CN107679335B - Real-time cutting force coefficient calculation method considering dynamic chip thickness under tool vibration - Google Patents
Real-time cutting force coefficient calculation method considering dynamic chip thickness under tool vibration Download PDFInfo
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Abstract
The invention discloses a real-time cutting force coefficient calculation method considering dynamic chip thickness under cutter vibration, which is used for solving the technical problem of poor practicability of the conventional cutting force coefficient calculation method. The technical scheme includes that the rigidity of a system is measured through a hammering experiment, cutting force of a workpiece in the cutting process is recorded, vibration displacement of a cutter is calculated in real time according to a kinetic equation, dynamic chip thickness is calculated by combining a time lag effect, a theoretical equation of the cutting force is calculated by combining the chip thickness and a cutting force coefficient, a relation is established between the theoretical equation and the actually measured cutting force, and an unknown cutting force coefficient is calculated by solving a regular equation. The method can effectively utilize cutting force data, calculate a group of cutting force coefficients every time the cutter rotates for one circle, simultaneously consider the rigidity characteristic changes of different 'main shaft-chuck-cutter' systems, improve the utilization efficiency of the data, provide a large amount of cutting force data for later statistical processing, enrich the data basis of a cutting database and have good practicability.
Description
Technical Field
The invention relates to a cutting force coefficient calculation method, in particular to a real-time cutting force coefficient calculation method considering dynamic chip thickness under cutter vibration.
Background
The document "Cutting force coefficients determination using Cutting, Procedia CIRP62(2017) 205-. Aiming at the continuous cutting process of turning, the method takes the influence of vibration caused by weak rigidity of a cutter in the cutting process into consideration to calculate the cutting force coefficient. In particular, due to the weak rigidity of the turning process tool, the undeformed chip thickness of the cutting layer of the turning process can dynamically change due to vibration of the tool. The method measures the vibration condition of a cutter by using a plurality of sensors, calculates the real-time dynamic chip thickness according to the installation condition of the sensors, and calculates the cutting force coefficient by combining the measured force signal and the relationship between the force and the cutting force coefficient and the undeformed chip thickness. Compared with a more traditional method, the method considers the dynamic characteristic of the system, and the calculation process considers the virtually-changed undeformed chip thickness, so that continuous monitoring of the calculation output is possible. However, the method uses a large number of sensors, particularly displacement sensors which are difficult to use in the milling process of tool rotation, and in addition, the calculation process of the method is not suitable for milling the widely-used interrupted cutting.
Disclosure of Invention
In order to overcome the defect that the existing cutting force coefficient calculation method is poor in practicability, the invention provides a real-time cutting force coefficient calculation method considering dynamic chip thickness under cutter vibration. The method comprises the steps of firstly measuring the rigidity of a system through a hammering experiment, recording the cutting force of a workpiece in the cutting process, simultaneously calculating the vibration displacement of a cutter in real time according to a kinetic equation, calculating the dynamic chip thickness by combining a time-lag effect, finally calculating a theoretical equation of the cutting force by combining the chip thickness and the cutting force coefficient, establishing a connection with the actually measured cutting force, and solving a regular equation to calculate the unknown cutting force coefficient. The method can effectively utilize cutting force data, calculate a group of cutting force coefficients every time the cutter rotates for one circle, and simultaneously consider the rigidity characteristic changes of different 'main shaft-chuck-cutter' systems, thereby improving the utilization efficiency of the data, providing a large amount of cutting force data for later statistical processing, enriching the data basis of a cutting database and having good practicability.
The technical scheme adopted by the invention for solving the technical problems is as follows: a real-time cutting force coefficient calculation method considering dynamic chip thickness under cutter vibration is characterized by comprising the following steps:
step one, tool geometric parameters are provided by a manufacturer providing tools simultaneously or obtained through tool measurement. In the process of establishing a system dynamics model, the end part of a cutter is regarded as a two-degree-of-freedom spring oscillator model, and the bottom modal stiffness, the damping and the modal mass parameters of the cutter arranged on a main shaft chuck are measured by using a hammering experiment, so that a system dynamics equation is determined:
wherein m isx、myModal masses in the x and y directions, respectively, cx、cyModal damping, k, in the x and y directions respectivelyx、kyModal stiffnesses in the x and y directions, respectively.
Secondly, side milling the workpiece by using constant cutting parameters meeting requirements, and measuring real-time cutting force by using a cutting dynamometer, wherein the cutting force is a force F under a fixed coordinate systemxt(tk)、Fyt(tk)、Fzt(tk)。
Step three, determining each sampling point tkAngle of rotation of the tool, force Fxt(tk)、Fyt(tk)、Fzt(tk) Conversion into forces F in the tool coordinate systemtc(tk) Radial force Frc(tk) Tangential force Fac(tk)：
Wherein,
step four, utilizing the system dynamics equation (1) and the cutting force F obtained by the system in real timext(tk)、Fyt(tk) Solving the real-time vibration displacement of the cutter by using a classic four-stage Runge-Kutta method, and then utilizingCalculating the dynamic chip thickness by using the real-time vibration displacement of the cutter:
wherein T is the time difference of the continuous two cutter teeth of the cutter. The true chip thickness on the tool edge at this time is:
h(tk)＝hsta(tk)+hdyn(tk) (4)
step five, combining the cutting force data and the dynamic chip thickness of each point to construct a regular equation: the formula for calculating the cutting force by the cutting force coefficient under the dynamic chip thickness corresponds to the value of each sampling point force, and a regular equation is constructed:
wherein, apFor axial cutting depth of the cutter.
And solving a regular equation to finally obtain the cutting force coefficient.
The invention has the beneficial effects that: the method comprises the steps of firstly measuring the rigidity of a system through a hammering experiment, recording the cutting force of a workpiece in the cutting process, simultaneously calculating the vibration displacement of a cutter in real time according to a kinetic equation, calculating the dynamic chip thickness by combining a time-lag effect, finally calculating a theoretical equation of the cutting force by combining the chip thickness and the cutting force coefficient, establishing a connection with the actually measured cutting force, and solving a regular equation to calculate the unknown cutting force coefficient. The method can effectively utilize cutting force data, calculate a group of cutting force coefficients every time the cutter rotates for one circle, and simultaneously consider the rigidity characteristic changes of different 'main shaft-chuck-cutter' systems, thereby improving the utilization efficiency of the data, providing a large amount of cutting force data for later statistical processing, enriching the data basis of a cutting database and having good practicability.
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Drawings
FIG. 1 is a flow chart of a method for calculating a real-time cutting force coefficient in consideration of dynamic chip thickness under tool vibration according to the present invention.
Detailed Description
Refer to fig. 1. The real-time cutting force coefficient calculation method considering the dynamic chip thickness under the vibration of the cutter comprises the following specific steps:
1. and determining geometrical and dynamic parameters of the tool.
The tool geometry is provided by the manufacturer of the tool at the same time or is obtained by tool measurements. In the process of establishing a system dynamics model, the end part of a cutter is regarded as a two-degree-of-freedom spring oscillator model, and the bottom modal stiffness, the damping and the modal mass parameters of the cutter arranged on a main shaft chuck are measured by using a hammering experiment, so that a system dynamics equation is determined:
wherein m isx、myModal masses in the x and y directions, respectively, cx、cyModal damping, k, in the x and y directions respectivelyx、kyModal stiffnesses in the x and y directions, respectively.
2. And (6) measuring the cutting force.
Side milling the workpiece with constant cutting parameters meeting the requirements, and measuring the real-time cutting force by a cutting dynamometer, wherein the group of cutting forces is a force F under a fixed coordinate systemxt(tk)、Fyt(tk)、Fzt(tk). The function is as follows: the constant cutting parameters can reduce the variables required in the calculation process, reduce the calculation difficulty of the verification identification method, and the dynamometer can synchronously measure xc,yc,zcThe cutting force in three directions has the characteristics of stable force measuring signals, strong anti-interference capability and convenient installation.
3. And converting the cutting force.
Determining each sampling point tkAngle of rotation of the tool, force Fxt(tk)、Fyt(tk)、Fzt(tk) Conversion into forces F in the tool coordinate systemtc(tk) Radial force Frc(tk) Tangential force Fac(tk)：
Wherein,
the function is as follows: the cutting force under the static coordinate system is converted into the cutting force under the rotating coordinate system, namely the cutting force in the right-angle cutting process, namely the interaction result of the material and the cutter, so that convenience is provided for the establishment of a linear equation and the solution below.
4. And calculating the vibration of the tool.
Cutting force F obtained in real time by using system dynamics equation (1) and systemxt(tk)、Fyt(tk) And solving the real-time vibration condition of the cutter. In this case, a numerical solution of a differential equation can be used, and the classical four-stage fourth-order Runge-Kutta method is used in the present invention. And then calculating the dynamic chip thickness by utilizing the real-time vibration displacement of the cutter:
wherein T is the time difference of the continuous two cutter teeth of the cutter. The true chip thickness on the tool edge at this time is:
h(tk)＝hsra(tk)+hdyn(tk) (4)
the function is as follows: the tool displacement obtained by solving the system dynamics equation is independent of additional sensors and has higher accuracy, especially because the later calculation process requires the dynamic chip thickness of the cutting process, which is obtained by the vibration displacement calculation of the tool later.
5. And establishing a regular equation and solving a cutting force coefficient.
And (3) combining the cutting force data and the dynamic chip thickness of each point to construct a regular equation: the formula for calculating the cutting force by the cutting force coefficient under the dynamic chip thickness corresponds to the value of each sampling point force, and a regular equation is constructed:
wherein, apFor axial cutting depth of the cutter.
And solving a regular equation to finally obtain the cutting force coefficient.
The function is as follows: one group of cutting force coefficients are six unknown variables, and under the condition that the sampling frequency in actual processing collection is high enough, the number of equations which can be constructed in each period is actually far larger than the number of the unknown variables, so that a regular equation can be directly formed.
The algorithm provided by the invention requires that the cutting width is not too large no matter the complexity of the workpiece in the process of data acquisition, and has the following functions: because the cutter usually has a plurality of cutter teeth, when the cutting width is too large, the condition that the cutter teeth cut simultaneously inevitably occurs, in this case, the stress condition of each cutter tooth cannot be calculated exactly, the formula relation between the thickness of the chip on each cutter tooth and the force cannot be obtained, and meanwhile, if the cutter teeth cut, the position cut by the cutter cannot be found exactly, namely, the origin of calculation is obtained. The algorithm provided by the invention is mainly based on the end mill, mainly aims at the spiral edge of the general end mill, does not consider the contact effect caused by the shapes of the cutters such as a ball head and the like, and therefore, the algorithm cannot be applied to the cutters except the end mill. The reason is that: the shape of the helical edge of these tools changes the direction and magnitude of the force applied to the tool, requiring special conversion processing. And the calculation of the undeformed chip thickness is influenced significantly by the change in the shape of the tool edge.
The method for calculating the cutting force coefficient of the heterogeneous system considering the system rigidity is suitable for machining materials which are difficult to machine, such as titanium alloy, high-temperature alloy and the like, and comprises the fine machining stage and the rough machining stage. The reason is that: the titanium alloy and the high-temperature alloy have the outstanding characteristics of larger processing resistance and obvious processing heat effect, and the cutting tool processing requirement adopts smaller cutting depth and width, thus meeting the requirement of the algorithm on processing parameters.
Claims (1)
1. A real-time cutting force coefficient calculation method considering dynamic chip thickness under tool vibration is characterized by comprising the following steps:
firstly, geometrical parameters of the cutter are provided by a manufacturer providing the cutter at the same time or obtained by measuring the cutter; in the process of establishing a system dynamics model, the end part of a cutter is regarded as a two-degree-of-freedom spring oscillator model, and the bottom modal stiffness, the damping and the modal mass parameters of the cutter arranged on a main shaft chuck are measured by using a hammering experiment, so that a system dynamics equation is determined:
wherein m isx、myModal masses in the x and y directions, respectively, cx、cyModal damping, k, in the x and y directions respectivelyx、kyModal stiffness in the x and y directions, respectively;
secondly, side milling the workpiece by using constant cutting parameters meeting requirements, and measuring real-time cutting force by using a cutting dynamometer, wherein the cutting force is a force F under a fixed coordinate systemxt(tk)、Fyt(tk)、Fzt(tk)；
Step three, determining each sampling point tkAngle of rotation of the tool, force Fxt(tk)、Fyt(tk)、Fzt(tk) Conversion into forces F in the tool coordinate systemtc(tk) Radial force Frc(tk) Tangential force Fac(tk)：
Wherein,
step four, utilizing the system dynamics equation (1) and the cutting force F obtained by the system in real timext(tk)、Fyt(tk) Solving the real-time vibration displacement of the cutter by using a classic four-stage Runge-Kutta method, and then calculating the dynamic chip thickness by using the real-time vibration displacement of the cutter:
wherein T is the time difference of the continuous two cutter teeth cutting in of the cutter; the true chip thickness on the tool edge at this time is:
h(tk)＝hsta(tk)+hdyn(tk) (4)
step five, combining the cutting force data and the dynamic chip thickness of each point to construct a regular equation: the formula for calculating the cutting force by the cutting force coefficient under the dynamic chip thickness corresponds to the value of each sampling point force, and a regular equation is constructed:
wherein, apCutting the cutter axially;
and solving a regular equation to finally obtain the cutting force coefficient.
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| CN109357826B (en) * | 2018-09-26 | 2020-06-19 | 江苏师范大学 | Research method for coupling characteristics of turning tool-workpiece nonlinear vibration system |
| CN109902448B (en) * | 2019-04-24 | 2022-05-17 | 西北工业大学 | Machine tool machining process energy consumption model modeling method considering cutter abrasion |
| CN111666650B (en) * | 2020-04-22 | 2023-08-29 | 航天材料及工艺研究所 | Cutting parameter and cutter parameter matching method based on mould pressing high silica milling |
| CN114119501B (en) * | 2021-11-05 | 2023-03-17 | 苏州大学 | Method and system for measuring non-deformed cutting thickness of micro-milling |
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| CN103823945A (en) * | 2014-03-13 | 2014-05-28 | 大连理工大学 | Flutter stability domain modeling approach for face cutting process |
| CN104298799A (en) * | 2014-05-07 | 2015-01-21 | 上海交通大学 | Method for designing key geometric parameters of end mill on basis of machining vibration |
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