A method for calculating tension distribution of a traction rope on a curved ring pulley

Abstract

The application discloses a tension distribution calculation method of a traction rope on a curved annular rope groove wheel, belongs to the rope groove wheel field, and solves the problem that a traditional friction force distribution calculation method cannot effectively calculate the friction force distribution of a rope groove wheel. The technical scheme for solving the problem mainly comprises the following steps: a parameterized model of the curved annular rope groove wheel is established, the curved path of the curved groove is parameterized, the micro-element method is adopted to analyze the force of the traction rope, the resultant force of the traction rope in the circumferential, radial and axial directions of the curved annular rope groove wheel is analyzed, the tension attenuation formula of the micro-arc segment is deduced, the tension attenuation is iterated according to the tension attenuation of the micro-arc segment, the tension value is calculated, and the tension distribution formula can be obtained after the tension value is fitted. The application is mainly used for accurately calculating the tension distribution of the traction rope on the curved annular rope groove wheel.

Description

Technical Field

[0001] This invention demonstrates a method for calculating the tension distribution of a traction rope on a curved annular grooved rope pulley, belonging to the field of grooved rope pulley technology. Background Technology

[0002] An electric traction device is a lifting device that integrates an electric motor and a grooved rope pulley. During operation, the traction rope is wound around the groove of the pulley, and the friction between the traction rope and the pulley keeps the rope taut, thus achieving the purpose of traction. The friction between the pulley and the traction rope is the decisive factor affecting the lifting and traction efficiency and stability during operation. Traditional grooved rope pulleys typically have a circular groove path around the pulley body. This structure often severely limits the operational capacity of the pulley system due to insufficient friction. Based on this, a curved path grooved rope pulley, by setting curved annular grooves around the pulley body, can provide greater frictional driving force and a higher safety factor, offering a more reliable option for related operations.

[0003] Existing methods for calculating the friction distribution of traditional grooved rope pulleys mainly rely on the traditional Euler formula, which ignores the combined influence of the axial bending path and groove shape on the rope force. Therefore, they are not suitable for curved annular grooved rope pulleys. In addition, existing calculation methods lack effective theoretical foundations and calculation tools when solving the tension distribution law of traction ropes, and cannot provide strong support for the structural design of curved annular grooved rope pulleys. Summary of the Invention

[0004] The purpose of this invention is to solve the problem that traditional friction distribution calculation methods cannot effectively calculate the friction distribution of a grooved rope wheel. To this end, a method for calculating the tension distribution of the traction rope on a curved annular grooved rope wheel is provided, which can accurately calculate the friction distribution on the surface of the curved annular grooved rope wheel.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] A method for calculating the tension distribution of a traction rope on a curved annular grooved sheave, wherein the outer periphery of the curved annular grooved sheave is provided with a curved groove for the traction rope to be wound, the curved groove including two annular walls with wavy curves, and the method for calculating the force exerted by the curved groove on the traction rope includes:

[0007] S1. Parameterize the curved annular grooved sheave and establish the model parametric equations of the curved annular grooved sheave;

[0008] S2. Mark several nodes on the traction rope, calculate the tension F at each node, calculate the angle θ between the tangent of the traction rope at each node and the radial section of the curved annular grooved rope wheel, and calculate the angle between the tangent of the traction rope at each node and the central axis of the curved annular grooved rope wheel.

[0009] S3. Using the infinitesimal element method, select micro-arc segments at each node of the traction rope. Based on Newton's third law and Coulomb's law, perform force analysis on the micro-arc segments in the circumferential, radial, and axial directions of the curved annular rope groove wheel. The tension attenuation dF of the micro-arc segments is obtained through the force analysis. The tension attenuation dF of each micro-arc segment in contact with the curved annular rope groove wheel is the friction force experienced by the micro-arc segment.

[0010] S4. Based on the tension attenuation dF of the micro-arc segment, and through iterative calculation of the tension F at each node of the traction rope, the tension value T at each node of the traction rope is obtained.

[0011] S5. Perform an exponential fit on the tension values ​​T of all nodes to obtain the distribution formula T(t) of the tension at the nodes of the traction rope.

[0012] Preferably, the parametric equation in S1 is used to fully express the curved path of the traction rope, and the specific expression of the parametric equation is as follows:

[0013]

[0014] Where R represents the radius of the curved annular grooved rope wheel, the curved path of the traction rope is a trigonometric function waveform, A represents the amplitude of the trigonometric function waveform path, and N represents the number of waveforms on the curved groove.

[0015] Preferably, in S2, the included angle θ and Used to determine the direction of the tension, the included angle θ, and The calculation method is as follows:

[0016]

[0017] Where T curve T represents the tangent vector of the micro-arc segment. circle This represents the tangent vector of the corresponding node of the curved annular grooved rope wheel.

[0018] Preferably, the resultant force of the traction rope in the circumferential, radial, and axial directions of the curved annular rope groove pulley in S3 is shown by the following formula:

[0019] In the circumferential direction of the curved annular grooved rope pulley:

[0020]

[0021] In the radial direction of the curved annular rope grooved pulley:

[0022]

[0023] In the axial direction of the curved annular rope grooved pulley:

[0024]

[0025] Where F represents the tension in the traction rope; F N1 F N2 This represents the supporting force of the two annular walls on the traction rope; F f dα represents the frictional force on the traction rope; f represents the coefficient of friction; dα represents the central angle of the curved annular groove wheel corresponding to the micro-arc segment; dβ represents the central angle of the curved groove corresponding to the micro-arc segment; γ represents the angle between the annular wall and the radial section; k represents the position of the micro-arc segment; rev represents the equivalent friction coefficient correction.

[0026] Solving the above system of equations yields the tensile force attenuation dF in the micro-arc segment, specifically the formula:

[0027]

[0028] Preferably, the formulas for calculating the central angle dα of the curved annular grooved sheave corresponding to the micro-arc segment and the central angle dβ of the curved groove corresponding to the micro-arc segment are as follows:

[0029]

[0030] Where n is the number of discrete nodes, k i Δs i The curvature and arc length of the waveform corresponding to the micro-arc segments at the corresponding nodes are respectively.

[0031] Preferably, k is used to determine the position of the arc where the force analysis node is located, and the calculation method is as follows:

[0032]

[0033] As a preferred embodiment, the equivalent friction coefficient correction rev is calculated by conducting a friction experiment on the curved annular rope grooved pulley, taking a section of the traction rope in contact with the curved annular rope grooved pulley, and using the tensions T' and T at both ends of the traction rope section under the wrap angle α of this section of the traction rope. The calculation formula is as follows:

[0034]

[0035] Preferably, the tension T on the traction rope at each node in S4 is... i The tension T experienced by the traction rope at the previous node can be used as a measure. i-1 The calculation is performed in conjunction with the tensile force attenuation dF, and the specific formula is shown below:

[0036] T i =Ti-1 -dF.

[0037] Preferably, in step S5, the tension formula for each node of the traction rope is obtained through exponential fitting:

[0038] T(t) = T0e -λt ;

[0039] Where T0 represents the tension value of the initial node, λ represents the attenuation coefficient, and t represents the index value of the node, with the initial node index value being 0.

[0040] The beneficial effects of using the present invention are:

[0041] This invention establishes a parameterized model of the curved annular rope grooved wheel, parameterizing the bending path of the curved groove. This allows for a complete representation of the curved path of the groove, particularly its bending characteristics in the axial direction of the curved annular rope grooved wheel. This enables a more accurate description of the force on the traction rope on the friction wheel, clarifying the force change process between the traction rope and the curved annular rope grooved wheel during operation. Furthermore, the invention employs the infinitesimal element method to analyze the force at the contact point between the traction rope and the curved annular rope grooved wheel, analyzing the resultant force of the traction rope in the circumferential, radial, and axial directions of the curved annular rope grooved wheel. This allows for the derivation of the tension attenuation formula for the micro-arc segment, providing a model for the surface friction distribution of the curved annular rope grooved wheel. This invention lays the foundation for precise calculations. Secondly, based on the tension attenuation of the micro-arc segment and through iterative calculations and exponential fitting using software, the tension formula for each node on the traction rope can be derived. This allows for precise analysis of the frictional force distribution on the surface of the curved annular rope groove wheel, revealing the influence of the curved groove bending path and groove shape on the frictional force distribution on the surface of the curved annular rope groove wheel. This invention not only improves the accuracy of calculating the frictional force distribution on the surface of the curved annular rope groove wheel, but also provides strong support for the structural design and optimization of the curved groove of the friction wheel. This enables the electric traction device to have a higher load capacity, pull heavier goods, and improve the safety of the electric traction device.

[0042] Other features and advantages of the present invention will be disclosed in detail in the following detailed description and accompanying drawings. Attached Figure Description

[0043] The invention will be further described below with reference to the accompanying drawings:

[0044] Figure 1 This is a flowchart of a method for calculating the tension distribution of a traction rope on a curved annular rope groove pulley according to the present invention;

[0045] Figure 2 This is a schematic diagram of the curved annular rope grooved pulley in this invention. Figure 1 ;

[0046] Figure 3This is a schematic diagram of the curved annular rope grooved pulley in this invention. Figure 2 ;

[0047] Figure 4 This is a force analysis diagram of the contact portion between the micro-arc traction rope and the curved annular rope groove wheel in this invention;

[0048] Figure 5 This is a flowchart illustrating the iterative calculations performed by software in this invention;

[0049] Figure 6 This is a tension fitting diagram of the traction rope node on the curved annular rope groove wheel in this invention;

[0050] Figure 7 This is a tension fitting diagram of the traction rope node on a conventional rope grooved pulley in this invention.

[0051] Reference numerals: 1. Curved annular grooved rope wheel; 11. Curved groove; 12. Annular wall. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be explained and described below with reference to the accompanying drawings. However, the following embodiments are only preferred embodiments of the present invention and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments in the implementation methods without creative effort are all within the protection scope of the present invention.

[0053] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0054] 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 connection; 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; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0055] like Figures 1 to 7As shown, this embodiment illustrates a method for calculating the surface friction distribution of a curved annular grooved rope wheel 1. The curved annular grooved rope wheel 1 has a circumferentially curved groove 11, which has a wavy curve along its axial direction. The curved groove 11 includes two wavy annular wall surfaces 12. (Refer to...) Figure 2 As shown; it is of course understandable that, in other embodiments, the two annular walls 12 of the curved groove 11 of the curved annular rope groove wheel 1 may also be composed of curved annular retaining rings.

[0056] The calculation method for the surface friction distribution of the curved annular rope groove wheel 1 described in this embodiment is as follows:

[0057] First, the curved annular rope grooved pulley 1 is parameterized, and the model parametric equations of the curved annular rope grooved pulley 1 are established. The parametric equations are used to fully express the curved path of the traction rope. The specific expressions of the parametric equations are as follows:

[0058]

[0059] Where R represents the radius of the curved annular rope groove wheel 1, the curved path of the traction rope is a trigonometric function waveform, A represents the amplitude of the trigonometric function waveform path, and N represents the number of waveforms on the curved groove 11.

[0060] like Figure 4 As shown, mark several nodes on the traction rope, calculate the tension F at each node, calculate the angle θ between the tangent of the traction rope at each node and the radial section of the curved annular grooved sheave 1, and calculate the angle between the tangent of the traction rope at each node and the central axis of the curved annular grooved sheave 1. included angle θ and The calculation method is as follows:

[0061]

[0062] Where T curve T represents the tangent vector of the micro-arc segment. circle This represents the tangent vector of the corresponding node of the curved annular grooved rope wheel.

[0063] like Figure 4 As shown, considering the influence of the bending path of the curved groove 11 on the traction rope during operation, the direction of the force on the traction rope will change with the change of the node. Therefore, the infinitesimal element method is used to select a micro-arc segment at each node of the traction rope. Based on Newton's third law and Coulomb's law, the force analysis of the micro-arc segment in the circumferential, radial and axial directions of the curved annular rope groove wheel 1 is carried out, and the tension attenuation dF of the micro-arc segment is obtained through the force analysis.

[0064] The resultant force of the traction rope in the circumferential, radial, and axial directions of the curved annular grooved rope sheave 1 is shown in the following formula:

[0065] In the circumferential direction of the curved annular grooved rope pulley 1:

[0066]

[0067] In the radial direction of the curved annular grooved rope pulley 1:

[0068]

[0069] In the axial direction of the curved annular rope grooved pulley 1:

[0070]

[0071] Where F represents the tension in the traction rope; F N1 F N2 This represents the supporting force of 12 pairs of traction ropes on the two annular walls; F f dα represents the frictional force on the traction rope; f represents the coefficient of friction; dα represents the central angle of the curved annular rope groove wheel 1 corresponding to the micro-arc segment; dβ represents the central angle of the curved groove corresponding to the micro-arc segment; γ represents the angle between the annular wall 12 and the radial section; k represents the position of the micro-arc segment; rev represents the equivalent friction coefficient correction.

[0072] Solving the above system of equations yields the tensile force attenuation dF in the micro-arc segment, specifically the formula:

[0073]

[0074] Before calculating the tension attenuation dF, the central angle dα of the curved annular rope groove wheel corresponding to the micro-arc segment, the central angle dβ of the curved groove corresponding to the micro-arc segment, the position k of the micro-arc segment, and the equivalent friction coefficient correction rev can be calculated first.

[0075] The formulas for calculating the central angle dα of the curved annular grooved sheave corresponding to the micro-arc segment and the central angle dβ of the curved groove corresponding to the micro-arc segment are as follows:

[0076]

[0077] Where n is the number of discrete nodes, k i Δs i The curvature and arc length of the waveform corresponding to the micro-arc segments at the corresponding nodes are respectively.

[0078] The formula for calculating the position k of the micro-arc segment is as follows:

[0079]

[0080] The equivalent friction coefficient correction rev is calculated by conducting friction experiments on a curved annular rope grooved pulley. A section of the traction rope in contact with the curved annular rope grooved pulley is obtained, and the calculation is performed using the tensions T' and T at both ends of the traction rope section under the wrap angle δ. The calculation formula is as follows:

[0081]

[0082] Substituting the above calculation results into the formula for calculating the tension attenuation dF, we can obtain the tension attenuation dF of each micro-arc segment in contact with the curved annular grooved sheave, which is the frictional force experienced by the micro-arc segment.

[0083] To verify the above calculation results, an iterative program was written using software such as MATLAB, and the tension at each node on the traction rope was iteratively calculated based on the obtained micro-arc segment tension attenuation formula. The tension T on the traction rope at each node was calculated. i The tension T on the traction rope at the previous node i-1 The specific formula is shown below:

[0084] T i =T i-1 -dF.

[0085] By performing an exponential fit on the tension values ​​of each node obtained above, the tension expressions for each node of the traction rope are obtained, as shown below:

[0086] T(t) = T0e -λt ;

[0087] Where T0 represents the tension value of the initial node, λ represents the attenuation coefficient, and t represents the index value of the node, with the initial node index value being 0.

[0088] In the specific experimental calculation process, the relevant parameters of the curved annular rope grooved wheel 1 are shown in Table 1 below:

[0089]

[0090] Table 1: Relevant parameters of curved annular rope grooved pulley 1

[0091] Based on the above parameters and using the above calculation method, a force analysis is performed on the micro-arc segment, with reference to... Figure 4 As shown, iterative calculations were then performed using MATLAB to obtain the tension values ​​at each node on the traction rope, and an exponential fit was performed. The resulting node tension value fitting curve is referenced. Figure 6 As shown, the tension values ​​for each node are expressed as follows:

[0092] T(t) = 4900.2512e-2.9377α ;

[0093] This embodiment establishes a parameterized model of the curved annular rope groove wheel 1, parameterizing the bending path of the curved groove 11. This allows for a complete representation of the curved path of the groove 11, particularly its bending characteristics in the axial direction of the curved annular rope groove wheel 1. This enables a more accurate description of the force on the traction rope in the curved annular rope groove, clarifying the force change process between the traction rope and the curved annular rope groove wheel 1 during operation. Furthermore, the infinitesimal element method is used to analyze the force at the contact point between the traction rope and the curved annular rope groove wheel 1, analyzing the resultant force of the traction rope in the circumferential, radial, and axial directions of the curved annular rope groove wheel 1. This allows for the derivation of the tension attenuation formula for the micro-arc segment, representing the surface friction force of the curved annular rope groove wheel 1. The accurate calculation of the distribution lays the foundation; secondly, based on the tension attenuation of the micro-arc segment, and through iterative calculation and exponential fitting using software, the tension formula of each node on the traction rope can be obtained, thereby enabling precise analysis of the frictional force distribution on the surface of the curved annular rope groove wheel 1, and clarifying the influence of the bending path and groove shape of the curved groove 11 on the frictional force distribution on the surface of the curved annular rope groove wheel 1; through this invention, not only can the calculation accuracy of the frictional force distribution on the surface of the curved annular rope groove wheel 1 be improved, but it can also provide strong support for the structural design and optimization of the curved annular rope groove 11, thereby enabling the electric traction device to have a higher load and pull heavier goods, which helps to improve the safety of the electric traction device.

[0094] This embodiment can provide a more accurate calculation of the structure than the traditional Euler formula, and can be used as a more accurate calculation method for the curved annular rope groove wheel 1.

[0095] Regarding the applicability of this calculation method, it was used to calculate ordinary straight grooved rope pulleys during the experiment. It should be noted that the rope grooves of the straight grooved rope pulley are complete annular on the outer circumference of the pulley, that is, the number of waveforms and amplitude of the rope grooves are both 0. The relevant parameters of the calculated straight grooved rope pulley are shown in Table 2 below:

[0096]

[0097] Table 2: Relevant parameters of straight grooved rope pulleys

[0098] Using the calculation method of this invention, a nodal tension fitting curve is obtained, with reference to... Figure 7 As shown, the expression is as follows:

[0099] T(t)=4900.0502e -0.5875α ;

[0100] The fitting result is consistent with the result obtained by Euler's formula after groove correction, indicating that the calculation method of the present invention has a wider range of applicability.

[0101] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Those skilled in the art should understand that the present invention includes, but is not limited to, the contents described in the accompanying drawings and the specific embodiments above. Any modifications that do not depart from the functional and structural principles of the present invention will be included within the scope of the claims.

Claims

1. A method for calculating the tension distribution of a traction rope on a curved annular grooved sheave, characterized in that, The outer periphery of the curved annular rope grooved wheel is provided with a curved groove for the traction rope to be wound. The curved groove includes two annular walls with wavy curves. The method for calculating the force exerted on the traction rope by the curved groove includes: S1. Parameterize the curved annular grooved rope pulley and establish the model parametric equations of the curved annular grooved rope pulley; S2. Mark several nodes on the traction rope, calculate the tension F at each node, and calculate the angle between the tangent of the traction rope at each node and the radial section of the curved annular grooved rope pulley. Calculate the angle between the tangent of the traction rope at each node and the central axis of the curved annular rope grooved pulley. ; S3. Using the infinitesimal element method, select micro-arc segments at each node of the traction rope. Based on Newton's third law and Coulomb's law, perform force analysis on the micro-arc segments in the circumferential, radial, and axial directions of the curved annular rope groove wheel, and obtain the tension attenuation of the micro-arc segments through the force analysis. ; S4. Based on the tension attenuation of the micro-arc segment The tension F at each node of the traction rope is calculated iteratively using an iterative program to obtain the tension value T at each node of the traction rope. S5. Perform an exponential fit on the tension values ​​T at all nodes to derive the distribution formula for the tension at the nodes of the traction rope. .

2. The method for calculating the tension distribution of the traction rope on a curved annular grooved rope pulley according to claim 1, characterized in that, The parametric equations in S1 are used to fully express the curved path of the traction rope. The specific expressions of the parametric equations are as follows: ； Where R represents the radius of the curved annular grooved rope wheel, the curved path of the traction rope is a trigonometric function waveform, A represents the amplitude of the trigonometric function waveform path, and N represents the number of waveforms on the curved groove.

3. The method for calculating the tension distribution of the traction rope on a curved annular grooved rope pulley according to claim 2, characterized in that, The included angle in S2 and Used to determine the direction and angle of tension. and The calculation method is as follows: ； ； in This represents the tangent vector of the micro-arc segment. This represents the tangent vector of the corresponding node of the curved annular grooved rope wheel, where x, y, and z are the radial, axial, and vertical coordinates of the curved groove path node in the three-dimensional coordinate system, respectively.

4. The method for calculating the tension distribution of the traction rope on a curved annular grooved rope pulley according to claim 3, characterized in that, The resultant force of the traction rope in the S3 along the circumferential, radial, and axial directions of the curved annular rope groove pulley is shown in the following formula: In the circumferential direction of the curved annular grooved rope pulley: ； In the radial direction of the curved annular rope grooved pulley: ； In the axial direction of the curved annular rope grooved pulley: ； Where F represents the tension in the traction rope; , This represents the supporting force of the two annular walls on the traction rope; This represents the coefficient of friction; This represents the central angle of the curved annular grooved rope wheel corresponding to the micro-arc segment; This represents the central angle of the groove on the surface corresponding to the micro-arc segment; This indicates the angle between the annular wall and the radial section plane; This indicates the position of the micro-arc segment; This indicates the correction for the equivalent coefficient of friction; Solving the above system of equations yields the tensile force attenuation in the micro-arc segment. The specific formula is as follows: 。 5. The method for calculating the tension distribution of the traction rope on a curved annular grooved rope pulley according to claim 4, characterized in that, The central angle of the curved annular grooved rope wheel corresponding to the micro-arc segment The central angle of the groove corresponding to the micro-arc segment The calculation formula is as follows: ； ； in The number of discrete nodes. , The curvature and arc length of the waveform corresponding to the micro-arc segments at the corresponding nodes are respectively.

6. The method for calculating the tension distribution of the traction rope on a curved annular grooved rope pulley according to claim 4, characterized in that, The The calculation method for determining the location of the arc where the force analysis node is located is as follows: 。 7. The method for calculating the tension distribution of the traction rope on a curved annular rope grooved pulley according to claim 4, characterized in that, Correction for equivalent friction coefficient Friction experiments were conducted on a curved annular grooved rope pulley. A section of the traction rope in contact with the pulley was obtained. Under the wrap angle δ of this section of the traction rope, the tension at both ends of this section of the traction rope was utilized. and The calculation is performed using the following formula: 。 8. The method for calculating the tension distribution of the traction rope on a curved annular rope grooved pulley according to claim 1, characterized in that, The tension on the traction rope at each node in S4 The tension on the traction rope at the previous node With tensile attenuation The calculation is performed using the formula shown below: 。 9. The method for calculating the tension distribution of the traction rope on a curved annular rope grooved pulley according to claim 1, characterized in that, In step S5, the tension formula for each node of the traction rope is obtained through exponential fitting: ； in This represents the tension value at the initial node. This represents the attenuation coefficient. This represents the index value of the node; the initial index value of the node is 0.

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