UNIVERSAL BEVEL GEAR TOOTH PROFILE CONTROLLING DEVICE

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1 UNIVERSAL BEVEL GEAR TOOTH PROFILE CONTROLLING DEVICE HOLLANDA DÉNES, MÁTÉ MÁRTON, TOLVALY-RO CA FERENC FORGÓ ZOLTÁN, POPA-MÜLLER IZOLDA Department of Mechanical Engineering, SAPIENTIA - Hungarian University of Transylvania, Faculty of Technological and Human Sciences, Department of Mechanical Engineering, 4300 Tg. Mure; - Pta. Trandafirilor 61, Romania hollanda@ms.sapientia.ro Keywords: bevel gear, tooth profile, controlling, spherical involute, octoid profile 1. General remarks Tooth profile precision mainly influences the behaviours of cylindrical and bevel gears betimes its exploitation. Tooth profile errors contribute to the modifying of many parameters like gearing ratio, load capacity, gearing noise level, tooth flanks wear and so on. A general accepted and applied method of controlling of bevel gears, actually not exists [2,4]. The majority of existing papers where bevel gear tooth control problems are considered, certain control methods are described as follows: tooth thickness, tooth radial beat, pitch and tooth direction measurement. But opinions are different regarding the tooth profile control. Some papers affirm the impossibility of controlling of bevel gear tooth profile. Argumentation is based on the non-existence of an adequate gauge [5,6]. In this case only the bearing area will be controlled. Other papers [2,3,4,5] prove that bevel gear tooth profiles can be measured using universal control devices like microscopes or the universal cylindrical involute gear control instrument. Specific bibliography contains papers that describe bevel gear tooth profile controlling devices too, developed for spherical involute, octoid l" 5 ' and octoid 2" Dd profiles [1,2,4,5], But these could not be extended for common industrial usage. 2. Microscope based tooth profile control Controlling process of bevel gear tooth profile can be performed using the universal microscope. The controlled bevel gear is fastened on the table of microscope that way that the generatrix of the complement cone is parallel to the table's plain. In order to realise that, a specific device will be used (figure 1.) As a consequence, generatrix of the pitch cone will be perpendicular on the microscope's table [5]. 115

2 Figure 1. The microscope's auxiliary device Figure 2. Positioning on the involute - controlling device Measuring position are found when one of the reticule traces overlaps the symmetry axis of the tooth. After the bevel gear is blocked in the position described before, coordinates of a finite set of points on the tooth profile will be measured. The disadvantage of the presented method consists in the difficulty of processing of measured data. 3. Method of control using the universal involute measuring device Tredgold's approximation referring to the geometric calculus of bevel gears can be used by the control of the tooth profile. By this measuring procedure, the bevel gear tooth profile is defined in a plane perpendicular to the generatrix of the pitch cone. The positioning of the inspected bevel gear must ensure that pitch cone's generatrix is parallel to the axis of the disk who materialise the basic circle (figure 2.). It happens if bevel gear's axis will be declined by the half top angle of the pitch [2]. This control method induces errors. Intersecting the pitch cone with the measuring plane, three different curves can be obtained, in dependence with the half-top angle value of the pitch cone: an ellipse if 8<45, a parabola if 5=45 and a hyperbola if 8>45 (figure 3.). When measuring, the intersection curve is replaced by a basic circle with radius r b = r'cosa. This will be the mobile centroid. Unfortunately it touches the intersection curve only in the medium position, in point P. 116

Another source of error by the presented method is that the intersection of the bevel gear tooth flank and the measuring plane is not a plain involute, but involute measuring devices still indicate

3 Another source of error by the presented method is that the intersection of the bevel gear tooth flank and the measuring plane is not a plain involute, but involute measuring devices still indicate the aberration related to the plain involute. This method can be successful applied if exists a gauge bevel gear with identical dimensions to that measured. First the gauge-gear's tooth profile will be measured, followed by the considered bevel gear. After that the obtained results will be compared. In this way, errors caused by the measuring principle are identical for both objects. 4. Profile control using special equipments Another special equipment for measuring bevel gear tooth profile is based on theoretical measuring principles, developed by the Klingelnberg Co. in The principle sketch of the equipment PKF200 is presented in figure 4 [2]. Using this equipment control, spherical involute and spherical octoide tooth profiles can be controlled. To perform the control of a bevel gear with spherical involute tooth profile, the equipment will be set in accordance with the half top angle of the basic cone. During the rolling movement, the feeler remains fix for a perfect spherical involute profile, and as consequence the sensor will indicate zero position. The equipment can be put in function moving the driver-slider (figure 4.). This will rotate the cradle with the help of a steel ribbon fastened to both. In the same time the balancing aim will be rotate too. The measured bevel gear is fastened to this. During these movements, the rolling cone -having the same axis with die measured bevel gear- rolls on the track of the plain gear. The movement of the feeler along the profile can be realised by an adjustable ruler and roller placed under the driver-slider. 117

4 Data recording - device ^ Cross slide Guide Feeler Bevel gear Guiding slide Plane gear Figure 4. The principle - sketch of PKF200 equipment On account of a very complicated structure and a designing error-in our opinion, the equipment couldn't be extended and it is not in use. Profile of bevel gear tooth can be proved using a Maag KP-42 equipment too. The principle of measuring is here also still based on the rolling of the tested bevel gear on the plain gear that holds the feeler [2]. 5. The proofing of the spherical involute profile Heidenreich & Harbeck had realised a special equipment intended for controlling straight teethed bevel gears. The principle of functioning is presented in figure 5. The deviation from the tooth direction can be also measured. Based on a very brief description of the equipment [1] can be deduced that it leans on the theoretical generating of the spherical involute. A rolling movement is realised between the basis cone of the measured gear and the plain of the plain gear. The feeler end the sensor are fastened on the cross slider that can move along the driver slider. The driver slider moves along its track disposed on the plain gear. 6. Profile controlling using numerical software Gleason Inc. from USA has developed a method of control based on the achievement of an amount of co-ordinates of 45 points on the investigated tooth flank. Measuring points are disposed on 5 parallel lines oriented along the tooth direction, each containing 9 points. On the height of tooth appear in consequence 9 lines each containing 5 points. A 3D measuring device must be used. 118

5 Feeler Rolling track Cradle Rolling cone.. ^ ^ k Dnving Balancing > S^/ band beam Driving slide Roller Figure 5. H&H measuring device Using numerical software in order to compute the measured co-ordinates, the precision of the Gleason type bevel gears (whose tooth direction is an arc of circle) can be determined. 7. Profile control performing using the proposed instrument The working principle of all existent control devices had coincided, less or more, with the working principle of the bevel gear cutting machines. The disadvantage of the presented control instruments consists in performing the relative movement between the measured gear and the corresponding plain gear through mechanical solutions. The structures of presented instruments are complicated, and as consequence the measuring precision is relatively low. This is the reason because in the actual bevel gear industry these instruments are not used This paper presents a method and a universal instrument that ensures the increasing of measuring precision through simplifying the construction of the proposed device. It is able to perform measuring of octoid I, octoid II and spherical involute profiles, on straight or curve teethed bevel gears. The rolling between the imaginary plain gear and the controlled bevel gear is realised applying solutions that differ from those classics mechanical. The proposed control method ensures the estimation of the teeth profile aberration relatively to the theoretical profile. The aberration will be estimated as the difference between the measured co-ordinates and the theoretical co-ordinates of the tooth flank points. The controlling device (figure 6.) is composed by a body (1) sustaining a turning table (2), who's axis coincides with the axis of the imaginary plain gear. On this table is to be found a slider (3) that can be translated in the radial direction. This slider sustains a vertical 119

$A circular slider (6) on the body ensures the rotating of the shaft around its axis. In the case of spherical involute 8 \ bevel gears, the basis cone f rolls over the centroid plain 8 v /.$

6 table (4) that facilitates the translation of the feeler (S) until it arrives in the rolling plane of the imaginary plain bevel gear. The measured bevel gear (8) is fastened on the shaft (7). A circular slider (6) on the body ensures the rotating of the shaft around its axis. In the case of spherical involute 8 \ bevel gears, the basis cone f rolls over the centroid plain 8 v /.^'isc f the plain gear. Otherwise, / ijtsi \ by measuring octoid profile \ / \ \ bevel gears, die generatrix of \ i; J; I \ \ the pitch cone is to be found MUíí 5^) I \ \ in the centroid plane. ^^^Rp^ / \ \ By the measuring, turning / \ \ table (2) and bevel gear (8) 1. are revolved over their own ,,, axes. The circular movements are realised by Figure 6. The proposed device two electrical motors in a manner that ensure the correlation between the angular speeds, in accordance with the gearing ratio between the measured gear and its imaginary plain gear Visualisation of data recorded is performed through a computer that performs the data processing and lists the aberration values and the associate diagrams. This universal bevel gear profile measuring device, under way to be patented by "Oficiul de Stat pentru Invenfii?i Mdrci Bucurejti" The National Patent Office can be used to determine the profile aberrations by all types of existing bevel gears. REFERENCES 1. APITZ, G.: Kegelreder mit geraden und schragen Zahnen. Heidenreich & Harbeck Weikzeugmaschinenfabrik, (1969). 2. ERNEY, GY.: A fogaskerekek mérése és gyártásellenőrzése. Műszaki Könyvkiadó, Budapest, (1959). 3. HOLLAND A, D.: Contribupi la studiul profilului sculei utilizatá la prelucrarea rofilor din(ate conice cu dinfi drepfi in evolvents sfericá $i la stabilirea schemei structurale a ma$inii-unelte pentru executarea sculei cu acest profil. TezS de doctorat. Universitatea din Bra ov, (1973). 4. MINCIU, C.: Precizia i controlul angrenajelor. Editura Tehnicá, Bucurejti, (1984). 5. RUZICKA, V. Controlul rotilor dintate. Editura Tehnicá, Bucure^ti, (1959). 6. SAUER, L., 1 COL.: Angrenaje. Vol. II. Editura Tehnicá, Bucurejti, (1970). 120

Lecture (7) on. Gear Measurement. By Dr. Emad M. Saad. Industrial Engineering Dept. Faculty of Engineering. Fayoum University.

Lecture (7) on. Gear Measurement. By Dr. Emad M. Saad. Industrial Engineering Dept. Faculty of Engineering. Fayoum University. 1 Lecture (7) on Gear Measurement Fayoum University By Dr. Emad M. Saad Industrial Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Industrial Engineering Dept. 2015-2016