutter cutting experiment plan and results

[0172] In order to obtain the instantaneous cutting energy consumption of the milling cutter under vibration, the CNC milling machine XK7124 three-axis milling machining center was used to conduct a face milling experiment on 45 steel. The milling cutter is the M4003-050-B22-04-6.5 face milling cutter produced by Walter Company, the blade is SDMT1204AZN-D57WKP35G, the number of teeth is 4, and the milling method is dry down milling. The face milling cutter structure and cutter tooth error are shown in Figure 1 and Figure 2 The experimental parameters are shown in Table 1, and the cutting trajectory of the face milling cutter is shown in Figure 4 The experimental results of cutting vibration, cutting force and cutting energy consumption are shown in Figure 5 shown.

[0173] Table 1 Milling experimental parameters

[0174]

[0175] Figure 2 In the figure, l is the length of the cutting edge of the cutter, b is the length of the wiper edge, and r is a is the radius of the tool tip, c is the blade thickness, α is the main clearance angle, s i is the tip of any tooth, s zmax is the tip point of the lowest axial tooth, s rmax is the tip point of the largest radial tooth, Δz i is the axial error of the cutter teeth, Δr i is the radial error of the cutter teeth, θ i For x i Axis and x d The angle between the axes. max is the maximum turning radius of the cutter teeth, r i is the turning radius of tooth i.

[0176] Figure 3 In, p r is the base surface, p s is the cutting plane, p o is an orthogonal plane, p f is the feed plane, s is the main cutting edge, s' is the secondary cutting edge, λ s is the blade inclination angle, κ r is the principal deflection angle, κ r ' is the secondary deflection angle, γ o is the rake angle, α o The back angle.

[0177] Figure 4In the figure, Δt1 to Δt7 are different time periods. Δt1 is the idle period before milling starts, Δt2 is the period when the milling cutter starts to cut in, Δt3 is the period when the milling cutter is fully cut in, Δt4 is the stable milling period, Δt5 is the period when the milling cutter starts to cut out, Δt6 is the period when the milling cutter is fully cut out, and Δt7 is the idle period after milling ends.

[0178] According to the cutting vibration, cutting force and cutting energy consumption experiment of face milling cutter, the experimental results of vibration acceleration, cutting force and cutting energy consumption are obtained, and according to Figure 4 Divide it into time periods, and the results are as follows Figure 5 shown.

[0179] Implementation Example 2: Instantaneous cutting energy composition of face milling cutter

[0180] During the milling process, the input energy and output energy of the milling cutter exist in various forms. The energy input by the main transmission system and feed system of the machine tool is transmitted to the milling cutter and the workpiece through the milling cutter body, the functional interface of each tooth and the cutting layer. The total input energy is composed of torque energy, machine tool feed energy in the three directions of x, y and z, additional vibration energy in the three directions and additional energy of the machine tool. The output energy is composed of the internal energy and centrifugal force energy consumption of the milling cutter caused by the deformation of the milling cutter structure, the main cutting force energy consumption of the milling cutter and the additional energy consumption of the milling cutter energy consumption.

[0181] There are many transmission and conversion relationships between the instantaneous energy input and output of the milling cutter, such as Figure 6 shown.

[0182] Depend on Figure 6 It can be seen that the energy input of the milling cutter during instantaneous cutting is:

[0183] P(t)=P M (t)+P1(t)+P2(t)+P3(t) (1)

[0184] Where P(t) is the total energy input into the milling cutter, P M (t) is the energy of torque input into the milling cutter, P1(t) is the energy of machine tool feed system input into the milling cutter, P2(t) is the vibration energy of the milling process system, and P3(t) is the additional energy provided by the machine tool required for the energy consumption of the milling cutter.

[0185] Among them, P1(t) and P2(t) can be expressed by the following formulas respectively.

[0186] P1(t)=P x (t)+P y (t)+P z (t) (2)

[0187] Where P x (t) is the feeding energy in the x direction, P y(t) is the feeding energy in the y direction, P z (t) is the feed energy in z direction.

[0188] P2(t)=P vx (t)+P vy (t)+P vz (t) (3)

[0189] Where P vx (t) is the vibration energy in the x direction, P vy (t) is the vibration energy in the y direction, P vz (t) is the vibration energy in the z direction.

[0190] The energy consumed by the milling cutter during instantaneous cutting P E (t) is:

[0191] P E (t) = P ie (t)+P ce (t)+P c (t)+P d (t) (4)

[0192] Where P ie (t) is the energy consumption of milling cutter deformation, P ce (t) is the vibration energy consumption of the milling cutter, P c (t) is the energy consumption of milling cutter cutting force, P d (t) is the additional energy consumption of the milling cutter.

[0193] Among them, the instantaneous cutting force energy consumption of the main cutting edge of the milling cutter is P c (t) can be expressed by the following formula:

[0194]

[0195] In the formula, is the instantaneous cutting force energy consumption of tooth i, is the instantaneous shear energy consumption of tooth i, is the instantaneous friction energy consumption between tooth i and the workpiece.

[0196] The input energy of the cutting teeth is:

[0197]

[0198] In the formula, The energy input into the milling cutter of the machine tool feed system is transferred to the energy of the cutter tooth i. is the energy consumption of tooth i along the x direction, is the energy consumption of tooth i along the y direction, is the energy consumption of tooth i along the z direction.

[0199] The output energy of the cutting teeth is:

[0200]

[0201] In the formula, is the energy consumed by the cutting tooth in cutting volume, The heat generated by the cutting process.

[0202]

[0203] In the formula, is the energy consumption of blade wear, The heat generated by the friction and wear of the cutting teeth.

[0204] Depend on Figure 6 According to equations (1) to (8-1), the instantaneous cutting position and energy distribution of the milling cutter under vibration are as follows: Figure 7 As shown in the figure, the milling cutter offset under vibration is as follows Figure 8 shown.

[0205] Figure 7 In the figure, o-xyz is the workpiece coordinate system, o b -x b y b z b is the cutting coordinate system, o c -x c y c z c is the milling cutter coordinate system without vibration, o d -x d y d z d is the milling cutter coordinate system under vibration, o i -x i y i z i is the tooth coordinate system, n is the spindle speed, v is f is the feed speed.

[0206] Figure 8 A x (t), A y (t), A z (t) are x b Axis, y b Axis, z b The vibration displacement in the axial direction, θ(t) is the inclination angle, and θ1(t) is the inclination angle in the x direction. b -oz b The angle of the plane projection, θ2(t) is the inclination angle in y b -oz b The angle of the plane projection, θ d (t) is the direction angle of the milling cutter, φc (t) is the position angle of the vibration-free milling cutter coordinate system, φ d (t) is the position angle of the vibration milling cutter coordinate system.

[0207] Depend on Figure 7 and Figure 8 , under the action of vibration, the equation of the cutting edge of tooth i at time t in the workpiece coordinate system is:

[0208] [x(t) y(t) z(t) 1] T =M3M2T3T2M1T1[x i y i z i 1] T (8-2)

[0209] Among them, (x i ,y i , z i ) is the coordinate of any point of the cutting edge in the cutter tooth coordinate system. M1 is the translation matrix between the cutter tooth coordinate system and the non-vibration milling cutter coordinate system, M2 is the translation matrix between the vibrating milling cutter coordinate system and the cutting coordinate system, M3 is the translation matrix between the cutting coordinate system and the workpiece coordinate system, T1 is the rotation matrix between the cutter tooth coordinate system and the non-vibration milling cutter coordinate system, T2 is the rotation matrix between the non-vibration milling cutter coordinate system and the vibrating milling cutter coordinate system, and T3 is the rotation matrix between the vibrating milling cutter coordinate system and the cutting coordinate system.

[0210] Implementation Example 3: Calculation Method of Instantaneous Velocity Vector and Force Vector of Face Milling Cutter Teeth

[0211] Under the influence of milling vibration, the cutting edge area involved in the cutting task changes with time. The cutting edge that is mainly responsible for removing materials is defined as the main cutting edge, and the cutting edge that is responsible for improving the surface quality of the machined surface is defined as the secondary cutting edge. Figure 3 shown.

[0212] Depend on Fig. 9 It can be obtained that the machining transition surface G formed by the cutter tooth i under vibration is i (x(t),y(t),z(t)) is:

[0213]

[0214] In the formula, l i (x(t), y(t), z(t)) is the cutting edge equation of the cutter tooth in the workpiece coordinate system, t0 is the cutting-in moment when the cutter tooth i forms the machining surface, and t1 is the cutting-out moment when the cutter tooth i forms the machining surface.

[0215] The coordinates of the upper boundary point m1 of the main cutting edge in the workpiece coordinate system are:

[0216]

[0217] In the formula, z m1 (t) is the coordinate of point m1 along the z-axis.

[0218] The coordinates of the lower boundary point m0 ​​of the main cutting edge in the workpiece coordinate system are:

[0219]

[0220] In the formula, z m0 (t) is the coordinate of point m0 ​​along the z-axis.

[0221] From the above formula, we can get the main cutting edge equation l im (x(t),y(t),z(t)) is:

[0222]

[0223] In the workpiece coordinate system, the coordinates of the lower boundary point b0 of the secondary cutting edge are the same as those of the lower boundary point m0 ​​of the main cutting edge.

[0224] The coordinates b1 (x(t), y(t), z(t)) of the upper boundary point b1 of the secondary cutting edge in the workpiece coordinate system are:

[0225]

[0226] The secondary cutting edge equation is:

[0227]

[0228] In the workpiece coordinate system, the position coordinates of point m (x(t), y(t), z(t)) satisfy:

[0229]

[0230] In the tooth coordinate system, the instantaneous cutting layer thickness h of the main cutting edge is Di1 (x i ,y i ,z i )for:

[0231]

[0232] Taking the cutting layer microelement of tooth i as an example, the cutting layer area of ​​the main cutting edge is:

[0233]

[0234] In the workpiece coordinate system, the position coordinates of point b satisfy:

[0235]

[0236] In the tooth coordinate system, the instantaneous cutting layer thickness h of the secondary cutting edge is Di2 (x i ,y i ,z i )for:

[0237]

[0238] The cutting layer area of ​​the secondary cutting edge is:

[0239]

[0240] In the formula, z im0 is the ordinate of point m0 ​​in the cutter tooth coordinate system, j i (x i ,y i ,z i ) is the secondary cutting edge equation of tooth i. From the above formula, we can get the instantaneous cutting layer area A of the milling cutter. D (t) is:

[0241]

[0242] The relationship between the instantaneous cutting velocity vector, the instantaneous shear velocity vector and the instantaneous friction velocity vector at the selected point m of the main cutting edge of the cutter tooth and the selected point b of the secondary cutting edge is as follows: Fig.12 shown.

[0243] Fig.12 In, P rm is the base surface of point m; P om is the cutting plane of point m; P sm is the normal plane of point m; v m (t) is the instantaneous net velocity of m; is the instantaneous cutting speed at point m; is the instantaneous shear velocity at point m; is the instantaneous friction velocity at point m; is the angle between the instantaneous cutting speed and the instantaneous resultant speed at point m; is the instantaneous shear angle at point m; θ m (t) is the instantaneous friction angle at point m.

[0244] Depend on Fig.12 It can be obtained that the instantaneous total velocity v at point m in the workpiece coordinate system is m (t) is:

[0245]

[0246] In the formula, v x(t) is the velocity in the x direction, v y (t) is the velocity in the y direction, v z (t) is the velocity in the z direction.

[0247] Instantaneous cutting speed at point m in the workpiece coordinate system for:

[0248]

[0249] Instantaneous shear velocity at point m of the main cutting edge for:

[0250]

[0251] θ s (t) = π / 4 + γ o -β (25)

[0252]

[0253] Where: γ o is the blade rake angle, β is the friction coefficient, a is the lattice constant (2.9506×10 -10 m), h is Planck's constant (h = 6.62607015 × 10 -34 J·s), kB is the Boltzmann constant (kB=1.380649×10 -23 J / K), T is temperature, υ is the frequency of atomic forced vibration, F N is the normal stress at the characteristic point of the cutting edge.

[0254] The relationship between the instantaneous cutting force vector and the instantaneous shear force vector at the selected point m of the main cutting edge of tooth i and the selected point b of the secondary cutting edge is as follows: Fig.13 shown.

[0255] In the tooth coordinate system, the instantaneous cutting force at the selected points of the main and secondary cutting edges is:

[0256]

[0257] In the formula, The cutting force at the selected point of the main cutting edge, is the cutting force at the selected point of the secondary cutting edge, k is the cutting force correction coefficient; F p is the unit cutting force.

[0258] In the tooth coordinate system, the instantaneous shear force at the selected points of the main and secondary cutting edges is:

[0259]

[0260] In the formula, h Di1 (x i,y i ,z i ) is the instantaneous cutting layer thickness of the main cutting edge, h Di2 (x i ,y i ,z i ) is the instantaneous cutting layer thickness of the secondary cutting edge, The cutting force at the selected point of the main cutting edge, is the shear force at the selected point of the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge.

[0261] Implementation Example 4: Calculation Method of Instantaneous Cutting Energy Efficiency of Face Milling Cutter

[0262] The instantaneous cutting force energy consumption of the main and secondary cutting edges of the cutter teeth are:

[0263]

[0264] In the formula, is the cutting force energy consumption of the main cutting edge, is the cutting force energy consumption of the secondary cutting edge.

[0265] Milling cutter instantaneous cutting force energy consumption P c (t) is:

[0266]

[0267] The instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth is:

[0268]

[0269] In the formula, is the shear energy consumption of the main cutting edge, is the shear energy consumption of the secondary cutting edge.

[0270] Milling cutter instantaneous shear energy consumption P s (t) is:

[0271]

[0272] The total energy consumption of the spindle and feed of the machine tool is calculated based on the experimentally measured energy consumption of the x-axis, y-axis, z-axis and spindle. The total energy consumption during the stable cutting period is as follows: Figure 42-48 shown.

[0273] From equations (31) to (33), it can be obtained that the cutting force energy consumption of the milling cutter during the stable cutting period is as follows: Figure 49-55 shown.

[0274] The shear energy consumption of the milling cutter during the stable cutting period is as follows: Figure 56-62 shown.

[0275] The efficiency of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy is η c (t) is:

[0276]

[0277] The efficiency of the milling cutter's instantaneous cutting force energy converted into instantaneous shear energy is η sc (t) is:

[0278]

[0279] Implementation Example 5: Variation characteristics of instantaneous cutting force energy efficiency and shear energy efficiency of face milling cutter

[0280] The cutting force efficiency during the stable cutting period is as follows: Figure 14-20 shown.

[0281] Depend on Figure 14-20 It can be seen that the RMS value of the cutting force energy efficiency in each cutting period remains between 31.8% and 34.0%, indicating that most of the total power of the machine tool is used to support auxiliary functions such as machine tool movement, control system, cooling, lubrication, etc., and only a part is used for direct cutting operations.

[0282] Depend on Figure 21-27 It can be seen that the root mean square value of shear energy efficiency in each cutting period is maintained between 68.0% and 69.8%, and is relatively stable. This shows that the cutting energy of the milling cutter is effectively converted into the energy of shearing and removing materials, completing the plastic deformation and cutting of the material, with a high energy utilization rate, and under the current cutting parameters and workpiece material conditions, the material deformation and energy consumption in the shearing area during the stable cutting stage have reached a relatively balanced state.

[0283] Implementation Example 6: Experimental Verification of Instantaneous Cutting Force Energy Efficiency of Face Milling Cutter

[0284] According to the cutting force and cutting energy consumption experiment of face milling cutter, the cutting force and energy consumption during the stable cutting period are measured as follows: Figure 28-34 The cutting force energy efficiency is calculated using the cutting force energy consumption measured in the above experiment. The results are shown in Figure 35-41 shown.

[0285] Depend on Figure 21-41It can be seen that the cutting force energy consumption measured experimentally is slightly larger than the cutting force energy efficiency calculated according to the theoretical model. This is because the friction force in the actual cutting process will be affected by multiple factors such as cutting speed, temperature and workpiece surface state, resulting in nonlinear changes, which will increase the friction energy consumption. In addition, the wear of the tool will further increase the friction energy consumption. The cutting force energy consumption includes shear energy consumption and friction energy consumption. Therefore, the cutting force energy consumption in the actual cutting process is greater than that in the theoretical calculation, resulting in a higher cutting force energy efficiency.

[0286] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter, characterized in that: The following steps are involved: S1. Reveal the composition of face milling cutter cutting energy: Determine that the total input energy is composed of the machine tool feed energy in the three directions of torque energy x, y, and z, the additional vibration energy in the three directions, and the additional energy of the machine tool; the output energy is composed of the milling cutter internal energy and centrifugal force energy consumption caused by the milling cutter structure deformation, the milling cutter main cutting force energy consumption, and the additional energy consumption of the milling cutter energy consumption; clarify the transmission and conversion relationship between the energies; S2. Construct the instantaneous cutting posture and energy distribution model of the face milling cutter: establish the workpiece coordinate system, cutting coordinate system, milling cutter coordinate system without vibration, milling cutter coordinate system under vibration and cutter tooth coordinate system, and determine the equation of the cutter tooth cutting edge under vibration in the workpiece coordinate system; S3, solving the instantaneous velocity vector and force vector of the face milling cutter teeth: defining the main and auxiliary cutting edges, constructing their instantaneous cutting boundaries, solving the coordinates and equations of the upper and lower boundary points of the main and auxiliary cutting edges, determining the instantaneous cutting layer thickness and area, and then solving the instantaneous cutting velocity vector, instantaneous shear velocity vector, instantaneous friction velocity vector, instantaneous cutting force vector and instantaneous shear force vector; S4. Construct a solution method for the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter: respectively calculate the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the main and auxiliary cutting edges of the cutter teeth, and then obtain the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the milling cutter; S5. Construct a solution method for the instantaneous cutting force energy efficiency and shear energy efficiency of the milling cutter: calculate the efficiency of the instantaneous input energy of the milling cutter converted into the instantaneous cutting force energy and the efficiency of the instantaneous cutting force energy of the milling cutter converted into the instantaneous shear energy, and reveal their changing characteristics; S6. Conduct experimental verification of the instantaneous cutting force energy efficiency of the face milling cutter: compare the cutting force energy consumption measured experimentally with the cutting force energy efficiency calculated by the theoretical model, and analyze the reasons for the difference.

2. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: In S3, the number of teeth of the milling cutter is 4, the blade model is SDMT1204AZN-D57WKP35G, and the experimental parameters are speed n=2400rpm, feed rate f=0.16mm / z, cutting depth a p =0.4mm, cutting width a e =25mm.

3. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: In the composition of the face milling cutter cutting energy, the calculation formula for the total input energy P(t) is: P(t)=P M (t)+P1(t)+P2(t)+P3(t), Among them, P M (t) is the energy of torque input into the milling cutter, P1(t) is the energy of machine tool feed system input into the milling cutter, P2(t) is the vibration energy of the milling process system, and P3(t) is the additional energy provided by the machine tool required for the energy consumption of the milling cutter; The energy consumed by the milling cutter during instantaneous cutting P E (t) is: P E (t)=P ie (t)+P ce (t)+P c (t)+P d (t), Among them, P ie (t) is the energy consumption of milling cutter deformation, P ce (t) is the vibration energy consumption of the milling cutter, P c (t) is the energy consumption of milling cutter cutting force, P d (t) is the additional energy consumption of the milling cutter.

4. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: When constructing the instantaneous cutting posture and energy distribution model of the face milling cutter, the equation of the cutting edge of tooth i in the workpiece coordinate system at time t under the action of vibration is determined by the translation matrices M1, M2, M3 and rotation matrices T1, T2, T3 between the tooth coordinate system and the non-vibration milling cutter coordinate system, the vibrating milling cutter coordinate system and the cutting coordinate system, and the cutting coordinate system and the workpiece coordinate system.

5. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: When solving the instantaneous velocity vector and force vector of the face milling cutter tooth, in the workpiece coordinate system, the instantaneous total velocity v of the selected point m of the main cutting edge is m (t) is: In the formula, v x (t) is the velocity in the x direction, v y (t) is the velocity in the y direction, v z (t) is the velocity in the z direction.

6. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: When solving the instantaneous velocity vector and force vector of the face milling cutter tooth, the instantaneous cutting force at the selected point of the main cutting edge in the tooth coordinate system is: In the formula, The cutting force at the selected point of the main cutting edge, is the cutting force at the selected point of the secondary cutting edge, k is the cutting force correction coefficient; F p is the unit cutting force; In the tooth coordinate system, the instantaneous shear force at the selected points of the main and secondary cutting edges is: In the formula, h Di1 (x i ,y i ,z i ) is the instantaneous cutting layer thickness of the main cutting edge, h Di2 (x i ,y i ,z i ) is the instantaneous cutting layer thickness of the secondary cutting edge, The cutting force at the selected point of the main cutting edge, is the shear force at the selected point of the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge.

7. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: The instantaneous cutting force energy consumption of the main and secondary cutting edges of the cutter teeth are: In the formula, is the cutting force energy consumption of the main cutting edge, is the cutting force energy consumption of the secondary cutting edge, The instantaneous cutting speed of the selected point m is the main cutting edge. Select the instantaneous cutting speed of point b for the secondary cutting edge.

8. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 7, characterized in that: Milling cutter instantaneous cutting force energy consumption P c (t) is:

9. The method for identifying the instantaneous cutting energy efficiency evolution characteristics of a high-efficiency face milling cutter according to claim 1, characterized in that: The instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth is: In the formula, is the shear energy consumption of the main cutting edge, is the shear energy consumption of the secondary cutting edge, The instantaneous shear velocity of the selected point m of the main cutting edge is, is the instantaneous shear velocity of the selected point b on the secondary cutting edge, τ is the shear stress, is the shear angle of the main cutting edge, is the shear angle of the secondary cutting edge; Milling cutter instantaneous shear energy consumption P s (t) is: The efficiency of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy is η c (t) is: The efficiency of the milling cutter's instantaneous cutting force energy converted into instantaneous shear energy is η sc (t) is:

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