90 CHAPTER 5 PREVENTION OF TOOTH DAMAGE IN HELICAL GEAR BY PROFILE MODIFICATION 5.1 INTRODUCTION In any gear drive the absolute and the relative transmission error variations normally increases with an increase in pressure angle. Thus a gear with higher pressure angle tends to be more sensitive to pitting damage. The contact stress and the bending stresses are the sources of failure in the helical gear. Tooth surface wear mainly occurs near the dedendum and the amount of wear increases as the number of teeth in meshing increases. Increase in module results in reduction of tooth deflection and root stresses. Tip relief is provided for minimizing the contact stress and to enable smooth running of the gear pair. Composite profile design reduces the bending stresses, tooth deflection and contact stresses in the helical gear teeth. This chapter is dedicated to analyze the performance of composite profile i.e the combination of both involute profile and cycloid profile for preventing pinion failure in the gearboxes used in the wind turbine generator. A comparative study was carried out with the following four options to choose the best profile for the helical gear pair drive engaged in WTG. i) A conventional pinion made of involute profile with tiny tip relief.
91 ii) A pinion made of composite profile with tip relief. iii) A least module helical pinion with next higher module helical pinion comprising of tip relief. iv) A higher module helical pinion made of composite profile with tip relief. 5.2 PROBLEM PHASE Wind Turbine Generator of 225 kw capacity built with gearbox comprised of one planetary stage and two helical stages are selected for investigation. The rst-helical stage called slow-speed line has 119/23 teeth gear combination and the second-helical stage called high-speed line has 94/19 teeth gear combination to achieve a nal speed ratio of 1:25.60. This increase in gearbox speed induces abnormal noise and vibration during the operation of the gearbox at full load, in addition, both drive and non-drive ank of high-speed pinion experience more standstill or pressure marks and have scuf ng wear and pitting wear which ultimately leads to frequent pinion failure. Besides failure of pinion in the high-speed stage when the WTG is in operational mode, it requires huge man-hours and machine stoppage for servicing the gearbox. Frequent turbine stoppages lead to enormous power generation losses, customer dissatisfaction and so on. Sometimes, the damaged high-speed pinion certainly affects smooth functioning of its mating gear, bearings, and other stage gear trains. Further, gear failure in the intermediate stage warrant either the replacement of that gear in the gearbox or overhauling of the gearbox. This complicates and leads to heavy repairing cost of the wind turbine generator because of the tower height and weight of the gearbox. De-erection of nacelle
92 necessitates a huge-capacity crane of the order of 200 400 tonne at the wind turbine site to swap the gearbox in the turbine unit. The survey undertaken during this research work confirms that the frequent pinion failure occurs in the existing 94/19 teeth gear pair used in the high-speed stage. The particular gear pair is made of ve module having 20 pressure angle with tiny tip relief. So, an attempt has been made to modify the helical gear profile for higher module with increased tip relief and introduction of a composite pro le to avoid the pinion failure. Recent days gear manufacturers and research consultants have explored the possibilities of the development of advanced materials, new heat treatment methods, design of stronger tooth pro le, and new gear manufacturing process. The objective of this research study is to find out the solution for preventing pinion failure in the gearboxes used in the WTG through pro le modi cation. 5.3 CONSTRUCTION OF COMPOSITE PROFILE 5.3.1 Tip Relief Tooth modi cation is a method by which the tooth pro le is changed from theoretical involute curve by reducing a tiny amount at the tooth tip. In general, tooth modi cation methods are used to reduce the meshing vibration and noise of the gear train. Pro le modi cations are done towards involute curve, lead crowning towards face width and end relief. Figure 5.1 shows 2-Dimensional (2D) geometry of half size tooth having tooth tip relief S o, length h o, S is the tooth tip thickness and in the radial direction from the tip h f which are symmetrical on both sides of the tooth.
93 Figure 5.1 Two-dimensional geometry of half-size tooth 5.3.2 Cycloid Pro le The spur gear comprises of involute cycloid conjugate pro le (Figure 5.2). It consists of an involute pro le near the pitch point which is just above and below the pitch point and a cycloid tooth pro le on the remaining portion of addendum and dedendum. Figure 5.2 Spur gear involute cycloid conjugate pro le
94 Figure 5.3 shows the basic rack form of involute cycloid composite pro le gear. The rack for the composite tooth pro le gear is of the form PQR consisting of a straight line PQ and a cycloid curve QR which is drawn by rolling a circle on the X-axis (the base pitch line). The tooth strength is improved by proper selection of parameters such as pressure angle and rolling circle (Gitin Maitra 1998). The addendum and dedendum of the rack are symmetrical to each other with respect to the pitch point P because of the interchangeability of the gear. Using the coordinate system shown in Figure 5.3 the cycloid curve PQR is expressed by the Equations (5.1) to (5.3) x = a ( sin ) + X 0 (5.1) y = a (1 Cos ) (5.2) and X 0 = 2a inv 0 (5.3) Figure 5.3 Cycloid curve co-ordinate systems
95 Where a is the radius of the rolling circle, is the rotational angle of the rolling circle and is the inclination of the straight line PQ to 0 the Y-axis, which is equal to the cutter (hob) pressure angle of the involute. X 0 is the distance between the pitch point P and the point where the cycloid curve begins. 5.3.3 Helical Gear Pro le The addendum and dedendum are symmetrical and conjugate in cycloid pro le, whereas a special concept called helical composite pro le comprising epi-cycloid with involute pro le in addendum and involute pro le alone in dedendum was introduced as shown in Figure 5.4 (i.e. an addendum is having a small portion of involute pro le just above the pitch point and the remaining pro le with an epi-cycloid pro le). Pinion of 19 teeth 5 modules and 18 teeth 5.5 modules encompassing this composite pro le have been considered for analysis in this research study. Figure 5.4 Composite pro le in helical gear comprising epi-cycloid with involute pro le
96 5.4 DESIGNING THE MODIFIED HELICAL GEAR PROFILE Conventional helical pinion is made up of 5 mm module whereas the modi ed helical pinion is formed with 5 mm module with composite profile and 5.5 mm module pinion with both the involute and composite profile with tip relief for the same centre distance. Hence, higher module pinion with lesser addendum modi cation co-efficient is analyzed in this research study. Tip relief is introduced on pro le for noise reduction, which will minimize the contact stress as well. Tables 5.1 and 5.2 give the speci cations of the conventional and the proposed gears used in this investigation. Table 5.1 Specifications of 94/19 teeth gear pair Description Conventional helical gear pair with involute profile Modified helical gear pair with composite profile Number of teeth (Z 1 /Z 2 ) 94/19 94/19 Normal module (mn) 5 5 Face width (b) in mm 100 100 Normal pressure angle ( ) 20 20 Helix angle ( ) 14 14 Centre distance (a 1 ) in mm 299 299 Pitch circle diameter (d) in mm 97.908 97.908 Addendum modification co-efficient 1.06/0.65 1.06/0.65 (X 1 /X 2 ) Pinion tip circle diameter (d a ) in mm 114.408 114.408 Total contact ratio (eps g) 2.865 2.865 Gear ratio (u) 4.947 4.947 Rotational speed (n) in rpm 1040 1040 Torque (T) in Nm 2066 2066 Rolling circle radius (a) in mm - 6.5 Rotational angle of the circle ( ) - 20 Addendum (h a ) in mm 8.25 8.25 Dedendum (h f ) in mm 3 3.15 Material and heat treatment 18CrNiMo7 Case hardened and tempered 18CrNiMo7 Case hardened and tempered Method of finishing teeth Profile grinding Profile grinding
97 Table 5.2 Specifications of 85/18 teeth gear pair Description Modified helical gear pair with involute profile Modified helical gear pair with composite profile Number of teeth (Z 1 /Z 2 ) 85/18 85/18 Normal module (mn) 5.5 5.5 Face width (b) in mm 100 100 Normal pressure angle ( ) 20 13 Helix angle ( ) 14 14 Centre distance (a 1 ) in mm 299 299 Pinion Pitch Circle Diameter (d) in mm 102.031 102.031 Addendum modification coefficient 0.6/0.79 0.6/0.79 (X 1 /X 2 ) Pinion tip circle diameter (d a ) in mm 119.631 119.631 Total contact ratio (eps g) 2.719 2.719 Gear ratio (u) 4.722 4.722 Rotational speed (n) in rpm 1040 1040 Torque (T )in Nm 2066 2066 Rolling circle radius (a) in mm - 7.25 Rotational angle of the circle ( ) - 15 Addendum (h a ) in mm 8.8 8.8 Dedendum (h f ) in mm 3.575 3.7 Material and heat treatment 18CrNiMo7 Case hardened and tempered 18CrNiMo7 Case hardened and tempered Method of finishing teeth Profile grinding Profile grinding 5.5 FORCE ANALYSIS The load-transmitting capability of gear tooth is analyzed and checked for designing a gear system. The effective circumferential force on the tooth at the pitch circle of the gear while in meshing is estimated. Two kinds of stresses are induced in gear pair during the power transmission from one shaft to another. They are: i) Bending stress-induced on gear teeth due to the tangential force developed by the power. ii) Surface contact stress or compressive stress.
98 of the tooth. The load is assumed as uniformly distributed along the face width 5.6 FORCE COMPONENTS The force exerted by the helical gear on its mating gear acts normal to the contacting surface if the friction is neglected. However, a normal force in case of helical gear has three components that is apart from the tangential and radial components that are present in the spur gear, a third component parallel to the axis of the shaft called axial or thrust force exists. These force components are shown in Figure 5.5. For the given data various forces were derived from standard Equations (5.4) to (5.8). Figure 5.5 Forces in helical gear Torque T = P 60/2 n (5.4) Tangential force F t = 2 T/d (5.5) Normal force F n = F t / (cos cos ) (5.6) Radial force F r = F t (tan /cos ) (5.7) Axial force F a = F t tan (5.8)
99 These force components are computed for a power value of 225 kw at speed 1040 rpm and are presented in Table 5.3. Figure 5.6 presents the tangential forces that act along the line of contact in the meshed model of helical pinion as recommended by ANSI/AGMA 1012 G05 standard. Table 5.3 Force components in helical gear Profile Tangential force in Newton (N) Normal force in Newton (N) Radial force in Newton (N) Axial force in Newton (N) In use 19 teeth involute 41340 37692 15507 10307 Proposed 19 teeth involute cycloid composite 41340 37692 15507 10307 Proposed 18 teeth involute 40508 36934 15195 10099 Proposed 18 teeth involute cycloid composite 40508 38297 9638 10099 Figure 5.6 Tangential forces in helical pinion
100 5.7 FINITE-ELEMENT ANALYSIS Since the solid 186 elements have quadratic displacement behavior and is well suited to model irregular meshes, this solid 186 element type with 20 nodes is selected to describe the helical gear and its tooth de ection in ANSYS software version 11.0. As the gears are made out of heat-treated alloy steel, carburized and case-hardened alloy steel (18CrNiMo7) is taken for analysing the root stress concentrations. The material properties are given in Table 5.4. The maximum stresses on the tensile and compressive sides of the tooth are considered for analysis. Table 5.4 Material properties Gear material 18CrNiMo7 Density 7870 kg/m 3 Young s modulus (E) 206000 N/mm 2 Poisson s ratio (n y ) 0.30 Yield strength (R p ) 850 N/m 2 20 Nodes 3D solid element with three degrees of freedom per node (UX, UY, and UZ) is stacked to model through the thickness discontinuities. To obtain the individual tooth bending stresses, tooth de ection, and stiffness, single tooth of both the pinion and the wheel with solid rim have been meshed in Finite-Element Analysis (FEA) as per ANSI/AGMA 1012 G05 standards as given in Figure 5.6. Virtual model analysis in ANSYS software is carried out for all the four models. The meshed model of all the four gear teeth is shown in Figures 5.7 to 5.10. The elements in the 19 teeth x 5mm module gear model having involute profile are 68,181 (Figure 5.7) and in 19 teeth x 5mm module gear model having composite profile are 42,382 (Figure 5.8). Similarly, for
101 18 teeth x 5.5 mm module gear model having involute profile are 66,801 (Figure 5.9) and 18 teeth x 5.5 mm module gear model having composite profile are 36,395 (Figure 5.10). Figure 5.7 Meshed model of 19 teeth 5 module involute pinion Figure 5.8 Meshed model of 19 teeth 5 module composite pinion
102 Figure 5.9 Meshed model of 18 teeth 5.5 module involute pinion with tip relief Figure 5.10 Meshed model of 18 teeth 5.5 module composite pinion with tip relief
103 5.8 RESULTS AND DISCUSSION The visual presentation of the induced tooth de ection and bending stresses in pinion having different number of teeth and modules are depicted in Figures 5.11 and 5.12 respectively. The induced tooth de ection and bending stresses (von Mises) given in Table 5.5 were obtained using Finite Element Analysis. It is observed from the ANSYS study and also from Table 5.5 that the 18 teeth 5.5 mm module pinion generated with helical composite pro le has a smaller amount of tooth de ection (0.006 mm), lesser root stress (150 N/mm 2 von Mises) with higher tooth stiffness (6.75 10 6 N/mm) as compared with that of the existing 19 teeth 5 mm module conventional involute pinion. Figure 5.11 Tooth deflections of pinions
104 Figure 5.12 Bending stress of pinions Table 5.5 FEA results at maximum speed (1040 rpm) of pinion Gear strength 19 teeth 5 module 18 teeth 5.5 module Involute Composite Involute Composite Tooth deflection in mm 0.007 0.009 0.007 0.006 5.36 Stiffness (N/mm) 10 6 4.59 10 6 5.78 10 6 6.75 10 6 Bending stress (N/mm 2 ) 1057 796 459 150 Permissible tooth root stress (N/mm 2 ) 825.50 825.50 820.72 820.72 Figure 5.13 predicts the trend how the tooth de ection varies at maximum speed for pinion with different teeth and modules. The de ection decreases in the modi ed pinion having 18 teeth 5.5 mm module with composite pro le. Figure 5.14 shows bending stresses in pinions at maximum
105 speed. Bending stress (von Mises) decreases drastically in pinion having helical composite pro le with 18 teeth 5.5 mm module. Figure 5.15 indicates how the tooth stiffness is varying for the change in profile and module. Figure 5.13 Tooth deflection trend Figure 5.14 Bending stress trend
106 Figure 5.15 Tooth stiffness trend 5.9 CONCLUSION The following conclusion is arrived from the foregoing analysis and investigation pertaining to the tooth de ection, stiffness, and bending stresses of the pinion having different modules: i. The bending stresses (von Mises) of the modi ed composite pro le gear pair having 5.5 mm module is comparatively less than that of the conventional helical gear pair. ii. The modi ed 18-teeth pinion having 5.5 mm module with composite pro le exhibits less tooth de ection under load condition and more tooth stiffness.
107 iii. iv. The bending stress of conventional 19-teeth helical pinion having 5 mm module exceeds the permissible tooth root stress (Table 5.5), which is the root cause for the failure of the pinion very often. However any fault in the cutter design for generating composite pro le leads to misalignment in the gearbox assembly. Therefore, care must be taken in the gear-making process; otherwise it would not at all serve the purpose.