TWI482920B - Clearance Calculation of Helical Rotor Between Twin Screw Compressor - Google Patents

Description

Calculation method of gap between spiral rotors of twin-screw compressor

The invention relates to a method for calculating a gap, in particular to a method for calculating a gap between spiral rotors of a twin-screw compressor.

The twin-screw compressor uses a pair of conjugated male and female spiral rotors to engage, inhale, compress and exhaust, and has high reliability, easy operation and maintenance, good transmission dynamic balance, and strong adaptability. It is widely used in the power system of medical equipment, food processing machines and even automobiles by transmitting a variety of mixed liquids.

Since the twin-screw compressor uses a pair of conjugated male and female spiral rotors to mesh, the gap between the conjugated male and female spiral rotors not only affects the efficiency of the twin-screw compressor, but also avoids the male and female spirals. The rotor interferes or seizes due to machining or assembly errors and thermal expansion and stress deformation during operation.

The measurement method of the gap between the male and female spiral rotors is often contacted by the male and female spiral rotors, and placed in the gap piece for measurement, or the mathematical equation is used to solve the theoretical tooth shape data. However, The above method is very wasteful.

In order to improve the above shortcomings, the relevant industry has developed the Republic of China. Invented No. I325037 "Two-dimensional Rotor Tooth Profile Positioning and Gap Analysis Method" invention patent, based on the four-point linear straight tooth profile method, introduced B-Spline curve surface model, reflecting the actual male and female male and female spiral rotor The amount of clearance is provided to provide design and processing manufacturer reference.

However, the four-point linear straight tooth positioning method is carried out by using a male spiral rotor shaft center, a female spiral rotor shaft center, a male spiral rotor tooth tip, and a female spiral rotor tooth bottom coaxial positioning method, wherein the male spiral rotor tooth tip It is defined as the farthest point of the male spiral rotor curve from the center of the male spiral rotor shaft; otherwise, the female spiral rotor tooth bottom is defined as the point where the mother spiral rotor curve is closest to the center of the female rotor shaft, and a large number of numerical search solutions are needed to find the rotor teeth. The shortest gap distance between the faces is still very complicated and inconvenient to use.

Accordingly, it is an object of the present invention to provide a gap calculation method between spiral rotors of a twin-screw compressor which is easy to operate and simple.

Accordingly, the present invention proposes a method for calculating a gap between helical rotors of a twin-screw compressor, the twin-screw compressor including a male spiral rotor having a male helical tooth surface, and a meshing with the male spiral rotor and having a female spiral a mother spiral rotor of the tooth surface, and a gap band along the contact line is formed between the male spiral tooth surface and the female spiral tooth surface, and the gap band calculation method comprises the following steps: step (A2) is generated separately a male rotor tooth type in which the spiral rotor and the female spiral rotor mesh with each other, and a female rotor tooth type; the step (A3) is inversely calculated according to the gear envelope theory on the axis perpendicular to the axis of the male spiral rotor and the female spiral rotor Axis right angle section a pair of male racks having a male rotor tooth type and a pair of female racks having a female rotor tooth type; and a step (A4) projecting the male rack and the female rack respectively to the male spiral tooth surface and On the plane orthogonal to the parent spiral tooth surface, a pair of male rotor right angle racks of the male spiral rotor are generated, and a pair of female rotor teeth orthogonal angle racks of the female spiral rotor are calculated, and the male rotor tooth right angle rack is calculated a normal gap between the female rotor teeth and a right angle rack, and correspondingly distributing the normal gap to the contact line to obtain a contact between the male spiral tooth surface of the male spiral rotor and the female spiral tooth surface of the female spiral rotor The gap of the line.

The invention has the beneficial effects that: according to the gear envelopment theory, the male rotor tooth right angle rack and the female rotor tooth right angle rack respectively corresponding to the male rotor tooth type and the female rotor tooth type are generated, and then the male and female spiral rotor meshing positions are assembled. The male rotor tooth right angle rack and the female rotor tooth right angle rack, and the normal gap between the male rotor tooth right angle rack and the female rotor tooth right angle rack is deduced to the three-dimensional contact line, and a three-dimensional contact line gap distribution map is presented, which is not only calculated The time taken is short and the accuracy is high.

2‧‧‧ twin screw compressor

21‧‧‧Male spiral rotor

211‧‧‧Male spiral tooth surface

212‧‧‧Male rotor blade

213‧‧‧Male rotor tooth type

214‧‧‧Male rotor toothed rectangular rack

215‧‧ ‧ male teeth right angle section

22‧‧‧Female spiral rotor

221‧‧‧Female spiral tooth surface

222‧‧‧Female rotor blade

223‧‧‧Female rotor tooth type

224‧‧‧Female rotor toothed rectangular rack

225‧‧‧Female teeth right angle section

23‧‧‧Contact line

31‧‧‧Steps

311‧‧ steps

312‧‧ steps

313‧‧ steps

314‧‧ steps

32‧‧‧Steps

33‧‧‧Steps

34‧‧‧Steps

341‧‧ steps

342‧‧ steps

343‧‧ steps

T‧‧‧ axis right angle section

A‧‧‧Male rack

B‧‧‧Female rack

Other features and advantages of the present invention will be apparent from the embodiments of the drawings, wherein: Figure 1 is a cross-sectional view illustrating a twin-screw compressor; Figure 2 is a side view illustrating the aspect of the contact line Figure 3 is a flow chart showing a preferred embodiment of the method for calculating the gap between the helical rotors of the twin-screw compressor of the present invention; Figure 4 is a schematic view showing the state of the data of the male rotor, wherein the X-axis value table Male rotor point data x coordinate, Y-axis value table male rotor point Figure y coordinates; Figure 5 is a schematic diagram showing the state of the parent rotor point data, where the X-axis value table parent rotor point data x coordinate, Y-axis value table female rotor point data y coordinate; Figure 6 is a schematic diagram illustrating The left half of the male rotor point data; Figure 7 is a schematic diagram showing the right half of the male rotor point data; Figure 8 is a schematic diagram showing a male rotor blade and a female rotor blade; Figure 9 is a The schematic diagram illustrates a male rotor tooth profile and a female rotor tooth profile which are meshed by a cubic spline curve; FIG. 10 is a schematic view showing a state of a right angle section of the shaft, a right angle section of the male tooth and a right angle section of the parent tooth; Figure 11 is a schematic view showing a pair of racks of the male rotor tooth type and the female rotor tooth type; Fig. 12 is a schematic view showing the assembly of a male rotor tooth right angle rack and a female rotor tooth right angle rack. Figure 13 is a schematic view showing a method of calculating the gap value between the right-angle rack of the male rotor and the right-angle rack of the female rotor; Figure 14 is a schematic view showing the between the right-angle rack of the male-rotor and the right-angle rack of the female rotor The aspect of the gap distribution, In the middle, the X-axis value table, the female rotor tooth, the right-angle rack x coordinate, the Y-axis value table, the female rotor tooth, the right-angle rack, the y coordinate; and FIG. 15 is a schematic diagram showing the gap distribution diagram of the three-dimensional contact line, wherein the horizontal axis Numerical table contact line x coordinate; vertical axis value table contact line y coordinate; depth axis value table contact line z coordinate.

Before the present invention is described in detail, it should be noted that in the following description, similar elements are denoted by the same reference numerals.

1 and 2, a preferred embodiment of a method for calculating a gap between helical rotors of a twin-screw compressor 2 of the present invention, the twin-screw compressor 2 includes a male spiral rotor 21 having a male helical tooth surface 211, and a female spiral rotor 22 that meshes with the male spiral rotor 21 and has a female helical tooth surface 221, and the male helical tooth surface 211 that is engaged with the female helical tooth surface 221 forms a contact as shown in FIG. Line 23.

Referring to FIG. 3, the gap calculation method first performs step 31. The step 31 includes a step 311, a step 312, a step 313, and a step 314 in sequence.

The step 311 is to measure the male spiral rotor 21 (shown in FIG. 1) and the female spiral rotor 22 (shown in FIG. 1) by using three-dimensional measurement, and obtain several pairs as shown in FIGS. 4 and 5, respectively. The male rotor point data of the male spiral rotor 21 and the plurality of female rotor point data corresponding to the female spiral rotor 22 should be used.

In this step 312, the distance between two adjacent male rotor point data and the distance between two adjacent female rotor point data are respectively calculated by using the following calculation formula, and if the distance between two adjacent male rotor point data is less than an error value, the distance is deleted. One of the male rotor point data of the two adjacent male rotor point data, if the distance between the data of the two adjacent female rotor points is less than the error value, one of the parent rotor point data of the two adjacent female rotor point data is deleted.

In the above formula, Indicates the distance between two adjacent male rotor point data or two adjacent female rotor point data, x _i , y _i represent the x and y coordinates of the i-th point data, and e represents the error value. Wherein, the error value is freely given according to the degree of density distribution of the gap distribution, or the information of the male rotor point and the data of the female rotor point are automatically interpolated.

Since the preferred embodiment is to measure the tooth groove of the male spiral rotor 21 to obtain the male rotor point data, the step 313 is to first calculate the radius value of the male rotor point data and obtain the minimum value. The serial number of the common rotor point data of the radius value is used to divide the information of the male rotor point into the left half of the male rotor point data and the right half of the male rotor point data as shown in Figs.

Then, the left half of the male rotor point data shown in Fig. 6 is rotated by an angle of 2 p / z ₁ ( z ₁ is the number of teeth of the male spiral rotor 21), and the right half of the male rotor point data shown in Fig. 7 is reorganized and displayed. a male rotor blade 212 on the right side of FIG. 8; and the female rotor point data is arranged into a female rotor blade 222 shown on the left side of FIG. 8, the apex of the male rotor blade 212 and the bottom point of the female rotor blade 222 It is in the same horizontal position.

Referring to FIG. 3, proceeding to step 32, the un-deleted the common rotor point data and the parent rotor point data are respectively fitted with a Cubic Spline to produce an intermeshing as shown in FIG. The male rotor tooth type 213 and a female rotor tooth type 223.

The general equation r of the male rotor tooth profile 213 and the female rotor tooth profile 223 can be expressed as follows:

Where u is the curve parameter of the fitting curve of each segment (rotor tooth shape direction parameter), u _s is the upper limit range of the curve parameter of each segment fitting equation, which is between the two adjacent male rotor point data and the parent rotor point data The chord lengths, c _{k , x} and c _{k , y} are the coefficients of the fitted equations x ( u ) and y ( u ), respectively, and k is the order of the fitted equation ( k =0~3). Therefore, in the above formula, if the common rotor tooth type 213 and the female rotor tooth type 223 have a number of different discrete point data items, there are a total of ( m -1) fitting equations.

Referring to Figures 3, 10, and 11, next, step 33 is performed, according to the inverse calculation of the gear envelope theory, with the interpolation calculation, at a right angle to the axis of the male spiral rotor 21 and the female spiral rotor 22. A pair of male racks A corresponding to the male rotor tooth type 213 and a pair of female racks B corresponding to the female rotor tooth type 223 are formed in the section T. For convenience of explanation, the male rotor tooth profile 213 and the female rotor tooth profile 223 in FIG. 10 are drawn in a simplified manner.

Referring to Figures 3, 11, and 12. Finally, step 34 is performed. The step 34 includes a step 341, a step 342, and a step 343 in sequence. In this step 341, the male rack A is projected onto a male right-angled section 215 perpendicular to the male helical tooth surface 211 (shown in FIG. 1), and the female rack B is projected to the following equation. A male tooth orthogonal section 225 perpendicular to the female helical tooth surface 221 (shown in FIG. 1) produces a male rotor tooth right angle rack 214 and a female rotor tooth right angle rack 224, respectively.

r _ni =[ x _ti , y _ti cos b ,1], i =1,2

Where b is the pitch helix angle of the rotor, r _{n 1} and r _{n 2 are} the male rotor tooth right angle rack 214 and the female rotor tooth right angle rack 224 are respectively at the male tooth right angle section 215, and the female tooth is at right angles The equation on section 225, x _ti is the x coordinate of the male rack A or the female rack B, and y _ti is the y coordinate of the male rack A or the female rack B.

The step 342 is based on the meshing position of the male rotor tooth profile 213 and the female rotor tooth profile 223, and as shown in FIG. 12, the male rotor tooth right angle rack 214 is coupled to the male tooth orthogonal section 215. The female rotor tooth right angle rack 224 on the female tooth right angle section 225. And calculating the normal clearance of the female rotor point data to the male rotor tooth rectangular rack 214 based on the female rotor point data of the female rotor tooth rectangular rack 224 located on the female tooth right angle section 225.

Referring to FIG. 13, in order to accelerate the solution time of the normal gap, it is necessary to first determine that the unit normal vector of the parent rotor point data of the female rotor tooth orthogonal rack 224 passes through the male rotor point data of the male rotor tooth orthogonal rack 214. Which point is the interval. among them, Is the position of a point j ( j =1~ m ₂ , m ₂ is the number of points of the parent rotor point data) of the parent rotor point data, and It is the position of a point i and the next point i+1 ( i =1~ m ₁ , m ₁ is the number of points of the male rotor point data) on the data of the male rotor point, for The unit normal vector of the point. Unit normal vector when the following judgment formula is satisfied Will pass the male rotor point data point interval [ i , i +1]:

Where a ₁ and a ₂ are the parent rotor point data To the male rotor point data , Vector. Then, the parent rotor point data is substituted into the following formula, and the parent rotor point data can be obtained. The normal gap amount d ^{( j )} to the male rotor tooth rectangular rack 214.

The normal gap amount d ^{( j ) is} sequentially drawn on the female rotor tooth rectangular rack 224 according to the normal direction of each point, and the female rotor tooth rectangular rack gap diagram as shown in FIG. 14 can be drawn.

Referring to FIGS. 3, 10, and 13, the step 343 is to project the parent rotor point data and the normal gap amount d ^{( j ) of} the female rotor point data to the male rotor tooth rectangular rack 214 to a right angle section. T, the tangential rack equation r _t2 ( u ) as shown in the following equation is obtained: r _{t 2} ( u )=[ x _{n 2} ( u ), y _{n 2} ( u )/cos b ,1]

Where x _{n 2} ( u ) is the normal vector x coordinate of the female rotor tooth rectangular rack 224, and y _{n 2} ( u ) is the normal vector y coordinate of the female rotor tooth rectangular rack 224.

Then, through the coordinate transformation matrix and the meshing equation f ( u , f ₂ )=0, the female rotor tooth equation r ₂ ( u , f ₂ ( u ) of the female rotor tooth rectangular rack 224 in the female spiral rotor coordinate system is obtained. The corresponding meshing angle f _{2 is} substituted into the following equation to obtain the contact line equation r _f under the fixed coordinate system.

r _f =[ x _f , y _f , z _f ]=[ x ₂ cos f ₂ + y ₂ sin f ₂ , - x ₂ sin f ₂ + y ₂ cos f ₂ , p ₂ f ₂ ]

Where x _f is the x coordinate of the contact line 23 (shown in Figure 2), y _f is the y coordinate of the contact line 23, z _f is the z coordinate of the contact line 23, and x ₂ is the female rotor tooth rectangular rack 224 in the mother The female rotor tooth type x coordinate equation in the spiral rotor coordinate system, y ₂ is the female rotor tooth right angle rack 224 in the female spiral rotor coordinate system, the female rotor tooth type y coordinate equation, and z ₂ is the female rotor tooth right angle rack 224 is the parent rotor tooth z-coordinate equation in the female spiral rotor coordinate system, p ₂ = r _{p 2} cot b is the parent rotor spiral parameter.

Then, the linear parameter u of the parent rotor point data is brought into the above formula, and the contact line point coordinates corresponding to the parent rotor point data can be obtained. And then the normal vector of the parent rotor point data on the contact line 23 (shown in Figure 2) By multiplying the normal gap value d ^{( j )} , the male spiral tooth surface 211 (shown in FIG. 1) and the female spiral rotor 22 of the male spiral rotor 21 (shown in FIG. 1) as shown in FIG. 15 can be obtained (shown in The gap between the female helical flank 221 (shown in Figure 1) of Figure 1) is as follows:

among them, , Any point normal vector for the parent rotor The x and y components, and The normal gap vector equation x of the parent helical tooth surface 221 to the male helical tooth surface 211, The normal gap vector y equation for the parent helical tooth surface 221 to the male helical tooth surface 211, The normal gap vector z equation for the parent helical tooth surface 221 to the male helical tooth surface 211, Is the x coordinate of any point on the contact line 23, It is the y coordinate of any point on the contact line 23, and m ₂ is the number of gap data.

In order to verify the efficacy of the present invention, the inventors analyzed the types of three different male spiral rotors 21 and female spiral rotors 22 with Holloyd's well-known processing software HPMS (Holroyd Profile Management Software) in accordance with a preferred embodiment of the present invention, and The results are shown in the following table, wherein the field in this embodiment represents the gap value calculated by the method of the preferred embodiment, and the HPMS field is the gap value of the HPMS operation, the maximum gap of the A type, and the maximum B type. The gap and the C-shaped maximum gap represent the maximum gap between the male spiral rotor 21 and the female spiral rotor 22 of the three different types.

As can be seen from the following table, the error between the preferred embodiment of the present invention and the processing software HPMS is less than 10%, thereby demonstrating that the accuracy of the present embodiment is not significantly different from that of the existing processing software HPMS.

In summary, the method for calculating the gap between the helical rotors of the twin-screw compressor 2 of the present invention generates the male rotor orthogonal racks 214 corresponding to the male rotor tooth profile 213 and the female rotor tooth profile 223, respectively, according to the gear envelope theory. The female rotor tooth right angle rack 224 is further assembled with the male and female helical rotors 21, 22 at the meshing position of the male rotor tooth right angle rack 214 and the female rotor tooth right angle rack 224, and the male rotor tooth right angle rack 214 and the female rotor are used. The gap of the right-angled rack 224 is derived onto the contact line 23, and the gap distribution map of the three-dimensional contact line 23 is presented. Not only is the calculation time short and the accuracy is high, the object of the present invention can be achieved.

The above is only the preferred embodiment of the present invention, and the scope of the present invention is not limited thereto, that is, the simple equivalent changes and modifications made by the patent application scope and patent specification content of the present invention, All remain within the scope of the invention patent.

31‧‧‧Steps

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343‧‧ steps

Claims (4)

A method for calculating a gap between spiral rotors of a twin-screw compressor, the twin-screw compressor comprising a male spiral rotor having a male spiral tooth surface, and a female meshing with the male spiral rotor and having a female spiral tooth surface a spiral rotor, and a mesh line is formed between the male helical tooth surface and the female spiral tooth surface, and the gap calculation method comprises the following steps: (A2) generating a corresponding three-spoke curve corresponding to the male spiral rotor and the female a male rotor tooth type of a spiral rotor and meshing with each other, and a female rotor tooth type; (A3) an inverse calculation of the axis of the shaft perpendicular to the axis of the male spiral rotor and the female spiral rotor according to the gear envelopment theory a male rack corresponding to the male rotor tooth type, and a pair of female racks of the female rotor tooth type; and (A4) respectively projecting the male rack and the female rack to the male spiral tooth surface and the female On the plane orthogonal to the spiral tooth surface, a pair of male rotor right angle racks of the male spiral rotor are generated, and a pair of female rotor teeth right angle racks of the female spiral rotor are calculated, and the male rotor tooth right angle rack is calculated and Mother turn Method right angle between the teeth of the rack corresponding to the gap, and the gap is distributed to the normal to the line of contact, to obtain a well-gap helical teeth of the male and female screw rotor surface of the female helical screw rotor tooth surfaces of the contact line. The method for calculating a gap between two helical rotors of a twin-screw compressor according to claim 1, further comprising a step (A1) before the step (A2), the step (A1) sequentially comprising a step (A11) ), a step (A12), a step (A13), and a step (A14), the step (A11) The three-dimensional measurement is used to measure the male spiral rotor and the female spiral rotor to obtain a plurality of male rotor point data corresponding to the male spiral rotor and a plurality of female rotor point data corresponding to the female spiral rotor. This step (A12) Calculate the distance between the data of two adjacent male rotor points and the distance between the data of two adjacent parent rotor points. If the distance between the data of two adjacent male rotor points is less than an error value, delete the data of two adjacent male rotor points. One of the male rotor point data, if the distance between the data of the two adjacent female rotor points is less than the error value, one of the parent rotor point data of the two adjacent female rotor point data is deleted, and the step (A13) is to use the male rotor The point data and the female rotor point data are respectively arranged into a shape of a male rotor blade and a female rotor blade, and the step (A14) is to rotate the apex of the male rotor blade and the bottom point of the female rotor to the same In the horizontal position. a method for calculating a gap between two helical rotors of a twin-screw compressor according to claim 2, wherein the step (A2) is to delete the male rotor point data and the female rotor that are not deleted by three cubic-like curves, respectively. Point data fitting produces the male rotor tooth profile and the female rotor tooth profile. The method for calculating the gap between the two helical rotors of the twin-screw compressor of claim 3, wherein the step (A4) comprises a step (A41), a step (A42), and a step (A43), which Step (A41) is: projecting the male rack onto a right-angled cross section perpendicular to the male spiral tooth surface, and projecting the female rack onto a right-angle cross section perpendicular to the female spiral tooth surface. And the male rotor tooth right angle rack and the female rotor tooth right angle rack are respectively formed on the right angle section of the male tooth and the female tooth, and the step (A42) is based on the male rotor tooth type and the female rotor tooth. a type of meshing position is coupled to the male rotor toothed rectangular rack on the right angle section of the male tooth, and the female rotor tooth right angle rack on the right angle section of the female tooth, and the female rotor located on the right angle section of the female tooth Calculating the parent rotor point data to the normal gap of the male rotor tooth rectangular rack based on the parent rotor point data of the tooth right angle rack, and the step (A43) is to use the female rotor point data and the The parent rotor point data is projected onto the normal gap of the male rotor tooth rectangular rack to a right angle section, and then converted to a contact line of the male spiral tooth surface of the male spiral rotor and the female spiral tooth surface of the female spiral rotor, and Multiplying the parent rotor point data by the normal vector of the parent rotor point data to the normal gap of the male rotor tooth rectangular rack, the male spiral tooth surface of the male spiral rotor and the mother of the female spiral rotor can be obtained. The gap between the spiral flank surfaces.