CN105736059B - High-speed dynamic balance ability optimization design method for gas turbine pull rod rotor with end face teeth - Google Patents

Abstract

The invention discloses a high-speed dynamic balance ability optimization design method for a gas turbine pull rod rotor with end face teeth. The high-speed dynamic balance ability optimization design method is used for optimizing the high-speed dynamic balance ability of the gas turbine pull rod rotor. According to the method, an objective function for optimizing the installation angles of wheel discs of the gas turbine rotor is provided, the installation angles of the wheel discs are optimized through the genetic algorithm, the unbalance centrifugal force on the gas turbine rotor and the bending moment exerted on the midpoint of the rotor by the unbalance centrifugal force are lowered, the multi-objective genetic algorithm is adopted for optimizing the installation angles of the wheel discs of the gas turbine rotor, the unbalance response amplitude of the rotor is obviously lowered after optimization than that before optimization, and the axle vibration amplitude on a bearing of the rotor is far smaller than the allowable maximum amplitude of dynamic balance. Theoretically, the rotor can directly pass in-plant high-speed dynamic balance without other means such as balance weights through the optimization scheme, and the in-plant high-speed dynamic balance efficiency is improved. According to the method, the in-plant dynamic balance testing ability and efficiency of the rotor can be obviously improved for manufacturing enterprises.

Description

Optimal Design Method for High Speed Dynamic Balance Capability of Gas Turbine Tie Rod Rotor with Face Teeth

Technical field:

The invention relates to the technical field of gas turbines, in particular to a design method for optimizing the high-speed dynamic balance capability of a tie-rod rotor of a gas turbine with end teeth.

Background technique:

The tie-rod rotor of a heavy-duty gas turbine is a typical combined rotor. A central tie rod or multiple circumferential tie rods pass through the discs at all levels. The discs are compressed to hold the combined rotor together. Due to the light weight, easy assembly and good cooling effect of the rotor with this structure, it has been widely used in gas turbines and aero-engines. The imprecise mechanical processing in the manufacturing process of gas turbine discs causes unbalanced quantities on the rotors. At high speeds, a large unbalanced excitation force is generated, causing the unit to vibrate. For the gas turbine rotor structure with face teeth connected, the efficiency of high-speed dynamic balancing of the rotor can be improved by adjusting the installation angle of the face teeth.

Invention content:

The purpose of the present invention is to provide a method for optimizing the high-speed dynamic balance capability of a tie-rod rotor of a gas turbine with end teeth. The method provides the relationship between the radial circular runout of the wheel disc and the unbalance of the rotor, and provides a reference for determining the unbalance of the rotor. According to the relationship between the two, the installation angles of the wheel discs at all levels are optimized to minimize the unbalanced centrifugal force and unbalanced moment generated by the unbalanced amount, thereby reducing the vibration response amplitude of the rotor bearing and achieving the purpose of reducing rotor vibration.

In order to achieve the above object, the present invention takes the following technical solutions to achieve:

A method for optimizing the high-speed dynamic balance capability of a gas turbine tie-rod rotor with face teeth, including the following steps:

1) Determine the initial size and phase distribution of the unbalance of different components of the entire rotor according to the radial circular runout e of the front shaft head, the rear shaft head and the discs at all levels of the tie rod rotor of the gas turbine;

2) According to the initial size and phase distribution of the unbalance, determine the unbalanced centrifugal force to be optimized and the bending moment from each unbalanced centrifugal force to the midpoint of the rotor as the objective function;

3) Compile the genetic algorithm optimization program according to the objective function, and use the genetic algorithm to obtain the minimum value of the objective function and the corresponding installation angle of the wheel face teeth;

4) By comparing the unbalanced response of the rotor at the initial installation angle and the optimized installation angle, after optimization, the peak value of the first-order response of the shaft vibration amplitude at the compressor end bearing decreases by more than 95%, and the first-order response peak value of the shaft vibration amplitude at the turbine end bearing decreases The amplitude is greater than 95%; after optimization, the peak value of the second-order response of the shaft vibration amplitude at the compressor end bearing is greater than 95%, and the second-order response peak value of the shaft amplitude at the turbine end bearing is greater than 80%. Balanced effectiveness.

A further improvement of the present invention is that the tie rod rotor of the gas turbine has an end-face tooth structure, and adjacent disks are connected through end-face teeth, and the end-face tooth connection structure is used to adjust the installation angle of the disks.

A further improvement of the present invention is that in step 1), the relationship between the radial circular runout e and the unbalance is:

Among them, q is the unbalance, e is the radial runout, and m is the mass of the wheel of this stage.

A further improvement of the present invention is that in step 2), the optimization objective function is:

The vector sum of unbalanced centrifugal force and unbalanced force bending moment is expressed as:

Among them, q(i) represents the unbalance of each level of roulette/g mm; α(i) represents the phase of unbalance/°, which is a variable in the genetic algorithm, that is, the corresponding roulette installation angle; k represents the roulette Number of stages; ω is the rotor speed/r·min ^-1 ; L(i) represents the distance/mm from the unbalance of each stage to the midpoint of the rotor; i ranges from 1 to 25; F _x is the x direction Unbalanced centrifugal force/N; F _y is the unbalanced centrifugal force in the y direction/N; F is the total unbalanced centrifugal force/N; M _x is the unbalanced force bending moment in the x direction/N m; M _y is the unbalanced force in the y direction Moment/N·m; M is total unbalanced moment/N·m.

Compared with prior art, the beneficial effect of the present invention is:

The invention provides a method for optimizing the dynamic balance capability of a gas turbine tie rod rotor with a face tooth structure, and the method provides a method for optimizing the dynamic balance capability of the rotor with a face tooth structure by adjusting the installation angle of the wheel disc face teeth. Through this optimization method, the peak value of the first-order response of the shaft vibration amplitude at the compressor end bearing before and after optimization decreases by more than 95%, and the peak value of the first-order response of the shaft vibration amplitude at the turbine end bearing decreases by more than 95%; The second-order response peak value of the vibration amplitude decreases by more than 95%, and the second-order response peak value of the shaft vibration amplitude at the turbine end bearing decreases by more than 80%. Therefore, this method can effectively improve the factory's ability to perform rotor dynamic balancing. The method is suitable for rotor parts with face tooth structures in aerospace, electric power and other related industries, and has broad engineering application prospects.

Description of drawings:

Fig. 1 is a schematic diagram of a typical structure of a gas turbine rotor with a center tie rod. The figure shows the structure of the rotor face teeth and the center tie rod.

Fig. 2 is a schematic diagram of the unbalance amount of the gas turbine disc.

Figure 3 is a schematic diagram of the radial runout of various parts of the gas turbine rotor.

A total of 25 radial runout positions are given in the figure, where S1, S2, S3 are the radial runouts of the front and rear shaft heads, C21, C2...C15 are the radial runouts of the compressor wheel, and N1, N2, N3 are the middle The radial runout of the shaft, T1, T2, T3, T4 are the radial runout of the turbine disc.

Fig. 4 is a schematic diagram of generation of unbalanced bending moment of gas turbine rotor.

Figure 5 shows the shaft vibration amplitude at the compressor end bearing before and after the optimization of the unbalanced phase of the tie rod rotor of the gas turbine.

Figure 6 shows the shaft vibration amplitude at the turbine end bearing before and after the unbalanced phase optimization of the tie rod rotor of the gas turbine.

Figure 7 shows the shaft vibration amplitude at the bearing after the unbalance phase optimization of the tie rod rotor of the gas turbine.

Fig. 8 is a schematic diagram of the structure of the face gear.

detailed description:

The present invention will be described in further detail below in conjunction with the accompanying drawings.

Figure 1 is a schematic diagram of a typical structure of a central tie-rod rotor of a gas turbine. The discs of each stage of the rotor rely on the end face teeth to transmit torque, and the central tie rod is used to apply the pre-tightening force.

Referring to Fig. 2 to Fig. 8, the method for optimizing the design of the dynamic balance capability of the tie rod rotor of the gas turbine with the end tooth structure of the present invention includes the following steps:

1) Determination of the unbalance amount suffered by the gas turbine rotor.

In order to obtain the data of the unbalance of each component of the entire rotor, the eccentricity and unbalanced phase of each component are obtained according to the radial circular runout of the front and rear shaft heads of the gas turbine rotor and the discs at all levels provided by the manufacturer. Among them, the relationship between eccentricity δ and radial circular runout e is; According to the results of the eccentricity and unbalanced phase, the distribution of the initial unbalanced quantity of the entire rotor is determined. There are 25 positions where unbalanced quantities need to be added to each part of the entire rotor. The relationship between the unbalanced quantity and the eccentricity is: q=mδ, and then obtained The relationship between unbalance and radial runout is: Determine the unbalance of each component of the rotor, where q is the unbalance, e is the radial runout, and m is the mass of the disc at this stage. Fig. 2 gives a schematic diagram of the unbalance of the wheel disc, which produces unbalance components in the x-direction and y-direction. Figure 3 shows the distribution of the unbalanced amount of the entire rotor, and there are 25 unbalanced amounts applied to each position of the rotor.

2) Determination of the optimization objective function of gas turbine rotor unbalanced centrifugal force and unbalanced force bending moment.

The unbalance components of the unbalance in the x and y directions will generate unbalanced centrifugal forces F _x , F _y and unbalanced bending moments M _x , M _y in the corresponding directions. Figure 4 shows the mechanism of unbalanced bending moments. The unbalanced centrifugal force and unbalanced force bending moment cause the rotor to vibrate. According to the mechanism of unbalanced centrifugal force and unbalanced force bending moment, the optimization objective function of unbalanced centrifugal force and unbalanced force bending moment is determined as:

The vector sum of unbalanced centrifugal force and bending moment can be expressed as:

Among them, q(i) represents the unbalance of all levels of roulette/g mm; α(i) represents the phase of unbalance/°, which is a variable variable in the genetic algorithm; The distance between the unbalanced amount of each stage of the wheel disc and the position at the midpoint of the rotor/mm; ω is the rotor speed/r·min ^-1 ; the range of i is 1 to 25; F _x is the unbalanced centrifugal force in the x direction/N; F _y is the unbalanced centrifugal force in the y direction/N; F is the total unbalanced centrifugal force/N; M _x is the unbalanced moment in the x direction/N m; M _y is the unbalanced moment in the y direction/N m; Total unbalanced force bending moment/N·m.

3) Determination of the minimum value of unbalanced centrifugal force and bending moment and the corresponding wheel installation angle.

According to the unbalanced centrifugal force and unbalanced force bending moment to optimize the objective function, compile the genetic algorithm optimization program, where α(i) is the variable variable in the optimization algorithm. By adjusting the installation angles of the wheels at all levels, the minimum value of the objective function, that is, the minimum value of unbalanced centrifugal force and bending moment, is determined, and the corresponding installation angle is the required installation angle. It should be pointed out that for the special structure of the end-face tooth connection, since there are 180 teeth in the entire circle of the end-face teeth of the wheel disc, the calculated installation angle is rounded and the installation angle difference between adjacent wheel discs is an even number.

4) Comparing the unbalance response of the rotor under the initial installation angle and the optimized installation angle.

In order to verify the reliability of the optimized wheel disk installation angle, the rotor unbalance response calculation method is used to compare the unbalance response amplitude before and after optimization. After optimization, the unbalance response amplitude of the rotor decreases, and the shaft amplitude of the rotor at the bearing is smaller than that The maximum magnitude allowed when balancing.

The unbalanced response calculation of the installation angle after optimization is compared with the unbalanced response calculation results before optimization. The shaft vibration amplitude at the compressor end bearing before and after optimization is shown in Figure 5. After optimization, the peak value of the first-order response drops from 482 μm to 0.802 μm, which is more than 95%; the peak value of the second-order response drops from 60.90 μm before optimization to 2.91 μm , a drop greater than 95%.

The shaft amplitude values at the turbine end bearings before and after optimization are shown in Figure 6. After optimization, the peak value of the first-order response decreased from 521 μm to 0.843 μm, which is more than 95%; the peak value of the second-order response decreased from 9.48 μm before optimization to 1.88 μm . The decline is greater than 80%.

The optimized shaft vibration amplitudes at the compressor end and turbine end bearings are shown in Figure 7. After optimization, the peak value of the first-order response decreases, and the shaft vibration amplitudes at the turbine end and compressor end are both less than 1 μm; the optimized second-order response peak value is more optimized The shaft vibration amplitudes of the turbine end and the compressor end are both less than 3 μm when the front is lowered; when the operating speed is 3000 r/min, the shaft vibration amplitudes of the turbine end and the compressor end are both less than 2.3 μm.

Table 1 Comparison and analysis of single amplitude calculation results of unbalance response shaft vibration before and after optimization of gas turbine rotor

Claims (4)

1. The method for optimizing the high-speed dynamic balance capability of the gas turbine tie-rod rotor with face teeth, characterized in that it comprises the following steps: 1) Determine the initial size and phase distribution of the unbalance of different components of the entire rotor according to the radial circular runout e of the front shaft head, the rear shaft head and the discs at all levels of the tie rod rotor of the gas turbine; 2) According to the initial size and phase distribution of the unbalance, determine the unbalanced centrifugal force to be optimized and the bending moment from each unbalanced centrifugal force to the midpoint of the rotor as the objective function; 3) Compile the genetic algorithm optimization program according to the objective function, and use the genetic algorithm to obtain the minimum value of the objective function and the corresponding installation angle of the wheel face teeth; 4) By comparing the unbalanced response of the rotor at the initial installation angle and the optimized installation angle, after optimization, the peak value of the first-order response of the shaft vibration amplitude at the compressor end bearing decreases by more than 95%, and the first-order response peak value of the shaft vibration amplitude at the turbine end bearing decreases The amplitude is greater than 95%; after optimization, the peak value of the second-order response of the shaft vibration amplitude at the compressor end bearing is greater than 95%, and the second-order response peak value of the shaft amplitude at the turbine end bearing is greater than 80%. Balanced effectiveness. 2. The method for optimizing the high-speed dynamic balance capability of a gas turbine tie rod rotor with end teeth according to claim 1, wherein the gas turbine tie rod rotor has an end tooth structure, and adjacent discs are connected by end teeth. The tooth connection structure is used to adjust the installation angle of the wheel disc. 3. the gas turbine tie rod rotor high-speed dynamic balancing capability optimization design method with face teeth according to claim 1, is characterized in that, in step 1), the relationship between the radial runout e and the unbalance is: $\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$ Among them, q is the unbalance, e is the radial runout, and m is the mass of the wheel of this stage. 4. the gas turbine tie rod rotor high-speed dynamic balance capability optimization design method with face teeth according to claim 1, is characterized in that, in step 2), the optimization objective function is: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; c</span>}\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ {\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\end{array}\right.$ The vector sum of unbalanced centrifugal force and unbalanced force bending moment is expressed as: $\left\{\begin{array}{c}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\\ \mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\sqrt{{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\end{array}\right.$ Among them, q(i) represents the unbalance of each level of roulette/g mm; α(i) represents the phase of unbalance/°, which is a variable in the genetic algorithm, that is, the corresponding roulette installation angle; k represents the roulette Number of stages; ω is the rotor speed/r·min ^-1 ; L(i) represents the distance/mm from the unbalance of each stage to the midpoint of the rotor; i ranges from 1 to 25; F _x is the x direction Unbalanced centrifugal force/N; F _y is the unbalanced centrifugal force in the y direction/N; F is the total unbalanced centrifugal force/N; M _x is the unbalanced force bending moment in the x direction/N m; M _y is the unbalanced force in the y direction Moment/N·m; M is total unbalanced moment/N·m.