AUTOMATED DESIGNS OF SHIFTED SPIRAL BEVEL GEARS WITH PARAMETERIZED THREE DIMENSIONAL MODELS

HỘI NGHỊ KHCN TỒN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM AUTOMATED DESIGNS OF SHIFTED SPIRAL BEVEL GEARS WITH PARAMETERIZED THREE DIMENSIONAL MODELS Duc Phuc Truong School of Mechanical Engineering, Hanoi University of Science and Technology No Dai Co Viet Road, Hanoi, Vietnam Tel & Fax: +84 3869-2440 Email: phuc.truongduc@hust.edu.vn ABSTRACT: In this research, the author develops parameterized three dimensional (3-D) models for spiral bevel gears with the correct involute curve tooth profiles by using programing tool inside Pro Engineer software package In addition, the geometrical calculation of the spiral bevel gears presented in this paper includes the consideration of shifted coefficient and backlash of the gear teeth Therefore, it is considered to be more general and more sophisticated than that of standard bevel gears In this paper, the authors developed the fully parameterized 3-D models of the spiral bevel gears at both part level and assembly level These spiral bevel gears can be updated automatically if any input parameters of the gears are changed The result shows that parameterized 3-D models of different types of spiral bevel gears (such as skew bevel gear, Zerol bevel gear, spiral bevel gears, and straigh bevel gears) with correct involute curve tooth profile are generated at both part level model and assembly level model by using the method proposed in this paper The result demonstrates possibilities of developing a bevel gears design tool for 3-D CAD softwares Keywords: shifted spiral bevel gears, parameterized design, CAD/CAM, 3D model designing INTRODUCTION Together with the development of computer aided design (CAD) from two dimension (2-D) CAD to three dimensional (3-D) CAD, the parametric design is more and more developed Especially, the parametric design is developed for many mechanical components which have the common shape or characteristics such as bolt and nuts, cutting tool, bearing, gears, etc The parametric design of the standard mechanical component plays an important role in increasing the design efficiency and the productivity Gears are the most important mechanical components in the mechanical power transimission system The design of gear is generally time consuming Especially, the design of spiral bevel gears with the correct involute curve tooth profile is considered the most complex among the gear types AutoDesk Inventor [1] and Solidworks [2] are the most popular 3-D CAD softwares which include the gear design tool box or gear library However, the gears models provided in these softwares are the approximate models which consist of a lot of interference Trang 84 between the teeth of the mating gears The interference between the teeth is illustrated in the Figure In addition, the tooth profile of the gears in AutoDesk Inventor and Solidworks is arc curve which in not involute curve Therefore, the interference between the teeth of the mating gears can not be avoided Figure Interference between teeth of mating gears Figure gives the explaination for the difficulty of using the involute curves for the tooth profiles Usually, for a gear utilizing an involute HỘI NGHỊ KHCN TỒN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM tooth profile, the involute curve is always drawn from the base circle (i.e point B) to the addendum circle (i.e point A) On the other hand, the tooth profile is always drawn from the dedendum circle (i.e point D) to the addendum circle (i.e point A) Figure (a) shows the case that the base circle is smaller than the dedendum circle, the tooth profile (i.e curve DA) is shorter than the involute curve (i.e curve BA) Therefore, the whole tooth profile is (a) Base circle is smaller than dedendum circle (b) Base circle is larger than dedendum circle Figure Tooth profile for different cases of gear calculated from the involute curve geometry However, figure 2(b) shows the another case when gear has the base circle is larger than the dedendum circle In this case, the tooth profile consists of an two curves: (1) involute curve (i.e curve AB) and (2) a straight line (i.e line BD) It is difficult to create a general gear model with correct involute tooth profile to satisfy these two cases Therefore, the CAD software such as AutoDesk Inventor and Solidworks usually use an arc curve as an approximate curve for the tooth profile of a gear To address this problem, the author introduced a break point to split the involute curve into two curves during the programing [3] which provide the correct involute curve tooth profile for the gears Recently, Camnetisc Inc introduces the Gear Trax software [4] which provide 3-D gear models with correct involute curve tooth profiles This software utilizes the geometrical calculations of gears, and then creates workpiece and the tooth profile of the calculated gear and export to Solidworks software or Autodesk Inventor software Then, the users have to create the gear model by themselves in those softwares The disadvantage of the Gear Trax software is that the gear models exported to Solidworks or Autodesk Inventor are the “dead models” which not have “online” relations with input parameters; this means that the exported 3-D gear models can not be updated if any input parameters of the gears is changed This is inconvenient if the designer would like to modify some parameters of the gears In order to address these above disadvantages, a proper solution of parametric design of 3-D models for shifted bevel gears with correct involute curve tooth profile will be presented in this study Shifted bevel gears are more general than standard gears Therefore, the geometrical calculation of shifted bevel gears is much more complex than that of the standard one Moreover, the author also includes the calculation of backlash of the gear teeth in the geometrical calculation The objective of this paper is to develop fully parameterized 3-D models for shifted spiral bevel gears with correct involute curve tooth profile These spiral bevel gears are general case for straight bevel gears, skew bevel gears and Zerol bevel gears Therefore, we can change the input parameters of the spiral bevel gears in order to obtain the above bevel gear types In addition, these bevel gear models are fully parameterized models which automatically changed their shapes accordingly with the input parameters METHODOLOGY Figure shows the process to create the parameterized 3-D bevel gear models in this study It can be devided into two main steps: (1) geometrical calculation of the spiral bevel gears and (2) create the parametric 3-D models of spiral bevel gears in the Pro/Engineer software The results of parameterized 3-D spiral bevel gear models can be generated at both part level and assembly level In addition, a report file of the spiral bevel gears is also generated in the form of Microsoft Excel file Trang 85 HỘI NGHỊ KHCN TOÀN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM Figure Process to create the parameterized 3-D models for spiral bevel gears The input parameters of the spiral bevel gears are the major parameters for calculating the geometry of the bevel gears They include the following parameters: (1) (2) (3) (4) (5) (6) (7) Shaft angle:  Module: m Normal pressure angle: n Central spiral angle: m Number of teeth: z1, z2 Shifted coefficients: x1 = - x2 = x Normal backlash: cn d 02  z2 m The pitch cone angle (2.3) 0 is determined as follow:     sin  1    01  tan  z2   z  cos  sin  01    and  02    01 The calculations of the major parameters of the bevel gears by applying the gears theory [5-9] are summarized as follows: Cone distance Ra is determined as: Radial pressure angle s is determined by the following formula: Ra   tan  n   cos  m    s  tan 1  (2.1) Trang 86 d 01 d 02  sin  01 sin  02 (2.5) (2.6) Flank width b is equal to one-third of cone distance Ra The pitch diameter d0 is determined as follow: d01  z1m (2.4) (2.2) b Ra (2.7) HỘI NGHỊ KHCN TỒN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM Addendum is determined as follows: ha1  (1  x2 )m (2.8)  (1  x1 )m (2.9) Dedendum hd is determined as follows: hd1  (1.25  x1 )m (2.10) hd  (1.25  x2 )m (2.11) Addendum angle a is determined as follows: ) Ra  a  tan 1 ( (2.12) zv1  z1 cos  01 (2.20) zv  z2 cos  02 (2.21) The same as straight bevel gears, module of spiral bevel is given in in the large end of the teeth (the heel) Therefore, we have to calculate module for each section of spiral bevel gear Figure shows two sections (section A and section Q) of spiral bevel gear Dedendum angle d is determined as follows:  d  tan 1 ( Outer cone angle hd ) Ra a (2.13) is determined as:  a    a Root cone angle r (2.14) is determined as:  r    d (2.15) Outside diameter is determined as: d o  d  2ha cos  (2.16) Mounting distance X is determined as: X  Ra cos   sin  (2.17) Axial flank width Xb is determined as: Xb  b cos  a cos  a (2.18) Inner outside diameter di is determined as: 2b sin  a di   cos  a Figure For calculation of equivalent spur gears Section A is coincided with large end of the teeth Hence, we have the following relations: mA  m (2.22) d0 A  d0 (2.23) d 0vA  d0 cos  (2.24) haA  (2.25) hdA  hd (2.26) (2.19) Section Q is displaced from section A a distance Calculation of teeth number of equivalent spur q From Figure 4, we have pitch diameter at gear The virtual number of teeth is equal to the section Q as follow: actual number of teeth divided by the cosine of the pitch cone angle: d 0Q  d A  2q sin  (2.27) Module of spiral bevel gear at section Q is determined as: Trang 87 HỘI NGHỊ KHCN TỒN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM mQ  d 0Q z Apply for section C (with q = b) we the pitch (2.28) Apply for section B (with q = b/2) we the pitch diameter and module in section B as follows: d B  d A  b sin  (2.29) diameter and module in section C as follows: d 0C  d A  2b sin  mC  d 0C z (2.31) (2.32) Figure shows the process to create d mB  B z (2.30) parameterized 3-D models of spiral bevel gears in Pro Engineer software This process mainly comprises steps: (1) create the parameters for the sprial bevel gears pair, (2) create the 3-D spiral bevel gear model and programing the gear parameters at part level; (3) create the 3-D spiral bevel gear model and programing the gear pair at assembly level; (4) create the report file of gear parameters and export to Excel software Figure The process to create parametric 3-D models of spiral bevel gear in Pro Engineer software Table shows some of paramters of the spiral programming geometrical parameters of spiral bevel gears defined inside Pro/Engineer software, bevel gears inside Pro/ Engineer software and Table shows a part of program for Trang 88 HỘI NGHỊ KHCN TOÀN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM Table Parameters for spiral bevel gears No Name Symbol Value Description Note SHAFT_ANGLE  90 Shaft Angle MODULE m Module of the gears PRESSURE_ANGLE 0 20 Standard Pressure Angle SPIRAL_ANGLE m Major input 35 parameters to Spiral Angle calculate z1 TEETH_NUMBER_1 spiral bevel 16 Teeth Number gear geometry TEETH_NUMBER_2 z2 24 DIS_MOD_COE x 0.2 Profile Shifted Coefficient BACKLASH_N cnn 0.1 Normal Backlash PITCH_DIA_1 d01 30 10 PITCH_DIA_2 d02 11 PIT_CONE_ANGLE_1  01 Standard Pitch Diameter Some geometrical Pitch Cone Angle 12 PIT_CONE_ANGLE_2  02 13 CONE_DISTANCE Ra Cone Distance 14 FLANK_WIDTH b Flank Width … … … parameters of spiral bevel gears … … … Table A part of program of the geometrical parameters of spiral bevel gears inside Pro/Engineer software ………… ……… RADIAL_PRESSURE_ANGLE=ATAN(TAN(PRESSURE_ANGLE)/COS(SPI Calculate radial pressure angle RAL_ANGLE)) as in Eq (2.1) PITCH_DIA_1=TEETH_NUMBER_1*MODULE Calculate pitch diameter as in PITCH_DIA_2=TEETH_NUMBER_2*MODULE Eq (2.2) & (2.3) PIT_CONE_ANGLE_1=ATAN((SIN(SHAFT_ANGLE))/(TEETH_NUMBER_2/ TEETH_NUMBER_1+COS(SHAFT_ANGLE))) Calculate pitch cone angle as in Eq (2.4) & (2.5) PIT_CONE_ANGLE_2=SHAFT_ANGLE-PIT_CONE_ANGLE_1 CONE_DISTANCE=PITCH_DIA_2/(2*SIN(PIT_CONE_ANGLE_2)) Calculate FLANK_WIDTH=1/3*CONE_DISTANCE flank width as in Eq (2.6) & (2.7) cone distance and Trang 89 HỘI NGHỊ KHCN TỒN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM ADDENDUM_GEAR_1=(1-DIS_MOD_COE_2)*MODULE Calculate addendum, dedendum, ADDENDUM_GEAR_2=(1-DIS_MOD_COE_1)*MODULE and whole depth of the teeth as DEDENDUM_GEAR_1=(1.25-DIS_MOD_COE_1)*MODULE in Eq (2.8) to Eq (2.11) DEDENDUM_GEAR_2=(1.25-DIS_MOD_COE_2)*MODULE ………… ……… Set 3: RESULTS AND DISCUSSIONS Figure shows the 3-D models different types of spiral bevel gear In these gears, the tooth profile is correct involute curve, and the gears are fully parameterized Therefore, the gears are automatically updated their shape if any parameters of the gear is changed To demonstrate the this posibility, we create different type of bevel gears by only changing the input the parameters Set 1:  = 90, m = 3, 0 = 20, 0 = 35, z1 = 20, z2 = 30, x1 = - x2 = 0, cn = Set 2:  = 120, m = 3, 0 = 20, 0 = 35, z1 = 20, z2 = 30, x1 = - x2 = 0.2, cn = 0.1 Set 4: Set 5: Set 6:  = 90, m = 3, 0 = 20, 0 = 45, z1 = 30, z2 = 20, x1 = - x2 = -0.1, cn = 0.1 (Note that the side of spiral is changed for each gear)  = 90, m = 3, 0 = 20, 0 = 0, z1 = 16, z2 = 30, x1 = - x2 = 0.2, cn = 0.1 (Note that the gears pair is changed to Zerol bevel gears)  = 90, m = 6, 0 = 20, 0 = 35, z1 = 20, z2 = 30, x1 = - x2 = 0.2, cn = 0.1 (Note that the gears pair is changed to skew bevel gears)  = 90, m = 6, 0 = 20, 0 = 0, z1 = 20, z2 = 30, x1 = - x2 = 0.2, cn = (Note that the gears pair is changed to straight bevel gears) Set 1: Spiral bevel gears  = 90, 0 = 35 Set 2: Spiral bevel gears  = 120, 0 = 35 Set 3: Spiral bevel gears  = 90, 0 = 45 Set 4: Zerol bevel gears  = 90, 0 = 0 Trang 90 HỘI NGHỊ KHCN TỒN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM Set 5: Skew bevel gears  = 90, 0 = 35 Set 6: Straight bevel gears  = 90, 0 = 0 Figure Spiral bevel gear sets with different parameters CONCLUSION In this paper, the author develops fully parameterized 3-D models for different spiral bevel gears such as spiral bevel gears, straight bevel gears, skew bevel gears and Zerol bevel gears The tooth profile of the gear is correct involute curve In addition, the geometrical calculation of the spiral bevel gears also include the shifted coefficient and backlash which provides a general model for the spiral bevel gears The results of the parameterized 3-D bevel gear models are developed at both 3-D part level models and 3-D assembly level models which can be automatically updated if any parameter of the gear is changed This results demonstrate possibilities for further development of tool boxes for designing of bevel gears and also other gear types inside the 3-D CAD softwares REFERENCES [1] http://www.autodesk.com/products/inventor/o verview [2] http://www.solidworks.com/ [6] L Y Wang, “Elements of Gear Technology”, First Edition 1993, Editional Cooperater: Kohara Gear Industry Co.Ltd Japan [3] Truong Duc Phuc, “Parametric Design of 3-D Models for Shifted Spur Gears”, Proceeding of National Conference On Mechanical & Transportation Engineering, Vol.3, ISBN: 978-604-95-0041-1, Page 491-496 [7] G.M Maitra, “Handbook of Gear Design”, Tata McGraw-Hill Publishing Co.Ltd 1988 [4] http://camnetics.com/geartrax/ [9] Bevel Gears” Transactions of the ASME 174/ Vol 113, June 1991 [5] Faydor L Litvin, Alfonso Fuentes, “Geometry and Applied Theory”, Second Edition 2004, Cambridge University Press [8] Dennis P Townsend, “Dudley’s Gear Handbook”, Second Edition 1962, McGrawHill Inc Trang 91 HỘI NGHỊ KHCN TOÀN QUỐC VỀ CƠ KHÍ - ĐỘNG LỰC NĂM 2017 Ngày 14 tháng 10 năm 2017 Trường ĐH Bách Khoa – ĐHQG TP HCM TỰ ĐỘNG HÓA THIẾT KẾ BỘ TRUYỀN BÁNH RĂNG CƠN XOẮN DỊCH CHỈNH BẰNG MƠ HÌNH THAM SỐ CHIỀU TÓM TẮT Trong nghiên cứu này, tác giả xây dựng mơ hình tham số chiều truyền bánh côn xoắn với biên dạng thân khai chuẩn áp dụng công cụ lập trình phần mềm Pro Engineer Hơn nữa, việc tính tốn thơng số hình học truyền bánh xoắn có tính đến hệ số dịch chỉnh khe hở cạnh nên coi tổng quát phức tạp so với tính tốn truyền bánh xoắn tiêu chuẩn Trong báo này, tác giả phát triển mô hình tham số chiều truyền bánh côn xoắn cấp độ chi tiết bánh vẽ lắp truyền bánh Các mơ hình tham số chiều tự động thay đổi theo tham số đầu vào truyền bánh Dựa vào phương pháp đề báo, tác giả phát triển mô hình tham số chiều cho nhiều truyền bánh côn xoắn dịch chỉnh bánh côn xoắn, bánh côn nghiêng, bánh côn cong góc nghiêng khơng, bánh răng thẳng với biên rạng thân khai chuẩn Kết báo áp dụng để phát triển thành phần mềm thiết kế bánh tự động cho phần mềm thiết kế chiều Từ khóa: bánh xoắn dịch chỉnh, thiết kế tham số hóa, CAD/CAM, thiết kế mơ hình chiều Trang 92 ... fully parameterized 3-D models for different spiral bevel gears such as spiral bevel gears, straight bevel gears, skew bevel gears and Zerol bevel gears The tooth profile of the gear is correct... objective of this paper is to develop fully parameterized 3-D models for shifted spiral bevel gears with correct involute curve tooth profile These spiral bevel gears are general case for straight bevel. .. solution of parametric design of 3-D models for shifted bevel gears with correct involute curve tooth profile will be presented in this study Shifted bevel gears are more general than standard gears