CHECK METHOD OF WORM GEARS

Abstract

A check method of worm gears includes the following steps: identification of a real profile (PR) of a worm gear to be checked; scanning of the real profile (PR) in such a way to obtain a measured profile (PM), filtering of the measured profile (PM) with a low pass filter in such a way to obtain a primary profile (PP), filtering of the primary profile (PP) with a high pass filter in such a way to obtain a surface analysis profile (SA), calculation of three parameters (SA.sub.3; SA.sub.q; SA.sub.p) from said surface analysis profile (SA) and comparison of the three parameters (SA.sub.3; SA.sub.q; SA.sub.p) with preset threshold values (TSa; TSq; TSp) in such a way to reject the worm gear when at least one of the parameters exceeds the corresponding threshold value.

Claims

1. Check method of worm gears comprising the following steps: identification of a real profile (PR) of a gear to be checked, considering a plane that contains the axis of the gear, wherein the real profile (PR) is given by the intersection of the external lateral surface of the gear with the plane that contains the axis of the gear, scanning of the real profile (PR) by means of a feeler, such a way to obtain a measured profile (PM), filtering of the measured profile (PM) with a low pass filter with a preset cut-off frequency (fs), in such a way to obtain a primary profile (PP), filtering of the primary profile (PP) with a high pass filter with a preset cut-off frequency (fc), in such a way to obtain a surface analysis profile (SA), calculation of a median line of the surface analysis profile (SA), calculation of a first error quadratic average parameter (SA.sub.a) with the following expression: ${\mathrm{SA}}_a=\frac{{.Math.}_i.Math.x_i}{\mathrm{np}}$ wherein x.sub.i are the absolute deviations of the points of the surface analysis profile from the median line of the surface analysis profile; and np is the number of points considered in the assessment analysis; calculation of a second quadratic error parameter (SA.sub.q) with the following expression ${\mathrm{SA}}_q=\sqrt{{.Math.}_i.Math.x_i^2}$ calculation of a third peak average parameter (SA.sub.p) with the expression ${\mathrm{SA}}_p=\frac{{.Math.}_i.Math.p_i}{\mathrm{np}}$ wherein p.sub.i are the peak points, whose distance from the median line of the surface analysis profile is higher than the distances of at least four adjacent points; comparison of said first, second and third parameter (SA.sub.a; SA.sub.q; SA.sub.p) with corresponding preset threshold values (TSa; TSq; TSp) in such a way to reject the gear when at least one of said parameters exceeds the corresponding threshold value.

2. The method of claim 1, wherein said low pass filter and/or said high pass filter are Gauss filters.

3. The method of claim 2, wherein said cut-off frequency (fs) of the low pass filter is inversely proportional to a lower threshold wavelength value (s) equal to 7.

4. The method of claim 2, wherein said cut-off frequency (fc) of the high pass to filter is inversely proportional to an upper threshold wavelength value (s) and proportional to the number of points of the scan made with the feeler.

5. The method of claim 4, wherein said upper threshold wavelength value (s) is equal to the number of points of the scan made with the feeler divided by 10.

6. The method of claim 1, wherein the number of points considered in the is assessment analysis (np) is equal to approximately 80% of the number of points of the scan made with the feeler.

7. The method of claim 1, wherein said feeler makes a scan with a number of points higher than 2000, preferably equal to 3000.

8. The method of claim 1, wherein said threshold values (TSa; TSq; TSp) have the values shown in the following table: TABLE-US-00002 TSa 0.4 TSq 0.5 TSp 0.6

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0015] Additional features of the invention will appear manifest from the detailed description below, which refers to a merely illustrative, not limiting embodiment, as illustrated in the attached figures, wherein:

[0016] FIG. 1 shows a primary profile of involute obtained with a Gauss low pass filter.

[0017] FIG. 1A shows a median line calculated on the primary profile of involute of FIG. 1,

[0018] FIG. 2 shows a primary profile of helix obtained with a Gauss low pass filter.

[0019] FIG. 2A shows a median line calculated on the primary profile of helix of FIG. 2,

[0020] FIG. 3 shows a surface analysis profile of involute obtained with the Gauss high pass filter,

[0021] FIG. 4 shows a surface analysis profile of helix obtained a Gauss high pass filter,

[0022] FIG. 5 is a table with experimental measurements made on seven groups of worm screws,

[0023] FIG. 6 is a block diagram that diagramatically shows the method according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0024] With reference to FIG. 6, the method of the invention provides ter analyzing four different profiles of a worm screw (I). The profiles to be analyzed are:

[0025] Real Profile (PR),

[0026] Measured Profile (PM)

[0027] Primary Profile (PP)

[0028] Surface Analysis Profile (SA)

[0029] Real Profile

[0030] The real profile (PR) is identified by means of a measuring machine (2), considering a plane that contains the axis of the gear (1). The real profile (PR) is given by the intersection of the external lateral surface of the gear with the plane that contains the axis of the gear.

[0031] Measured Profile

[0032] After identifying the real profile (PR), a feeler (3) scans the real profile (PR) in such a way to obtain a measured profile (PM). Therefore the real profile (PR) is mechanically filtered according to the radius of the feeler. The measured profile (PM) represents a deviation from a theoretical profile.

[0033] For illustrative purposes, the measured profile (PM) is obtained from a worm gear (1) with MDM involute, using a feeler with cutting tool with 0.5 mm diameter, with a measurement software that collects a maximum of 3000 points on the involute and on the helical section of the screw.

[0034] The input data of the method according to the invention, i.e. the measured profile (PM), are not perfect virtual geometries (in this specific case, involute of circle and helix), but deviations from a perfect virtual geometry obtained with a sensor of the feeler that travels along a kinematic trajectory based on the construction data of the worm gear.

[0035] Primary Profile

[0036] The primary profile (PP) is obtained by filtering the measured profile (PM) with a low pass filter (4) with cut-off frequency (fs) that is inversely proportional to a lower threshold wavelength .sub.S. Therefore, the low pass filter lets the frequencies under the cut-off frequency (Fs) pass and removes the wavelengths under the lower threshold wavelength .sub.S because they are not relevant.

[0037] The primary profile is calculated for the entire scanning length of the measured profile (PM).

[0038] The low pass filter (4) can be a Gauss filter. In the Gauss filter, the definition of the weight in the spatial domain (x) is given by the following expression

[00001]$S\left(x\right)=\frac{1}{.Math..Math.}.Math.\exp \left[-{\left(\frac{x}{.Math..Math.}\right)}^2\right]$

[0039] wherein

[00002]$=\sqrt{\frac{\ln .Math..Math.2}{}}=0.4697$

[0040] is the wavelength that is inversely proportional to the cut-off frequency of the filter.

[0041] For illustrative purposes, a lower threshold wavelength =.sub.S=7 is chosen for the low pass filter.

[0042] FIG. 1 shows the primary profile of involute obtained with the Gauss low pass filter with lower threshold wavelength =.sub.S=7. FIG. 1A shows a median line calculated on the primary profile of involute of FIG. 1.

[0043] FIG. 2 shows the primary profile of helix obtained with the Gauss low pass filter. FIG. 2A shows a median line calculated on the primary profile of helix of FIG. 2.

[0044] Surface Analysis Profile

[0045] The surface analysis profile (SA) is obtained by filtering the primary profile (PP) with a high pass filter (5) with cut-off frequency (fc) that is inversely proportional to an upper threshold wavelength .sub.C.

[0046] Therefore the high pass filter lets the frequencies higher than the cut-off frequency (fc) pass and removes the wavelengths higher than the upper threshold wavelength .sub.C because they are not relevant.

[0047] The surface analysis profile (SA) is calculated for a length equal to approximately 80% of the scanning length of the measured profile.

[0048] The high pass filter (5) can be a Gauss filter like the low pass filter.

[0049] In the case of the high pass filter (5), the upper threshold wavelength .sub.C can be set by the user.

[0050] Advantageously, the upper threshold wavelength .sub.C is given by the number of points of the scan made by the feeler divided by 10, that is to say

[00003]${}_C=\frac{\left(\mathrm{number}.Math..Math.\mathrm{of}.Math..Math.\mathrm{scan}.Math..Math.\mathrm{points}\right)}{10}$

[0051] Advantageously, the number of scan points can be higher than 2000; in this specific example, if the number of scan points is 3000, the upper threshold wavelength is .sub.C=300.

[0052] FIGS. 3 and 4 respectively show the surface analysis profile (SA) of involute and of helix, obtained with the Gauss high pass filter, with upper threshold wavelength =.sub.C=300, wherein a median line (LM) calculated in a known way with a calculator (6) is shown.

[0053] The surface analysis profile (SA) is used to calculate [0054] a first error quadratic average parameter (SA.sub.a); [0055] a second quadratic error parameter (SA.sub.q) and [0056] a third peak average parameter (SA.sub.p).

[0057] The error quadratic average (SAO is obtained from the following expression:

[00004]${\mathrm{SA}}_a=\frac{{.Math.}_i.Math.x_i}{n_p}$

[0058] wherein

[0059] x.sub.i are the absolute deviations of the points of the SA) profile from the median line of the SA profile; and

[0060] n.sub.p is the number of points considered in the assessment analysis. Normally, in the (SA) profile the number of considered points is equal to approximately 80% of the number of scan points. Therefore, in this specific case, if the scan points are 3000, n.sub.p=2400

[0061] The quadratic error (SA.sub.q) is obtained from the following expression

[00005]${\mathrm{SA}}_q=\sqrt{\frac{{.Math.}_i.Math.x_i^2}{n_p}}$

[0062] The peak average (SA.sub.p) is obtained from the following expression

[00006]${\mathrm{SA}}_p=\frac{{.Math.}_i.Math.p_i}{n_p}$

[0063] wherein

[0064] p.sub.i are the peak points, whose distance from the median line of the SA profile is higher than the distances of at least four adjacent points.

[0065] The three parameters (SA.sub.a; SA.sub.q; SA.sub.p) are calculated with the calculator (6). After calculating the parameters (SA.sub.a; SA.sub.q; SA.sub.p), each of said parameters is compared with a corresponding threshold value (TSa; TSq; TSp) that is preset by the user. Such a comparison is made with a comparator (7).

[0066] If one of said parameters (SA.sub.a; SA.sub.q; SA.sub.p) is above its threshold value (TSa; TSq; TSp), then the worm gear (1) must be rejected.

[0067] The threshold values (ISa; TSq; TSp) are calculated by the user based on experimental tests according to the type of worm gear to be analyzed.

[0068] FIG. 5 shows the results of the tests made on seven groups of worm gears (A, B, C, F, D, E, G).

[0069] The chattermark of the screws mounted in a kit was measured with traditional instruments. Moreover, the following parameters were calculated: error arithmetical average (SA.sub.a), quadratic error (SA.sub.q) and peak average (SA.sub.p), on each side of the screw thread.

[0070] As shown in FIG. 5, the screws of groups C and F have unacceptable chattermark values, the screw of group B has borderline chattermark values; whereas the screws of groups A, D, E and G have very low chattermark values that are perfectly acceptable. These results are perfectly reflected in the values of the parameters (SA.sub.a; SA.sub.q; SA.sub.p) calculated with the method of the invention.

[0071] Therefore, according to said experimental results, the threshold values (TSa; TSq; TSp) of the three parameters (SA.sub.a; SA.sub.q; SA.sub.p) can be found.

[0072] For merely illustrative purposes, a table is given below, with the threshold values (TSa; TSq; TSp) calculated based on the experimental tests made on the groups of screws of FIG. 5.

TABLE-US-00001 TSa 0.4 TSq 0.5 TSp 0.6

[0073] Numerous equivalent variations and modifications can be made to the present embodiment of the invention, which are within the reach of an expert of the field and fall in any case within the scope of the invention as disclosed by the claims.