A forward calculation method for pre-tensioning amount of lead screw

Abstract

The disclosure provides a forward calculation method of a lead screw pre-tensioning amount, comprising: establishing a three-dimensional model of a lead screw transmission system and importing a finite element analysis model to obtain a thermal deformation simulation model of the lead screw; taking the heat generation of each heat source and the heat exchange coefficient of each heat exchange surface as the input conditions of the thermal deformation simulation model to obtain the thermal deformation result of the lead screw; calculating the front end displacement change value of the front end of the lead screw along the axial direction of the lead screw based on the thermal deformation result of the lead screw, and calculating the rear end displacement change value of the rear end of the lead screw along the axial direction of the lead screw based on the thermal deformation result of the lead screw; and calculating the pre-tensioning amount of the lead screw according to the front end displacement change value and the rear end displacement change value of the lead screw. In the forward calculation method of the lead screw pre-tensioning amount, the pre-tensioning amount of the lead screw is calculated based on the non-uniform distribution of the thermal deformation field of the lead screw, effectively solving the problem that the lead screw pre-tensioning amount cannot be accurately calculated in the forward design stage at the initial stage of machine tool design.

Description

Technical Field

[0001] This disclosure relates to the field of lead screw pretension calculation technology, and in particular to a forward calculation method for lead screw pretension. Background Technology

[0002] During assembly at room temperature, the lead screw is actively stretched by a preset amount (usually a negative T value) through a mechanical structure, generating pre-tension stress inside it. During operation, the lead screw expands due to heat, and the expansion offsets part of the pre-tension, thus keeping the effective length and pitch accuracy of the lead screw essentially unchanged.

[0003] Currently, when using lead screw drive systems, the preload of the lead screw is generally calculated according to the manufacturer's recommended value. However, this recommended preload calculation assumes a uniform distribution of temperature rise and thermal deformation in the lead screw. While this method is simple and quick, its accuracy is low, making it unsuitable for precision transmission applications. Additionally, some systems use a reverse calculation method, i.e., experimental measurement on a test platform. While this can obtain the preload, it doesn't address the issue of accurately calculating the lead screw preload during the initial forward design phase of machine tool design. Therefore, it is necessary to solve the problem of inaccurate calculation of lead screw preload during the initial forward design phase of machine tool design. Summary of the Invention

[0004] This disclosure aims to at least partially address one of the technical problems in the related art.

[0005] Therefore, the purpose of this disclosure is to provide a forward calculation method for the pretension of the lead screw.

[0006] To achieve the above objectives, this disclosure provides a forward calculation method for the pretension of a lead screw, comprising: identifying heat sources in the lead screw transmission system and calculating the heat generation of the heat sources; identifying heat exchange surfaces in the lead screw transmission system and calculating the heat transfer coefficients of the heat exchange surfaces; establishing a three-dimensional model of the lead screw transmission system and importing it into a finite element analysis model to obtain a thermal deformation simulation model of the lead screw; using the heat generation of the heat sources and the heat transfer coefficients of the heat exchange surfaces as input conditions for the thermal deformation simulation model to obtain the thermal deformation result of the lead screw; calculating the change in front displacement of the lead screw front end along the lead screw axis based on the thermal deformation result of the lead screw, and calculating the change in rear displacement of the lead screw rear end along the lead screw axis based on the thermal deformation result of the lead screw; and calculating the pretension of the lead screw based on the change in front displacement and the change in rear displacement.

[0007] Optionally, calculating the change in front displacement of the lead screw along the axial direction based on the thermal deformation result of the lead screw includes: determining the i-th bearing unit in the front bearing assembly of the lead screw in the lead screw transmission system, wherein the i-th bearing unit is the first bearing unit to bear the axial force along the direction from the rear end to the front end of the lead screw when the lead screw thermally expands; forming the front section of the lead screw by transversely cutting the front end of the lead screw with the virtual plane containing the center of the rolling element of the i-th bearing unit; and calculating the average displacement change of the front section of the lead screw as the front displacement change value based on the thermal deformation result of the lead screw.

[0008] Optionally, calculating the average displacement change value of the front end section of the lead screw based on the thermal deformation result of the lead screw as the front end displacement change value includes: dividing the front end section of the lead screw radially into an outer ring, a middle ring, and an inner ring; calculating a first front end displacement value of the outer ring along the lead screw axis, a second front end displacement value of the middle ring along the lead screw axis, and a third front end displacement value of the inner ring along the lead screw axis based on the thermal deformation result of the lead screw; assigning a first front end weighting coefficient to the first front end displacement value, and assigning a first front end weighting coefficient to the second front end displacement value; and assigning a first front end weighting coefficient to the second front end displacement value; and assigning a first front end weighting coefficient to the third front end displacement value; and assigning a first front end weighting coefficient to the second front end displacement value; and assigning a first front end weighting coefficient to the third front end weighting coefficient ... The first front-end weighting coefficient is assigned to the first front-end displacement value, and the second front-end weighting coefficient is assigned to the third front-end displacement value, wherein the first front-end weighting coefficient is greater than the second front-end weighting coefficient, and the second front-end weighting coefficient is greater than the third front-end weighting coefficient; the average displacement change value of the front-end section of the lead screw is calculated based on the first front-end displacement value and the first front-end weighting coefficient corresponding to the first front-end displacement value, the second front-end displacement value and the second front-end weighting coefficient corresponding to the second front-end displacement value, and the third front-end displacement value and the third front-end weighting coefficient corresponding to the third front-end displacement value, and the average displacement change value of the front-end section of the lead screw is calculated using a weighted average algorithm.

[0009] Optionally, calculating the average displacement change of the front end section of the lead screw based on the thermal deformation result of the lead screw as the front end displacement change value includes: calculating the average displacement change of the front end section of the lead screw based on a first formula, wherein the first formula is: ; wherein, the l front-point The average displacement change of the front end section of the lead screw, α k D is the weighting coefficient of the k-th front end. i-k This is the displacement value of the k-th front end.

[0010] Optionally, calculating the rear displacement change value of the lead screw rear end along the lead screw axis based on the thermal deformation result of the lead screw includes: determining the j-th bearing unit in the lead screw rear end bearing group of the lead screw transmission system, wherein the j-th bearing unit is the first bearing unit to bear the axial force along the direction from the front end to the rear end of the lead screw when the lead screw thermally expands; forming the rear end section of the lead screw by transversely cutting the virtual plane where the rolling element center of the j-th bearing unit is located across the rear end of the lead screw; and calculating the average displacement change value of the rear end section of the lead screw based on the thermal deformation result of the lead screw as the rear displacement change value.

[0011] Optionally, calculating the average displacement change value of the rear end section of the lead screw based on the thermal deformation result of the lead screw as the rear end displacement change value includes: dividing the rear end section of the lead screw radially into a rear end outer ring, a rear end middle ring, and a rear end inner ring; calculating the first rear end displacement value of the rear end outer ring along the lead screw axial direction, the second rear end displacement value of the rear end middle ring along the lead screw axial direction, and the third rear end displacement value of the rear end inner ring along the lead screw axial direction based on the thermal deformation result of the lead screw; assigning a first rear end weighting coefficient to the first rear end displacement value, and assigning a third rear end weighting coefficient to the second rear end displacement value... The first rear-end weighting coefficient is assigned to the first rear-end displacement value, and the second rear-end weighting coefficient is assigned to the third rear-end displacement value, wherein the first rear-end weighting coefficient is greater than the second rear-end weighting coefficient, and the second rear-end weighting coefficient is greater than the third rear-end weighting coefficient; the average displacement change value of the screw rear section is calculated based on the first rear-end displacement value and the first rear-end weighting coefficient corresponding to the first rear-end displacement value, the second rear-end displacement value and the second rear-end weighting coefficient corresponding to the second rear-end displacement value, and the third rear-end displacement value and the third rear-end weighting coefficient corresponding to the third rear-end displacement value, and a weighted average algorithm is used.

[0012] Optionally, calculating the average displacement change of the rear end section of the lead screw based on the thermal deformation result of the lead screw as the rear end displacement change value includes: calculating the average displacement change of the rear end section of the lead screw based on a second formula, wherein the second formula is: ; wherein, the l end-point The average displacement change of the rear end section of the lead screw, β k D is the weighting coefficient for the k-th back end. j-k This represents the displacement value of the k-th rear end.

[0013] Optionally, the step of calculating the pre-tension amount of the lead screw based on the displacement change value of the front end and the displacement change value of the rear end of the lead screw includes: taking the displacement value changing along the direction from the front end to the rear end of the lead screw as a positive value, and taking the displacement value changing along the direction from the rear end to the front end of the lead screw as a negative value; and calculating the pre-tension amount of the lead screw by subtracting the displacement change value of the front end of the lead screw from the displacement change value of the rear end of the lead screw.

[0014] Optionally, identifying heat sources in the lead screw drive system and calculating the heat generation of each heat source includes: taking the motor, front bearing, transmission nut, and rear bearing in the lead screw drive system as heat sources respectively, and calculating the heat generation of the motor heat source, the heat generation of the front bearing heat source, the heat generation of the transmission nut heat source, and the heat generation of the rear bearing heat source respectively; wherein, the motor is connected to the front end of the lead screw, the front bearing is sleeved on the front end of the lead screw, the transmission nut is threaded on the lead screw, and the rear bearing is sleeved on the rear end of the lead screw.

[0015] Optionally, identifying the heat transfer surfaces at various points in the lead screw drive system and calculating the heat transfer coefficient of the heat transfer surfaces includes: identifying the natural convection heat transfer surfaces at various points in the lead screw drive system and calculating the heat transfer coefficient of the natural convection heat transfer surfaces, and identifying the forced convection heat transfer surfaces at various points in the lead screw drive system and calculating the heat transfer coefficient of the natural convection heat transfer surfaces.

[0016] The technical solution provided in this disclosure may include the following beneficial effects: The heat generation of each heat source and the heat transfer coefficient of each heat exchange surface are used as input conditions for the thermal deformation simulation model to obtain the thermal deformation results of the lead screw. Based on the thermal deformation results, the displacement change of the lead screw front end along the lead screw axis and the displacement change of the lead screw rear end along the lead screw axis are calculated. Finally, the pre-tension of the lead screw is calculated based on the displacement changes of the front and rear ends. Thus, through theoretical calculation and finite element simulation analysis, the influence of heat generation of heat sources and heat transfer coefficient of heat exchange surfaces on the deformation of mechanical parts in the lead screw transmission system is evaluated. The non-uniformly distributed thermal deformation field of the lead screw is obtained, and the pre-tension of the lead screw is calculated based on the non-uniformly distributed thermal deformation field. This effectively solves the problem of inaccurate calculation of lead screw pre-tension in the initial forward design stage of machine tool design.

[0017] Additional aspects and advantages of this disclosure will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of this disclosure. Attached Figure Description

[0018] The above and / or additional aspects and advantages of this disclosure will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, in which: Figure 1 This is a flowchart illustrating a forward calculation method for the pretension of the lead screw according to an embodiment of this disclosure; Figure 2 This is a schematic diagram of the structure of a lead screw transmission system according to an embodiment of the present disclosure; Figure 3 This is a schematic diagram of the structure at a cross-section of a lead screw transmission system according to an embodiment of this disclosure; Figure 4 This is a schematic diagram of the structure at the front end cross section of the lead screw in a lead screw transmission system according to an embodiment of this disclosure; Figure 5 This is a schematic diagram of the structure at the rear end section of the lead screw in a lead screw transmission system according to an embodiment of this disclosure; As shown in the figure: 1. Lead screw, 101. Front section, 102. Rear section, 103. Outer ring of the front end of the lead screw, 104. Middle ring of the front end of the lead screw, 105. Inner ring of the front end of the lead screw, 106. Outer ring of the rear end of the lead screw, 107. Middle ring of the rear end of the lead screw, 108. Inner ring of the rear end of the lead screw. 2. Motor, 3. Front support, 4. Coupling, 5. Front bearing, 6. Front lock nut, 7. Front outer ring baffle, 8. Transmission nut, 9. Rear support, 10. Rear bearing, 11. Rear outer ring baffle, 12. Rear lock nut. Detailed Implementation

[0019] Embodiments of this disclosure are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are used only to explain this disclosure, and should not be construed as limiting this disclosure. Rather, embodiments of this disclosure include all variations, modifications, and equivalents falling within the spirit and scope of the appended claims.

[0020] like Figure 1 As shown in the embodiments of this disclosure, a forward calculation method for the pretension of a lead screw is proposed, including: S1: Identify the heat sources in the lead screw drive system and calculate the heat generated by the heat sources; S2: Identify the heat exchange surfaces in the lead screw drive system and calculate the heat transfer coefficient of the heat exchange surfaces; S3: Establish a three-dimensional model of the lead screw transmission system and import it into the finite element analysis model to obtain the thermal deformation simulation model of the lead screw; S4: The heat generation of each heat source and the heat transfer coefficient of each heat exchange surface are used as input conditions for the thermal deformation simulation model to obtain the thermal deformation results of the lead screw. S5: Calculate the change in displacement of the front end of the lead screw along the lead screw axis based on the thermal deformation results of the lead screw, and calculate the change in displacement of the rear end of the lead screw along the lead screw axis based on the thermal deformation results of the lead screw. S6: Calculate the pre-tension of the lead screw based on the displacement changes at the front and rear ends of the lead screw.

[0021] Understandably, the heat generation of each heat source and the heat transfer coefficient of each heat exchange surface are used as input conditions for the thermal deformation simulation model to obtain the thermal deformation results of the leadscrew. Based on the thermal deformation results, the displacement change of the leadcrew's front end along the leadcrew axis is calculated, as is the displacement change of the leadcrew's rear end along the leadcrew axis. Finally, the pre-tension of the leadscrew is calculated based on the displacement changes of the front and rear ends. Thus, through theoretical calculations and finite element simulation analysis, the influence of heat generation of heat sources and heat transfer coefficient of heat exchange surfaces on the deformation of mechanical parts in the leadscrew transmission system is evaluated. The non-uniformly distributed thermal deformation field of the leadscrew is obtained, and the pre-tension of the leadscrew is calculated based on this non-uniformly distributed thermal deformation field. This effectively solves the problem of not being able to accurately calculate the leadcrew pre-tension in the initial forward design stage of machine tool design.

[0022] It should be noted that in this embodiment, during the forward design phase in the early stage of machine tool design, the forward calculation method is used to obtain the pre-tension of the lead screw in the lead screw transmission system in the shortest time, avoiding the reverse acquisition of the lead screw pre-tension by building a test platform, thus reducing platform cost and time cost. At the same time, the pre-tension of the lead screw is calculated based on the non-uniformly distributed thermal deformation field of the lead screw, thereby ensuring high calculation accuracy of the pre-tension.

[0023] The lead screw 1 transmission system is a power output system based on lead screw 1. Specifically, such as... Figure 2 As shown, the lead screw 1 transmission system includes: lead screw 1, motor 2, front support 3, coupling 4, front bearing 5, front locking nut 6, front outer ring baffle 7, transmission nut 8, rear support 9, rear bearing 10, rear outer ring baffle 11, and rear locking nut 12.

[0024] The motor 2 is located at the front end of the front end support 3. The front end of the lead screw 1 extends from the rear end of the front end support 3 and is connected to the rotor shaft of the motor 2 through a coupling 4. At the same time, the front end of the lead screw 1 is rotatably arranged in the front end support 3 through the front end bearing 5, and the front end of the front end bearing 5 is locked by the front end locking nut 6 threaded on the front end of the lead screw 1. In addition, the rear end of the front end support 3 is sealed by the front end outer ring baffle 7.

[0025] The transmission nut 8 is threaded onto the middle of the lead screw 1. The rear end of the lead screw 1 extends into the rear end support 9 from the front end and is rotatably mounted in the rear end support 9 through the rear end bearing 10. The rear end of the rear end bearing 10 is locked by the rear end locking nut 12 threaded onto the rear end of the lead screw 1. In addition, the rear end of the rear end support 9 is covered by the rear end outer ring baffle 11.

[0026] After initial installation, the pre-tension of the lead screw 1 can be adjusted by tightening the rear locking nut 12 at its free length.

[0027] like Figure 3 As shown, in some embodiments, calculating the change in displacement of the lead screw tip along the lead screw axis based on the thermal deformation results of the lead screw includes: In the lead screw front bearing assembly of the lead screw transmission system, the i-th bearing unit is determined, wherein the i-th bearing unit is the first bearing unit to bear the axial force along the direction from the rear end to the front end of the lead screw when the lead screw thermally expands. The virtual plane containing the center of the rolling element of the i-th bearing unit is used to cross the front end of the lead screw to form the front end section 101 of the lead screw; The average displacement change of the front section 101 of the lead screw is calculated based on the thermal deformation results of the lead screw as the front displacement change value.

[0028] It is understandable that the virtual plane where the center of the rolling element of the i-th bearing unit is located is used to cross the front end of the screw to form the front end section 101 of the screw, and the average displacement change value of the front end section 101 of the screw is calculated based on the thermal deformation result of the screw as the front end displacement change value. Then, the accurate pre-tension amount of the screw is calculated based on the front end displacement change value of the screw.

[0029] It should be noted that after obtaining the thermal deformation displacement field of the lead screw through finite element analysis, the displacement values ​​at each point of the lead screw front section 101 on the virtual plane iplane are extracted so as to accurately obtain the displacement change value of the lead screw front end using the displacement values ​​at each point.

[0030] like Figure 4 As shown, in some embodiments, calculating the average displacement change value of the front end section 101 of the lead screw as the front end displacement change value based on the thermal deformation result of the lead screw includes: The front section 101 of the lead screw is divided radially into the outer ring 103, the middle ring 104, and the inner ring 105 of the lead screw front end. The first front displacement value of the outer ring 103 of the front end of the lead screw along the lead screw axis, the second front displacement value of the middle ring 104 of the front end of the lead screw along the lead screw axis, and the third front displacement value of the inner ring 105 of the front end of the lead screw along the lead screw axis are calculated based on the thermal deformation results of the lead screw. A first front-end weighting coefficient is assigned to the first front-end displacement value, a second front-end weighting coefficient is assigned to the second front-end displacement value, and a third front-end weighting coefficient is assigned to the third front-end displacement value, wherein the first front-end weighting coefficient is greater than the second front-end weighting coefficient, and the second front-end weighting coefficient is greater than the third front-end weighting coefficient. The average displacement change of the lead screw front section 101 is calculated based on the first front displacement value and the first front weighting coefficient corresponding to the first front displacement value, the second front displacement value and the second front weighting coefficient corresponding to the second front displacement value, and the third front displacement value and the third front weighting coefficient corresponding to the third front displacement value, and the weighted average algorithm is used.

[0031] Understandably, dividing the lead screw front section 101 into radially distributed lead screw front outer ring 103, lead screw front middle ring 104, and lead screw front inner ring 105, and calculating the first front displacement value of the lead screw front outer ring 103, the second front displacement value of the lead screw front middle ring 104, and the third front displacement value of the lead screw front inner ring 105 using a weighted average algorithm, yields the average displacement change value of the lead screw front section 101, thus providing an accurate and effective means for accurately assessing the lead screw pretension.

[0032] It should be noted that the thermal deformation of the outer ring 103 at the front end of the lead screw has the greatest impact on the thermal elongation of the lead screw. Therefore, the largest first front end weighting coefficient is adopted. Thus, by assigning different weighting coefficients, the average displacement change value of the front end section 101 of the lead screw can be accurately obtained.

[0033] In some embodiments, calculating the average displacement change of the lead screw's front end cross section based on the thermal deformation results of the lead screw as the front end displacement change value includes: The average displacement change of the lead screw front section is calculated based on the first formula, which is: ; Among them, l front-point α is the average displacement change of the front section of the lead screw. k D is the weighting coefficient of the k-th front end. i-k This is the displacement value of the k-th front end.

[0034] For example, the first front-end weighting coefficient α1 is 50%, the second front-end weighting coefficient α2 is 30%, and the third front-end weighting coefficient α3 is 20%.

[0035] like Figure 3 As shown, in some embodiments, calculating the change in rear displacement of the lead screw along the lead screw axis based on the thermal deformation results of the lead screw includes: In the lead screw rear bearing assembly of the lead screw transmission system, the j-th bearing unit is determined, wherein the j-th bearing unit is the first bearing unit to bear the axial force along the direction from the front end to the rear end of the lead screw when the lead screw thermally expands. The virtual plane containing the center of the rolling element of the j-th bearing unit is used to cross the rear end of the lead screw to form the rear end section 102 of the lead screw. The average displacement change of the rear section 102 of the lead screw is calculated based on the thermal deformation results of the lead screw as the rear displacement change value.

[0036] It is understandable that the virtual plane containing the center of the rolling element of the j-th bearing unit is used to cross the rear end of the screw to form the rear end section 102 of the screw, and the average displacement change value of the rear end section 102 of the screw is calculated based on the thermal deformation result of the screw as the rear end displacement change value. Then, the accurate pre-tension amount of the screw is calculated based on the rear end displacement change value of the screw.

[0037] It should be noted that after obtaining the thermal deformation displacement field of the lead screw through finite element analysis, the displacement values ​​at each point of the lead screw rear end section 102 on the virtual plane jplane are extracted so as to accurately obtain the displacement change value of the lead screw rear end using the displacement values ​​at each point.

[0038] like Figure 5 As shown, in some embodiments, calculating the average displacement change value of the rear section 102 of the lead screw as the rear displacement change value based on the thermal deformation result of the lead screw includes: The rear end section 102 of the lead screw is divided radially into the outer ring 106, the middle ring 107, and the inner ring 108 of the rear end of the lead screw. Based on the thermal deformation results of the lead screw, calculate the first rear displacement value of the outer ring 106 of the lead screw rear end along the lead screw axis, the second rear displacement value of the middle ring 107 of the lead screw rear end along the lead screw axis, and the third rear displacement value of the inner ring 108 of the lead screw rear end along the lead screw axis. A first back-end weighting coefficient is assigned to the first back-end displacement value, a second back-end weighting coefficient is assigned to the second back-end displacement value, and a third back-end weighting coefficient is assigned to the third back-end displacement value, wherein the first back-end weighting coefficient is greater than the second back-end weighting coefficient, and the second back-end weighting coefficient is greater than the third back-end weighting coefficient. The average displacement change of the lead screw rear section 102 is calculated based on the first rear displacement value and the corresponding first rear weighting coefficient, the second rear displacement value and the corresponding second rear weighting coefficient, and the third rear displacement value and the corresponding third rear weighting coefficient, using a weighted average algorithm.

[0039] Understandably, dividing the lead screw rear end section 102 into radially distributed lead screw rear end outer ring 106, lead screw rear end middle ring 107, and lead screw rear end inner ring 108, and calculating the first rear end displacement value of the lead screw rear end outer ring 106, the second rear end displacement value of the lead screw rear end middle ring 107, and the third rear end displacement value of the lead screw rear end inner ring 108 using a weighted average algorithm, yields the average displacement change value of the lead screw rear end section 102, thus providing an accurate and effective means for accurately assessing the lead screw pretension.

[0040] It should be noted that the thermal deformation of the outer ring 106 at the rear end of the lead screw has the greatest impact on the thermal elongation of the lead screw. Therefore, the largest first rear end weighting coefficient is adopted. Thus, by assigning different weighting coefficients, the average displacement change value of the section 102 at the rear end of the lead screw can be accurately obtained.

[0041] In some embodiments, calculating the average displacement change of the rear end section of the lead screw as the rear end displacement change based on the thermal deformation results of the lead screw includes: The average displacement change of the rear section of the leadscrew is calculated based on the second formula, which is: ; Among them, l end-point β is the average displacement change of the cross section at the rear end of the leadscrew. k D is the weighting coefficient for the k-th back end. j-k This represents the displacement value of the k-th rear end.

[0042] For example, the first back-end weighting coefficient β1 is 50%, the second back-end weighting coefficient β2 is 30%, and the third back-end weighting coefficient β3 is 20%.

[0043] In some embodiments, the pre-tension of the lead screw is calculated based on the displacement changes at the front and rear ends of the lead screw, including: The displacement value that changes along the direction from the front end to the rear end of the lead screw is taken as a positive value, and the displacement value that changes along the direction from the rear end to the front end of the lead screw is taken as a negative value. The pre-tension of the lead screw is calculated by subtracting the change in displacement at the front end of the lead screw from the change in displacement at the rear end of the lead screw.

[0044] For example, the first front displacement value D i-1 The second front displacement value D is -0.03mm. i-2 The third front displacement value D is -0.02mm. i-3 It is -0.01mm.

[0045] Based on the calculation using the first formula: .

[0046] For example, the first rear displacement value Dj-1 The displacement value D of the second rear end is 0.03 mm. j-2 The displacement value D at the third rear end is 0.02 mm. j-3 It is 0.01mm.

[0047] Based on the calculation using the second formula: .

[0048] The final calculated lead screw pretension is: l end-point -l front-point =0.046mm.

[0049] In some embodiments, identifying heat sources at various points in the lead screw drive system and calculating the heat generated by these heat sources includes: The motor, front bearing, transmission nut, and rear bearing in the lead screw transmission system are each taken as heat sources, and the heat generation of the motor heat source, the heat generation of the front bearing heat source, the heat generation of the transmission nut heat source, and the heat generation of the rear bearing heat source are calculated respectively. The motor and the front end of the lead screw are connected by a transmission. The front end bearing is sleeved on the front end of the lead screw, the transmission nut is threaded on the lead screw, and the rear end bearing is sleeved on the rear end of the lead screw.

[0050] Understandably, the motor, front bearing, transmission nut, and rear bearing in the lead screw drive system are each taken as a heat source, and the heat generation of the motor, front bearing, transmission nut, and rear bearing is calculated separately. Then, the heat generation of the motor, front bearing, transmission nut, and rear bearing is used as the input conditions for the thermal deformation simulation model to obtain accurate thermal deformation results of the lead screw.

[0051] For example, a 1kW motor generates 40W of heat, the front bearing generates 10W of heat, the drive nut generates 25W of heat, and the rear bearing generates 8W of heat.

[0052] In some embodiments, identifying heat transfer surfaces at various points in the lead screw drive system and calculating the heat transfer coefficients of these surfaces includes: Identify the natural convection heat transfer surfaces at various points in the lead screw drive system and calculate the heat transfer coefficient of the natural convection heat transfer surfaces; and identify the forced convection heat transfer surfaces at various points in the lead screw drive system and calculate the heat transfer coefficient of the natural convection heat transfer surfaces.

[0053] It should be noted that stationary parts exchange heat with the outside air through natural convection, while moving parts exchange heat with the outside air through forced convection.

[0054] Surfaces of moving parts, such as the surface of the motor rotor, coupling, front locking nut, lead screw, transmission nut, and rear locking nut.

[0055] For example, the convective heat transfer coefficient of the rotating cylindrical surface of the coupling is 45 W / m. 2 • K; The convective heat transfer coefficient of the rotating cylindrical surface of the lead screw is 120 W / m 2 • K; At air temperatures of 20-35℃, the natural convection heat transfer coefficient between the metal and air is 8 W / m². 2 ·K.

[0056] It should be noted that in the description of this disclosure, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Furthermore, in the description of this disclosure, unless otherwise stated, "a plurality of" means two or more.

[0057] 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 preferred embodiments of this disclosure 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 function involved, as will be understood by those skilled in the art to which embodiments of this disclosure pertain.

[0058] 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 this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0059] Although embodiments of the present disclosure have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present disclosure. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present disclosure.

Claims

1. A method for forward calculation of lead screw pretension, characterized in that, include: Identify the heat sources in the lead screw drive system and calculate the heat generation of the heat sources; Identify the heat exchange surfaces at various points in the lead screw drive system and calculate the heat transfer coefficient of the heat exchange surfaces; A three-dimensional model of the lead screw transmission system was established and imported into the finite element analysis model to obtain the thermal deformation simulation model of the lead screw. The heat generation of each heat source and the heat transfer coefficient of each heat exchange surface are used as input conditions for the thermal deformation simulation model to obtain the thermal deformation result of the lead screw. The front end section of the lead screw is divided radially into the outer ring of the lead screw front end, the middle ring of the lead screw front end, and the inner ring of the lead screw front end. Based on the thermal deformation results of the lead screw, calculate the first front displacement value of the outer ring of the lead screw front end along the lead screw axis, the second front displacement value of the middle ring of the lead screw front end along the lead screw axis, and the third front displacement value of the inner ring of the lead screw front end along the lead screw axis. A first front-end weighting coefficient is assigned to the first front-end displacement value, a second front-end weighting coefficient is assigned to the second front-end displacement value, and a third front-end weighting coefficient is assigned to the third front-end displacement value, wherein the first front-end weighting coefficient is greater than the second front-end weighting coefficient, and the second front-end weighting coefficient is greater than the third front-end weighting coefficient. The average displacement change of the lead screw front end section is calculated based on the first formula and used as the displacement change of the lead screw front end along the lead screw axis. The first formula is: ; wherein, the l front-point The average displacement change of the front end section of the lead screw, α k D is the weighting coefficient of the k-th front end. i-k This represents the k-th front displacement value; The displacement change of the rear end of the lead screw along the lead screw axis is calculated based on the thermal deformation results of the lead screw. The pre-tension of the lead screw is calculated based on the displacement changes at the front and rear ends of the lead screw.

2. The forward calculation method for the pretension of the lead screw according to claim 1, characterized in that, The calculation of the rear displacement change of the lead screw along the lead screw axis based on the thermal deformation result of the lead screw includes: In the lead screw drive system, the j-th bearing unit is determined in the lead screw rear bearing, wherein the j-th bearing unit is the first bearing unit to bear the axial force along the direction from the front end to the rear end of the lead screw when the lead screw thermally expands. The virtual plane containing the center of the rolling element of the j-th bearing unit is transversely cut across the rear end of the lead screw to form the rear end section of the lead screw; The average displacement change of the rear end section of the lead screw is calculated based on the thermal deformation results of the lead screw and is taken as the rear end displacement change value.

3. The forward calculation method for the pretension of the lead screw according to claim 2, characterized in that, The calculation of the average displacement change value of the rear end section of the lead screw based on the thermal deformation result of the lead screw as the rear end displacement change value includes: The rear end section of the lead screw is divided radially into the outer ring of the rear end of the lead screw, the middle ring of the rear end of the lead screw, and the inner ring of the rear end of the lead screw. Based on the thermal deformation results of the lead screw, calculate the first rear end displacement value of the outer ring of the rear end of the lead screw along the axial direction of the lead screw, the second rear end displacement value of the middle ring of the rear end of the lead screw along the axial direction of the lead screw, and the third rear end displacement value of the inner ring of the rear end of the lead screw along the axial direction of the lead screw. A first back-end weighting coefficient is assigned to the first back-end displacement value, a second back-end weighting coefficient is assigned to the second back-end displacement value, and a third back-end weighting coefficient is assigned to the third back-end displacement value, wherein the first back-end weighting coefficient is greater than the second back-end weighting coefficient, and the second back-end weighting coefficient is greater than the third back-end weighting coefficient. The average displacement change of the lead screw rear section is calculated based on the first rear displacement value and the first rear weighting coefficient corresponding to the first rear displacement value, the second rear displacement value and the second rear weighting coefficient corresponding to the second rear displacement value, and the third rear displacement value and the third rear weighting coefficient corresponding to the third rear displacement value, using a weighted average algorithm.

4. The forward calculation method for the pretension of the lead screw according to claim 3, characterized in that, The calculation of the average displacement change value of the rear end section of the lead screw based on the thermal deformation result of the lead screw as the rear end displacement change value includes: The average displacement change of the rear section of the lead screw is calculated based on the second formula, and the second formula is: ； Wherein, the l end-point The average displacement change of the rear end section of the lead screw, β k D is the weighting coefficient for the k-th back end. j-k This represents the k-th rear displacement value.

5. The forward calculation method for the pretension of the lead screw according to claim 1, characterized in that, The calculation of the pre-tension of the lead screw based on the displacement change values ​​of the front end and the rear end of the lead screw includes: The displacement value that changes along the direction from the front end to the rear end of the lead screw is taken as a positive value, and the displacement value that changes along the direction from the rear end to the front end of the lead screw is taken as a negative value. The pre-tension of the lead screw is calculated by subtracting the displacement change of the front end of the lead screw from the displacement change of the rear end of the lead screw.

6. The forward calculation method for the pretension of the lead screw according to claim 1, characterized in that, The process of identifying heat sources at various points in the lead screw drive system and calculating the heat generated by these heat sources includes: The motor, front bearing, transmission nut, and rear bearing in the lead screw transmission system are respectively used as heat sources, and the heat generation of the motor heat source, the heat generation of the front bearing heat source, the heat generation of the transmission nut heat source, and the heat generation of the rear bearing heat source are calculated respectively. The motor and the front end of the lead screw are connected by a transmission, the front end bearing is sleeved on the front end of the lead screw, the transmission nut is threaded on the lead screw, and the rear end bearing is sleeved on the rear end of the lead screw.

7. The forward calculation method for the pretension of the lead screw according to claim 1, characterized in that, The process of identifying the heat transfer surfaces at various points in the lead screw drive system and calculating the heat transfer coefficients of the heat transfer surfaces includes: Identify the natural convection heat transfer surfaces at various points in the lead screw drive system and calculate the heat transfer coefficient of the natural convection heat transfer surfaces; and identify the forced convection heat transfer surfaces at various points in the lead screw drive system and calculate the heat transfer coefficient of the natural convection heat transfer surfaces.

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