A method for modeling dynamics of a high-speed ball screw feed system in service state

Abstract

A kind of dynamics modeling method of high-speed ball screw feeding system in service state, the mass of moving part of ball screw feeding system is obtained;Based on the acceleration range value commonly used in numerical control system, the inertia force caused by different acceleration is quantitatively calculated;Quantitatively calculate the friction force related to speed;According to the inertia force caused by different acceleration of moving part, the friction force under different feeding speed and the initial pre-tightening force of screw nut pair and supporting bearing pair, the equivalent axial stiffness of screw nut pair and supporting bearing pair is calculated by combining elastic hertz contact theory;The dynamics model of ball screw feeding system is equivalent by using hybrid element method, and the equivalent dynamics model is obtained;According to d'Alembert principle and equivalent dynamics model, the variable coefficient dynamics equation of ball screw feeding system in service state is established;The invention can avoid vibration source frequency, realize the stable, accurate and fast response of system, and finally realize the high-precision and efficient machining of parts.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of machine tool equipment design and manufacturing technology, in particular to a kind of dynamics modeling method of high-speed ball screw feed system in service state. BACKGROUND

[0002] Ball screw feed system as the core key functional components of manufacturing industry work machine, has been widely applied in shipbuilding, aerospace, automobile and other manufacturing fields.

[0003] There are many dynamics model analyses of ball screw feed system in prior art, for example, patent application CN202111339195.9 discloses a ball screw feed system rolling joint dynamic characteristic parameter identification method, taking ball screw feed system as the analysis object, a twin finite element model of ball screw feed system considering the stiffness and damping of multiple rolling joints in each direction is established; an optimization identification model is constructed combined with modal test data, and particle swarm algorithm is used for solving, so as to identify the dynamic characteristic parameters of each rolling joint. However, for high-speed ball screw feed system, since it needs to have high acceleration and high speed to realize the stable, accurate and fast reciprocating motion of the moving part in service state, and finally completes the machining of the part, the inertia force caused by high acceleration and the friction force caused by high speed will change the pre-tightening force of the dynamic joint of the feed system, thereby changing the contact stiffness of the dynamic joint and affecting the modal frequency distribution of the feed system. Therefore, the modal frequency cannot be regarded as an ideal value to select the control parameters and high-precision and high-efficiency machining parameters of the system, otherwise it may cause the feed system to realize higher stability, accuracy and speed, and may cause machining chatter and other phenomena, ultimately affecting the machining quality of the part. SUMMARY

[0004] In view of the problems existing in the prior art, the present application provides a dynamics modeling method of high-speed ball screw feed system in service state, which can give the modal frequency distribution of ball screw feed system in service state, avoid the vibration source frequency, realize the stable, accurate and fast response of the system, and finally realize the high-precision and high-efficiency machining of the part.

[0005] In order to achieve the above-mentioned purpose, the present application realizes the following technical scheme:

[0006] A dynamics modeling method of high-speed ball screw feed system in service state, comprising the following steps:

[0007] Step 1, for ball screw feed system, the mass of moving part of ball screw feed system is obtained by establishing three-dimensional model using CAD software;

[0008] Step 2, based on the commonly used acceleration range value of numerical control system, the size of inertia force caused by different accelerations is quantitatively calculated;

[0009] Step 3, when the ball screw feeding system is in uniform motion, the friction force in the feeding direction of the system should be equal to the driving force output by the servo motor, and the friction force related to the speed is quantitatively calculated by combining the lead of the screw, the speed reduction ratio, the torque constant of the motor and the average value of the current under uniform speed running;

[0010] Step 4, according to the inertia force caused by different accelerations of the moving part, the friction force under different feeding speeds, and the initial pre-tightening force of the screw nut pair and the supporting bearing pair, the equivalent axial stiffness of the screw nut pair and the supporting bearing pair is calculated by combining the elastic Hertz contact theory;

[0011] Step 5, the dynamic combination part is equivalent to a spring damping unit, the screw lever is equivalent to a beam unit with 2 nodes and 4 degrees of freedom, and the moving part is equivalent to a concentrated mass unit. The mixed unit method is used to equivalent the dynamics model of the ball screw feeding system to obtain the equivalent dynamics model;

[0012] Step 6, according to the D'Alembert principle and the equivalent dynamics model, the variable coefficient dynamics equation of the ball screw feeding system in the service state is established.

[0013] The step 3 is specifically: since the friction force in the feeding direction of the ball screw feeding system is equal to the driving force output by the servo motor when the system is in uniform motion, the input driving torque T of the servo motor is s The friction force f(v) of the ball screw feeding system can be obtained by the following formula:

[0014] T s =k t ·I A (1)

[0015] In the formula: k t is the torque constant of the motor; I A is the average value of the current under uniform speed running, therefore, the friction force f(v) of the ball screw feeding system can be obtained by the following formula:

[0016]

[0017] In the formula: π is the constant of circular ratio, p is the lead of the screw, S dr is the speed reduction ratio.

[0018] The step 4 is specifically: assuming that the moving part moves in the Y direction with a speed v t , and a tThe formula (3) is used for calculating the equivalent axial stiffness of the screw nut pair, and the formula (4) and the formula (5) are used for calculating the equivalent axial stiffness of the front and rear support bearing pairs, and the change rule of the equivalent axial stiffness of the screw nut pair and the front and rear support bearing pairs with different accelerations and different feeding speeds is quantitatively given;

[0019]

[0020]

[0021]

[0022] In the formula, P Ca is the initial pre-tightening force of the nut pair, P d and C p are the rated dynamic load and the rated dynamic load coefficient of the nut pair respectively, and α con is the contact angle of the ball and the raceway, is the helix angle of the screw, i sn is the number of bearing circles of the single nut, d0 and d sb are the nominal diameter of the screw and the diameter of the ball respectively, F as is the pre-stretching axial force of the screw, α cb is the contact angle of the bearing pair, i b is the number of single-end bearing, n b is the number of balls of the single-end bearing, and K h is the Hertz contact coefficient.

[0023] The step 5 is specifically: the screw nut pair dynamic joint part and the front and rear support bearing pair dynamic joint part in the screw feeding system are equivalent to spring-damping units; the screw lever is equivalent to a beam unit with n nodes and 2n degrees of freedom, each node has one rotational degree of freedom and one axial movement degree of freedom; the moving parts are equivalent to concentrated mass units, and the dynamic model of the ball screw feeding system is equivalent by using the mixed unit method, and the equivalent dynamic model of the ball screw feeding system is established; the mass matrix of the equivalent beam unit is shown in the formula (6) and the formula (7), and is a function of the position of the moving parts;

[0024]

[0025]

[0026] In the formula, ρ ss is the material density of the beam unit, A ess is the equivalent cross-sectional area of the beam unit, I ρss is the polar moment of inertia, and yvari L is the distance between the lead screw and nut assembly and the front bearing support unit. fix This refers to the distance between the front and rear bearing support units.

[0027] Since the lead screw and nut pair and the motor not only bear the tension and compression functions, but also the torsional force, the stiffness matrices of the equivalent beam elements on both sides of the lead screw and nut pair are different. The stiffness matrices of the equivalent beam elements are shown in formulas (8) and (9):

[0028]

[0029]

[0030] In the formula: E ss For the elastic modulus, G ss Let p be the shear modulus and p be the lead of the lead screw.

[0031] The variable coefficient dynamic equation described in step 6 is as follows:

[0032]

[0033] In the formula: M, C, and K are the mass, damping, and stiffness matrices of the system, respectively; the mass matrix is ​​a function of the position of the moving part, i.e., it changes with y. vari The stiffness matrix changes with the position, velocity, and acceleration of the moving part; it is a variable value. q represents the vectors of acceleration, velocity, and position, respectively.

[0034] Compared with the prior art, the present invention has the following beneficial technical effects:

[0035] The dynamic modeling method for a high-speed ball screw feed system under service conditions, as described in this invention, provides the actual preload of the moving joint of the feed system and the variation range of the equivalent axial stiffness of the screw-nut pair and the support bearing pair under different accelerations and feed speeds during the use of high-end CNC machine tools. Furthermore, it provides the distribution law of the modal frequencies of the ball screw feed system, offering a theoretical basis for the selection of system control parameters, spindle speed, and cutting parameters. This overcomes the shortcomings of existing dynamic modeling methods for ball screw feed systems, which only treat the equivalent stiffness of the moving joint as a constant value and do not consider the influence of feed speed and feed acceleration on the preload, equivalent stiffness, and modal frequencies of the moving joint. It has the advantage of being able to provide the modal frequency distribution of the ball screw feed system under service conditions, avoiding vibration source frequencies, achieving stable, accurate, and fast system response, and ultimately realizing high-precision and high-efficiency machining of parts. Attached Figure Description

[0036] Figure 1This is a schematic diagram of the ball screw feed system.

[0037] Figure 2 This is a schematic diagram of the structure of a washer-type double nut in a ball screw feed system.

[0038] Figure 3 This is a schematic diagram of the support unit in the ball screw feed system.

[0039] Figure 4 This is the equivalent dynamic model of the ball screw feed system in this invention. Detailed Implementation

[0040] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. These descriptions are intended to explain the invention and not to limit it.

[0041] The present invention discloses a dynamic modeling method for a high-speed ball screw feed system under service conditions, which can accurately describe the dynamic characteristics of the feed system of a high-end CNC machine tool under actual working conditions. The method includes the following steps:

[0042] Step 1: For the ball screw feed system of CNC machine tool, based on the CAD model of the system, use 3D software to set the density of the material and calculate the mass m of the moving parts of the ball screw feed system.

[0043] Step 2: Calculate the mass m of the moving part of the system from Step 1, and combine it with the acceleration value a commonly used in CNC systems (here, acceleration value a is a range) to quantitatively calculate the magnitude m*a of the inertial force caused by different accelerations.

[0044] Step 3: When the ball screw feed system moves at a constant speed, the frictional force in the feed direction is equal to the driving force output by motor 5, and the driving torque T input by servo motor 5 is... s It can be obtained from the following formula:

[0045] T s =k t ·I A (1)

[0046] In the formula: k t I is the torque constant of the motor; A Since the current is the average value under constant speed operation, the frictional force f(v) of the ball screw feed system can be obtained by the following formula:

[0047]

[0048] In the formula: π is the constant of pi, p is the lead of the leadscrew, and S dr This is the reduction ratio.

[0049] Step 4, targeting Figure 1In the above, the assumed moving part 6 moves at a speed v t Move in the Y direction, with a t Accelerating in the Y direction, the inertial force under different accelerations and the frictional force under different feed speeds are calculated in step 1. With the help of the elastic Hertzian contact theory, the calculation formula for the equivalent axial stiffness of the lead screw nut pair 1 is derived as formula (3), and the calculation formula for the equivalent axial stiffness of the front / rear support bearing pair is derived as formula (4) and formula (5). The variation law of the equivalent axial stiffness of the lead screw nut pair 1, the front / rear support bearing pairs 2 and 3 with different accelerations and different feed speeds of the system is quantitatively given.

[0050]

[0051]

[0052]

[0053] In the formula: P Ca P is the initial preload of the nut assembly. d C p These are the rated dynamic load and rated dynamic load factor of the nut pair, respectively, α. con The contact angle between the ball and the raceway. Let i be the helix angle of the leadscrew. sn For the number of bearing turns of a single nut, d0 and d sb These are the nominal diameter of the lead screw and the diameter of the balls, respectively. as α is the axial force of the lead screw preload. cb i is the contact angle of the bearing pair. b n represents the number of single-end bearings. b K represents the number of balls in a single load-bearing bearing. h is the Hertzian contact coefficient.

[0054] Step 5, refer to Figure 1 , Figure 2 and Figure 3 The ball screw feed system's moving joints (screw nut assembly 1 and front / rear support bearing assemblies 2 and 3) are equivalent to spring-damped elements; the lever 4 is equivalent to a beam element with n nodes and 2n degrees of freedom, each node having one rotational degree of freedom and one axial translational degree of freedom; the moving parts are equivalent to lumped mass elements. Using the hybrid element method, the ball screw feed system's dynamic model is equivalently modeled, establishing an equivalent dynamic model for the ball screw feed system, such as... Figure 4 As shown; the mass matrix of the equivalent beam element is shown in formulas (6) and (7), and is a function of the position of the moving part;

[0055]

[0056]

[0057] In the formula: ρ ss Let A be the material density of the beam element. ess I is the equivalent cross-sectional area of ​​the beam element. ρss For the polar moment of inertia, y vari L is the distance between the lead screw nut assembly 1 and the front bearing support unit 2. fix This refers to the distance between the front / rear bearing support units 2 and 3.

[0058] Since the lever 4 between the lead screw and nut assembly 1 and the motor 5 not only bears the tension and compression functions but also the torsional force, the stiffness matrices of the equivalent beam elements on both sides of the lead screw and nut assembly are different. The stiffness matrices of the equivalent beam elements are shown in formulas (8) and (9):

[0059]

[0060]

[0061] In the formula: E ss For the elastic modulus, G ss Let p be the shear modulus and p be the lead of the lead screw.

[0062] Step 6: Based on d'Alembert's principle and the equivalent dynamic model, establish the variable coefficient dynamic equation of the ball screw feed system under service conditions, and solve the modal frequency distribution law of the ball screw feed system; based on the calculated modal frequency distribution law of the feed system, provide a theoretical basis for the selection of system control parameters, spindle speed and cutting parameters of the feed system, and finally realize high-precision and high-efficiency machining of parts.

[0063] Based on d'Alembert's principle and the equivalent dynamic model of the system established in step 5, the variable coefficient dynamic equation of the ball screw feed system considering the influence of the feed position, feed speed, and feed acceleration of the moving part is established as follows:

[0064]

[0065] In the formula: M, C, and K are the mass, damping, and stiffness matrices of the system, respectively; the mass matrix is ​​a function of the position of the moving part, i.e., it changes with y. vari The stiffness matrix changes with the position, velocity, and acceleration of the moving part; it is a variable value. q represents the vectors of acceleration, velocity, and position, respectively.

Claims

1. A dynamic modeling method for a high-speed ball screw feed system in service, characterized in that, Includes the following steps: Step 1: For the ball screw feed system, use CAD software to obtain the mass of the moving parts of the ball screw feed system through the established three-dimensional model; Step 2: Based on the commonly used acceleration range values ​​of CNC systems, quantitatively calculate the magnitude of the inertial force caused by different accelerations; Step 3: When the ball screw feed system moves at a constant speed, the frictional force in the feed direction of the system should be equal to the driving force output by the servo motor. Combining the lead of the ball screw, the reduction ratio, the torque constant of the motor, and the average value of the current under constant speed operation, the frictional force related to the speed is quantitatively calculated. Step 4: Based on the inertial force caused by different accelerations of the moving parts, the frictional force at different feed speeds, and the initial preload of the lead screw and nut pair and the support bearing pair, the equivalent axial stiffness of the lead screw and nut pair and the support bearing pair is calculated using the elastic Hertzian contact theory. Step 5: The moving joint is equivalent to a spring damping element, the ball screw lever is equivalent to a 2-node 4-DOF beam element, and the moving part is equivalent to a lumped mass element. The hybrid element method is used to perform dynamic model equivalence on the ball screw feed system to obtain the equivalent dynamic model. Step 6: Based on d'Alembert's principle and the equivalent dynamic model, establish the variable coefficient dynamic equation of the ball screw feed system under service conditions; Step 5 specifically involves: equipping the ball screw nut drive joint and the front / rear support bearing drive joint in the ball screw feed system as spring-damping units; equipping the lever as an n-node, 2n-degree-of-freedom beam unit, with each node having one rotational degree of freedom and one axial translational degree of freedom; equipping the moving parts as lumped mass units, and using the hybrid element method to perform dynamic model equivalence on the ball screw feed system, thus establishing an equivalent dynamic model of the ball screw feed system; the mass matrix of the equivalent beam unit, as shown in formulas (6) and (7), is a function of the position of the moving parts. In the formula: ρ ss Let A be the material density of the beam element. ess I is the equivalent cross-sectional area of ​​the beam element. ρss For the polar moment of inertia, y vari L is the distance between the lead screw and nut assembly and the front bearing support unit. fix This refers to the distance between the front and rear bearing support units. Since the lead screw and nut pair and the motor not only bear the tension and compression functions, but also the torsional force, the stiffness matrices of the equivalent beam elements on both sides of the lead screw and nut pair are different. The stiffness matrices of the equivalent beam elements are shown in formulas (8) and (9): In the formula: E ss For the elastic modulus, G ss Let p be the shear modulus and p be the lead of the lead screw.

2. The dynamic modeling method for a high-speed ball screw feed system in service state according to claim 1, characterized in that, Step 3 specifically involves: Since the frictional force in the feed direction of the ball screw feed system is equal to the driving force output by the servo motor when the system moves at a constant speed, the input driving torque T of the servo motor... s It can be obtained from the following formula: T s =k t ·I A (1) In the formula: k t I is the torque constant of the motor; A Since the current is the average value under constant speed operation, the frictional force f(v) of the ball screw feed system can be obtained by the following formula: In the formula: π is the constant of pi, p is the lead of the leadscrew, and S dr This is the reduction ratio.

3. The dynamic modeling method for a high-speed ball screw feed system in service state according to claim 1, characterized in that, Step 4 specifically involves: assuming the moving part moves at a speed of v t Move in the Y direction, with a t Accelerating in the Y direction, the inertial force under different accelerations and the frictional force under different feed speeds are calculated from step 1. With the help of the elastic Hertzian contact theory, the calculation formulas for the equivalent axial stiffness of the screw nut pair are derived as shown in formula (3), and the calculation formulas for the equivalent axial stiffness of the front / rear support bearing pair are shown in formula (4) and formula (5). The variation law of the equivalent axial stiffness of the screw nut pair and the front / rear support bearing pair with different accelerations and different feed speeds of the system is quantitatively given. In the formula: P Ca P is the initial preload of the nut assembly. d C p These are the rated dynamic load and rated dynamic load factor of the nut pair, respectively, α. con The contact angle between the ball and the raceway. Let i be the helix angle of the leadscrew. sn For the number of bearing turns of a single nut, d0 and d sb These are the nominal diameter of the lead screw and the diameter of the balls, respectively. as α is the axial force of the lead screw preload. cb i is the contact angle of the bearing pair. b n represents the number of single-end bearings. b K represents the number of balls in a single load-bearing bearing. h is the Hertzian contact coefficient.

4. The dynamic modeling method for a high-speed ball screw feed system in service state according to claim 1, characterized in that, The variable coefficient dynamic equation described in step 6 is as follows: In the formula: M, C, and K are the mass, damping, and stiffness matrices of the system, respectively; the mass matrix is ​​a function of the position of the moving part, i.e., it changes with y. vari The stiffness matrix changes with the position, velocity, and acceleration of the moving part; it is a variable value. q represents the vectors of acceleration, velocity, and position, respectively.

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