Expansion sleeve assembly flange connecting mechanism and design method

Abstract

The invention belongs to the technical field of couplings, and particularly relates to an expansion sleeve assembly flange connecting mechanism and a design method of the expansion sleeve assembly flange connecting mechanism. The expansion sleeve assembly flange connecting mechanism comprises an expansion sleeve assembly and a flange, the flange is coaxially arranged at the end part of the expansion sleeve assembly; the bolts are evenly distributed in the circumferential direction, and the bolts are arranged in the flange and the expansion sleeve assembly in the axial direction; the multiple limiting pins are evenly distributed in the circumferential direction, the limiting pins are arranged in the flange and the expansion sleeve assembly in the axial direction, and the sum of the maximum torque capable of being transmitted by the limiting pins within the preset deformation quantity and the friction torque capable of being transmitted by the bolts is larger than or equal to the rated torque.

Description

Technical Field

[0001] This invention belongs to the field of coupling technology, specifically, it relates to a flange connection mechanism for an expansion sleeve assembly and a design method for the flange connection mechanism for the expansion sleeve assembly. Background Technology

[0002] As the power of wind turbines increases, the torque requirements for the expansion sleeve assembly will also increase. Currently, the torque is transmitted between the contact surface of the expansion sleeve assembly and the flange through friction. Due to factors such as the instability of the friction coefficient and the instability of the bolt axial force, there is a risk of relative slippage between the contact surfaces of some expansion sleeve assemblies and the flange during wind farm operation. This will cause the bolt to break under shear load. The broken bolt will fly out with the high-speed rotating transmission shaft, which will pose a risk of damage to equipment near the expansion sleeve assembly. Summary of the Invention

[0003] To address the technical problems described above, this invention aims to provide a flange connection mechanism for an expansion sleeve assembly and a design method for such a mechanism.

[0004] According to the present invention, a flange connection mechanism for an expansion sleeve assembly is provided, comprising: Expansion sleeve assembly; A flange coaxially disposed at the end of the expansion sleeve assembly; A plurality of bolts are evenly distributed along the circumferential direction, and the bolts are arranged axially within the flange and the expansion sleeve assembly; Multiple limiting pins are evenly distributed along the circumference, and the limiting pins are axially arranged in the flange and the expansion sleeve assembly. The sum of the maximum torque that the limiting pins can transmit within a preset deformation range and the frictional torque that the bolts can transmit is greater than or equal to the rated torque.

[0005] In a specific embodiment, the maximum torque that the limiting pin can transmit within a preset deformation is calculated as follows: Calculate the maximum force F0 that the limiting pin can withstand without being sheared; Calculate the deformation δ1 of the limiting pin at L / 2 under the action of F0; If δ1 > δ, successively take F1 less than F0 as the new F0, calculate the deformation δ1 of the limiting pin at L / 2 under the action of the new F0, until δ1 ≤ δ; If δ1≤δ, then T3=N2F0r2; Wherein, L is the length of the limiting pin located outside the expansion sleeve assembly; δ is a preset deformation variable; T3 is the maximum torque that the limiting pin can transmit within a preset deformation range; N2 is the number of the limiting pins; r2 is the radius of the circle containing the limiting pin.

[0006] In one specific embodiment, the preset deformation δ is less than or equal to 0.01 mm.

[0007] In one specific embodiment, during the process of successively taking F1 that is less than F0, the magnitude is gradually reduced based on F0.

[0008] In one specific embodiment, during the process of successively taking F1 that is less than F0, the value of F0 is successively reduced by 1%.

[0009] In one specific embodiment, when calculating the maximum force F0 that the limiting pin can withstand without being sheared, the bending stress σ1 and shear stress τ1 of the limiting pin are compared with the yield strength σ. s The relationship between the pressure P and the limit pins 0 to L is used to obtain the pressure P. Under the pressure P, the limit pins 0 to L are integrated to obtain F0.

[0010] In one specific embodiment, both the expansion sleeve assembly and the flange are provided with pin holes for installing the limiting pin, and the limiting pin is disposed in the pin hole by means of an interference fit.

[0011] In one specific embodiment, the pin hole is a countersunk hole.

[0012] In one specific embodiment, the bolt includes a plurality of inner ring bolts and a plurality of outer ring bolts evenly distributed along the circumference, wherein the diameter of the circle containing the inner ring bolts is smaller than the diameter of the circle containing the outer ring bolts.

[0013] In one specific embodiment, the diameter of the circle containing the limiting pin is equal to the diameter of the circle containing the outer ring bolt.

[0014] According to the present invention, a design method for a flange connection mechanism of an expansion sleeve assembly is also provided, wherein the sum of the maximum torque that the limiting pin can transmit within a preset deformation and the frictional torque that the bolt can transmit is set to be greater than or equal to the rated torque, wherein the preset deformation is less than or equal to 0.01 mm.

[0015] Compared with the prior art, this application has at least the following advantages.

[0016] The expansion sleeve assembly flange connection mechanism uses a limit pin to bear shear load. The sum of the maximum torque that the limit pin can transmit within a preset deformation range and the frictional torque that the bolt can transmit is set to be greater than or equal to the rated torque. This solves the problem of insufficient friction between the current expansion sleeve assembly and the flange mating surface, and can effectively prevent the bolt from being sheared and avoid bolt breakage.

[0017] When the contact surface between the expansion sleeve assembly and the flange needs to transmit higher torque, the method of setting limit pins can be adopted. This eliminates the need to increase the outer diameter of the inner ring of the expansion sleeve assembly to increase the number of bolts and the distribution diameter. Therefore, the overall weight and inertia of the expansion sleeve can be reduced, which helps to reduce costs. Attached Figure Description

[0018] The present invention will now be described with reference to the accompanying drawings.

[0019] Figure 1 A top view schematic diagram of an embodiment of the expansion sleeve assembly flange connection mechanism provided by the present invention is shown; Figure 2 Showing Figure 1 A schematic diagram of the cross-section along direction A. Figure 3 A schematic diagram showing the separation of the expansion sleeve assembly from the flange is displayed; Figure 4 A three-dimensional schematic diagram of the expansion sleeve assembly is shown; Figure 5 A side view of the expansion sleeve assembly is shown; Figure 6 A top view of the expansion sleeve assembly is shown.

[0020] The reference numerals in the figure are as follows: 1. Expansion sleeve assembly; 11. Inner ring; 111. Connecting part; 112. Tapered part; 12. Outer ring; 2. Flange; 3. Bolt; 31. Inner ring bolt; 32. Outer ring bolt; 4. Limiting pin; 5. Pin hole; 100. Expansion sleeve assembly flange connection mechanism.

[0021] In this application, all drawings are schematic and are used only to illustrate the principles of the invention, and are not drawn to scale. Detailed Implementation

[0022] The invention will now be described with reference to the accompanying drawings.

[0023] It should be noted that the directional terms or qualifiers such as "up" and "down" used in this application are all specific to the referenced [reference]. Figure 2In this context, these terms are not used to define the absolute position of the components involved, but can vary depending on the specific circumstances. In this application, the directional term or qualifier "axial" refers to the direction indicated by the central axis of the expansion sleeve assembly, and "radial" refers to the direction perpendicular to the central axis of the expansion sleeve assembly.

[0024] Figure 1 and Figure 2 The structure of the expansion sleeve assembly flange connection mechanism 100 according to the present invention is shown. Figure 1 and Figure 2 As shown, the expansion sleeve assembly flange connection mechanism 100 includes an expansion sleeve assembly 1, a flange 2, a bolt 3, and a limit pin 4.

[0025] In this embodiment, the expansion sleeve assembly 1 includes a cylindrical inner ring 11 and an outer ring 12. The upper part of the inner ring 11 is configured as a connecting portion 111 for connection with the flange 2, and the lower part of the inner ring 11 is configured as a tapered portion 112 for connection with the outer ring 12. The inner wall of the outer ring 12 is configured as a tapered surface that matches the outer wall of the tapered portion 112. After the tapered portion 112 of the inner ring 11 is fitted inside the outer ring 12, by applying an axial force that brings the inner ring 11 and the outer ring 12 closer together, the outer wall of the tapered portion 112 can provide a radially outward force to the outer ring 12, while the inner wall of the outer ring 12 provides a radially inward force to the tapered portion 112.

[0026] Flange 2 is coaxially disposed on the upper part of the expansion sleeve assembly 1 and is coaxially connected to the connecting part 111 of the inner ring 11.

[0027] Multiple bolts 3 are evenly distributed along the circumference, and each bolt 3 is axially arranged within the flange 2 and the expansion sleeve assembly 1, thereby fixing the flange 2 and the expansion sleeve assembly 1 together. Furthermore, the bolts 3 are axially arranged within the inner ring 11 and the outer ring 12 of the expansion sleeve assembly 1. By tightening the bolts 3, an axial force can be provided to bring the inner ring 11 and the outer ring 12 closer to each other.

[0028] In a specific embodiment, such as Figure 1 As shown, bolt 3 includes multiple inner ring bolts 31 and multiple outer ring bolts 32 evenly distributed along the circumference. The diameter of the circle containing the inner ring bolts 31 is smaller than the diameter of the circle containing the outer ring bolts 32.

[0029] Multiple limiting pins 4 are evenly distributed along the circumferential direction, and the limiting pins 4 are axially disposed within the flange 2 and the expansion sleeve assembly 1. That is, a portion of the limiting pin 4 is located within the expansion sleeve assembly 1, and another portion is located within the flange 2, thereby enabling the limiting pin 4 to withstand the shear stress from the expansion sleeve assembly 1 and the flange 2. Specifically, as shown... Figure 1 and Figure 2As shown, a pin hole 5 for installing a limit pin 4 is provided on the upper end face of the connecting part 111 of the inner ring 11 of the expansion sleeve assembly 1, and a pin hole 5 for installing a limit pin 4 is provided on the flange 2. During installation, the pin holes 5 of the flange 2 correspond one-to-one with the pin holes 5 of the connecting part 111, and the limit pin 4 is set in the pin hole 5 by an interference fit.

[0030] According to the present invention, the sum of the maximum torque that the limiting pin 4 can transmit within a preset deformation range and the frictional torque that the bolt 3 can transmit is greater than or equal to the rated torque. This configuration solves the problem of insufficient friction between the expansion sleeve assembly and the flange mating surface in the prior art, prevents relative rotation between the flange 2 and the expansion sleeve assembly 1, effectively prevents the bolt 3 from being sheared, and avoids bolt 3 breakage.

[0031] The calculation method for the maximum torque that the limit pin 4 can transmit within the preset deformation is as follows.

[0032] Step 1: Calculate the maximum force F0 that the limiting pin 4 can withstand without being sheared. In this embodiment, this is based on the bending stress σ1 and shear stress τ1 of the limiting pin 4 and its yield strength σ. s The relationship between the pressure P and the limit pin 4 is used to obtain the pressure P. Under the pressure P, the limit pin 4 is integrated from 0 to L to obtain F0.

[0033] Step 2: Calculate the deformation δ1 of the limiting pin 4 at L / 2 under the action of F0.

[0034] Step 3: If δ1 > δ, successively select F1 that is less than F0, and calculate the deformation δ1 of the limiting pin 4 at L / 2 under the action of F1, until δ1 ≤ δ. During the process of successively selecting F1 that is less than F0, the magnitude is gradually reduced from F0. In this embodiment, during the process of successively selecting F1 that is less than F0, the magnitude is gradually reduced by 1% from F0.

[0035] Step 4: If δ1≤δ, then T3=N2F0r2.

[0036] Where L is the length of the limiting pin 4 located outside the tightening sleeve assembly 1, such as Figure 5 As shown; δ is a preset deformation. In this embodiment, the preset deformation δ is less than or equal to 0.01 mm. Preferably, the preset deformation δ is less than or equal to 0.01 mm and greater than or equal to 0.001 mm. T3 is the maximum torque that the limiting pin 4 can transmit within the preset deformation range; N2 represents the quantity of limit pins 4; r2 is the radius of the circle containing the limiting pin 4.

[0037] In one embodiment, the limiting pin 4 is a resilient pin, and more specifically, an open resilient pin. In another embodiment, the limiting pin 4 is a solid cylindrical pin.

[0038] In one specific embodiment, the pin hole 5 is a countersunk hole.

[0039] In this embodiment, multiple limiting pins 4 are evenly distributed along the circumference, and the diameter of the circle where the limiting pins 4 are located is equal to the diameter of the circle where the outer ring bolt 32 is located.

[0040] In a specific embodiment provided by the present invention, a countersunk hole is designed on the upper end face of the connecting part 111 of the inner ring 11 as a pin hole 5, and a countersunk hole is designed on the flange 2 as a pin hole 5. The number of countersunk holes on the connecting part 111 and the flange 2 are equal and correspond one-to-one, and the diameter and depth are as equal as possible. The pin holes 5 are evenly distributed along the circumferential direction. The diameter and tolerance of the pin holes 5 are designed as Y(-a, -0.05). Where Y is the diameter of the pin hole 5, and a is a positive number, which is determined according to the deformation of the limiting pin 4.

[0041] The countersunk hole on the inner ring 11 and the countersunk hole on the flange 2 both have a chamfer of C1, which serves as a guide.

[0042] The limiting pin 4 is an open elastic pin. The diameter and wall thickness of the limiting pin 4 are rationally designed based on the required load-bearing capacity. The outer diameter and tolerance of the limiting pin 4 are designed as Y(0.05, +a), where Y is the outer diameter of the limiting pin 4, and a is a positive number determined based on the deformation of the limiting pin 4. A small interference fit is used between the outer circle of the limiting pin and the countersunk hole.

[0043] The assembly process of the limiting pin 4 and the expansion sleeve assembly 1 is as follows. First, place the outer ring 12 on the assembly table, apply grease between the conical surfaces of the inner ring 11 and the outer ring 12, and ensure that the threaded holes of the inner ring 11 and the outer ring 12 correspond one-to-one. Place the inner ring 11 with its conical portion 112 facing down inside the outer ring 12, ensuring contact between the conical surfaces of the inner ring 11 and the outer ring 12. Place four inner ring bolts 31 symmetrically in the inner ring hole of the inner ring 11 using a cross-shaped method for positioning. Then, place the limiting pin 4 on the pin hole 5 of the connecting portion 111 of the inner ring 11, as shown. Figure 4 As shown, one hand can use pliers to hold the limiting pin 4, aligning the lower part of the limiting pin 4 with the pin hole 5, while the other hand uses a copper or lead hammer to gently tap the limiting pin 4, causing it to enter the pin hole 5 of the connecting part 111 and making the end of the limiting pin 4 contact the bottom of the pin hole 5 of the connecting part 111. Figure 5 As shown.

[0044] The assembly process between flange 2 and expansion sleeve assembly 1 is as follows: Remove the aforementioned four inner ring bolts 31 that serve as positioning bolts from the inner ring 11, then suspend flange 2 and align the pin holes 5 on flange 2 with the limiting pins 4 on the inner ring 11, as follows. Figure 3 As shown. Then, gently place flange 2 on top of inner ring 11, maintaining a certain distance from the upper end face of inner ring 11. Then, pass the outer ring bolts 32 downwards from above flange 2 and screw them into all the outer ring threaded holes of the expansion sleeve assembly 1. Tighten the outer ring bolts 32 symmetrically using a cross-tightening method, gradually reducing the distance between the lower end face of flange 2 and the upper end face of inner ring 11, and trying to keep the distance as uniform as possible. After several rounds of tightening, the lower end face of flange 2 and the upper end face of inner ring 11 are completely in contact. Then, install all the inner ring bolts 31 in the inner ring threaded holes of flange 2 and expansion sleeve assembly 1. At this time, it is not necessary to tighten them. At this point, the assembly between flange 2 and expansion sleeve assembly 1 is complete.

[0045] According to the present invention, a design method for a flange connection mechanism of an expansion sleeve assembly is also provided, wherein the sum of the maximum torque that the limiting pin can transmit within a preset deformation and the frictional torque that the bolt can transmit is set to be greater than or equal to the rated torque, wherein the preset deformation is less than or equal to 0.01 mm.

[0046] In a specific embodiment, the maximum torque that the limiting pin 4 can transmit within a preset deformation is calculated as follows.

[0047] Assuming there is no limit pin 4, after the bolt 3 is tightened, there is no relative sliding between the mating surfaces of the expansion sleeve assembly 1 and the flange 2. At this time, the expansion sleeve applies a total torque T0, the frictional torque that the inner ring bolt 31 can transmit is T1, and the frictional torque that the outer ring bolt 32 can transmit is T2. It can be known that T0 = T1 + T2.

[0048] The friction coefficient between the mating surfaces of flange 2 and expansion sleeve assembly 1 is μ. The number of inner ring bolts 31 and outer ring bolts 32 is equal, N1. The distribution radius of the inner ring bolts 31 is r1 (i.e., the radius of the circle containing multiple inner ring bolts 31 is r1), and the distribution radius of the outer ring bolts 32 is r2 (i.e., the radius of the circle containing multiple outer ring bolts 32 is r2). The axial force of a single bolt 3 is F1. It can be known that T1=μN1F1r1 and T2=μN1F1r2. After setting the limit pin 4, the total number of limit pins 4 is N2. Assume that the maximum torque that all limit pins 4 can transmit is T3, and the yield strength of the limit pin 4 is σ. s In the process of transmitting torque, a single limiting pin 4 bears bending stress and shear stress. For example... Figure 5 and Figure 6 As shown, suppose a certain limiting pin 4 is subjected to a uniformly distributed pressure P along a length L, and the direction of the force is as follows. Figure 6As shown. The outer diameter of the limiting pin 4 is D, and the inner diameter is d. The calculation steps for the maximum torque T3 are as follows.

[0049] (1) Calculate the bending stress σ1 and shear stress τ1 of the limiting pin 4 at the mating surface of the expansion sleeve assembly 1 and the flange 2. These two stresses are represented by parameters such as P, L, D and d. It is easy to understand that the use of parameters such as P, L, D and d to represent bending stress σ1 and shear stress τ1 is well known to those skilled in the art, and will not be elaborated here.

[0050] (2) Based on the strength theory, take an appropriate safety factor k, and establish the relationship between bending stress σ1 and shear stress τ1 and yield strength σ s The equations between these equations can then be used to determine the maximum allowable pressure P under the given safety factor k. It is easy to understand that by choosing an appropriate safety factor k, equations can be established between bending stress σ1 and shear stress τ1 and yield strength σs, which are well-known to those skilled in the art and will not be elaborated upon here.

[0051] (3) Under pressure P, the length (0~L) of the limiting pin 4 is integrated to obtain the force F0 on the limiting pin 4.

[0052] (4) Using the deflection calculation method, the deformation δ1 at L / 2 of the limiting pin 4 is calculated. The allowable deformation δ (preset deformation δ) of the limiting pin 4 is at the micrometer level (i.e. δ is between 0.001 mm and 0.01 mm).

[0053] (5) If δ1≤δ, then the maximum force that a single limit pin 4 can withstand is the force F0 calculated in step (3). At this time, the maximum torque that all limit pins 4 can transmit is T3=N2F0r2.

[0054] If δ1 > δ, then reduce the force F0 calculated in step (3) by 1% to obtain a new force F0, and then substitute it into step (4) to recalculate the new deformation δ1. If δ1 ≤ δ, then the maximum torque T3 = N2F0r2; otherwise, perform iterative calculation, reduce the force F0 calculated in step (3) by 2% to obtain a new force F0, and then repeat steps (4) and (5). Until δ1 ≤ δ is satisfied. In each iterative calculation, increase the reduction rate by 1% based on the force F0 calculated in step (3), and then repeat steps (4) and (5).

[0055] The final T3 is the maximum torque that the limit pin 4 can transmit within the preset deformation range.

[0056] T4 = T0 + T3, where T4 is the total torque that can be transmitted between flange 2 and expansion sleeve assembly 1, and T4 is greater than or equal to the rated torque between flange 2 and expansion sleeve assembly 1.

[0057] In the description of this invention, it should be understood that 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. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0058] 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.

[0059] In the description of this specification, 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 invention. 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.

[0060] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A flange connection mechanism for an expansion sleeve assembly, characterized in that, include: Expansion sleeve assembly (1); A flange (2) is coaxially disposed at the end of the expansion sleeve assembly (1); A plurality of bolts (3) are evenly distributed along the circumferential direction, and the bolts (3) are arranged axially within the flange (2) and the expansion sleeve assembly (1); Multiple limiting pins (4) are evenly distributed along the circumference. The limiting pins (4) are arranged axially in the flange (2) and the expansion sleeve assembly (1). The sum of the maximum torque that the limiting pins (4) can transmit within a preset deformation and the frictional torque that the bolt (3) can transmit is greater than or equal to the rated torque.

2. The expansion sleeve assembly flange connection mechanism according to claim 1, characterized in that, The calculation method for the maximum torque that the limiting pin (4) can transmit within the preset deformation is as follows: Calculate the maximum force F0 that the limiting pin (4) can withstand without being sheared; Calculate the deformation δ1 of the limiting pin (4) at L / 2 under the action of F0; If δ1 > δ, successively take F1 less than F0 as the new F0, calculate the deformation δ1 of the limit pin (4) at L / 2 under the action of the new F0, until δ1 ≤ δ; If δ1≤δ, then T3=N2F0r2; Wherein, L is the length of the limiting pin (4) located outside the expansion sleeve assembly (1); δ is a preset deformation variable; T3 is the maximum torque that the limiting pin (4) can transmit within the preset deformation range; N2 is the number of the limiting pins (4); r2 is the radius of the circle containing the limiting pin (4).

3. The expansion sleeve assembly flange connection mechanism according to claim 2, characterized in that, The preset deformation δ is less than or equal to 0.01 mm.

4. The expansion sleeve assembly flange connection mechanism according to claim 2, characterized in that, In the process of successively taking F1 values ​​less than F0, the amplitude is gradually reduced from F0.

5. The expansion sleeve assembly flange connection mechanism according to claim 4, characterized in that, In the process of successively taking F1 that is less than F0, the value of F0 is successively reduced by 1%.

6. The expansion sleeve assembly flange connection mechanism according to claim 2, characterized in that, When calculating the maximum force F0 that the limiting pin (4) can withstand without being sheared, the bending stress σ1 and shear stress τ1 of the limiting pin (4) are compared with the yield strength σ. s The pressure P is obtained from the relationship between the limiting pins (4)0 to L under the pressure P, and F0 is obtained by integrating the limiting pins (4)0 to L.

7. The expansion sleeve assembly flange connection mechanism according to any one of claims 1 to 6, characterized in that, Both the expansion sleeve assembly (1) and the flange (2) are provided with pin holes (5) for installing the limiting pin (4), and the limiting pin (4) is set in the pin hole (5) by an interference fit.

8. The expansion sleeve assembly flange connection mechanism according to claim 7, characterized in that, The pin hole (5) is a countersunk hole.

9. The expansion sleeve assembly flange connection mechanism according to any one of claims 1 to 6, characterized in that, The bolt (3) includes a plurality of inner ring bolts (31) and a plurality of outer ring bolts (32) evenly distributed along the circumference, wherein the diameter of the circle in which the inner ring bolts (31) are located is smaller than the diameter of the circle in which the outer ring bolts (32) are located.

10. The expansion sleeve assembly flange connection mechanism according to claim 9, characterized in that, The diameter of the circle containing the limiting pin (4) is equal to the diameter of the circle containing the outer ring bolt (32).

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