JP3286567B2 - Screw compressor rotor inspection method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention inspects male and female rotors of an oilless screw compressor (also called a Lysholm compressor) that rotates while maintaining a small gap by a timing gear in a casing. It is about the method.

[0002]

2. Description of the Related Art Conventionally, prior to an assembling process of a screw compressor, in order to control the quality of each male and female rotor, machining inspection and coating of a rotor without a coating film (hereinafter abbreviated as a bare rotor) are performed. Assembling is performed by inspecting the thickness of the coating film on a rotor provided with the film (hereinafter abbreviated as a covered rotor).

A description will now be given of a bare rotor machining inspection. In the machining of a bare rotor, it is required to precisely cut a tooth having a special shape such as a screw shape. For this purpose, a dedicated processing machine is used as the processing machine, but it is necessary to inspect the processing accuracy (difference from the design value). Inspection items include lead bending, tooth thickness, cross-sectional shape, etc. However, since the tooth shape is formed by a three-dimensional multi-curved surface, conventionally, the rotation of the work (rotor) one point at a time using a three-dimensional measuring device. And moving the tracing stylus of the three-dimensional measuring device to obtain data of many measurement points, obtain an error by comparing the measured value with the value of the master rotor, and perform the processing accuracy determination and the pass / fail determination. . The result obtained by the measurement is fed back to the processing machine and used for changing the set value.

Next, the inspection of the thickness of the coating film will be described. Coating is a process to prevent the wear of the bare rotor, improve sealability, and impart corrosion resistance. Surface treatment is performed to improve the adhesion of the coating film to the bare rotor after machining inspection, and the spray nozzle is attached to the coating device. Is positioned with respect to the tooth profile and sprayed with paint.

[0005] As a thickness test of a coating film, a multipoint measurement was performed using a film thickness gauge. The film thickness meter measures the film thickness by pressing the probe vertically to the coating surface, and the measurement is performed by the operator pressing one point at a time. The measurement data is recorded while corresponding to the measurement position, and the absolute value (average value), variation (bias), etc. of the film thickness are obtained and fed back to the coating device to change the set value.
It is used to determine the pass / fail of the coating film thickness distribution.

[0006] In the final assembling process to the casing performed after the above, as described in Japanese Patent Application Laid-Open No. 1-155089, the brake is applied to one of the covered rotors without at least one timing gear. The other covered rotor is rotated in the forward and reverse directions, and a minute gap between both covered rotors is set using the rotation angle difference (rotation phase difference) of the male and female covered rotors measured by an encoder or the like during the rotation (timing adjustment). Or it is also called distribution adjustment). In the setting of the minute gap, pressure oil is applied between the other timing gear and the covered rotor to which the timing gear is fixed while restraining one timing gear to loosen the interference fit therebetween,
By hitting the tooth surface of the other timing gear with a hammer, a relative displacement is caused between the other timing gear and the covered rotor to which the timing gear is fixed, and a shim (thickness gauge) is set. It is inserted between both covered rotors to check if the minute gap between both covered rotors is the desired one (value) (shim measurement), and repeats hammering and shim measurement to reduce the minute gap between both covered rotors. The desired (value) was being made.

Prior to the assembling process, the male and female covered rotors are individually checked for meshing. In the meshing inspection, the two covered rotors are combined (positioned) in a prescribed distance between the axes and in the axial direction, and a shim is manually inserted into the meshing position between the two covered rotors one point at a time, and a minute gap ( The final judgment is made by measuring the backlash.

[0008]

The above-mentioned conventional bare-rotor machining inspection is automated using a three-dimensional measuring device, but it is time-consuming, and the conventional coating film thickness inspection and meshing inspection are manually performed. Therefore, it takes time and effort, and there is a problem in the accuracy of the measured value.

Furthermore, since the measuring instruments used for each inspection are different and each inspection is performed independently, it is difficult to utilize the inspection results in the next step, and it is difficult to perform a consistent evaluation.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide a method for inspecting a rotor of a screw compressor, which requires less time, has high measurement accuracy, can use a common measuring instrument for each inspection, and can perform consistent evaluation. To provide.

[0011]

A feature of the present invention to achieve the above object is to provide a method for inspecting male and female rotors in a screw compressor rotating while maintaining a minute gap by a timing gear, At least one of the timing gears is not provided, and the other rotor is rotated in each of forward and reverse directions while a brake is applied to one of the rotors. Measuring the minute gap between the male and female master rotors without the coating film, and the minute gap between the male master rotor and the female rotor without the coating film. Gap measurement data and minute gap measurement data between the female master rotor and the male rotor without a coating film The male and female between the two rotors and a minute gap measurement data measured respectively, lies in the respective measurement data is displayed on the same measured data obtaining machining status of the male rotor and the female rotor.

Another feature of the present invention that achieves the above object is that a minute gap measurement data between the male and female master rotors without the coating film and the male master rotor and the coating film are provided. The micro-gap measurement data between the female rotor and the micro-gap measurement data between the female master rotor and the male rotor provided with the coating film and the micro-gap measurement data between the male and female rotors are measured, respectively. The object of the present invention is to display the measurement data on the same measurement data to obtain the machining status of each of the male and female rotors.

[0013] Further, a feature of the present invention that achieves the above object is that the other master rotor rotated in each of the forward and reverse directions, the rotor not provided with the coating film, and the rotor provided with the coating film have at least two features.
The method is to measure the minute gaps by multiplying torques of different values each time, and to calculate and find the minute gaps when there is no torque value by extrapolation from those data.

Further, a feature of the present invention that achieves the above object is that the axial length of each of the male and female master rotors is such that each of the female and male rotors or coating films having no coating film is provided. It is characterized in that it is a value obtained by dividing the lead length of each of the provided female and male rotors by the number of their teeth.

[0015]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The inspection method of the present invention will be described below with reference to an embodiment shown in the drawings. FIG. 1 shows a measurement state of a minute gap between rotors and a measurement system configuration in a screw rotor engagement test according to an embodiment of the inspection method of the present invention.

In the following description, various combinations of a master rotor, a bare rotor without a coating film, a covered rotor with a coating film, and the like are provided for males and females. However, in the case of a general description that does not take a specific combination, it is simply referred to as a rotor to simplify the description.

In FIG. 1, the male rotor 1 and the female rotor 2 are positioned and fixed at predetermined positions between the axes and in the axial direction by rotor supports 11 to 14 having conical tips. The rotor supports 11 to 14 are supported by bearings 15 to 18 and housings 19 and 20 in the radial and thrust directions. In the measurement of the minute gap between the rotors, the types of the rotor 1 and the rotor 2 are changed, but the positional relationship between the male and female is not changed. The encoder 3 measures the rotation of the male rotor 1 and the encoder 4 measures the rotation of the female rotor 2 in the form of pulses.

The detection pulses from the encoders 3 and 4 are divided by interpolators (dividers) 21 and 22 and transmitted to a personal computer 24 via a bus system 23 containing a counter board.
The data is stored in a memory (RAM) in the personal computer, and is stored in the memory (ROM) in the personal computer. The processing is performed as the rotation angle measurement values θM and θF of the rotors 1 and 2. The two rotation angle measurement values θM and θF are calculated by the CPU as a rotation angle difference Δθ (= θF−θM) based on the rotation angle of the male rotor.

When measuring the rotation of the rotor, the servo motor 5
, And the driving force is transmitted to the pulley 7 and the belt 9 to rotate the male rotor 1. At this time, an appropriate torque is generated in the torque motor 6 in order to reliably apply the male and female rotors 1 and 2 to each other and transmitted to the female rotor 2 via the pulley 8 and the belt 10. Control of the servo motor 5 and the torque motor 6 is performed by motor drivers 25 and 26 based on instructions from the personal computer 24.

Next, processing of the screw compressor rotor,
The procedure of the inspection method will be described with reference to FIG. First, FIG.
It is a flow chart explaining the whole flow of processing and inspection of a rotor. The male and female master rotors are inspected in advance (32), and data on the forward plane and the reverse plane is obtained. Details of this processing are shown in FIG. 3, and as a result, curves A and B in FIG. 6 are obtained.

Next, the rotor is processed (34), and the processing accuracy of the processed rotor is inspected (36). The details of this processing are also shown in FIG. 3, and as a result, curves C to F in FIG. 6 are obtained.

Next, the rotor is coated (3)
8) Obtain the coating film thickness accuracy (40). The details of this processing are shown in FIG. 4, and as a result, the HK curves of FIG. 6 are obtained. Further, final assembly is performed (42), and a minute gap between both rotors 1 and 2 is measured (44). The above processing is repeated for the processing of each rotor.

In the data processing, when the processing accuracy of the rotor is inspected (36), whether the processing accuracy of the rotor is obtained in the rotor processing in the preceding process (whether the reference value is cleared).
Is used to determine The machining accuracy is determined by the four points of the forward / reverse plane of the male / female rotor (C-F curves in FIG. 6) and (AB curve).
And the difference between

Working accuracy of male rotor (advance surface) ... (CA) (error) (reverse surface) ... (DB) Processing accuracy of female rotor (advance surface) ... (EA) (error) ( (Reverse surface) ... (FB) Male / female combination (forward surface) ... (CA) + (EA) = (TA) (error) (reverse surface) ... (DB) + ( It is checked that the value of (FB) = (SB) is equal to or less than the reference value.

The above data can also be used to change the rotor coating thickness setting. That is, a value obtained by subtracting the processing error from the design value film thickness may be set as the target value.

Next, the measurement of the minute gap between the rotors 1 and 2 (step 44 in FIG. 2) will be described. The minute gap measurement is performed by continuously rotating the male rotor 1 in the normal direction, and then rotating the male rotor 1 in the reverse direction, and taking in the measured values of the rotation angles θM and θF of the rotors 1 and 2 at every constant sampling. In FIG.
(A) shows the rotation direction of the rotors 1 and 2 and the direction of the torque applied to the female rotor 2 by the torque motor 6 when the two rotors 1 and 2 are rotated in the forward direction CW, and (b) in the reverse direction CCW.

The measured value obtained in the torque added state has a reduced measurement accuracy due to the occurrence of distortion in each of the rotors 1 and 2. Therefore, it is necessary to perform the following contact correction. That is, while the rotation of the servomotor 5 is stopped, the torque value is changed by the torque motor 6 to rotate the female rotor 2, and the rotation angle difference Δθ (= θ
F-θM). As shown in FIG. 7, a forward or reverse torque is applied to at least two points, and the rotation angle difference Δθ at that time is applied.
And a correction value of the rotation angle difference Δθ when the torque is 0 (state without distortion) is obtained by the external search method. The interval between the rotation angle differences in FIGS. 7A and 7B indicates the minute gap between the rotors. Therefore, the correction value of the rotation angle difference Δθn of the forward surface is Δθn−a, and the correction value of the rotation angle difference Δθr of the reverse surface is Δθr−b.

Next, inspection of the master rotor (3)
Details of the procedure of 2) and the inspection of the processing accuracy of the rotor (36) will be described with reference to FIG. First, in the inspection of the master rotor, a male master rotor (Mm) 1 created according to the design drawing
With the female master rotor (Fm) 2 and forward rotation
(n) and respective rotation angles θM and θF (θM
mn, θMmr, θFmn, θFmr)
2) After performing the contact correction (324), a rotation angle difference Δθ is obtained (326). In the contact correction, the contact measurement and the correction value calculation may basically be performed only once. However,
Correction is performed for all data (either during or after measurement).

FIG. 6 shows measurement data of the minute gap between the rotors after the contact correction method using various combinations. FIG.
Indicates the rotation angle difference Δθ between the rotation angle of the male rotor 1 and the rotation angle of the female rotor 2. By setting the rotation angle of the male rotor 1 to 360 ° × the number of teeth of the female rotor, the total meshing can be measured. In FIG. 6 (a), the curve A is for forward rotation and the curve B is for reverse rotation. Therefore, the male master rotor 1 and the female master are converted by converting the distance G0 between the curves A and B into a distance. A minute gap between the rotors 2 can be obtained.

In each of the curves including curves A and B described below, the rotation angle difference .DELTA..theta. Undulates depending on the processing accuracy of each rotor. For simplification, each curve is shown as a straight line in FIG. Was.
Incidentally, since the master rotor is a reference, it is machined with high accuracy, and the curves A and B are almost flat. However, since the bare rotor and the covered rotor are machined with arbitrary accuracy, those curves are the same as those of the master rotor. Ripples more than curves A and B.

Now, since the curves A and B are data obtained by the master rotor, the RAM of the personal computer 24 is used to judge a measured value obtained as a true value (target value) of the bare rotor or the covered rotor below. (328 in FIG. 3).

Next, measurement for determining the machining accuracy of the bare rotor is performed. Bear rotor (Mb) as male rotor 1
The female rotor 2 is a combination of the master rotor (Fm) and the measured values (θMb) of the forward and reverse rotation angles θM and θF.
n, θMbr, θFmn, θFmr) (36 in FIG. 3).
1). The rotation angle difference Δθ in this combination is obtained (36
3). Male bare rotor 1 in the same manner as curves A and B
Is rotated forward and backward to rotate the female master rotor 2 to obtain measurement data, which is stored in the memory of the personal computer 24 (365). FIG. 6A shows curves A and B.
Are displayed on the same data as curves C and D.

Next, the measured values (θMmn, θMmr, θFbn, θFbr) of the forward and reverse rotation angles θM, θF in the combination of the male master rotor 1 and the female bear rotor 2 are taken (3).
66), the rotation angle difference Δθ when this combination is obtained is obtained (368), and the result is stored in the memory of the personal computer 24 (369).

Next, a machining error is calculated based on the measured data of the minute gap between the rotors, and as a result, the HK curves of FIG. 6 are obtained (370).

In FIG. 6, the difference between the curves C and A and the difference between the curves D and B represent the processing error of the male bear rotor. Since the value of the curve C is smaller than the value of the curve A, the advancing surface of the male bare rotor 1 is excessively shaved. Curve D
Is smaller than the value of the curve B, the reverse surface of the male bear rotor 1 is also excessively cut.

Curves E and F in FIG. 6B show the rotation angle difference Δθ when the male master rotor 1 and the female bear rotor 2 are combined. As can be seen from the curves A and B, the female bearer rotor 2 also has a processing error, and the advancing surface is excessively shaved, whereas the reverse surface has a value of the curve F smaller than the value of the curve B and is insufficiently cut. Is shown.

FIG. 6 (c) shows the processing error between the curves C and E and the curves D and F at each position of the rotation angle θM of the male rotor based on the curves A and B between the master rotors 1 and 2. Are added in a vector, and are shown by curves S and T as a total machining error on the forward plane and the reverse plane.

These processing errors are stored in the memory of the personal computer 24 (371) and fed back to the processing machines of the bare rotors 1 and 2 to improve the processing accuracy.

Next, the details of the coating processing status of the male and female covered rotors 1 and 2 in which the bare rotors 1 and 2 have been coated, that is, the measurement of the coating film thickness (Step 40 in FIG. 2) will be described with reference to FIG. .

Since the male covered rotor 1 is to be considered, the master rotor Fm is used as the female rotor 2,
The measured values (θMcn, θM) of the forward and reverse rotation angles θM, θF in combination with the covered rotor Mc as the male rotor 1
cr, θFmn, θFmr) (401 in FIG. 4). The rotation angle difference Δθ in this combination is obtained (403) and stored (404). A curve H in FIG. 6A is a rotation angle difference Δθ on the forward plane when the covered rotor 1 is rotated forward, and a curve I is a rotation angle difference Δθ on the reverse plane when the covered rotor 1 is rotated reversely. This is the measurement data. The distance between the curves C and H is the coating thickness on the advancing surface, and the distance between the curves D and I is the coating thickness on the reversing surface.

Next, in order to obtain a coating thickness of the female covered rotor 2 by obtaining a rotation angle difference Δθ using the male rotor 1 as a master rotor and the female rotor 2 as a covered rotor, the male master rotor 1 and the female covered rotor 2 are formed. The measured values of the rotation angles θM and θF (θMmn, θ
Mmr, θFcn, θFcr) are taken in (405), the rotation angle difference Δθ when this combination is obtained is obtained (407), and the result is stored in the memory of the personal computer 24 (40).
8). As shown in FIG. 6B, the rotation angle difference Δθ at this time is
Are superimposed on the measured data (curves E and F) when the female bare rotor 2 is used. Curves E and J,
The distance corresponding to the interval between the curves F and K is the coating film thickness on the advancing surface and the reversing surface of the female covered rotor 2, respectively.

Next, a processing error is calculated based on the measurement data of the minute gap between the rotors, and as a result, the X and Y curves of FIG. 6 are obtained (409).

Curves X and Y in FIG. 6 (c) show the film thickness of the coating film on the advancing surface and the reversing surface with the same calculation and display based on the curves A and B of the master rotors 1 and 2. It is a thing. A distance corresponding to the distance G1 between the curves X and Y is a minute gap between the covered rotors 1 and 2, that is, a minute gap between the coating film surfaces of the male and female rotors 1 and 2. The curves X and Y in FIG. 6C are obtained by synthesizing the measurement data shown in FIGS. 6A and 6B as described above. , 2 are combined to obtain the rotation angle difference Δθ, the result is the interval G1 between the curves X and Y.

Therefore, a minute gap between the covered rotors 1 and 2 and a coating film thickness can be obtained without performing measurement by a combination of the male and female covered rotors 1 and 2. Since the target coating film thickness is data known by design, the coating process status can be easily determined.

Curves S and T in FIG. 6C indicate the positions of the ground surfaces (metal surfaces) of the bare rotors 1 and 2. Since the coating film wears over time, the ground surface (metal surface) of the screw rotor is found, and the distance between the ground surfaces is set in adjusting the minute gap between the covered rotors 1 and 2 at the time of final assembly. Thereby, the reliability and durability of the screw compressor can be improved.

Although the inspection method described above is for a case where a minimum gap is considered in the engagement (combination) of the male and female rotors, another embodiment for performing measurement over the entire tooth surface of the rotor will be described below.

If the screw compressor is used continuously for a long time, a temperature rise occurs. In compressing the fluid, a temperature difference appears between the inlet and the outlet of the fluid, and a difference appears in the amount of thermal expansion between the suction side and the discharge side of the screw rotor. I will. Therefore, there is a type in which the expansion of the screw rotor due to compression heat is predicted and a taper process is performed to secure an optimum clearance during operation.

Since the rotation angle difference Δθ is obtained by bringing the rotors 1 and 2 into contact with each other, the male and female rotors 1
2 are engaged with each other without shifting in the axial direction as shown in FIG.
Measurement data can be obtained only on the suction side, and a minute gap cannot be measured in the middle of the full winding angle or on the discharge side.

Therefore, in order to measure the small gap at all the winding angles of the male and female rotors 1 and 2 subjected to the taper processing, FIG.
Rotor supports 11 to 14 and their bearings 15 to
As shown in FIG. 8A, male or female master rotors 1 and 2 are connected to female or male bear rotors 2 and 1 and covered rotors 2 and 1 by using housings 19 and 20 which can move the axial direction 18. The rotation may be performed while being shifted in the axial direction, and the rotation angle difference may be obtained as shown in FIG.

As shown in FIG. 8B, the measurement may be performed using male or female master rotors 1 and 2 having a short length L. The length L of the master rotor may be set to L = the lead length of the teeth of the screw rotors 1 and 2 / the number of teeth. As in the case of FIG. 8A, the measurement by the master rotor is performed by rotating the master rotor 1 or 2 in the axial direction as shown in FIG. 8C.

The inspection methods shown in FIGS. 8 (a) and 8 (c) are not limited to those subjected to taper processing, but also to screw processing machines of straight processing which do not care about the difference in thermal expansion between the suction side and the discharge side. Applicable to inspection. In this case, the male rotor 1
By comparing the minute gap for each rotation angle θM, it is possible to detect the twist of the lead and the variation in the thickness of the coating film from the tendency of expansion and contraction of the minute gap.

This comparison may be a numerical table in which the minute gap for each rotation angle θM of the male rotor 1 can be compared at an appropriate axial position, and a format in which each measurement data is displayed on the same measurement data. Is not limited to the shape shown in FIG.

As described above, without using a three-dimensional measuring device, a film thickness gauge and a shim (thickness gauge),
By engaging the master rotor and determining the rotation angle difference,
It is possible to carry out a consistent inspection (evaluation) of a bare rotor or a covered rotor with high accuracy, easily and without taking much time, and it is also possible to achieve automation by a personal computer. Further, the inspection result can be fed back to the processing machine and reflected on the improvement of the processing accuracy.

[0054]

As described above, according to the present invention, the inspection of the rotor does not take much time, the measurement accuracy is high, a measuring instrument common to each inspection can be used, and a consistent evaluation can be performed. .

[Brief description of the drawings]

FIG. 1 is a view showing an embodiment of a rotor inspection device for a screw compressor according to the present invention.

FIG. 2 is a flowchart for explaining the overall flow of a method of processing and inspecting a raw material according to the embodiment of FIG. 1;

FIG. 3 is a diagram showing details of a processing procedure for processing accuracy inspection of the rotor of FIG. 2;

FIG. 4 is a diagram showing details of a processing procedure of a coating film thickness accuracy inspection of FIG . 2;

FIG. 5 is a view showing a state of measuring a minute gap between rotors in the embodiment of FIG. 1;

FIG. 6 is a diagram showing measurement data of a minute gap between rotors in the embodiment of FIG. 1;

FIG. 7 is a diagram showing the relationship between the application of torque to the rotor and the method of obtaining the rotor-to-rotor micro-gap measurement data during the rotor-to-rotor micro-gap measurement in the embodiment of FIG. 1;

FIG. 8 is a diagram showing another embodiment of the inspection method of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Male rotor 2 ... Female rotor 3,4 ... Encoder 5 ... Servo motor 6 ... Torque motor 7,8 ... Pulley 9,10 ... Belt 11-14 ... Rotor supporter 15-18 ... Bearing 19,20 ... Housing 21 , 22 ... interpolator (divider) 23 ... bus system 24 ... personal computer 25, 26 ... motor driver

──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Hiroyasu Obata 1007 Kamigo, Ebina-shi, Kanagawa Prefecture Hitachi Techno Engineering Co., Ltd. Ebina Office (56) References JP-A-1-155089 (JP, A) JP-A-5-107151 (JP, A) JP-A 1-282441 (JP, A) JP-A 1-210839 (JP, A) A) (58) Field surveyed (Int. Cl. ⁷ , DB name) G01M 13/00 G01B 21/16 F04C 18/16

Claims (4)

(57) [Claims] A method for inspecting male and female rotors of a screw compressor rotating while maintaining a small gap by a timing gear, wherein a brake is applied to one of the rotors without at least one of the timing gears. The other rotor is rotated in each of the forward and reverse directions while being hung, and a minute gap between the two rotors is measured by using a difference in rotation angle between the male and female rotors measured during the rotation, and a coating film is provided. The micro-gap measurement data between the male and female master rotors, the micro-gap measurement data between the male master rotor and the female rotor without the coating film, and the female master rotor and the coating film are provided. The gap data between the male and female rotors and the gap data between the male and female rotors were measured. Rotor inspection method of the screw compressor, characterized in that each measurement data is displayed on the same measured data obtaining machining status of the male rotor and the female rotor. 2. A method for inspecting male and female rotors of a screw compressor rotating while maintaining a small gap by a timing gear, wherein at least one of the rotors is braked without the one timing gear. The other rotor is rotated in each of the forward and reverse directions, and the minute gap between the two rotors is measured by using the rotation angle difference between the male and female rotors measured during the rotation. And small gap measurement data between the two master rotors and the female master rotor and the small gap measurement data between the female rotor provided with the coating film, and the male rotor provided with the female master rotor and the coating film Between the male and female rotors, and the small gap measurement data between the male and female rotors. Rotor inspection method of the screw compressor, characterized in that to display the data on the same measured data obtaining machining status of each rotor of said male and female. 3. The method according to claim 1, wherein a torque having a different value is applied at least twice to the other master rotor, the rotor not provided with the coating film, and the rotor provided with the coating film, which are rotated in forward and reverse directions. A method for inspecting a rotor of a screw compressor, wherein a minute gap in the case where there is no torque value is calculated and obtained from the data by extrapolation to measure the minute gap. 4. An axial length of each of said male and female master rotors according to claim 1 or 2, wherein said male and female master rotors have female and male rotors provided with no coating film or female and male rotors provided with a coating film. A rotor inspection method for a screw compressor, wherein the value is obtained by dividing a lead length of a rotor by the number of teeth.