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

Abstract

The application discloses a high-efficiency face milling cutter instantaneous cutting energy efficiency evolution characteristic identification method, comprising the following steps: S1, revealing the composition of the face milling cutter cutting energy: determining that the input total energy is composed of the torque energy, the machine tool feeding energy in x, y and z directions, the three-direction additional vibration energy and the machine tool additional energy; the application solves the instantaneous cutting boundary, the instantaneous speed vector and the force vector of the main and auxiliary cutting edges of the cutter under the vibration action, and then solves the milling cutter cutting force energy consumption and the shearing energy consumption, reveals the instantaneous change of the milling cutter cutting energy consumption, obtains the change characteristics of the milling cutter instantaneous cutting energy efficiency and the shearing energy efficiency, reveals the energy transmission efficiency in the material removal process, solves the problems that the existing method cannot accurately reveal the instantaneous change characteristics of the milling cutter cutting energy consumption and the vibration and the cutter tooth error are ignored, thereby leading to the problem that the calculation error of the cutting energy consumption is too large.

Description

Technical Field

[0001] The present 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 surface quality. Face milling cutters, as a type of high-efficiency milling cutter, are mainly used for high-speed milling. Face milling cutters use intermittent cutting as the cutter teeth repeatedly cut in and out of the workpiece, generating a continuous impact that causes the milling cutter and its teeth to be constantly under the influence of vibration. This causes their instantaneous cutting behavior to change dynamically, resulting in constant changes in instantaneous cutting energy consumption, which directly affects the energy utilization of the milling cutter. Therefore, establishing a method to identify the instantaneous cutting energy efficiency of milling cutters under vibration is of great significance to improving the energy utilization of milling cutters and achieving efficient cutting of milling cutters.

[0003] The instantaneous cutting energy efficiency of a milling cutter directly reflects the level and variation characteristics of the milling cutter's energy utilization. It is related to the milling cutter's instantaneous cutting layer parameters, instantaneous cutting force energy consumption, instantaneous shear energy consumption, and instantaneous input energy of the milling cutter. The instantaneous cutting energy efficiency of a milling cutter includes cutting force energy efficiency and shear energy efficiency, and mainly reflects the relationship between various energies during the milling cutter's cutting of a workpiece. Among them, cutting force energy efficiency refers to the proportion of cutting force energy consumption in the input energy, and shear energy efficiency refers to the proportion of shear energy consumption in the cutting force energy consumption. The root mean square of the cutting force energy efficiency and the shear energy efficiency are used to evaluate the milling cutter's cutting energy efficiency. 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 of the milling cutter.

[0004] 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 cutting force energy consumption and the experimental results; or use the cutting power to integrate time to calculate the cumulative cutting energy consumption, which cannot reveal the instantaneous change of the milling cutter cutting energy consumption.

[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 the cutting vibration, cutting force and cutting energy consumption of the face milling cutter based on 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 the action of 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 objectives, the present invention provides the following technical solution: a method for identifying the evolution characteristics of the instantaneous cutting energy efficiency of a high-efficiency face milling cutter, comprising the following steps: S1, revealing the composition of the face milling cutter's cutting energy: determining that the total input energy is composed of the torque energy in the three directions of x, y, and z, the machine tool feed energy in the three directions, the additional vibration energy, and the machine tool additional energy; the output energy is composed of the milling cutter's internal energy and centrifugal force energy consumption caused by the milling cutter's structural deformation, the milling cutter's main cutting force energy consumption, and the additional energy consumption of the milling cutter's energy consumption; and clarifying the transmission and conversion relationship between the various 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. Calculate the instantaneous velocity vector and force vector of the face milling cutter teeth: define the primary and secondary cutting edges, construct their instantaneous cutting boundaries, calculate the coordinates and equations of the upper and lower boundary points of the primary and secondary cutting edges, determine the instantaneous cutting layer thickness and area, and then calculate 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 method for calculating the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter: calculate the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth respectively, 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 milling cutter's instantaneous input energy converted into instantaneous cutting force energy and the efficiency of the milling cutter's instantaneous cutting force energy converted into 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, the experimental parameters are speed n=2400rpm, feed rate f=0.16mm / z, cutting depth a p =0.4mm, cutting width a e =25mm.

[0014] Preferably, in the face milling cutter cutting energy composition, 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 to the milling cutter, P1(t) is the energy input to the milling cutter by the machine tool feed system, 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 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.

[0021] Preferably, when calculating 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:

[0022]

[0023] Where, 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 calculating 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:

[0025]

[0026]

[0027] Where, 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] Where 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] Where, 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] Where, 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 is the main cutting edge, 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 η of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy c (t) is:

[0042]

[0043] The efficiency of the milling cutter's instantaneous cutting force energy converted into instantaneous shear energy 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, since the friction force is affected by factors such as cutting speed, temperature and workpiece surface state, as well as tool wear, the cutting force energy consumption measured experimentally is greater than that calculated theoretically, 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 face milling experiments, this method reveals the instantaneous cutting energy composition, transfer and conversion characteristics of the face milling cutter, considers the influence of milling vibration and tooth error on the cutting energy of the milling cutter, and solves the instantaneous cutting boundaries, instantaneous velocity vectors and force vectors 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, revealing the instantaneous change of the milling cutter cutting energy consumption, obtaining the change characteristics of the instantaneous cutting energy efficiency and shear energy efficiency of the milling cutter, and revealing the energy transfer efficiency in the material removal process. It solves the problem that the existing methods cannot accurately reveal the instantaneous change characteristics of the milling cutter cutting energy consumption and the problem that 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 Provides a structural diagram of the face milling cutter cutting trajectory and time period division 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 embodiment 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 Provides instantaneous cutting posture and energy distribution diagram of the milling cutter under vibration for the embodiment of the present invention; Figure 8 Provides a coordinate offset diagram of a milling cutter under vibration for an embodiment of the present invention; Figure 9 Provide instantaneous cutting boundary diagrams of the primary and secondary cutting edges of the cutter teeth for embodiments of the present invention; Figure 10 Provide instantaneous cutting layer diagrams of the primary and secondary cutting edges of the cutter teeth for embodiments of the present invention; Figure 11 A diagram of a method for intercepting the microelement of a tooth cutting edge is provided for an embodiment of the present invention; Figure 12 Provide instantaneous velocity vector diagrams of primary and secondary cutting edges for embodiments of the present invention; Figure 13 Provide instantaneous force vector diagrams of the primary and secondary cutting edges for the embodiment of the present invention; Figure 14 Provided for an embodiment of the present invention are (a) a cutting force energy efficiency diagram for a period of Δt4; Figure 15 Provide (b)Δt for the embodiment of the present invention 41 Cutting force energy efficiency diagram for each period; Figure 16 Provide (c)Δt for the embodiment of the present invention 42 Cutting force energy efficiency diagram for each period; Figure 17 Provide (d)Δt for the embodiment of the present invention 43 Cutting force energy efficiency diagram for each period; Figure 18 Provide (e)Δt for the embodiment of the present invention 44Cutting force energy efficiency diagram for each period; Figure 19 Provide (f)Δt for the embodiment of the present invention 45 Cutting force energy efficiency diagram for each period; Figure 20 Provide (g)Δt for the embodiment of the present invention 46 Cutting force energy efficiency diagram for each period; Figure 21 Provided for an embodiment of the present invention are (a) a shear energy efficiency diagram for a period of Δt4; Figure 22 Provide (b)Δt for the embodiment of the present invention 41 Time period shear energy efficiency diagram; Figure 23 Provide (c)Δt for the embodiment of the present invention 42 Time-period shear energy efficiency diagram; Figure 24 Provide (d)Δt for the embodiment of the present invention 43 Time period shear energy efficiency diagram; Figure 25 Provide (e)Δt for the embodiment of the present invention 44 Time-period shear energy efficiency diagram; Figure 26 Provide (f)Δt for the embodiment of the present invention 45 Time-period shear energy efficiency diagram; Figure 27 Provide (g)Δt for the embodiment of the present invention 46 Time-period shear energy efficiency diagram; Figure 28 (a) cutting force energy consumption diagram of the experiment during the Δt4 period is provided for the embodiment of the present invention; Figure 29 Provide (b)Δt for the embodiment of the present invention 41 Cutting force and energy consumption diagram of time period experiment; Figure 30 Provide (c)Δt for the embodiment of the present invention 42 Cutting force and energy consumption diagram of time period experiment; Figure 31 Provide (d)Δt for the embodiment of the present invention 43 Cutting force and energy consumption diagram of time period experiment; Figure 32 Provide (e)Δt for the embodiment of the present invention 44 Cutting force and energy consumption diagram of time period experiment; Figure 33 Provide (f)Δt for the embodiment of the present invention 45 Cutting force and energy consumption diagram of time period experiment; Figure 34 Provide (g)Δt for the embodiment of the present invention 46 Cutting force and energy consumption diagram of time period experiment; Figure 35 (a) an experimental cutting force energy efficiency diagram during the Δt4 period is provided for an embodiment of the present invention; Figure 36 Provide (b)Δt for the embodiment of the present invention 41 Cutting force energy efficiency diagram of time period experiment; Figure 37 Provide (c)Δt for the embodiment of the present invention 42 Cutting force energy efficiency diagram of time period experiment; Figure 38 Provide (d)Δt for the embodiment of the present invention 43 Cutting force energy efficiency diagram of time period experiment; Figure 39 Provide (e)Δt for the embodiment of the present invention44 Cutting force energy efficiency diagram of time period experiment; Figure 40 Provide (f)Δt for the embodiment of the present invention 45 Cutting force energy efficiency diagram of time period experiment; Figure 41 Provide (g)Δt for the embodiment of the present invention 46 Cutting force energy efficiency diagram of time period experiment; Figure 42 Provided for the embodiment of the present invention are (a) a total energy consumption diagram for the Δt4 period; Figure 43 Provide (b)Δt for the embodiment of the present invention 41 Total energy consumption graph for each period; Figure 44 Provide (c)Δt for the embodiment of the present invention 42 Total energy consumption graph for each period; Figure 45 Provide (d)Δt for the embodiment of the present invention 43 Total energy consumption graph for each period; Figure 46 Provide (e)Δt for the embodiment of the present invention 44 Total energy consumption graph for each period; Figure 47 Provide (f)Δt for the embodiment of the present invention 45 Total energy consumption graph for each period; Figure 48 Provide (g)Δt for the embodiment of the present invention 46 Total energy consumption graph for each period; Figure 49 Provided for an embodiment of the present invention are (a) a cutting force energy consumption diagram for a period of Δt4; Figure 50 Provide (b)Δt for the embodiment of the present invention 41 Cutting force and energy consumption diagram for each period; Figure 51 Provide (c)Δt for the embodiment of the present invention 42 Cutting force and energy consumption diagram for each period; Figure 52 Provide (d)Δt for the embodiment of the present invention 43 Cutting force and energy consumption diagram for each period; Figure 53 Provide (e)Δt for the embodiment of the present invention 44 Cutting force and energy consumption diagram for each period; Figure 54 Provide (f)Δt for the embodiment of the present invention 45 Cutting force and energy consumption diagram for each period; Figure 55 Provide (g)Δt for the embodiment of the present invention 46 Cutting force and energy consumption diagram for each period; Figure 56 Provided for the embodiment of the present invention are (a) a shear energy consumption diagram for the Δt4 period; Figure 57 Provide (b)Δt for the embodiment of the present invention 41 Time period shear energy consumption diagram; Figure 58 Provide (c)Δt for the embodiment of the present invention 42 Time period shear energy consumption diagram; Figure 59 Provide (d)Δt for the embodiment of the present invention 43 Time period shear energy consumption diagram; Figure 60 Provide (e)Δt for the embodiment of the present invention 44 Time period shear energy consumption diagram; Figure 61 Provide (f)Δt for the embodiment of the present invention 45 Time period shear energy consumption diagram; Figure 62 Provide (g)Δt for the embodiment of the present invention 46 Time period shear energy consumption diagram. DETAILED DESCRIPTION

[0049] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts 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 evolution characteristics of the instantaneous cutting energy efficiency 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 torque energy in the three directions of x, y, and z, the machine tool feed energy, the additional vibration energy in the three directions, and the machine tool additional energy; the output energy is composed of the milling cutter internal energy and centrifugal force energy consumption caused by 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 each energy;

[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. Calculate the instantaneous velocity vector and force vector of the face milling cutter teeth: define the primary and secondary cutting edges, construct their instantaneous cutting boundaries, calculate the coordinates and equations of the upper and lower boundary points of the primary and secondary cutting edges, determine the instantaneous cutting layer thickness and area, and then calculate 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 method for calculating the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter: calculate the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth respectively, 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 milling cutter's instantaneous input energy converted into instantaneous cutting force energy and the efficiency of the milling cutter's instantaneous cutting force energy converted into 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 experimental plan and results:

[0058] In order to obtain the instantaneous cutting energy consumption of the milling cutter under vibration, a 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 as follows 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 tooth, b is the length of the wiper edge, and r is the length of the cutter tooth. a is the radius of the tool tip, c is the thickness of the blade, α is the main clearance angle, s i is the tip point of any tooth, s zmax is the tip point of the lowest tooth in the axial direction, s rmax is the tip point of the largest radial tooth, Δz i is the axial error of the cutter tooth, Δr i is the radial error of the cutter teeth, θ i is 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 cutting 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 cutting 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 face milling cutter cutting vibration, cutting force and cutting energy consumption experiment, the vibration acceleration, cutting force and cutting energy consumption experimental results 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 the face milling cutter consists of:

[0067] During the milling process, the cutter's input and output energy take on various forms. Energy input from the machine's main drive and feed systems is transferred to the cutter and workpiece via the cutter body, the functional interfaces of each tooth, and the cutting layer. Total input energy consists of torque energy, machine feed energy in the x, y, and z directions, additional vibration energy in these three directions, and additional machine energy. Output energy is comprised of the cutter's internal energy and centrifugal force energy caused by structural deformation, the main cutting force energy, and the additional energy consumed by the cutter's 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 to the milling cutter, P M (t) is the energy of torque input to the milling cutter, P1(t) is the energy input to the milling cutter by the machine tool feed system, 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 feed energy in the y direction, P z (t) is the feed energy in the 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 P c (t) can be expressed by the following formula:

[0081]

[0082] Where, 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] Where, The energy of the milling cutter input into 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] Where, is the energy consumed by the cutting tooth to cut the volume, The heat generated by the cutting process of the blade.

[0089]

[0090] Where, is the energy consumption of tooth wear, The heat generated by the friction and wear of the 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, 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 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, 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 non-vibration 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 on the cutting edge in the tooth coordinate system. M1 is the translation matrix between the 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 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 part of the cutting edge that is mainly responsible for removing materials is defined as the main cutting edge, and the part of the cutting edge that is responsible for improving the quality of the machined surface is defined as the secondary cutting edge. Figure 3 shown.

[0099] Depend on Figure 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] Where, l i The cutting edge equation of the cutter tooth in the workpiece coordinate system (x(t), y(t), z(t)), t0 is the moment when the cutter tooth i cuts into the machined surface, and t1 is the moment when the cutter tooth i cuts out of the machined surface.

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

[0103]

[0104] Where 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] Where 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 equation of the secondary cutting edge 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 element 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, instantaneous shear velocity vector and 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: Figure 12 shown.

[0130] Figure 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 Figure 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] Where, 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 tooth 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: Figure 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] Where, 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] Where 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] Where, 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] Where, 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 is the main cutting edge, 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 η of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy c (t) is:

[0160]

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

[0162]

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

[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 motion, control system, cooling, and lubrication, while only a part is used for direct cutting operations.

[0166] Depend on Figure 21-27 The RMS value of shear energy efficiency during each cutting period remains relatively stable, ranging from 68.0% to 69.8%. This indicates that the milling cutter's cutting energy is effectively converted into shearing energy for material removal, completing both plastic deformation and cutting. This results in high energy utilization, and under current cutting parameters and workpiece material conditions, a relatively balanced state of material deformation and energy consumption in the shear zone is achieved during the stable cutting phase.

[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: Figures 35-41 shown.

[0170] Depend on Figure 21-41 The experimentally measured cutting force energy consumption is slightly higher than the cutting force energy efficiency calculated using the theoretical model. This is because friction in the actual cutting process is affected by multiple factors, such as cutting speed, temperature, and workpiece surface condition, resulting in nonlinear variations and increased friction energy consumption. Furthermore, tool wear further exacerbates friction energy consumption. Since cutting force energy consumption includes both shear and friction energy, the actual cutting force energy consumption is greater than that calculated theoretically, leading to a higher calculated cutting force energy efficiency.

[0171] Implementation Example 1: Face Milling Cutting Experiment Plan and Results

[0172] In order to obtain the instantaneous cutting energy consumption of the milling cutter under vibration, a 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 as follows 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 tooth, b is the length of the wiper edge, and r is the length of the cutter tooth. a is the radius of the tool tip, c is the thickness of the blade, α is the main clearance angle, s i is the tip point of any tooth, s zmax is the tip point of the lowest tooth in the axial direction, s rmax is the tip point of the largest radial tooth, Δz i is the axial error of the cutter tooth, Δr i is the radial error of the cutter teeth, θ i is 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 cutting 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 cutting 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 face milling cutter cutting vibration, cutting force and cutting energy consumption experiment, the vibration acceleration, cutting force and cutting energy consumption experimental results 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 cutter's input and output energy take on various forms. Energy input from the machine's main drive and feed systems is transferred to the cutter and workpiece via the cutter body, the functional interfaces of each tooth, and the cutting layer. Total input energy consists of torque energy, machine feed energy in the x, y, and z directions, additional vibration energy in these three directions, and additional machine energy. Output energy is comprised of the cutter's internal energy and centrifugal force energy caused by structural deformation, the main cutting force energy, and the additional energy consumed by the cutter's 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 to the milling cutter, P M (t) is the energy of torque input to the milling cutter, P1(t) is the energy input to the milling cutter by the machine tool feed system, 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 feed energy in the y direction, P z (t) is the feed energy in the 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 P c (t) can be expressed by the following formula:

[0194]

[0195] Where, 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] Where, The energy of the milling cutter input into 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] Where, is the energy consumed by the cutting tooth to cut the volume, The heat generated by the cutting process of the blade.

[0202]

[0203] Where, is the energy consumption of tooth wear, The heat generated by the friction and wear of the 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, 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 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, 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 non-vibration 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 on the cutting edge in the tooth coordinate system. M1 is the translation matrix between the 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 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 part of the cutting edge that is mainly responsible for removing materials is defined as the main cutting edge, and the part of the cutting edge that is responsible for improving the quality of the machined surface is defined as the secondary cutting edge. Figure 3 shown.

[0212] Depend on Figure 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] Where, l i The cutting edge equation of the cutter tooth in the workpiece coordinate system (x(t), y(t), z(t)), t0 is the moment when the cutter tooth i cuts into the machined surface, and t1 is the moment when the cutter tooth i cuts out of the machined surface.

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

[0216]

[0217] Where 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] Where 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 equation of the secondary cutting edge 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 element 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] Where 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, instantaneous shear velocity vector and 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: Figure 12 shown.

[0243] Figure 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 Figure 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] Where, 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 rake angle of the blade, 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 atomic forced vibration frequency, 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: Figure 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] Where, 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] Where 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 for 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] Where, 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] Where, 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: Figures 42-48 shown.

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

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

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

[0276]

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

[0278]

[0279] Implementation Example 5: Variation Characteristics of Instantaneous Cutting Force Energy Efficiency and Shear Energy Efficiency of Face Milling Cutters

[0280] The cutting force energy 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 motion, control system, cooling, and lubrication, while only a part is used for direct cutting operations.

[0282] Depend on Figure 21-27 The RMS value of shear energy efficiency during each cutting period remains relatively stable, ranging from 68.0% to 69.8%. This indicates that the milling cutter's cutting energy is effectively converted into shearing energy for material removal, completing both plastic deformation and cutting. This results in high energy utilization, and under current cutting parameters and workpiece material conditions, a relatively balanced state of material deformation and energy consumption in the shear zone is achieved during the stable cutting phase.

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

[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 Figures 35-41 shown.

[0285] Depend on Figure 21-41The experimentally measured cutting force energy consumption is slightly higher than the cutting force energy efficiency calculated using the theoretical model. This is because friction in the actual cutting process is affected by multiple factors, such as cutting speed, temperature, and workpiece surface condition, resulting in nonlinear variations and increased friction energy consumption. Furthermore, tool wear further exacerbates friction energy consumption. Since cutting force energy consumption includes both shear and friction energy, the actual cutting force energy consumption is greater than that calculated theoretically, leading to a higher calculated cutting force energy efficiency.

[0286] While 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 these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for identifying the evolution characteristics of instantaneous cutting energy efficiency 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 torque energy in the three directions of x, y, and z, the machine tool feed energy, the additional vibration energy in the three directions, and the machine tool additional energy; the output energy is composed of the milling cutter internal energy and centrifugal force energy consumption caused by 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 each energy; 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. Calculate the instantaneous velocity vector and force vector of the face milling cutter teeth: define the primary and secondary cutting edges, construct their instantaneous cutting boundaries, calculate the coordinates and equations of the upper and lower boundary points of the primary and secondary cutting edges, determine the instantaneous cutting layer thickness and area, and then calculate 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 method for calculating the instantaneous cutting force energy consumption and shear energy consumption of the milling cutter: calculate the instantaneous cutting force energy consumption and the instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth respectively, 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 milling cutter's instantaneous input energy converted into instantaneous cutting force energy and the efficiency of the milling cutter's instantaneous cutting force energy converted into 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 milling cutter teeth is 4, the blade model is SDMT1204AZN-D57WKP35G, and the experimental parameters are speed n = 2400 rpm, feed rate f = 0.16 mm / 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 to the milling cutter, P1(t) is the energy input to the milling cutter by the machine tool feed system, 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 calculating the instantaneous velocity vector and force vector of the face milling cutter tooth, the instantaneous total velocity v of the selected point m of the main cutting edge in the workpiece coordinate system is m (t) is: Where, 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, wherein: 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: Where, 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: Where 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: Where, 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, wherein: The instantaneous shear energy consumption of the main and secondary cutting edges of the cutter teeth is: Where, 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 is the main cutting edge, 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 η of the milling cutter's instantaneous input energy converted into instantaneous cutting force energy c (t) is: The efficiency of the milling cutter's instantaneous cutting force energy converted into instantaneous shear energy η sc (t) is:

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