ISSUES ON CYLINDRICAL GEARINGS WITH ASYMMETRIC TEETH

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1 ISSUES ON CYLINDRICAL GEARINGS WITH ASYMMETRIC TEETH Asistent Eng. Sándor RAVAI NAGY, Prof. Eng. Mircea LOBONTIU, Ph.D. North University of Baia Mare, ROMANIA Abstract: This scientific paper approaches some issues relating to the manufacturing of the gearbox with gears with asymmetric teeth. The flanks of gears from the gearbox have been grinded. After its manufacturing, the gearbox with gears with asymmetric teeth can be tested both in laboratory conditions and while used with industrial equipment. There have been created the premises of a correct dimensioning of the gears with asymmetric teeth. Key words: gears with asymmetric teeth, testing method and device, gearbox, manufacturing. 1. INTRODUCTION In some fields (Aeolian, aviation, heavy duty transmissions) gears with asymmetric teeth are promoted for their improved resistance to torque transfer. The asymmetry is expressed by the pressure angle which is different from 20 on one of the flanks. Following the theoretical and static testing already carried out on the gears with asymmetric teethwe have reached a final step, resulted in the possibility of executing a gearbox based on two gears with asymmetric teeth. The execution of the gearbox is highly important because by this the manufacturing technologies of the gears with asymmetric teeth can be tested and the possibilities to study these gears also in dynamic conditions are opened. 2. ISSUES CONCERNING THE BENDING STRESS DIMENSIONING OF THE TOOTED GEARS WITH ASYMMETRIC TEETH The bending stress calculation for the gears with symmetric teeth is standardized and is presented in detail in STAS 12268, DIN 3990, and ISO The above mentioned standards perform the stress calculation by taking into consideration only the bending of a subsequent tooth making corrections by using the contact ratio coefficient. The calculation is based on the fact that the gear tooth is bent at maximum values in the moment when the point of contact between teeth reaches the point "E" (Fig.3) at recess, or point A on approach, that is when the nominal force Fn acts on the tooth top [1]. The tooth is seen as a shaped recessed beam clamped in the gear body and charged with normal force Fn. During calculation process, the following assumptions are made: the force is applied to the tooth top and is taken over by one tooth only, and the restraint section sf, the dangerous section is where the lines are laid out under an angle of 30 in relation to the tooth axis are tangent to the contact profile, i.e. the "S1S2 area [1], [2]. When highlighting the loading of the tooth, the normal force "F n " (fig.1) moves on its working line to the "F" point and splits into the radial force F ra, whose effect is ignored, and in the tangential force F ta, which will bend the tooth root. 61

2 a.) b.) Fig.1 Hypothesis regarding stress calculation for gears with asymmetric teeth The flexural unit stress is given by the expression (1) [1]: Fta hf σ b = (1) 2 SnF b 6 Or, in the case of gears with asymmetric teeth, the (1) formula changes into: Fta hf σ b = k σ (2) 2 SnF b 6 where: k σ the correction coefficient of the asymmetric tooth, a coefficient which will take into account the shape of the tooth This coefficient will be experimentally determined according to modules and teeth numbers. The sizing relation presented in (rel.1.) and used for the gears with symmetric teeth for being applicable to the gears with asymmetrical teeth (with some corrections) must be completed with some correction coefficients which take into account the asymmetric shape of the tooth when performing the tooth bending stress calculation and when checking the resistance to contact pressure. For determining the coefficient k σ, a correction coefficient of the asymmetric tooth, we have developed a test method and device with which one can analyze the behaviour of the tooth and the maximum load value that makes the tooth break. The system simulates the static gearing of a rack with a segment of a gear. 62

3 3. ISSUES CONCERNING THE FLEXURAL STRENGTH TEST The testing device presented in fig.2 is contrived and designed to be used on the presses that perform tests under compression. The device consists of the motherboard "1" which has abutments located on it: sample abutment "2"; rack abutment "5"; Sample 4 is placed in the sample abutment and secured with a vice grip type device, named fixation frame 6. In the rack abutment 2 the single toothed rack slips over. The head of the press will press down the top of the rack. The behaviour under load of the tooth can be followed with the monitoring system of the press. Fig.2 Device for testing the flexural strength of the gear teeth The shape of the test sample used within the presented test method is obtained by keeping in mind that the tooth of the gear is maximally bent when the place of contact reaches the E position. In this point, the nominal force F n actuates the tooth top (fig.1, fig.3). The test sample objectifies an entire tooth. Given the technological needs, the test samples can be made on CNC Machine Tools, with a small and low-cost manufacturing cycle. In the point "E", the tangent to the basic circle of the involute defining the tooth flank is perpendicular to the rack side and the tangent passes through the pitch point "C". The gauge dimensions of the test sample A E and B E are set according to the dimensions of the testing device. During the test, the following stages have been identified (fig.4): 1. stage of elastic deformation of the tooth; 2. stage of occurrence of first plastic deformations of the tooth in the fillet area; 3. stage of occurrence of plastic deformations on the tooth flank; 4. - fracture, shearing of the tooth made by the tooth of the rack. According to carried out tests, the tooth shearing occurs at the top of the tooth rack. 63

4 Fig.3 The test sample shape for the flexural tests Stage 1. Stage 2. Stage 3. Fig.4 Stages of tooth damaging From the results of the experiment on a gear z=30 teeth, m=5 mm, b=8mm, the material: C45 improved we can present the following results (Table 1): The asymmetric tooth flexural strength shows an increase of 11,5% table 1. Summary of experimental results The pressure angle of the gear tooth z = 30, m = 5 mm Maximum tangential force 20º - 20º (symmetrical tooth) 41.2 kn 20º - 30º (asymmetric tooth) 47.5kN 4. TECHNOLOGICAL ASPECTS IN PROCESSING GEARS WITH ASYMMETRIC TEETH Grinding gears with asymmetric teeth used for the gearbox developed to be prototype rigorously pursues the general technology for gear manufacturing. Instead, technologies applied to key stages will have a distinct specific character, due to the gear teeth asymmetry. First of all, the toothed gears were roughened through the method of profiling and processing cavity by cavity with the side-milling cutter for asymmetric teeth, and then machined through grinding, by using the gear grinding method Niles with a biconic-type abrasive wheel. 64

5 4.a. Milling gears with asymmetric teeth The key point in milling of gears with asymmetric teeth by using asymmetric involute gear milling cutters consists in our ability to design and execute them, because currently there are no mills of this type on the market. The gear milling cutter profiles have been obtained via graphics. 4.a.1. The graphic method of determining the profile of the involute gear milling cutters with asymmetric profile The graphic design method consists in determination the tooth space profile of the gear with asymmetric teeth, a profile that will be transposed on the outer circumference of the involute gear milling cutters. The parts of the involute gear milling cutters, the outer diameter, the diameter of bore, the grooved wedge dimensions, the tolerances in sizes can be chosen according to the involute gear milling cutters standard [8], [9] STAS 2763, and DIN The profile of the gear is generated by a CAD medium, since there is no tooth space symmetry, and the involute gear milling cutters profile is chosen to be the centre of the contact profile of the root surface. Thus, there is the specific adjustment of the technological system for manufacturing gears with asymmetric teeth, presented in Fig.5. Fig.5 The technological system for manufacturing gears with asymmetric teeth One can choose to set tooth spaces so that these to be in a good position for processing, but in this case the technological adjustment will be more difficult. In Fig.5 we present the two tooth space setting cases. a) following the axis of tooth space symmetry, in this case κ 1 κ 2, the cutting depth h will be exactly the tooth space depth and only the milling cutter must be adjusted according to the symmetry axis of the blank, by using the L tehn.1 coordinate. b) following the favourable position needed by the chip removing process for obtaining tooth spaces. In this case, the angles κ 1 and κ 2 are equal, but the depth will differ from the tooth space depth, and the reference plane of the milling cutter will not run through the axis of the blank, it will be parallel to that, and the milling cutter will be rigged according to the L tehn.2 coordinate. 4.a.2. The technological milling system adjustment for gears with asymmetric teeth through the copying method with a profiled involute gear milling cutters with asymmetric profile. The milling cutter position adjustment to the blank of the gear with asymmetric teeth is done in three stages: stage 1. Positioning the involute gear milling cutters and of the reference plane according to the symmetry axis of the blank. We bring into contact one side of the 65

6 milling cutter and the outer diameter of the wheel blank. After this, we carry out the Ltehn. shifting and we get the position between the gear blank and the milling cutter. stage 2. Adjusting the involute gear milling cutters to achieve the tooth space depth. The outer diameter of the cutter reaches the surface of the gear blank, after which the coordinate h, the tooth space depth, is adjusted from this position. stage 3. Perform the cutting process along face width of the gear. The figure 6 present photos of the technological system for manufacturing of the gears with asymmetric teeth by using involute gear milling cutters with asymmetric profile. The above mentioned gears have the following characteristics: z 1 =26 teeth, z 2 =32 teeth, α m+ =40º, α m- =20º, A=145mm, (m=5). Fig.6. Technological system for manufacturing gears with asymmetric teeth through the method of copying by using a involute gear milling cutters with asymmetric profile 4.b. Grinding gears with asymmetric teeth with a biconic type abrasive wheel, through the Niles method Finishing by grinding is essential for the quality of the pieces. The specialized bibliography does not present grinding solutions for these types of gears [3], [7]. Given the kinematic structures of gear-tooth grinding machines, this paper advances the technological solution of the biconic-type abrasive wheel grinding, through the Niles method. In case of the Niles method, this means either tool profiling with features specific to each flank (asymmetrical profile of the biconic grinding wheel), or adjustments of the machine tool specific to each pressure angle afferent to each flank. For the standard profiling of the abrasive wheel, the grinding of both flanks will require identical profiling of the grinding wheel flanks and two riggings of the kinematic chains of the machine tool that will grind each flank. The moments of successive grinding of each flank are presented in fig.7 and 8. The adjustment is based on the kinematic chain with change gears for dividing and rolling, in conformity with the base circles of each flank. The b + rolling stroke must also be set for grinding the flank m +, and will be different from the b- stroke for grinding the flank m - (20 ). This is due to the different lengths of the involutes belonging to the two flanks of a tooth. After each gear tooth flank grinding, the same adjustments for the opposite flank are made. 66

7 Putting the gear blank and the grinding wheel into gear is done as a result of rotation ω and translation V r that the blank makes, according to fig.7 and 8. From the correlation of the two movements the rolling motion derives, being described by the equation: r V = ω r w, (3) where r w is the technological rolling radius. Each flank grinding is done within the angular interval ψ + and ψ respectively, that is defined by the points between which the grinding wheel flank is tangential to the involute of the grinded flank. Fig.7 Stroke for the modified flank m - Fig.8. Stroke for the modified flank m + After the complete machining of the gear with asymmetric teeth, the following results have been obtained (table 2): z 1 =26 series 1 Variation of the tooth profile (f fr ) flank 40º flank 20º flank 40º flank 20º 0º 180º 0º 180º 0º 180º 0º 180º table 2. The control results of the grinded gear. Variation of the tooth Radial direction (F βr ) run-out Roughness of the toothing Ra Rz (F rr ) [µm] [µm] [µm] [µm] [µm] [µm] [µm] [µm] [mm] [µm] [µm] ,025 0,290 0,502 1,716 2,569 Result checking of the technological adjustment of the tool depth feed for removing the tooling allowance was done by measurement over rolls, determined graphically, within tolerances allowed for gears with symmetric teeth. Fig.9 Technological adjustment of the biconic grinding wheel with 20 half-angular, to grind asymmetrical gears through the Niles method. 67

8 Researches on such testing gearings require technology solutions that can be generalized for a stable manufacturing technology. The above mentioned technological solutions have been applied in the development stages of the gearbox with gears with asymmetric teeth. 5. CONCLUSION Following our investigations, experiments and tests in correlation with our publications [4], [5], [6], we can bring forward the following conclusions: a) Gears with asymmetric teeth have the bending strength increased by 11.5% b) For dimensioning cylindrical gears with asymmetric teeth a correction coefficient k σ and, respectively, a method to test them are defined. c) Gears with asymmetric teeth can be milled off with fly cutters with asymmetric profile and can be grinded through the Niles method. d) Tests should be extended for various gearing angles, modules and numbers of teeth. REFERENCES 1. Antal, A., Tataru, O. Elemente privind proiectarea angrenajelor. Editura ICPIAF SA, Cluj Napoca, Gafitanu, M., s.a. Organe de masini. Vol. II., Editura Tehnică, Bucuresti, Henriot, G. Traité theorique et pratique les engrenages. Tome I-II, Paris, Dunod, Ravai Nagy, S. Manufacturing gears with asymmetric teeth through the method of copying, and designing side-milling cutters for gears with asymmetric teeth. International Multidisciplinary conference IMC2011, 9 th edition, Baia Mare Romania Nyiregyhaza Hungary, May 19-21, 2011, ISBN , (pp ) 5. Ravai Nagy, S., Lobontiu, M. Manufacture of gears with asymmetric teeth on CNC machine tools. Annals of the Oradea University, Fascicle of Management and Technological Engineering, Volume IX (XIX), 2010, NR.2, IMT Oradea 2010, Oradea, ISSN , (pp ) 6. Ravai Nagy, S., Lobontiu, M. Approach to the test of flexural strength of the teeth of gears with asymetric teeth. Annals of the Oradea University, Fascicle of Management and Technological Engineering, Volume X (XX), 2011, NR.2, IMT Oradea 2011, Oradea, ISSN , (pp ) 7. Sauer, L., s.a. Angrenaje. Editura Tehnică, Bucuresti, STAS 2763/1-83 Scule pentru danturare. Freze disc modul. Conditii tehnice generale de calitate. (Toothing tools. Fly cutters. General technical requirements for quality) 9. STAS 2763/2-83 Scule pentru danturare. Freze disc modul. Dimensiuni. (Toothing tools. Fly cutters. Dimensions) 68