Method for determining the assembly interference of a composite flywheel rotor multi-ring

Abstract

The application discloses a kind of composite flywheel rotor multi-ring assembly interference amount determination method, comprising the following steps: step 1, determine the size of flywheel rotating shaft;Step 2, calculate the stress of composite rim winding, obtain the displacement of each ring static assembly due to interference amount by calculating the assembly of multi-ring flywheel, calculate the stress of each ring;Step 3, calculate the size change of multi-ring flywheel assembly, the size after assembly is regarded as the size of flywheel in working condition, calculate the displacement of flywheel in working condition;Step 4, calculate the stress caused by the displacement difference of each ring contact part;The stress obtained by superimposing static initial stress and the stress caused by displacement difference due to centrifugal force is regarded as the stress of flywheel in working condition;Step 5, determine the maximum interference amount according to the strength of each ring material.The present application can accurately determine the interference amount of composite flywheel rotor multi-ring assembly.

Description

Technical Field

[0001] This invention relates to mechanical strength analysis, and more particularly to a method for strength analysis and structural design of a multi-ring composite material flywheel rotor. Background Technology

[0002] Flywheel energy storage is widely used in backup power supplies (UPS), rail transit energy conservation, and power frequency regulation due to its rapid response, high power density, and long lifespan. The rotor system is the core of flywheel energy storage, directly affecting the energy density and operational safety of the system. To increase the energy storage density of flywheel systems, flywheel rotors are being developed towards higher speeds and lighter weights. As the rotational speed increases, the stress on the flywheel rotor system also increases. To reduce rotor stress, flywheel rotors employ a multi-ring interference fit structure. To ensure the safe and stable operation of the flywheel rotor, the stress and displacement distribution under the multi-ring fit must be comprehensively considered. The selection of the interference fit has a significant impact on the stress and displacement of the flywheel, making it a crucial aspect of flywheel design.

[0003] Prior art CN112560168A discloses a method, apparatus, device, and storage medium for determining the interference fit of a wheel hub bearing unit. The method includes: determining a minimum interference fit based on the applied radial load, the inner diameter, the effective width, and the rated radial static load; determining a maximum interference fit based on the equivalent outer diameter of the inner ring, the diameter of the mating surface, the equivalent inner diameter of the inner flange shaft, the elastic modulus, the fracture limits of the quenched inner ring and the quenched inner flange shaft, and the safety factor; correcting the maximum and minimum interference fits; and determining the interference fit range of the wheel hub bearing unit based on the corrected minimum and maximum interference fits. Through this method, a reasonable interference fit range for the wheel hub bearing unit can be determined, ensuring that the manufactured wheel hub bearing units are within a reasonable interference fit range and preventing loosening and breakage of the inner ring of the wheel hub bearing unit.

[0004] Existing technology CN109598032A discloses a method for determining the interference fit of a helicopter rotor blade root bushing, belonging to the technical field of helicopter rotor blade structure design. The method includes: obtaining the outer diameter of the rotor root bushing, the inner and outer diameters of the inner bushing fitted inside the rotor root bushing, and obtaining the elastic modulus of the bushing; determining the relationship between the interference fit and the pressure between the rotor root bushing and the inner bushing; determining the relationship between the maximum static friction force and the pressure; obtaining the axial component force at the bushing root under helicopter rotor blade rotation; calculating the interference fit when the axial component force is less than or equal to the pressure; and designing the inner and outer diameters of the rotor root bushing and the inner bushing based on the interference fit. This invention uses a combined cylinder theoretical model for interference fit calculation. The calculation model is closer to reality, and the calculation results are more accurate. It can effectively solve the problem of multiple iterations in bushing interference fit design, considering multiple aspects from the early design stage, avoiding subsequent maintenance and design changes due to malfunctions.

[0005] Existing methods for determining interference fit cannot solve the problem of determining the interference fit in multi-ring assembly of composite material flywheel rotors. Summary of the Invention

[0006] To address the shortcomings and gaps in existing technologies in related fields, this invention provides a method for determining the interference fit of multi-ring assembly in composite material flywheel rotors. The objective of this invention is achieved through the following technical solution:

[0007] Step 1: Determine the generator size based on the flywheel's power and speed. Then, determine the flywheel shaft size based on the flywheel's structure and the generator's dimensions. Finally, determine the dimensions of the hub and rim based on material strength.

[0008] Step 2: Calculate the rim winding stress of the composite material, set the interference fit in the multi-ring flywheel assembly, and calculate the static initial stress after the multi-ring flywheel assembly.

[0009] Step 3: Calculate the dimensional changes of the multi-ring flywheel after assembly, take the assembled dimensions as the dimensions of the flywheel in the working state, and calculate the displacement of the flywheel in the working state.

[0010] Step 4: Calculate the stress caused by the displacement difference of each ring contact surface. The stress obtained by superimposing the static initial stress and the stress caused by the displacement difference due to centrifugal force is taken as the flywheel stress under working conditions.

[0011] Step 5: Determine the maximum interference amount based on the strength of the material of each part of the ring, determine the minimum interference amount based on the interference criterion that the strain must not exceed the interference amount, and calculate the minimum stress value of each part of the ring to determine the interference amount.

[0012] In step 1, after selecting the motor based on its power and speed, the size ratio is determined according to the speed and structure to obtain the generator's dimensions. The formula for calculating these dimensions is as follows:

[0013]

[0014] Where: D—motor armature diameter; l—motor armature length; ω—flywheel speed; P—flywheel power; k—motor coefficient; size ratio—

[0015] In step 2, the static initial stress of the multi-ring flywheel is determined based on the material characteristics, and the tension force T per unit area is calculated using the following formula:

[0016]

[0017] In the formula: —The pressure between the nth and n+1th layers after winding to the (n+1)th layer; T —Tension force per unit area; r n+1 —Inner diameter of the (n+1)th fiber layer; R n+1 —Outer diameter of the (n+1)th fiber layer; K —Elastic modulus ratio, (where E) r E is Young's modulus. θ (Elastomer).

[0018] The pressure at each ring contact point is calculated based on the displacement difference after assembly. The stress in the multi-ring section is then calculated using this pressure. The displacement is calculated using the following formula:

[0019]

[0020] Where: u—displacement caused by interference after static assembly; r i —Inner diameter of the ring; R o —Outer diameter of the ring; v —Poisson's ratio; p1 —External pressure on the rim; p2 —Internal pressure on the rim; r —Rim radius.

[0021] The formula for calculating the pressure on each ring contact surface is as follows:

[0022]

[0023] In the formula: p — the pressure between the two rims; δ — the interference fit between the two rims; r i —Inner diameter of the i-th rim; R i —Outer diameter of the i-th layer rim.

[0024] The formula for calculating the stress in each ring section is as follows:

[0025]

[0026]

[0027] Where: σ r —Radial stress of each ring under internal pressure; σ θ —Circumferential stress when each ring is subjected to internal pressure.

[0028] In step 3, the dimensions of the multi-ring flywheel assembly can be obtained from the displacement after assembly in step 2. The dimensions of the flywheel in the working state are the assembled dimensions. In the working state, the inner diameter of each ring is r2 and the outer diameter of each ring is R2. The formula for calculating the displacement in the working state is:

[0029]

[0030] When calculating the pressure, the interference fit is the difference in displacement of the contact parts of each ring in the working state after the multi-ring assembly. The stress caused by the difference in displacement of each ring in the working state is obtained through the stress of each ring in step 2. The stress calculation formula for the outer ring is:

[0031]

[0032]

[0033] In the formula: —Radial stress of each ring under external pressure —Circumferential stress of each ring under external pressure.

[0034] When calculating the stress caused by the difference between interference fit and displacement, the stress of each ring under internal pressure is solved by the stress formula in step 2, and the stress of each ring under external pressure is solved by the above formula.

[0035] In step 5, the difference in displacement between each ring must not exceed the initial interference. From the stress expression in step 2, it can be seen that the larger the interference, the greater the static initial stress. When the flywheel speed is low, the static initial stress accounts for a large proportion of the flywheel's stress, and the minimum interference can be selected. When the flywheel speed is high, the static initial stress accounts for a small proportion of the flywheel's stress, and the interference needs to be selected based on the material strength of each part of the flywheel rotor.

[0036] This invention determines the flywheel dimensions based on known power and speed, calculates the static stress and displacement after assembly, uses the assembled dimensions as the flywheel dimensions under operating conditions, and calculates the stress under operating conditions. The interference fit is adjusted to minimize flywheel stress, thus ensuring safe and stable operation of the flywheel at high speeds. Attached Figure Description

[0037] Figure 1 This is a schematic diagram illustrating the principle of the present invention;

[0038] Figure 2This is a stress diagram of the static initial stress under different interference fits in this invention;

[0039] Figure 3 This is a stress diagram showing the working stress of the present invention under different interference fits. Detailed Implementation

[0040] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that process equipment or devices not specifically specified in the following embodiments are all conventional equipment or devices in the art. Furthermore, it should be understood that one or more method steps mentioned in the present invention do not exclude the existence of other method steps before or after the combined steps, or the insertion of other method steps between these explicitly mentioned steps, unless otherwise stated; it should also be understood that the combined connection relationship between one or more devices / apparatus mentioned in the present invention does not exclude the existence of other devices / apparatus before or after the combined devices / apparatus, or the insertion of other devices / apparatus between these explicitly mentioned two devices / apparatus, unless otherwise stated. Moreover, unless otherwise stated, the numbering of each method step is only a convenient tool for identifying each method step, and not for limiting the order of the method steps or limiting the scope of the present invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the present invention. To make the objectives, technical solutions, and advantages of this invention clearer, the examples are described in detail below with reference to the accompanying drawings.

[0041] Reference Figure 1 A method for determining the interference fit of a multi-ring assembly includes the following steps:

[0042] (a) The size of the generator is determined by the power and speed of the flywheel. The size ratio is determined based on the speed and structure to obtain the size of the generator. The formula for calculating the size is as follows:

[0043]

[0044] Where: D—motor armature diameter; l—motor armature length; ω—flywheel speed; P—flywheel power; k—motor coefficient; size ratio—

[0045] The dimensions of the flywheel shaft are determined based on the flywheel's structure and the generator's dimensions. The dimensions of the hub and rim are determined based on material strength.

[0046] (II) Determine the unit area tension force T based on the material characteristics. The formula for calculating the pressure generated by winding is as follows:

[0047]

[0048] In the formula: —The pressure between the nth and n+1th layers after winding to the n+1th layer; T —Tension force per unit area; r n+1 —Inner diameter of the (n+1)th fiber layer; R n+1 —Outer diameter of the (n+1)th fiber layer; K —Elastic modulus ratio, (where E) r E is Young's modulus. θ (Elastomer).

[0049] The pressure at each ring contact point is calculated based on the displacement difference after assembly. The stress in the multi-ring section is then calculated using this pressure. The displacement is calculated using the following formula:

[0050]

[0051] Where: u—displacement caused by interference after static assembly; r i —Inner diameter of the ring; R o —Outer diameter of the ring; v —Poisson's ratio; p1 —External pressure on the rim; p2 —Internal pressure on the rim; r —Rim radius.

[0052] The formula for calculating the pressure on each ring contact surface is:

[0053]

[0054] In the formula: p — the pressure between the two rims; δ — the interference fit between the two rims; r i —Inner diameter of the i-th rim; R i —Outer diameter of the i-th layer rim.

[0055] The formula for calculating the stress in each ring section is as follows:

[0056]

[0057]

[0058] In the formula: σ r —Radial stress of each ring under internal pressure; σ θ —Circumferential stress when each ring is subjected to internal pressure.

[0059] (III) The dimensions of the multi-ring flywheel after assembly can be obtained from the displacement after assembly in step 2. The dimensions of the flywheel in the working state are the dimensions after assembly. In the working state, the inner diameter of each ring is r2 and the outer diameter of each ring is R2. The formula for calculating the displacement in the working state is:

[0060]

[0061] (iv) When calculating the pressure, the interference fit is the difference in displacement of the contact parts of each ring in the working state after the multi-ring assembly. The stress caused by the difference in displacement of each ring in the working state is obtained by calculating the stress of each ring in step 2. The stress calculation formula for the outer ring is:

[0062]

[0063]

[0064] In the formula: —Radial stress of each ring under external pressure, —Circumferential stress of each ring under external pressure.

[0065] When calculating the stress caused by the difference between interference fit and displacement, the stress of each ring under internal pressure is solved by the stress formula in step 2, and the stress of each ring under external pressure is solved by the above formula.

[0066] (v) The difference in displacement between each ring must not exceed the initial interference. From the stress expression in step 2, it can be seen that the larger the interference, the greater the static initial stress. When the flywheel speed is low, the static initial stress accounts for a large proportion of the flywheel's stress, and the minimum interference can be selected. When the flywheel speed is high, the static initial stress accounts for a small proportion of the flywheel's stress, and the interference needs to be selected based on the material strength of each part of the flywheel rotor.

[0067] The above description is merely a specific embodiment of this application. Under the guidance of the above teachings, those skilled in the art can make other improvements or modifications based on the above embodiments. Those skilled in the art should understand that the above specific description is only to better explain the purpose of this application, and the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for determining the interference fit of a multi-ring assembly of a composite material flywheel rotor, characterized in that, Includes the following steps: Step 1: Determine the dimensions of the flywheel shaft; the formula for calculating the generator dimensions in Step 1 is: ； Where: D—motor armature diameter; l—motor armature length; ω—flywheel speed; P—flywheel power; k—motor coefficient; size ratio— ; Step 2: Calculate the rim winding stress of the composite material. For the multi-ring flywheel assembly, calculate the displacement of each ring after static assembly due to interference fit, and calculate the pressure of each ring. The calculation method for the displacement of each ring after static assembly due to interference fit is as follows: ； Where: u—displacement caused by interference after static assembly; r i —Inner diameter of the i-th rim; R o —Outer diameter of the ring; v —Poisson's ratio; p1 —External pressure on the rim; p2 —Internal pressure on the rim; r —Rim radius; The calculation methods for the pressure of each ring are as follows: ； In the formula: p — the pressure between the two rims; δ — the interference fit between the two rims; r i —Inner diameter of the i-th rim; R i —Outer diameter of the i-th layer rim; The formula for calculating the composite material rim winding pressure in step 2 is as follows: ； In the formula: —The pressure between the nth and n+1th layers after winding to the (n+1)th layer; T —Tension force per unit area; r n+1 —Inner diameter of the (n+1)th fiber layer; R n+1 —Outer diameter of the (n+1)th fiber layer; K —Elastic modulus ratio, E r E is Young's modulus. θ It is the elastic modulus; Step 3: Calculate the dimensional changes of the multi-ring flywheel after assembly, and use the assembled dimensions as the dimensions of the flywheel in the working state. Calculate the displacement of the flywheel in the working state. The formula for calculating the displacement of the flywheel in the working state in Step 3 is: ； In the formula: r2—inner diameter of each ring under working conditions; R2—outer diameter of each ring under working conditions; Step 4: Calculate the stress caused by the displacement difference of each ring contact part; superimpose the static initial stress and the stress caused by the displacement difference due to centrifugal force to obtain the stress as the flywheel stress in the working state; The stress calculation method for each ring is as follows: ； ； Where: σ r —Radial stress of each ring under internal pressure; σ θ —Circumferential stress in each ring when subjected to internal pressure; Calculate the stress caused by the displacement difference at the contact surfaces of each ring; the stress calculation formula for the outer ring is: ； ； In the formula: —Radial stress of each ring under external pressure —Circumferential stress in each ring under external pressure; Step 5: Determine the maximum interference fit based on the strength of each ring material.

2. The method for determining the interference fit of multi-ring assembly of composite material flywheel rotor according to claim 1, characterized in that, In step 5, the stress of each ring under static assembly obtained in step 2 above, and the stress of each ring under working conditions obtained in step 4 above are used to determine the interference fit based on the minimum stress value of each part of the ring.

3. The method for determining the interference fit of multi-ring assembly of composite material flywheel rotor according to claim 2, characterized in that, Furthermore, the maximum interference is determined based on the strength of the material of each ring, and the minimum interference is determined based on the interference criterion, ensuring that the displacement does not exceed the interference amount. In step 5, the difference in displacement between the ring parts must not be greater than the initial interference.

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