International Journal of Engineering Trends and Technology (IJETT) – Volume 5 Number 6 - Nov 2013 Parametric Modelling and Static Structural Analysis of Four Speed, Constant Mesh, Manual Gear Box Santosh Ukamnal#1, Ketan Nalawade#2, P. Baskar*3 # P G Scholar, M. Tech in Automotive Engineering VIT University, Vellore, India * Assistant Professor, School of Mechanical and Building Sciences VIT University, Vellore, India Abstract— Gears are one of the important part in the power transmission systems. Good design of transmission enebles better engine performance. Gear box is most widely used in automotive sector. This paper deals with the modeling in Pro Engineer and static structural analysis in Ansys Workbench 12.1 of four speed constant mesh gear box for 305cc engine, in order to conclude the stresses induced in the gears while transmitting power. involute is always at the point of tangency of the string with the base circle. A tangent to the involute is always normal to the string, which is the instantaneous radius of curvature of the involute curve. Keywords— Pro Engineer, Von Mises Stress, Ansys Workbench 12.1 I. INTRODUCTION Power transmission has always been of high importance. Gears are used in past, present and they will be used in future automobiles, due to their high reability, torque handling capacity and rapid shifting of gears. As the world moves on there is always new demands, which are to be fulfilled. People now prefer cars with low weight and low engine sound. This opens up a demand for quite power transmission. Higher reliability and lighter weight gears are necessary to make automobile light in weight as lighter automobiles continue to be in demand. Spur gears are the most commonly used gears to transmit power and rotational motion between parallel shafts. The tooth of gear is cut parallel to the shaft. The simplest motion of two external spur gears can be seen by an example of two external rotating cylinders, if sufficient friction is present at the rolling interface. Fig 1. Involute profile generated on the base circle [1] Figure 1 shows the way in which involute curve is formed. These represent gear teeth. The cylinders from which the strings are unwrapped are called the base circles of the respective gears. The base circles should always be smaller than the pitch circles, which are at radii of the original rolling cylinders. C. Gear Mesh Geometry A. Law of Gearing Fundamental law of gearing states that “angular velocity ratio between the gears of a gear set must remain constant throughout the mesh”. The angular velocity ratio m equals to the ratio of the pitch radius of the input gear to that of the output gear. Mv= = The surfaces of the rolling cylinders will become the pitch circles, and their diameters become the pitch diameters of the gears. B. Involute Profile Forms The involute of a circle is a curve that can be generated by unwrapping a taut string from a cylinder. The string is always tangent to the base circle. The centre of the curvature of the ISSN: 2231-5381 Fig 2. Gear mesh geometry [1] Gear mesh geometry is the most complicated part of gears, because most of the loss in power transmission occurs at this point. Figure 2 shows a pair of involute tooth coming in contact and also leaving contact. From the figure 2 it can be seen that common normal for both the contact points passes from the same pitch point. Mesh between the gear and the http://www.ijettjournal.org Page 320 International Journal of Engineering Trends and Technology (IJETT) – Volume 5 Number 6 - Nov 2013 pinion, is defined by the points of beginning and leaving contact. The distance along the line of action between the two contact points in mesh is called length of action. After defining and relating all the gear parameters we can then as needed in sketched features. The figure below shows the screen shot from Pro/E after the completion of this step. II. MODELLING OF GEAR First and the foremost step in this is to model a spur gear. The most complicated part in spur gear is the involute profile of its teeth. There are number of ways of creating involute profile of a spur gear. In this the spur gear model was designed in Pro Engineer design modeler. A. Model and Relation The word Relation and Equation itself gives the idea about relating the feature with the help of equations. Relations are used to express dependencies between the dimensions of a feature. Following are steps involved in this modelling procedure. First Step while modelling is define the parameters in PRO-E. The Parameters are N = No. of teeth Phi = Pressure Angle D = Pitch circle diameter P= Diametrical Pitch As shown in figure Fig 4. Image showing relations Next step is extrude feature. After defining the gear parameters, next step is to extrude circular disc having a diameter equal to addendum diameter and thickness equal to face width. To do this a circle is to be drawn with centre on the sketch references and then go to Tools / Relations menu to define relations between the sketch dimensions and the part parameters. After defining these relations, the circle should have a diameter equal to the addendum diameter of the gear blank. Next step is to define a datum curve showing the involute profile for radius Ri ≤ R≤ Ro. Go to the Insert => Model Datum => Curve menu. Select from Equation, when prompted for a co-ordinate system for a part “PART_CSYS_DEF”. Set the co-ordinate system to cylindrical system. At this point, a notepad window (shown below in the figure 5) will pop up, Fig 3. Image showing parameters For the remaining parameters, which are to be related to basic where one can enter all the equations for the datum curve. parameters, relations can be defined in Tools / Relations menu. Enter the equations listed above for R, θ and Z in terms of t, (a Formulas for the remaining parameters are written below. parametric variable ranging from 0 to 1) and other part Tools => Relations [2] parameters. For the involute profile, the equations will be [2]: Z = D/m Gamma = t*sqrt(Ro^2-Ri^2) (mm) ha = m R = sqrt(gamma*gamma+Ri*Ri) hf = 1.16 * m Theta = theta0+((gamma/Ri)*(180/pi))-atan(gamma/Ri) Ro = ( D / 2 ) + ha (mm) Z=0 Rd = ( D / 2 ) - hf (mm) Ri = ( D / 2 ) * cos ( PHI ) (mm) g_c = sqrt(( D ^ 2 ) / 4 - Ri ^ 2) theta_0 = (360 / (4 * Z)) - ((g_c / Ri) * (180 / pi)) + atan(g_c/ Ri) (degrees) Where, Z = Number of teeth Hf = dedendum height Ha = addendum height Ro= Radius of addendum circle Rd = Radius of dedendum circle Phi = Pressure Angle Fig 5. Image of equation of involute curve in notpad D = pitch diameter When all the datum curve equations are entered, close notepad and click preview, a curve on the flat surface of the ISSN: 2231-5381 http://www.ijettjournal.org Page 321 International Journal of Engineering Trends and Technology (IJETT) – Volume 5 Number 6 - Nov 2013 gear blank should be seen like the one shown in the figure 6 below. Fig 6: Involute corve on the flat surfce of the gear blank After this, define the root circle and make the cut in such away that shown in figure 7 below. Fig 9: Generated gear model in Pro-E The gear model, with involute pfofile teeth, which is generated in Pro Engineer by using relations and parameters option is shown in the figure 9. Like above mentioned methods, all the gears of the gear box are generated. The next step is assembly. B. Assembly In this section, the generated gears will be assembled to defined mesh geometry. 1) Defining of Axis: Two axes, i.e. output and input gear axes must be generated by providing the distance between them before proceeding to the next step which is shown in figure 10. The distance between toe axes of this gear box is is 70mm. Fig 7: Image showing the cut section of the gear After a single tooth space is generated, it has to be patterned along the centre axis of the gear blank. Using the pattern option in Pro/E and by selecting the following option, one can easily pattern the tooth space, as needed depending on the number of teeth. Pattern Type => Axis Pattern: Axis, which goes through the centre of the gear blank => Number of copies Figure 8 shows the preview and the spur gear model created after patterning the tooth space. Fig 10: Axes with distance between two shafts 2) Adding gears and constraints: The gears that are modelled are added to the assembly by Assemble option. Once the gear is added, change the constraint to Pin and align the axis of the gear to one of the generated axes which is as shown in the figure 11. Fig 8: Paterning of the geat teeth ISSN: 2231-5381 http://www.ijettjournal.org Page 322 International Journal of Engineering Trends and Technology (IJETT) – Volume 5 Number 6 - Nov 2013 Fig 14: Standard view of the assembled gear box Fig 11: Input gear with given constraints Once the constraint to input gear is over, again using the option Assemble, the corresponding gear on the output shaft is also added. The constraint chosen is pin and mate the lateral surfaces of the gear as shown in the figure 12. III. ANALYSIS OF GEARS The analysis of meshing gears at different gear ratios present in the gear box is done in ANSYS Workbench 12.1. The assembled model in Pro-E is saved in STEP format, which has to be imported in the Ansys. After the importing is done, following steps has to be accomplished: A. Selection of Material The material that is chosen for gear must have high strength, high hardness and low ductility and should offer high resistance to surface fatigue and wear. To satisfy both core and surface properties, the gear material is generally subjected surface hardening process. Most commonly used gear materials which have application in the automotive industry are 8620steel and 4320 steel [3]. Fig 12: Geometric meshing of two gears TABLE I PROPERTIES OF 4320 STEEL 4320 Steel Hardness Young’s Modulus 0.2% Yield Strength UTS 654 BHN 201 GPa 1250 MPa 1912 MPa TABLE III PROPERTIES OF 4320 STEEL 620 Steel Hardness 615 BHN Young’s Modulus 208 GPa 0.2% Yield Strength 1125 MPa UTS 1869 MPa Before proceeding further with the analysis, the properties of the selected materials is updated in the library. Here the 4320 Steel is chosen as the gear material because of its higher Yield Strength. Fig 13: Final assembly of gear box In the above said manner, remaining gears of the input and output shafts, input shaft and output shaft are assembled with gear shifter as shown in the figure 13. The standard view of the total assemble model is shown in the figure 14. As this gear box is constant mesh gear box, all the gears are constantly meshing at all times. ISSN: 2231-5381 B. Defining Contact Type of contact surface has to be defined in order to carry forward with the analysis. When the two gears are mating the power is transferred by rolling and sliding mechanism. Here we choose frictionless contact, between two mating gears, http://www.ijettjournal.org Page 323 International Journal of Engineering Trends and Technology (IJETT) – Volume 5 Number 6 - Nov 2013 assuming that there is no friction between gear teeth [4]. This can be provided by adding lubricant in the gear box. C. Meshing the Model The meshing of model is done before proceeding to next step. The meshed gear pair is shown in figure 15. In this step the gear model is divided into number of small elements, and these elements are further analysed. Fig 17: Firctionless support provided for input gear E. Defining Loads To define the loads which is in the form of torque, engine specifications has to be noted. Specifications of the engine is as follows: TABLE III SPECIFICATION OF ENGINE Fig 15: Meshing of gears D. Defining Supports 1) Fixed Support: One of the gear must be completely fixed in order to apply the loads. For this purpose the fixed support is given to the inner surface of the driver gear which is located on the output shaft as shown in figure. Type of Engine Manufacturer’s Name Max Torque Capacity Four stroke, Gasoline Engine Briggs and Stratton 20 Nm at 3600 rpm 305cc The torque produced by the engine is transmitted to the wheels by transmission unit, which consists of clutch, gear box, final drive and differential. The gear ratio for the top gear in the gear box is taken as unity (1:1) and the ratio of the final drive is taken as top gear transmission ratio (7.35:1). If we divide the transmission ratio at each gear by top gear transmission ratio, we will arrive at the gear box gear ratios at each gear [5]. Multiplying the torque produced by the engine with the respective gear box gear ratio, torque transmitted at each gear can be calculated. The transmission ratio, gear box ratio and torque transmitted is given in the table below. The load distribution along the face width is assumed uniform and plane strain method is adopted [6]. TABLE IV TORQUE TRANSMITTED BY EACH GEAR IN THE GEAR BOX Fig 16: Fixed support provided for output gear 2) Frictionless Support: The input gear must rotate on the application of the torque. Hence a friction less support is given on the inner surface of the driving gear which is on input shaft as shown in figure. Gear Number Transmission Gear Ratio Torque Transmitted 31.48:1 18.7:1 Gear Box Gear Ratio 4.2829:1 2.5442:1 First Gear Second Gear Third Gear Fourth Gear 11.4:1 7.35:1 1.551:1 1:1 31.02 Nm 20 Nm 85.65 Nm 50.884 Nm F. Solving the Problem The effect of case hardness, case depth and the oil film thickness is neglected. The surface asperities and waviness is neglected [7]. ISSN: 2231-5381 http://www.ijettjournal.org Page 324 International Journal of Engineering Trends and Technology (IJETT) – Volume 5 Number 6 - Nov 2013 The meshed and applied boundary conditioned model is solver for the results by clicking Solve option present in the Ansys Workbench. This process can be very helpful in contact problems as it needs model with high accuracy. It also decreases the lead times and improves overall engineering productivity. G. Generating Equivalent Von-Mises Stress and Factor of Safety In the solution part of the analysis, the option for Equivalent Stress and Stress Tool will be present. Once selected, the results have to be evaluated. Thus the results are displayed on the screen. Which shows that the gear box so designed can be able to transmit the power from engine to drive shaft. IV. RESULTS AND CONCLUSION The Von-Mises stress of the gears in mesh for power transmission is as shown in the figure. V. FUTURE SCOPE While analysisng the gear box, the dynimic loads must also be taken into account. The analysis of the gear box can be further extended to the dynamic loads as well. Vibration effects on each gear pair can also be analysed. REFERENCES [1] [2] [3] [4] [5] [6] [7] Mechanical Engineering, Sighley’s Mechanical Engineering Design, McGraw Hill Publications, Eighth Edition, pp 569.661. Shreyash D. Patel, Finite Element Analysis of Stresses in Involute Spur and Helical Gear, Master of Science in Mechanical Engineering, The University of Texas at Arlington, December 2010. Hong Lin, Robert R. Binoniemi, Gregory A. Fett, Thomas Woodard and Mick Deis, “Mechanical Properties of Gear Steels and Other Perspective Light Weight Materials for Gear Applications”, SAE Technical Paper Series, ISSN 0148-7191, November 2006. Walton, D., Tessema, A.A., Hooke, C.J., and Shippen, J. Load sharing in metallic and non-metallic gears. Proc. Instn Mech. Engrs, Journal of Mechanical Engineering Science, 1994, 208 (C2), 81-87. Harald Naunheimer, Bernd Bertsche, Joachim Ryborz, Wolfgang Novak Automotive Transmissions, ISBN 978-3-642-16213-8, pp 101105, Second Edition. Cornell R.W., Compliance and stress sensitivity of spur gear teeth, ASME Trans., J. Mech. Des., April 1981. M. Rameshkumar, G. Venkatesan and P. Sivakumar, Finite Element Analysis of High Contact Ratio Gear, AGMA Technical Paper, ISBN: 978-1-55589-981-3, October 2010. Fig 18: Equivalent Von-Mises stress for fourth gear 354.63MPa The maximum stresses induced in each gear ratio i.e. each gear of the gear box is as given in the table. TABLE V EQUIVALENT VON-MISES STRESS AND FACTOR OF SAFETY FOR EACH GEAR IN THE GEAR B OX Gear Number First Gear Second Gear Third Gear Fourth Gear Equivalent VonMises Stress (MPa) 670.17 251 829.6 354.62 Factor Of Safety 1.8652 4.9801 1.5067 3.5249 In this study, a three dimensional deformable-body of spur gear was developed in Pro-E modelling and analysed in Ansys Workbench 12.1 software.From the results obtained, following results can be drawn: 1) It is easy and more accurate to design the complicated involute profiles by using relational equation modelling in Pro Engineer. 2) The laod can be applied in terms of torque or moment instead of line loads on a single tooth of the gear. 3) From the results of Von-Mises stress induced in each gear of the gear box, it can be observed that the maximum strress is below the yield stress of the material which is 1250 MPa. ISSN: 2231-5381 http://www.ijettjournal.org Page 325