CN113407894A - Screw rotor tooth space gap thermal state variation calculation method - Google Patents

Screw rotor tooth space gap thermal state variation calculation method Download PDF

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CN113407894A
CN113407894A CN202110712586.4A CN202110712586A CN113407894A CN 113407894 A CN113407894 A CN 113407894A CN 202110712586 A CN202110712586 A CN 202110712586A CN 113407894 A CN113407894 A CN 113407894A
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rotor
cold
point
thermal deformation
axis
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徐明照
袁玮玮
刁安娜
翁恺
高培文
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Shanghai Qiyao Screw Machinery Co ltd
Shanghai Marine Diesel Engine Research Institute
711th Research Institute of CSIC
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Shanghai Qiyao Screw Machinery Co ltd
711th Research Institute of CSIC
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Abstract

The method for calculating the thermal state variation of the clearance between the teeth of the screw rotor comprises the following steps: receiving initial coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor and given temperature working condition; calculating to obtain coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor under a given temperature working condition; the coordinate data under the given temperature working condition is subtracted from the initial coordinate data to obtain the thermal deformation of a plurality of points on the end face; respectively calculating the thermal deformation of each point in the normal vector direction of the tooth surface of the rotor according to the thermal deformation of each point on the end surface of the cold-state end surface profile of the female rotor and the male rotor; and adding the thermal deformation quantities of corresponding points on the cold-state end face molded lines of the female rotor and the male rotor in the normal vector direction of the tooth surface to obtain the thermal state variation quantity of the clearance between the teeth of the screw rotor. According to the invention, the calculation of the thermal state variation of the clearance between the teeth of the screw rotor can be rapidly completed according to the given temperature working condition parameters and the cold state end face molded line of the rotor.

Description

Screw rotor tooth space gap thermal state variation calculation method
Technical Field
The invention relates to a screw compressor technology.
Background
The screw compressor belongs to a positive displacement compressor, and realizes the compression of gas along with the continuous reduction of the closed volume in the rotation process by forming the closed volume between a female rotor and a male rotor and a shell. The high efficiency of the screw compressor is mainly ensured by precise meshing between rotors, however, when the difference between the working condition temperature and the standard design temperature is large, the rotor profile is changed due to thermal deformation, so that the gap between the rotor teeth is changed, the leakage of the place with large gap is increased, the faults such as rotor seizure and cylinder cleaning are easy to occur in the place with small gap, and the operation efficiency and the reliability of the main machine are obviously reduced.
At present, the following two methods are mainly used for solving the problem of rotor thermal deformation:
(1) method of controlling temperature
The method has the advantages that the method can normally use standard line cutters when the rotor is machined, so that the machining cost and the machining efficiency are kept at a better level, and the defects are that the configuration cost of a compressor unit is increased, and the field process complexity of a project is increased;
(2) method for preparing a target
And customizing the rotor type line according to the actual working condition temperature, ensuring that the rotor type line is close to the standard type line in the hot state through theoretical calculation, and reversely deducing the non-standard rotor type line in the cold state processing. The screw compressor has the advantages that the process arrangement of the compressor unit is not required to be adjusted, the interference of temperature to the clearance between the rotor teeth is solved through customized design, and the efficient operation of the screw compressor is ensured. The disadvantage is that high requirements are made on the design capability and the processing capability of the rotor.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a method for calculating the thermal state variation of the tooth space of the screw rotor, which can calculate the thermal state variation of the tooth space of the screw rotor according to the given temperature working condition parameter and the coordinate data of the cold-state end surface molded line of the rotor.
The method for calculating the thermal state variation of the clearance between the teeth of the screw rotor comprises the following steps:
receiving initial coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor and given temperature working condition;
calculating to obtain coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor under a given temperature working condition;
the method comprises the following steps of (1) subtracting coordinate data and initial coordinate data of a plurality of points forming initial cold-state end face molded lines of a female rotor and a male rotor under a given temperature working condition to obtain thermal deformation of the plurality of points on an end face;
respectively calculating the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor in the normal vector direction of the tooth surface of the rotor according to the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor on the end surface;
and adding the thermal deformation quantities of corresponding points on the cold-state end face molded lines of the female rotor and the male rotor in the normal vector direction of the rotor tooth surface to obtain the thermal state variation quantity of the screw rotor inter-tooth space.
The invention has at least the following advantages and characteristics:
according to the method for calculating the thermal state variation of the clearance between the teeth of the screw rotor, provided by the embodiment of the invention, the calculation of the thermal state variation of the clearance between the teeth of the screw rotor can be quickly finished according to the given working condition parameters of the temperature and the molded line of the cold end face of the rotor, the design value of the cold state clearance of the rotor can be checked according to the calculation result of the thermal state variation of the clearance between the teeth of the rotor, the accuracy of the clearance design of the screw compressor is improved, the subsequent calculation of the leakage between the teeth of the rotor can be corrected, the more accurate calculation result of the leakage between the teeth of the rotor can be obtained, and the accuracy of the performance prediction of the screw compressor can be improved.
Drawings
Fig. 1 is a schematic flow chart illustrating a method for calculating a thermal state variation of a tooth space of a screw rotor according to an embodiment of the present invention.
Fig. 2 shows a point on the cold end profile of a rotor according to an embodiment of the present invention.
Fig. 3 shows an included angle θ between a tangent T2 of a point o2 along a spiral line S2 and a rotor central axis CL at a rotor cold end face profile according to an embodiment of the present invention.
Fig. 4 shows a spatial coordinate system o2x2y2z2 established at a point o2 on a cold end profile of a rotor in accordance with an embodiment of the present invention.
Detailed Description
The method for calculating the thermal state variation of the clearance between the teeth of the screw rotor comprises the following steps of:
receiving initial coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor and given temperature working condition;
calculating to obtain coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor under a given temperature working condition;
the method comprises the following steps of (1) subtracting coordinate data of a plurality of points forming cold-state end face molded lines of a female rotor and a male rotor from initial coordinate data under a given temperature working condition to obtain thermal deformation of the plurality of points on an end face;
respectively calculating the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor in the normal vector direction of the tooth surface of the rotor according to the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor on the end surface;
and adding the thermal deformation quantities of corresponding points on the cold-state end face molded lines of the female rotor and the male rotor in the normal vector direction of the rotor tooth surface to obtain the thermal state variation quantity of the screw rotor inter-tooth space.
The method for calculating the thermal state variation of the clearance between the teeth of the screw rotor according to the present invention will be described in detail with reference to a specific embodiment. Referring to fig. 2, the method for calculating the thermal state variation of the clearance between the teeth of the screw rotor includes the following steps:
a. receiving a given temperature working condition, wherein the given temperature working condition comprises the following two temperature working parameters, namely the highest rotor temperature t1And the ambient temperature t0；
b. Initial coordinate data of multiple points of cold-state end face molded lines of the female rotor and the male rotor are introduced, and coordinates of the points on the end faces are all expressed as (x)00，y00) Shown, as in fig. 2 (fig. 2 is only an example of a male rotor); the initial coordinate data is in the coordinate system ox1y1The coordinate of the lower part is shown in the specification, wherein o is the axis of the rotor, the direction of the x1 axis is the horizontal direction, and the direction of the y1 axis is the vertical direction;
c. receiving the set cold working clearance value s of the screw rotor0；
d. According to the linear expansion coefficients of the materials of the female rotor and the male rotor, coordinate data of a plurality of points forming the cold-state end face molded lines of the female rotor and the male rotor under a given temperature working condition (namely, the coordinate data of a plurality of points forming the hot-state end face molded lines of the female rotor and the male rotor are obtained) are obtained through calculation, and the coordinate of each point under the given temperature working condition is expressed by (x)01，y01) Represents;
e. coordinate data (x) of multiple points of cold-state end face molded lines forming the female rotor and the male rotor under a given temperature working condition01，y01) With initial coordinate data (x)00，y00) Subtracting the cold-state end surface profile of the male rotor and the female rotor to obtain the thermal deformation amount of a plurality of points on the rotor end surface, wherein the thermal deformation amount of each point on the rotor end surface is (delta x)0，Δy0) Represents;
f. according to the thermal deformation (delta x) of each point on the cold-state end surface profile of the female rotor and the male rotor on the end surface0，Δy0) Respectively calculating the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor in the normal vector direction of the tooth surface of the rotor, and the specific process is as follows:
for each point on the cold-state end surface molded lines of the female rotor and the male rotor, firstly, the component Deltax of the thermal deformation vector l of the point on the normal vector direction of the rotor tooth surface on the x2 axis is calculated2And a component Δ y on the y2 axis2The formula is as follows:
Figure BDA0003134287010000041
wherein:
(Δx0，Δy0) Is the amount of thermal deformation of the point on the end face;
the y2 axis is the y2 axis in the rectangular coordinate system x2y2z2 with the point as the origin, the direction of the y2 axis is the vertical direction (i.e. parallel to the y1 axis), the direction of the z2 axis is the tangential vector direction of the point along the spiral line, the x2 axis is respectively perpendicular to the y2 axis and the z2 axis, and the x2 axis is determined by the right-hand rule in the embodiment;
k is the tangent slope of the point on the cold-state end face molded line;
theta is an included angle between a tangent vector of the point (which is also the initial point of the rotor spiral line) along the spiral line and the central axis of the rotor, and the calculation formula of theta is as follows:
Figure BDA0003134287010000042
(x00，y00) B is the pitch of the helix for the received initial coordinate data of the point;
Figure BDA0003134287010000043
is the point (x)00，y00) The angle between the vertical direction (i.e. the y1 axis) and the line connecting the rotor axis is calculated as:
Figure BDA0003134287010000044
in the above formula (x)00，y00) Located in a coordinate system ox1y1The second quadrant and the third quadrant take a plus sign, and the second quadrant and the fourth quadrant take a minus sign;
FIG. 2 shows a point (x)00，y00) The angle between the vertical direction (y1 axis) and the line between the axis o of the rotor
Figure BDA0003134287010000051
And point (x)00，y00) Tangent L1 at cold end face profile M1;
then, calculating a thermal deformation vector l in the normal vector direction of each rotor tooth surface, wherein the thermal deformation vector l is as follows:
Figure BDA0003134287010000052
fig. 3 and 4 illustrate a spiral line S2 starting from a point o2, an included angle θ between a tangent vector T2 of the point o2 along the spiral line S2 and a rotor central axis CL, a coordinate system x2y2z2 established by using a point o2 as an origin, and a thermal deformation vector l of the point o2 in a normal vector direction of a rotor tooth surface by taking a point o2 on a rotor cold-state end face molded line as an example;
g. according to the meshing principle, the thermal deformation quantities of corresponding points (namely two mutually meshed points) on cold-state end face molded lines of the female rotor and the male rotor on a normal vector of a rotor tooth surface are added to obtain the thermal state variation quantity l of the rotor tooth space clearancetotComprises the following steps:
ltot＝lM+lF
in the formula:
lM-the amount of thermal deformation of the male rotor profile corresponding point in the tooth flank normal vector direction;
lF-the amount of thermal deformation of the female rotor profile corresponding point in the tooth flank normal vector direction;
h. the calculated rotor tooth space gap thermal state variation and the set screw rotor cold state processing gap value s are compared0And comparing, judging whether the design requirements are met, and if the design requirements are not met, resetting the cold machining clearance value of the screw rotor.
In the present embodiment, the method for calculating the thermal state variation of the clearance between the teeth of the screw rotor is implemented by computer programming.
According to the method for calculating the thermal state variation of the clearance between the teeth of the screw rotor in the above embodiment, the given temperature working condition parameter is received, the initial coordinate data of the plurality of points of the designed cold-state end face molded line of the screw rotor is imported, and the initial coordinate data of the plurality of points of the hot-state end face molded line of the rotor is calculated according to the thermal expansion theory, so that the thermal deformation of the plurality of points of the end face molded line on the end face of the rotor is obtained. And calculating the thermal deformation of the points in the normal vector direction of the tooth surface of the rotor according to the thermal deformation of the points on the cold-state end surface contour lines of the female rotor and the male rotor on the end surface of the rotor, so as to obtain the thermal deformation of the gaps between the teeth of the female rotor and the teeth of the male rotor, and carrying out comparative analysis on the set cold-state gap value, thereby completing the design checking calculation of the cold-state gap.
By using the method for calculating the thermal state variation of the clearance between the teeth of the screw rotor, the calculation of the thermal state variation of the clearance between the teeth of the rotor can be quickly finished only by setting specific working condition parameters, so that the design of a non-standard line of the high-temperature screw rotor can be checked, the clearance between the teeth of the rotor in a thermal state is ensured to be in a reasonable range, the design correctness of a customization method is improved, and theoretical guidance is provided for the design of the rotor of the screw compressor applied to the high-temperature working condition.

Claims (3)

1. The method for calculating the thermal state variation of the clearance between the teeth of the screw rotor is characterized by comprising the following steps:
receiving initial coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor and given temperature working condition;
calculating to obtain coordinate data of a plurality of points of cold-state end face molded lines forming the female rotor and the male rotor under a given temperature working condition;
the method comprises the following steps of (1) subtracting coordinate data of a plurality of points forming cold-state end face molded lines of a female rotor and a male rotor from initial coordinate data under a given temperature working condition to obtain thermal deformation of the plurality of points on an end face;
respectively calculating the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor in the normal vector direction of the tooth surface of the rotor according to the thermal deformation of each point on the cold-state end surface molded lines of the female rotor and the male rotor on the end surface;
and adding the thermal deformation quantities of corresponding points on the cold-state end face molded lines of the female rotor and the male rotor in the normal vector direction of the rotor tooth surface to obtain the thermal state variation quantity of the screw rotor inter-tooth space.
2. The method of claim 1, wherein the given temperature condition comprises a maximum rotor temperature t1And the ambient temperature t0。
3. The method for calculating the thermal state variation of the clearance between the teeth of the screw rotor according to claim 1, wherein calculating the thermal deformation of each point on the cold-state end face molded lines of the female rotor and the male rotor in the normal vector direction of the tooth surface of the rotor comprises the following steps:
for each point on the cold-state end surface molded lines of the female rotor and the male rotor, firstly, calculating the component Deltax of the thermal deformation l of the point on the normal vector direction of the rotor tooth surface on the x2 axis2And a component Δ y on the y2 axis2：
Figure FDA0003134286000000011
Wherein:
(Δx0，Δy0) Is the amount of thermal deformation of the point on the end face;
the y2 axis is the y2 axis in a rectangular coordinate system x2y2z2 with the point as the origin, the direction of the y2 axis is the vertical direction, the direction of the z2 axis is the tangential vector direction of the point along the spiral line, and the x2 axis is respectively vertical to the y2 axis and the z2 axis;
k is the tangent slope of the point on the cold-state end face molded line; theta is an included angle between a tangent vector of the point along the spiral line and the central axis of the rotor, and the calculation formula of theta is as follows:
Figure FDA0003134286000000021
(x00，y00) B is the pitch of the helix for the received initial coordinate data of the point;
Figure FDA0003134286000000022
is the included angle between the connecting line between the point and the rotor axis and the vertical direction;
then, calculating a thermal deformation vector l of the point in the normal vector direction of the rotor tooth surface, wherein the thermal deformation vector l is as follows:
Figure FDA0003134286000000023
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114372321A (en) * 2021-12-13 2022-04-19 中国船舶重工集团公司第七一一研究所 Temperature design method for water interlayer shell of double-screw compressor

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CN110374870A (en) * 2019-07-22 2019-10-25 陕西汉机精密机械股份有限公司 It is a kind of based on engagement-pixelation discrete logarithm twin-screw compressor screw rotor clearance method for arranging

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Publication number Priority date Publication date Assignee Title
CN114372321A (en) * 2021-12-13 2022-04-19 中国船舶重工集团公司第七一一研究所 Temperature design method for water interlayer shell of double-screw compressor

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