Cooling strategy formulating method for nut inner-cooling ball screw pair

Abstract

The invention provides a cooling strategy making method for a nut inner cooling ball screw pair. The cooling strategy making method comprises the following steps that the friction heat generation amount, the convective heat transfer coefficient and the convective heat transfer amount of a nut pair are calculated according to structure parameters and working conditions of the nut inner cooling ball screw pair; the Newton cooling theory is utilized, a correction coefficient k is added, the steady-state temperature of the nut is obtained through calculation, and a thermodynamic model of the cooling ball screw pair in the nut is established; according to the relation between the nut steady-state temperature and the cooling liquid flow speed and the relation between the nut steady-state temperature and the cooling liquid temperature of the nut internal cooling ball screw pair under different working condition parameters, a correction coefficient k is calculated through back-stepping of a calculation formula of the nut steady-state temperature, and a thermodynamic model of the nut internal cooling ball screw pair is updated; and substituting the expected steady-state temperature of the nut into the updated thermodynamic model of the cooling ball screw pair in the nut, solving the required lowest cooling liquid flow rate and cooling liquid temperature, and formulating a cooling strategy of the cooling ball screw pair in the nut under different working conditions.

Description

Technical Field

[0001] This invention relates to the field of ball screw pair cooling technology, and more specifically to a method for formulating a cooling strategy for ball screw pairs with internal cooling of the nut. Background Technology

[0002] A ball screw assembly, also known as a ball screw pair or ball screw joint, consists of a screw and a nut. It is a core rolling component of industrial machine tools, a high-precision, high-stability transmission component. Frictional heat is the main cause of thermal deformation in ball screw assemblies. The heat sources mainly include frictional heat between the balls and the screw raceway, frictional heat between the balls and the nut raceway, frictional heat between the balls themselves, and motor heat. The nut accounts for over 60% of the total heat generation; therefore, cooling the ball screw assembly is crucial for maintaining the accuracy of CNC machine tools.

[0003] In recent years, my country's ball screw pairs have been developing towards high speed and high precision. The main methods to improve the precision retention of ball screw pairs are internal cooling of the nut and hollow forced cooling. Especially when the screw is in a high-speed state, the thermal expansion caused by the heat generation phenomenon has a particularly serious impact on the screw precision. Therefore, the calculation of the steady-state temperature of the ball screw pair with internal cooling of the nut and the formulation of cooling strategies are particularly important.

[0004] In the prior art, patent number CN201911113905.9 discloses a hydrostatic lubrication and cooling ball screw assembly and method. It includes a screw, a nut fitted around the screw, and helical raceways on the outer surface of the screw and the inner surface of the nut, with balls disposed within the raceways. It also includes pressurized oil. The nut has a through-hole in the middle, communicating with the helical raceways. A rectangular hydrostatic oil chamber is formed on the inner side of the nut, penetrating the inner wall of the nut. Pressurized oil enters the hydrostatic oil chamber at a set pressure from the inlet and flows out from both ends of the nut to remove heat from the balls and raceways. Sealing caps are fixed at both ends of the nut, fitted around the screw. The inner surface of the sealing cap maintains a certain gap with the outer surface of the screw, and the inner surface of the sealing cap has an oil-sealing plug. This invention fills the nut with pressurized oil, forcibly flowing through all contact parts of the balls, thereby achieving forced lubrication and cooling.

[0005] Although the ball screw pair cooling method disclosed in this invention can cool the ball screw pair, it mainly relies on experience in selecting the coolant flow rate and temperature, and lacks an optimal method for cooling the ball screw pair inside the nut under different operating conditions. This results in low cooling efficiency and increased usage costs.

[0006] Based on this, the present invention proposes a cooling strategy formulation method for ball screw pairs with internal cooling of the nut. Summary of the Invention

[0007] To solve the above-mentioned technical problems, this invention provides a method for formulating a cooling strategy for ball screw pairs with internal cooling of the nut.

[0008] The technical solution adopted in this invention is as follows:

[0009] A method for formulating a cooling strategy for ball screw pairs with internal cooling of the nut includes the following steps:

[0010] Calculate the frictional heat generation, convective heat transfer coefficient, and steady-state heat of the nut pair based on the structural parameters and operating conditions of the ball screw pair with internal cooling in the nut.

[0011] Using Newton's cooling theory and adding a correction factor k, the steady-state temperature of the nut is calculated based on the calculated frictional heat generation, convective heat transfer coefficient and steady-state heat of the nut pair, and a thermodynamic model of the ball screw pair with internal cooling in the nut is established.

[0012] Combining the relationship between the steady-state temperature of the nut and the coolant flow rate and the steady-state temperature of the nut and the coolant temperature under different operating conditions, the correction coefficient k is calculated by back-deriving the formula for calculating the steady-state temperature of the nut, and the thermodynamic model of the ball screw pair with internal cooling is updated based on the calculated correction coefficient k.

[0013] The desired steady-state temperature of the nut is input into the updated thermodynamic model of the internally cooled ball screw pair to solve for the minimum required coolant flow rate and coolant temperature, and to formulate cooling strategies for the internally cooled ball screw pair under different operating conditions.

[0014] Furthermore, the calculation method for the frictional heat generated by the nut pair is as follows: determine the total frictional torque based on the structural parameters and operating coefficients of the ball screw pair, and then determine the frictional heat generated by the nut pair based on the total frictional torque; wherein, the total frictional torque consists of the frictional torque of the ball screw pair itself and the frictional torque for overcoming elastic hysteresis and local differential slippage.

[0015] Furthermore, the formula for calculating the total frictional torque is:

[0016] ,

[0017] In the formula, This represents the total frictional torque; This indicates the frictional torque inherent in the ball screw assembly. This represents the frictional torque used to overcome elastic hysteresis and local differential sliding.

[0018] Among them, the frictional torque of the ball screw pair itself The calculation formula is:

[0019] ,

[0020] In the formula, Indicates the coefficient of friction; Indicates the lead screw efficiency; This represents the axial load torque generated by overcoming friction, where the axial load torque generated by overcoming friction is... The calculation formula is:

[0021] ,

[0022] In the formula, Indicates the lead screw pitch; Indicates axial load;

[0023] Frictional torque to overcome elastic hysteresis and local differential sliding The calculation formula is:

[0024] ,

[0025] In the formula, This indicates the preload.

[0026] The formula for calculating the heat generated by friction between the nuts is:

[0027] ,

[0028] In the formula, This indicates the heat generated by friction between the nut and nut pairs; Indicates the lead screw speed; This represents the total frictional torque.

[0029] Furthermore, the formula for calculating the convective heat transfer coefficient is:

[0030] ,

[0031] In the formula, Indicates the convective heat transfer coefficient; Represents the Nuschelt number, Indicates the thermal conductivity of the coolant. Indicates the dimensional characteristics of the cooling pipes;

[0032] The natural convection heat transfer criterion equation is as follows:

[0033] ,

[0034] In the formula, Represents the Reynolds coefficient; This represents the Prandtl coefficient of the coolant;

[0035] The forced convection heat transfer criterion equation is:

[0036] Laminar flow state: ,

[0037] Turbulent state: ,

[0038] In the formula, Prandtl coefficient representing the initial temperature of the wall surface; This represents the correction factor.

[0039] Furthermore, during the operation of the internally cooled ball screw pair, the temperature exchange between the internally cooled nut and the cooling medium is forced convection heat transfer; the rotational motion of the ball screw pair and the natural cooling caused by the air are natural convection heat transfer.

[0040] The expression for the natural convection heat transfer coefficient is:

[0041] ,

[0042] The expression for the forced convection heat transfer coefficient is:

[0043] Laminar flow state: ,

[0044] Turbulent state: ,

[0045] Furthermore, the expression for steady-state heat is:

[0046] ,

[0047] In the formula, This indicates the heat generated by friction between the nut and the nut assembly, i.e., the heat generated by friction without cooling. Represents steady-state heat; This indicates convective heat transfer; Indicates the natural convection heat transfer coefficient; Indicates the forced convection heat transfer coefficient; This indicates the temperature difference between the air and the outer surface of the nut; This indicates the temperature difference between the coolant and the wall of the cooling pipe; This indicates the contact area between air and the outer wall of the nut; This indicates the contact area between the coolant and the cooling pipes; Indicates the correction factor;

[0048] Among them, steady-state heat The calculation formula is as follows:

[0049] ,

[0050] In the formula, This indicates the specific heat capacity of the nut; Indicates the mass of the nut; Indicates the steady-state temperature of the nut; This indicates the initial temperature of the nut.

[0051] Furthermore, the formula for calculating the steady-state temperature of the nut is:

[0052] ,

[0053] In the formula, This indicates the heat generated by friction without cooling; Indicates the natural convection heat transfer coefficient; Indicates the forced convection heat transfer coefficient; This indicates the temperature difference between the air and the outer surface of the nut; This indicates the temperature difference between the coolant and the wall of the cooling pipe; This indicates the contact area between air and the outer wall of the nut; This indicates the contact area between the coolant and the cooling pipes; Indicates the correction factor; This indicates the specific heat capacity of the nut; Indicates the mass of the nut; Indicates the steady-state temperature of the nut; This indicates the initial temperature of the nut.

[0054] Furthermore, the relationship model between the steady-state temperature of the nut and the coolant flow rate is as follows:

[0055] ,

[0056] In the formula, Indicates the coolant flow rate;

[0057] The relationship model between the steady-state temperature of the nut and the coolant temperature is as follows:

[0058] ,

[0059] In the formula, This indicates the temperature of the coolant.

[0060] The beneficial effects of this invention are:

[0061] (1) This invention utilizes Newton's cooling theory to consider the forced convection heat transfer of coolant flow and the natural convection heat transfer of air flow, and establishes a complete thermodynamic model of the ball screw pair with internal cooling in the nut. It can calculate the steady-state temperature of the ball screw pair with internal cooling in the nut under different working conditions, with high accuracy and high efficiency.

[0062] (2) This invention establishes a model of the relationship between steady-state temperature and coolant flow rate, and steady-state temperature and coolant temperature through simulation and experiment. It provides a method for formulating the optimal cooling strategy for ball screw pairs with internal cooling of nuts. The cooling efficiency is higher, and it can be better combined with the application scenario for targeted calculation. The flow rate and temperature of the coolant can be adjusted appropriately to meet the principle of economy. Attached Figure Description

[0063] Figure 1 This is a schematic diagram of the internal cooling nut structure applicable to the embodiments of this application.

[0064] Figure 2 A flowchart illustrating the method for developing a cooling strategy for ball screws with internal cooling of the nut, as provided in an embodiment of this application.

[0065] Figure 3 The diagram showing the relationship between nut temperature rise and coolant flow rate is provided for an embodiment of this application.

[0066] Figure 4 A graph showing the relationship between nut temperature rise and coolant temperature provided in an embodiment of this application.

[0067] Explanation of reference numerals in the attached figures:

[0068] 101-Nut; 102-Flange; 103-Internal cooling pipe; 104-Coolant inlet; 105-Coolant outlet. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] The following is a combination of... Figure 1 The possible system frameworks applicable to the embodiments of this application are described.

[0071] like Figure 1 As shown, this illustration illustrates a schematic diagram of an internal cooling nut structure used in an embodiment of this application. Specifically, the internal cooling nut structure includes a nut 101, a flange 102, a cooling pipe 103, a coolant inlet 104, and a coolant outlet 105. The flange 102 is disposed at one end of the nut 101, the cooling pipe 103 is disposed inside the nut 101, and the coolant inlet 104 and coolant outlet 105 are disposed on the flange 102, respectively communicating with both ends of the cooling pipe 103. It should also be noted that the cooling pipe 103 is a cylindrical coolant pipe.

[0072] The nut has four axial through holes inside, and two circular grooves on the two end faces that connect the four through holes in pairs. End caps are installed on the two end faces of the nut by screws, connecting the through holes and grooves to form an internal cooling circulation channel, i.e., cooling pipe 103. Rotary sealing rings and retaining rings are provided on the end caps and end faces. The sealing device is installed in a sealed manner with the nut, ensuring the assembly process of the two and facilitating later maintenance and replacement.

[0073] The internally cooled nut structure adopts a series cooling pipe arrangement, resulting in excellent cooling performance. The coolant is symmetrically distributed along the nut raceway, ensuring uniform cooling. The cooling pipes avoid structures such as the reverser and ball bearings, resulting in a reasonable and stable structure. By connecting through holes and grooves to form a cooling channel, the machining difficulty is low, the manufacturing cost is low, and it is easy to maintain later. It allows the cooling medium to be introduced for forced cooling immediately after the ball screw pair generates heat due to friction, avoiding uneven deformation of the screw nut due to heat. The loop design of the coolant inlet and outlet effectively reduces environmental pollution. By ensuring a certain pressure difference between the coolant inlet and outlet, the coolant can flow in the pipe at different speeds and flow states according to different application scenarios, thus realizing the real-time cooling function of the ball screw pair.

[0074] During cooling, the coolant enters through the coolant inlet 104 under the action of the pressure pump, passes through the series cooling pipes inside the nut, and is discharged through the coolant outlet 105, which plays a role in cooling the ball screw nut in time during the running-in process of the ball screw pair.

[0075] This embodiment simplifies the structure of the reverser, nut raceway, coolant inlet and outlet sealing device, etc.

[0076] based on Figure 1 The nut shown is internally cooled ball screw assembly. Figure 2 An exemplary flowchart illustrates a method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut, as provided in an embodiment of this application. Figure 2 As shown, the present invention provides a method for formulating a cooling strategy for ball screw pairs with internal cooling of the nut, which specifically includes the following steps:

[0077] S1: Calculate the frictional heat generation, convective heat transfer coefficient, and convective heat transfer of the nut pair based on the structural parameters and operating conditions of the ball screw pair with internal cooling.

[0078] Specifically, the calculation method for the heat generated by friction between the nut pair in S1 is as follows:

[0079] First, the total frictional torque is determined based on the structural parameters and operating coefficients of the ball screw pair. Then, the heat generated by friction in the nut pair is determined based on the total frictional torque. The total frictional torque consists of the frictional torque of the ball screw pair itself and the frictional torque used to overcome elastic hysteresis and local differential slippage.

[0080] The formula for calculating the total frictional torque is as follows:

[0081] ,

[0082] In the formula, This represents the total frictional torque; This indicates the frictional torque inherent in the ball screw assembly. It represents the frictional torque that overcomes elastic hysteresis and local differential sliding.

[0083] Among them, the frictional torque of the ball screw pair itself The calculation formula is:

[0084] ,

[0085] In the formula, Indicates the coefficient of friction; Indicates the lead screw efficiency; This represents the axial load torque generated by overcoming friction, where the axial load torque generated by overcoming friction is... The calculation formula is:

[0086] ,

[0087] In the formula, Indicates the lead screw pitch; Indicates axial load;

[0088] Frictional torque to overcome elastic hysteresis and local differential sliding The calculation formula is:

[0089] ,

[0090] In the formula, This indicates the preload.

[0091] Among them, the coefficient of friction of the ball screw pair Calculated by the following formula:

[0092] Oil lubrication: ,

[0093] Grease lubrication: ,

[0094] In the formula, lubrication parameters , Indicates the viscosity of the lubricant. Indicates the ball's sliding speed. This indicates the pressure at the contact point.

[0095] The formula for calculating the heat generated by friction of the nut pair (heat after the coolant is passed through) is as follows:

[0096] ,

[0097] In the formula, This indicates the heat generated by friction between the nut and nut pairs; Indicates the lead screw speed; This represents the total frictional torque.

[0098] In this invention, the method for calculating the convective heat transfer coefficient in S1 is as follows:

[0099] According to the Nusselt criterion, the relationship between the convective heat transfer coefficient and the cooling medium parameters (i.e., the thermal conductivity of the cooling medium) can be obtained. The formula for calculating the convective heat transfer coefficient is:

[0100] ,

[0101] In the formula, Indicates the convective heat transfer coefficient; Represents the Nuschelt number; Indicates the thermal conductivity of the cooling medium; This indicates the dimensional characteristics of the cooling pipe, where the dimensional characteristics of the cooling pipe are its diameter.

[0102] From the formula for calculating the heat transfer coefficient, it can be seen that, given the Nusselt number... Under these conditions, the convective heat transfer coefficient can be obtained by solving. .

[0103] For Nushert number It should be noted that the coolant flow rate affects the Reynolds number; different coolant flow rates correspond to different flow states, which in turn affect the convective heat transfer coefficient. The calculation involves the flow of coolant within cooling pipes. Specifically, the flow state is primarily related to the coolant velocity and the diameter of the cooling pipes. It should be noted that the Reynolds coefficient... <2300 indicates laminar flow; A value greater than 2300 indicates a turbulent flow state.

[0104] The formula for calculating the Reynolds coefficient of coolant flow is as follows:

[0105] ,

[0106] in, Indicates the density of the cooling medium; Indicates the flow rate of the cooling medium; This indicates the characteristic length, i.e., the diameter of the cooling pipe; This indicates the viscosity coefficient of the cooling medium.

[0107] According to Newton's theory of cooling, during the operation of the ball screw pair with internal cooling in the nut, the rotational motion of the ball screw pair and the natural cooling caused by the air constitute natural convection heat transfer. The criterion equation for natural convection heat transfer is:

[0108] ,

[0109] In the formula, Represents the Reynolds coefficient; This represents the Prandtl coefficient of the coolant.

[0110] During the operation of the internally cooled ball screw pair, the temperature exchange between the internally cooled nut and the cooling medium is forced convection heat transfer. The forced convection heat transfer criterion equation is:

[0111] Laminar flow state: ,

[0112] Turbulent state: ,

[0113] In the formula, Prandtl coefficient, representing the initial temperature of the wall surface (inner wall of the cooling pipe); This represents the correction factor.

[0114] S2: Utilizing Newton's theory of cooling and incorporating a correction factor. Based on the calculated frictional heat generation, convective heat transfer coefficient, and convective heat transfer of the nut pair, the steady-state temperature of the nut is calculated, and a thermodynamic model of the ball screw pair with internal cooling is established.

[0115] The formula for calculating Newton's cooling theory is as follows:

[0116] ,

[0117] In the formula, This indicates the amount of heat absorbed or released by an object; This represents the thermal conductivity coefficient, i.e., the convective heat transfer coefficient; This represents the temperature difference between the initial state and the steady state of an object. It represents the surface area of ​​an object in contact with the cooling medium.

[0118] According to the law of conservation of energy, the total heat generated minus the steady-state heat at steady state equals the convective heat transfer of the ball screw pair cooling the nut. Therefore, the corresponding expression for the steady-state heat of the ball screw pair cooling the nut at steady state is:

[0119] ,

[0120] In the formula, This indicates the total heat generated by friction in the nut assembly, i.e., the heat generated by friction when there is no cooling (no coolant flow). This represents steady-state heat (through coolant). This indicates convective heat transfer.

[0121] Indicates the natural convection heat transfer coefficient; Indicates the forced convection heat transfer coefficient; This indicates the temperature difference between the air and the outer surface of the nut; This indicates the temperature difference between the coolant and the wall of the cooling pipe; This indicates the contact area between air and the outer wall of the nut; This indicates the contact area between the coolant and the cooling pipes; This represents the correction factor.

[0122] Among them, the steady-state heat at steady state The formula for calculation is:

[0123] ,

[0124] In the formula, This indicates the specific heat capacity of the nut; Indicates the mass of the nut; Indicates the steady-state temperature of the nut; This indicates the initial temperature of the nut.

[0125] The expression for the natural convection heat transfer coefficient is:

[0126] ,

[0127] The expression for the forced convection heat transfer coefficient is:

[0128] Laminar flow state: ,

[0129] Turbulent state: ,

[0130] By combining the above formulas, the formula for calculating the steady-state temperature of the nut is:

[0131] ,

[0132] The formula for calculating the steady-state temperature of the nut shows that the steady-state temperature of the nut is only related to operating parameters such as rotational speed, axial load, coolant flow rate, and coolant temperature; the rest are fixed values.

[0133] S3: Combining the relationship between the steady-state temperature of the nut and the coolant flow rate and temperature of the ball screw pair under different operating conditions, the correction coefficient k is calculated by back-deriving the formula for calculating the steady-state temperature of the nut, and the thermodynamic model of the ball screw pair with internal cooling is updated based on the calculated correction coefficient k.

[0134] It should be noted that the main application scenarios for nut-cooled ball screw pairs are: small and medium-sized high-speed machining centers with high rotational speed and low axial load. Theoretical calculations and simulations should be combined with actual application scenarios.

[0135] Specifically, this invention analyzes the cooling effect using the fluid-steady-state thermal coupling simulation module of Ansys Workbench simulation software. The corresponding simulation steps are as follows:

[0136] First, to simplify the simulation process, this invention simplifies the inner raceway of the nut as a plane as the heat source, and uses the frictional heat generated by the nut pair calculated above as the heat source. The heat flux density is converted and applied to the heat source. Specialized cooling oils with different temperatures and flow rates are introduced into the nut cooling pipe. The material properties of the ball screw pair and the cooling medium are set and then imported into the Fluent fluid simulation module.

[0137] Then, the Fluent fluid simulation results were input into the settings of the fluid-steady-state thermal coupling simulation module, and the calculated convective heat transfer coefficient was used. Substituting these values, we finally obtained the steady-state thermal simulation results of the nut-cooled ball screw pair.

[0138] In this simulation, the axial load was set to 1000N, the rotational speed to 1000rpm, and the coolant temperature to 20℃. The steady-state temperature of the ball screw nut under different coolant flow rates was simulated to obtain the relationship model between the steady-state temperature of the nut and the coolant flow rate.

[0139] The simulation results of the relationship between coolant flow rate and nut steady-state temperature are as follows: Figure 3 As shown, the equation for the nonlinear curve fitting is:

[0140] ,

[0141] In the formula, This indicates the coolant flow rate.

[0142] The nonlinear curve fitting equation for the relationship between coolant flow rate and nut steady-state temperature is the model for the relationship between nut steady-state temperature and coolant flow rate.

[0143] In this simulation, the axial load was set to 1000N, the rotational speed to 1000rpm, and the coolant flow rate to 0.2m / s. The steady-state temperature of the ball screw nut under different coolant temperatures was simulated to obtain a model showing the relationship between the steady-state temperature of the nut and the coolant temperature.

[0144] The simulation results of the relationship between coolant flow rate and nut steady-state temperature are as follows: Figure 4 As shown, the linear curve fitting equation is:

[0145] ,

[0146] In the formula, This indicates the temperature of the coolant.

[0147] The linear curve fitting equation relating coolant flow rate and nut steady-state temperature is the nut steady-state temperature and coolant temperature model.

[0148] Based on the two simulation results above, the relationship models between the nut steady-state temperature and the coolant flow rate, and the relationship models between the nut steady-state temperature and the coolant temperature are obtained. The correction coefficient k is then calculated by back-deriving the formula for calculating the nut steady-state temperature, and the thermodynamic model of the cooling ball screw pair inside the nut is updated.

[0149] S4. Input the desired steady-state temperature of the nut into the updated thermodynamic model of the internally cooled ball screw pair to solve for the required minimum coolant flow rate and minimum coolant temperature, and formulate the cooling strategy for the internally cooled ball screw pair under different operating conditions. It should be noted that the desired steady-state temperature of the nut is a set value. For example, the desired steady-state temperature of the nut can be set to any value within the range of 20-40℃.

[0150] In this invention, the cooling strategy for the ball screw assembly under different operating conditions is determined by calculating the coolant flow rate and coolant temperature. Cooling is achieved by applying appropriate coolant flow rates and temperatures to the nut.

[0151] In this embodiment of the invention, the basic structural parameters of the nut-cooled ball screw pair used are shown in Table 1:

[0152] Table 1: Basic Structural Parameters of the Internally Cooled Ball Screw Pair

[0153] Screw mass / kg 14 Nominal diameter / mm 40 Lead / mm 16 Ball diameter / mm 3.969 Contact angle / ° 45 Overall length of lead screw / mm 1120 Effective length / mm 800 Screw material Cr Specific heat capacity of cooling medium / kJ / (kg*℃) 2.05 Thermal conductivity of cooling medium / W / (m*K) 0.15 Cooling medium specific density / kg / m³ 759 Kinematic viscosity of cooling medium / Pa*s 0.41e-3 Cooling pipe diameter / mm 8 Total length of cooling pipes / mm 450

[0154] The ball screw pair operates at a speed of 1000 rpm, without axial load, with a coolant flow rate of 0.2 m / s, a coolant temperature of 20°C, and a constant temperature chamber of 20°C. The steady-state temperature of the ball screw pair calculated using the thermodynamic model of the internal cooling ball screw pair of this invention is 26.45°C, while the actual measured steady-state temperature is 25.64°C, with a relative error of 3.16%.

[0155] In summary, this invention provides a method for formulating a cooling strategy for ball screw pairs with internal cooling in the nut. It utilizes Newton's cooling theory to consider both forced convection heat transfer from coolant flow and natural convection heat transfer from airflow, establishing a complete thermodynamic model for the ball screw pair with internal cooling in the nut. Through simulation and experimentation, it establishes models relating steady-state temperature to coolant flow rate and steady-state temperature to coolant temperature, providing a method for formulating the optimal cooling strategy for ball screw pairs with internal cooling in the nut, resulting in higher cooling efficiency.

[0156] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. "A plurality of" means two or more, unless otherwise explicitly specified.

[0157] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0158] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0159] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0160] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0161] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0162] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0163] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0164] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0165] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for formulating a cooling strategy for ball screw pairs with internal cooling of the nut, characterized in that, Includes the following steps: Calculate the frictional heat generation, convective heat transfer coefficient, and steady-state heat of the nut pair based on the structural parameters and operating conditions of the ball screw pair with internal cooling in the nut. Using Newton's cooling theory and adding a correction factor k, the steady-state temperature of the nut is calculated based on the calculated frictional heat generation, convective heat transfer coefficient and steady-state heat of the nut pair, and a thermodynamic model of the ball screw pair with internal cooling in the nut is established. Combining the relationship between the steady-state temperature of the nut and the coolant flow rate and the steady-state temperature of the nut and the coolant temperature under different operating conditions, the correction coefficient k is calculated by back-deriving the formula for calculating the steady-state temperature of the nut, and the thermodynamic model of the ball screw pair with internal cooling is updated based on the calculated correction coefficient k. The desired steady-state temperature of the nut is input into the updated thermodynamic model of the internally cooled ball screw pair to solve for the minimum required coolant flow rate and coolant temperature, and to formulate cooling strategies for the internally cooled ball screw pair under different operating conditions.

2. The method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut according to claim 1, characterized in that, The calculation method for the frictional heat generated by the nut pair is as follows: determine the total frictional torque based on the structural parameters and operating coefficients of the ball screw pair, and then determine the frictional heat generated by the nut pair based on the total frictional torque; wherein, the total frictional torque consists of the frictional torque of the ball screw pair itself and the frictional torque for overcoming elastic hysteresis and local differential slippage.

3. The cooling strategy formulation method for ball screw pairs with internal cooling of the nut according to claim 2, characterized in that, The formula for calculating the total frictional torque is: ， In the formula, This represents the total frictional torque; This indicates the frictional torque inherent in the ball screw assembly. This represents the frictional torque used to overcome elastic hysteresis and local differential sliding. Among them, the frictional torque of the ball screw pair itself The calculation formula is: ， In the formula, Indicates the coefficient of friction; Indicates the lead screw efficiency; This represents the axial load torque generated by overcoming friction, where the axial load torque generated by overcoming friction is... The calculation formula is: ， In the formula, Indicates the lead screw pitch; Indicates axial load; Frictional torque to overcome elastic hysteresis and local differential sliding The calculation formula is: ， In the formula, This indicates the preload. The formula for calculating the heat generated by friction between the nuts is: ， In the formula, This indicates the heat generated by friction between the nut and nut pairs; Indicates the lead screw speed; This represents the total frictional torque.

4. The method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut according to claim 3, characterized in that, The formula for calculating the convective heat transfer coefficient is: ， In the formula, Indicates the convective heat transfer coefficient; Represents the Nuschelt number, Indicates the thermal conductivity of the coolant. Indicates the dimensional characteristics of the cooling pipes; The natural convection heat transfer criterion equation is as follows: ， In the formula, Represents the Reynolds coefficient; This represents the Prandtl coefficient of the coolant; The forced convection heat transfer criterion equation is: Laminar flow state: , Turbulent state: , In the formula, Prandtl coefficient representing the initial temperature of the wall surface; This represents the correction factor.

5. The method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut according to claim 4, characterized in that, During the operation of the internally cooled ball screw pair, the temperature exchange between the internally cooled nut and the cooling medium is forced convection heat transfer; the rotational motion of the ball screw pair and the natural cooling caused by the air are natural convection heat transfer. The expression for the natural convection heat transfer coefficient is: ， The expression for the forced convection heat transfer coefficient is: Laminar flow state: , Turbulent state: .

6. The method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut according to claim 5, characterized in that, The expression for steady-state heat is: ， In the formula, This indicates the heat generated by friction between the nut and nut pairs; Represents steady-state heat; This indicates convective heat transfer; Indicates the natural convection heat transfer coefficient; Indicates the forced convection heat transfer coefficient; This indicates the temperature difference between the air and the outer surface of the nut; This indicates the temperature difference between the coolant and the wall of the cooling pipe; This indicates the contact area between air and the outer wall of the nut; This indicates the contact area between the coolant and the cooling pipes; Indicates the correction factor; Among them, steady-state heat The calculation formula is: ， In the formula, This indicates the specific heat capacity of the nut; Indicates the mass of the nut; Indicates the steady-state temperature of the nut; This indicates the initial temperature of the nut.

7. The method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut according to claim 6, characterized in that, The formula for calculating the steady-state temperature of the nut is: ， In the formula, This indicates the heat generated by friction without cooling; Indicates the natural convection heat transfer coefficient; Indicates the forced convection heat transfer coefficient; This indicates the temperature difference between the air and the outer surface of the nut; This indicates the temperature difference between the coolant and the wall of the cooling pipe; This indicates the contact area between air and the outer wall of the nut; This indicates the contact area between the coolant and the cooling pipes; Indicates the correction factor; This indicates the specific heat capacity of the nut; Indicates the mass of the nut; Indicates the steady-state temperature of the nut; This indicates the initial temperature of the nut.

8. The method for formulating a cooling strategy for a ball screw pair with internal cooling of the nut according to claim 7, characterized in that, The model relating the steady-state temperature of the nut to the coolant flow rate is as follows: ， In the formula, Indicates the coolant flow rate; The relationship model between the steady-state temperature of the nut and the coolant temperature is as follows: ， In the formula, This indicates the temperature of the coolant.

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