Methodology for Designing a Gearbox and its Analysis

Methodology for Designing a Gearbox and its Analysis

Neeraj Patel, Tarun Gupta

B.Tech,

Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, India.

AbstractRobust and Axiomatic design, a property based approach in design, is applied and integrated into a new methodology for developing Functional Requirements (FR) or Design Parameters (DP).The reliability of the design structure and design components are used as a functional requirements of the gearbox, in relation to the service and driving conditions, and also as a design constraints in analytical relationships. The different operating conditions of gearbox are used as case study in this paper. The same design structures have to operate under different operating conditions. In these circumstances, the carrying capacity as a functional requirement is related to driving conditions [5]. This paper unveils the more sophisticated methodology of the gearbox designing using the modern designing softwares.

KeywordsKISSsoft, Load spectrum, Gears, Shafts, Bearings

INTRODUCTION

Gears and gear drives have been known and used for millennia as critical components of mechanisms and machines. Over the last several decades the development of gearing has mostly focused in the following fields: the improving of material, manufacturing technology and tooling, thermal treatment, tooth surface engineering and coatings, tribology and lubricants, testing technology and diagnostics [4]. Gear design is a highly complicated art. The constant pressure to build less expensive, quieter running, lighter, and more powerful machinery has resulted in a steady change in gear designs [3]. At present much is known about gear load-carrying capacity, and many complicated processes for making gears are available. Gear design also included material selection, which should provide the required strength and durability of every component in the gear drive. The vast majority of gears are designed with the standard 20 pressure angle tooth proportions [4]. In this paper, two stage reduction helical gearbox has been designed. The gears and shaft design calculations are done with the help of KISSsoft. KISSsoft is a program for machine design calculations. KISSsoft have been incorporated with various calculation methods for the gear and shaft design separately. Here AGMA 2101-D04 (Metric Edition) has been selected as the calculation method. When the gear design completes, the next stage of gear drive development is fabrication of parts and assembly; this stage included technological process selection and tool design [4].

I. DESIGN PROCESS:

1. MATERIAL SELECTION

   The first step in the gearbox design process is to select the material. A material is to be selected by doing intensive research on the properties of the various materials. A material is to be selected keeping in mind the various parameters like strength, weight, durability, cost and other parameters. KISSsoft provide the user, list of the various materials which can be selected for the designing of gears.

   TABLE.I MATERIAL SPECIFICATION

   PROPERTIES	VALUE
   Surface hardness	HRC 61
   Allowable bending stress number (N/mm2 )	430
   Allowable contact stress number (N/mm2 )	1500
   Tensile strength (N/mm2 )	1200
   Yield point (N/mm2 )	850
   Youngs modulus (N/mm2 )	206000
   Poissons ratio	0.3

   Also there is a provision for the user to enter his own material properties and thus one can define his own material in the program. In this paper for the sake of designing gearbox, case-carburized steel is selected due to its better mechanical properties. Also the material selected for gears and shaft is to be same because of the fact, same material can be manufactured as a single unit.

2. INPUT PARAMETERS

   FOR 1ST REDUCTION

   Fig.1 Gear Pair 1

   TABLE.II INPUT PARAMETERS

   PARAMETERS	GEAR 1	GEAR 2
   Transmitted power (KW)	7.5	7.5
   Speed (1/min)	1278.9	403.9
   Torque(Nm)	56	177.3
   Overload factor	2.0	2.0
   Required service life(h)	2000	2000

   FOR 2ND REDUCTION

   Fig.2 Gear Pair 2 TABLE.III INPUT PARAMETERS

   PARAMETERS	GEAR 1	GEAR 2
   Transmitted power (KW)	7.5	7.5
   Speed (1/min)	400.1	126.4
   Torque(Nm)	179	566.8
   Overload factor	2.0	2.0
   Required service life(h)	2000	2000

   TABLE.IV INPUT SHAFT PARAMETERS

   PARAMETERS	VALUE
   Initial position	0.0
   Length (mm)	142
   Speed (1/min)	1279
   Sense of rotation	Counter clockwise

   Fig.3 Input shaft

   TABLE.V INTERMADIATE SHAFT PARAMETERS

   Fig.4 Intermediate Shaft TABLE.VI OUTPUT SHAFT PARAMETERS

   PARAMETERS	VALUE
   Initial position	0.0
   Length (mm)	183.2
   Speed (1/min)	125
   Sense of rotation	Counter clockwise

   Fig.5 Output Shaft

3. ROUGH SIZING OF GEARS

   PARAMETERS	GEAR 1	GEAR 2
   Centre distance (mm)	89	89
   Centre distance tolerance	ISO 286:2010 Measure js7	ISO 286:2010 Measure js7
   Normal diametral pitch (1/in)	11.28889	11.28889
   Transverse diametral pitch (1/in)	10.60809	10.60809
   Normal module (mm)	2.25	2.25
   Pressure angle ()	20	20
   Helix angle ()	20	20
   Number of teeth	18	57
   Facewidth (mm)	22.49	21.55
   Hand of gear	right	Left
   Accuracy grade	A8	A8
   Inner diameter	0.0	0.0
   Roughness average value, Flank (µm)	0.6	0.6
   Roughness average value, Root (µm)	3.0	3.0
   Mean roughness height, Flank (µm)	4.8	4.8
   Mean roughness height, Rot (µm)	20	20

   PARAMETERS	GEAR 1	GEAR 2
   Centre distance (mm)	89	89
   Centre distance tolerance	ISO 286:2010 Measure js7	ISO 286:2010 Measure js7
   Normal diametral pitch (1/in)	11.28889	11.28889
   Transverse diametral pitch (1/in)	10.60809	10.60809
   Normal module (mm)	2.25	2.25
   Pressure angle ()	20	20
   Helix angle ()	20	20
   Number of teeth	18	57
   Facewidth (mm)	22.49	21.55
   Hand of gear	right	Left
   Accuracy grade	A8	A8
   Inner diameter	0.0	0.0
   Roughness average value, Flank (µm)	0.6	0.6
   Roughness average value, Root (µm)	3.0	3.0
   Mean roughness height, Flank (µm)	4.8	4.8
   Mean roughness height, Root (µm)	20	20

   TABLE.VII 1ST REDUCTION PARAMETERS

   PARAMETERS	VALUE
   Initial position	0.0
   Length (mm)	142.350
   Speed (1/min)	400
   Sense of rotation	Clockwise

   Fig.6 Drawing Gear 1

   Fig.7 Drawing Gear 2

   TABLE.VIII 2ND REDUCTION PARAMETERS

   PARAMETERS	GEAR 3	GEAR 4
   Centre distance(mm)	100	100
   Centre distance tolerance	ISO 286:2010 Measure js7	ISO 286:2010 Measure js7
   Normal diametral pitch(1/in)	10.160	10.160
   Transverse diametral pitch(1/in)	9.54728	9.54728
   Normal module(mm)	2.5	2.5
   Pressure angle()	20	20
   Helix angle()	20	20
   Number of teeth	18	57
   Facewidth(mm)	45.88	44.38
   Hand of gear	Right	left
   Accuracy grade	A8	A8
   Inner diameter	0.0	0.0
   Roughness average value, Flank (µm)	0.6	0.6
   Roughness average value, Root (µm)	3.0	3.0
   Mean roughness height, Flank (µm)	4.8	4.8
   Mean roughness height Root(µm)	20	20

   Fig.8 Drawing Gear 3

   Fig.9 Drawing Gear 4

4. FINE SIZING OF GEARS

   FOR 1ST REDUCTION

   TABLE.IX PROFILE PARAMETERS

   PARAMETERS	GEAR 1	GEAR 2
   Reference profile	1.25 / 0.38 / 1.0 ISO 53.2:1997 Profile A	1.25 / 0.38 / 1.0 ISO 53.2:1997 Profile A
   Dedendum coefficient	1.25	1.25
   Root radius factor	0.380	0.380
   Addendum	1.0	1.0
   Tip radius factor	0.0	0.0
   Protuberance height factor	0.0	0.0
   Protuberance angle	0.0	0.0
   Tip form height coefficient	0.0	0.0
   Ramp angle	0.0	0.0

   Fig.10 Tooth Form Gear 1

   Fig.11 Tooth Form Gear 2

   (mm)
   Diameter of single contact point D (mm)	44.580	133.727
   Addendum contact ratio	0.874	0.657
   Minimal length of contact line (mm)	34.348	34.348
   Transverse contact ratio	1.531	1.531
   Transverse contact ratio with allowances	1.538	1.538
   Overlap ratio	1.043	1.043
   Total contact ratio	2.574	2.574
   Total contact ratio with allowances	2.581	2.581

   PARAMETERS	GEAR 1	GEAR 2
   Overall transmission ratio	-3.167	-3.167
   Gear ratio	3.167	3.167
   Transverse module(mm)	2.394	2.394
   Pressure angle at pitch circle ()	21.173	21.173
   Working transverse pressure angle ()	19.818	19.818
   Working pressure angle at normal section (°)	19.850	19.787
   Helix angle at operating pitch circle (°)	18.727	18.727
   Base helix angle (°)	18.747	18.747
   Reference centre distance (mm)	89.790	89.790
   Sum of profile shift coefficients	-0.3405	-0.3405
   Profile shift coefficient	0.1605	-0.5010
   Tooth thickness (Arc) (module)	1.6876	1.2061
   Tip alteration (mm)	-0.024	-0.024
   Reference diameter (mm)	43.099	136.481
   Base diameter (mm)	40.190	127.268
   Tip diameter (mm)	48.273	138.678
   Tip diameter allowances (mm)	0.0	0.0
   Tip form diameter (mm)	48.273	138.678
   Active tip diameter (mm)	48.273	138.678
   Operating pitch diameter (mm)	42.720	135.280
   Root diameter (mm)	38.196	128.601
   Generating Profile shift coefficient	0.1275	-0.5590
   Manufactured root diameter with xE (mm)	38.048	128.340
   Theoretical tip clearance (mm)	0.563	0.563
   Effective tip clearance (mm)	0.748	0.701
   Active root diameter (mm)	0.533	131.630
   Root form diameter (mm)	40.513	130.893
   Reserve (dNf-dFf)/2 (mm)	0.056	0.511
   Addendum (mm)	2.587	1.099
   Dedendum (mm)	2.451	3.940
   Roll angle at dFa (°)	38.123	24.800
   Roll angle at dNa (°)	38.123	24.800
   Roll angle to dNf (°)	7.684	15.185
   Roll angle at dFf (°)	6.696	13.448
   Tooth height (mm)	5.038	5.038
   Virtual gear no. of teeth	21.362	67.646
   Normal-tooth thickness at tip circle (mm)	1.434	1.807
   Normal-tooth thickness on tip form circle (mm)	1.488	1.900
   Normal space width at root circle (mm)	0.0	2.089
   Max. sliding velocity at tip (m/s)	1.080	0.813
   Specific sliding at the tip	0.378	0.284
   Specific sliding at the root	-0.284	-0.378
   Mean specific sliding	0.644	0.644
   Sliding factor on tip	0.378	0.284
   Sliding factor on root	-0.284	-0.378
   Pitch on reference circle (mm)	7.522	7.522
   Base pitch (mm)	7.014	7.014
   Transverse pitch on contact-path (mm)	7.014	7.014
   Lead height(mm)	372.009	1178.03
   Axial pitch (mm)	20.667	20.667
   Length of path of contact (mm)	10.740	10.740
   Length T1-A, T2-A (mm)	2.631	27.554
   Length T1-B (mm)	6.356	23.818
   Length T1-C (mm)	7.242	22.933
   Length T1-D (mm)	9.645	20.529
   Length T1-E (mm)	13.371	16.804
   Length T1-T2 (mm)	30.174	30.174
   Diameter of single contact point B	42.152	135.891

   PARAMETERS	GEAR 1	GEAR 2
   Overall transmission ratio	-3.167	-3.167
   Gear ratio	3.167	3.167
   Transverse module(mm)	2.394	2.394
   Pressure angle at pitch circle ()	21.173	21.173
   Working transverse pressure angle ()	19.818	19.818
   Working pressure angle at normal section (°)	19.850	19.787
   Helix angle at operating pitch circle (°)	18.727	18.727
   Base helix angle (°)	18.747	18.747
   Reference centre distance (mm)	89.790	89.790
   Sum of profile shift coefficients	-0.3405	-0.3405
   Profile shift coefficient	0.1605	-0.5010
   Tooth thickness (Arc) (module)	1.6876	1.2061
   Tip alteration (mm)	-0.024	-0.024
   Reference diameter (mm)	43.099	136.481
   Base diameter (mm)	40.190	127.268
   Tip diameter (mm)	48.273	138.678
   Tip diameter allowances (mm)	0.0	0.0
   Tip form diameter (mm)	48.273	138.678
   Active tip diameter (mm)	48.273	138.678
   Operating pitch diameter (mm)	42.720	135.280
   Root diameter (mm)	38.196	128.601
   Generating Profile shift coefficient	0.1275	-0.5590
   Manufactured root diameter with xE (mm)	38.048	128.340
   Theoretical tip clearance (mm)	0.563	0.563
   Effective tip clearance (mm)	0.748	0.701
   Active root diameter (mm)	40.533	131.630
   Root form diameter (mm)	40.513	130.893
   Reserve (dNf-dFf)/2 (mm)	0.056	0.511
   Addendum (mm)	2.587	1.099
   Dedendum (mm)	2.451	3.940
   Roll angle at dFa (°)	38.123	24.800
   Roll angle at dNa (°)	38.123	24.800
   Roll angle to dNf (°)	7.684	15.185
   Roll angle at dFf (°)	6.696	13.448
   Tooth height (mm)	5.038	5.038
   Virtual gear no. of teeth	21.362	67.646
   Normal-tooth thickness at tip circle (mm)	1.434	1.807
   Normal-tooth thickness on tip form circle (mm)	1.488	1.900
   Normal space width at root circle (mm)	0.0	2.089
   Max. sliding velocity at tip (m/s)	1.080	0.813
   Specific sliding at the tip	0.378	0.284
   Specific sliding at the root	-0.284	-0.378
   Mean specific sliding	0.644	0.644
   Sliding factor on tip	0.378	0.284
   Sliding factor on root	-0.284	-0.378
   Pitch on reference circle (mm)	7.522	7.522
   Base pitch (mm)	7.014	7.014
   Transverse pitch on contact-path (mm)	7.014	7.014
   Lead height(mm)	372.009	1178.03
   Axial pitch (mm)	20.667	20.667
   Length of path of contact (mm)	10.740	10.740
   Length T1-A, T2-A (mm)	2.631	27.554
   Length T1-B (mm)	6.356	23.818
   Length T1-C (mm)	7.242	22.933
   Length T1-D (mm)	9.645	20.529
   Length T1-E (mm)	13.371	16.804
   Length T1-T2 (mm)	30.174	30.174
   Diameter of single contact point B	42.152	135.891

   (mm)
   Diameter of single contact point D (mm)	44.580	133.727
   Addendum contact ratio	0.874	0.657
   Minimal length of contact line (mm)	34.348	34.348
   Transverse contact ratio	1.531	1.531
   Transverse contact ratio with allowances	1.538	1.538
   Overlap ratio	1.043	1.043
   Total contact ratio	2.574	2.574
   Total contact ratio with allowances	2.581	2.581

   TABLE.X RECTIFIED PARAMETERS

   Fig.12 Meshing of Gear 1 and 2

   FOR 2ND REDUCTION

   TABLE.XI PROFILE PARAMETERS

   PARAMETERS	GEAR 1	GEAR 2
   Reference profile	1.25 / 0.38 / 1.0 ISO 53.2:1997 Profile A	1.25 / 0.38 / 1.0 ISO 53.2:1997 Profile A
   Dedendum coefficient	1.25	1.25
   Root radius factor	0.380	0.380
   Addendum	1.0	1.0
   Tip radius factor	0.0	0.0
   Protuberance height factor	0.0	0.0
   Protuberance angle	0.0	0.0
   Tip form height coefficient	0.0	0.0
   Ramp angle	0.0	0.0

   Active root diameter (mm)	45.279	147.797
   Root form diameter (mm)	45.133	146.723
   Reserve (dNf-dFf)/2 (mm)	0.127	0.698
   Addendum (mm)	3.058	2.174
   Dedendum (mm)	2.565	3.449
   Roll angle at dFa (°)	38.965	26.684
   Roll angle at dNa (°)	38.965	24.684
   Roll angle to dNf (°)	9.765	17.461
   Roll angle at dFf (°)	7.879	15.563
   Tooth height (mm)	5.623	5.623
   Virtual gear no. of teeth	21.362	67.646
   Normal-tooth thickness at tip circle (mm)	1.562	2.019
   Normal-tooth thickness on tip form circle (mm)	1.562	2.019
   Normal space width at root circle (mm)	0.0	2.024
   Max. sliding velocity at tip (m/s)	0.352	0.279
   Specific sliding at the tip	0.378	0.640
   Specific sliding at the root	-1.776	-1.237
   Mean specific sliding	0.591	0.591
   Sliding factor on tip	0.350	0.277
   Sliding factor on root	-0.277	-0.350
   Pitch on reference circle (mm)	8.358	8.358
   Base pitch (mm)	7.794	7.794
   Transverse pitch on contact-path (mm)	7.794	7.794
   Lead height(mm)	413.343	1308.92
   Axial pitch (mm)	22.964	22.964
   Length of path of contact (mm)	11.438	11.438
   Length T1-A, T2-A (mm)	3.746	32.929
   Length T1-B (mm)	7.390	29.285
   Length T1-C (mm)	8.802	27.873
   Length T1-D (mm)	11.540	25.135
   Length T1-E (mm)	15.184	21.491
   Length T1-T2 (mm)	36.675	36.675
   Diameter of single contact point B (mm)	47.038	153.058
   Diameter of single contact point D (mm)	50.267	150.078
   Addendum contact ratio	0.819	0.649
   Minimal length of contact line (mm)	67.913	67.913
   Transverse contact ratio	1.468	1.468
   Transverse contact ratio with allowances	1.474	1.474
   Overlap ratio	1.933	1.933
   Total contact ratio	3.4	3.4
   Total contact ratio with allowances	3.406	3.406

   Active root diameter (mm)	45.279	147.797
   Root form diameter (mm)	45.133	146.723
   Reserve (dNf-dFf)/2 (mm)	0.127	0.698
   Addendum (mm)	3.058	2.174
   Dedendum (mm)	2.565	3.449
   Roll angle at dFa (°)	38.965	26.684
   Roll angle at dNa (°)	38.965	24.684
   Roll angle to dNf (°)	9.765	17.461
   Roll angle at dFf (°)	7.879	15.563
   Tooth height (mm)	5.623	5.623
   Virtual gear no. of teeth	21.362	67.646
   Normal-tooth thickness at tip circle (mm)	1.562	2.019
   Normal-tooth thickness on tip form circle (mm)	1.562	2.019
   Normal space width at root circle (mm)	0.0	2.024
   Max. sliding velocity at tip (m/s)	0.352	0.279
   Specific sliding at the tip	0.378	0.640
   Specific sliding at the root	-1.776	-1.237
   Mean specific sliding	0.591	0.591
   Sliding factor on tip	0.350	0.277
   Sliding factor on root	-0.277	-0.350
   Pitch on reference circle (mm)	8.358	8.358
   Base pitch (mm)	7.794	7.794
   Transverse pitch on contact-path (mm)	7.794	7.794
   Lead height(mm)	413.343	1308.92
   Axial pitch (mm)	22.964	22.964
   Length of path of contact (mm)	11.438	11.438
   Length T1-A, T2-A (mm)	3.746	32.929
   Length T1-B (mm)	7.390	29.285
   Length T1-C (mm)	8.802	27.873
   Length T1-D (mm)	11.540	25.135
   Length T1-E (mm)	15.184	21.491
   Length T1-T2 (mm)	36.675	36.675
   Diameter of single contact point B (mm)	47.038	153.058
   Diameter of single contact point D (mm)	50.267	150.078
   Addendum contact ratio	0.819	0.649
   Minimal length of contact line (mm)	67.913	67.913
   Transverse contact ratio	1.468	1.468
   Transverse contact ratio with allowances	1.474	1.474
   Overlap ratio	1.933	1.933
   Total contact ratio	3.4	3.4
   Total contact ratio with allowances	3.406	3.406

   Fig.13 Tooth Form Gear 3

   PARAMETERS	GEAR 1	GEAR 2
   Overall transmission ratio	-3.167	-3.167
   Gear ratio	3.167	3.167
   Transverse module(mm)	2.660	2.660
   Pressure angle at pitch circle()	21.173	21.173
   Working transverse pressure angle()	21.515	21.515
   Working pressure angle at normal section (°)	20.322	20.322
   Helix angle ()	20.043	20.043
   Base helix angle (°)	18.747	18.747
   Reference centre distance (mm)	99.767	99.767
   Sum of profile shift coefficients	0.2238	-0.1298
   Profile shift coefficient	1.7337	1.4763
   Tooth thickness (Arc) (module)	1.7337	1.4763
   Tip alteration (mm)	-0.002	-0.002
   Reference diameter (mm)	47.888	47.888
   Base diameter (mm)	44.655	141.409
   Tip diameter (mm)	54.003	155.993
   Tip form diameter (mm)	54.003	155.993
   Active tip diameter (mm)	54.003	155.993
   Operating pitch diameter (mm)	48.0	152.0
   Root diameter (mm)	42.757	144.747
   Generating Profile shift coefficient	0.1941	-0.1820
   Manufactured root diameter with xE (mm)	42.609	144.486
   Theoretical tip clearance (mm)	0.625	0.625
   Effective tip clearance (mm)	0.847	0.763

   PARAMETERS	GEAR 1	GEAR 2
   Overall transmission ratio	-3.167	-3.167
   Gear ratio	3.167	3.167
   Transverse module(mm)	2.660	2.660
   Pressure angle at pitch circle()	21.173	21.173
   Working transverse pressure angle()	21.515	21.515
   Working pressure angle at normal section (°)	20.322	20.322
   Helix angle ()	20.043	20.043
   Base helix angle (°)	18.747	18.747
   Reference centre distance (mm)	99.767	99.767
   Sum of profile shift coefficients	0.2238	-0.1298
   Profile shift coefficient	1.7337	1.4763
   Tooth thickness (Arc) (module)	1.7337	1.4763
   Tip alteration (mm)	-0.002	-0.002
   Reference diameter (mm)	47.888	47.888
   Base diameter (mm)	44.655	141.409
   Tip diameter (mm)	54.003	155.993
   Tip form diameter (mm)	54.003	155.993
   Active tip diameter (mm)	54.003	155.993
   Operating pitch diameter (mm)	48.0	152.0
   Root diameter (mm)	42.757	144.747
   Generating Profile shift coefficient	0.1941	-0.1820
   Manufactured root diameter with xE (mm)	42.609	144.486
   Theoretical tip clearance (mm)	0.625	0.625
   Effective tip clearance (mm)	0.847	0.763

   Fig.14 Tooth Form Gear 4 TABLE.XII RECTIFIED PARAMETERS

   Fig.15 Meshing of Gear 3 and 4

5. SHAFT AND BEARING DESIGN

   TABLE.XIII INPUT SHAFT PARAMETERS

   PARAMETERS	CYLINDER 1	CYLINDER 2	CYLINDER 3
   Diameter (mm)	20	25	20
   Length (mm)	40	84	18
   Surface roughness(µm)	8	8	8
   Keyway (mm)	10	18	–

   TABLE.XIV INPUT SHAFT FORCES PARAMETERS

   PARAMETERS	GEAR 1	COUPLING
   Position on shaft (mm)	56.0000	6.0000
   Position in global system (mm)	56.0000	6.0000
   Operating pitch diameter (mm)	43.0990	0.0000
   Helix angle (°)	19.8380	0.0000
   Working pressure angle at normal section (°)	18.7270	0.0000
   Position of contact (°)	0.0000	0.0000
   Length of load application (mm)	22.5000	0.0000
   Power (kW)	driving (Output)	7.5000 driven (Input)
   Torque (Nm)	55.9967	-55.9967
   Axial force (N)	937.469	0.0000
   Shearing force X (N)	-936.48	0.0000
   Shearing force Z (N)	-2598.5	0.0000
   Bending moment X (Nm)	-0.0000	0.0000
   Bending moment Z (Nm)	20.2020	0.0000

   TABLE.XV INPUT SHAFT BEARINGS PARAMETERS

   PARAMETERS	BEARING 1	BEARING 2
   Bearing type	SKF 4204 ATN9 Deep groove ball bearing (double row)	SKF 4204 ATN9 Deep groove ball bearing (double row)
   Bearing position (mm)	31.000	133.000
   Attachment of external ring	Free bearing	Fixed bearing
   Inner diameter (mm)	20.000	20.000
   External diameter (mm)	47.000	47.000
   Width (mm)	18.000	18.000
   Corner radius (mm)	1.000	1.000
   Basic static load rating	12.500	12.500
   Basic dynamic load rating	17.800	17.800
   Fatigue load rating	0.530	0.530
   Basic dynamic load rating (kN)	0.000	0.000
   Basic static load rating (kN)	0.000	0.000

   Fig.16 Load application

   Fig.17 Force diagram

   Fig.18 Torque diagram

   TABLE.XVI INTERMEDIATE SHAFT PARAMETERS

   PARAMETERS	CYLIN DER 1	CYLIN DER 2	CYLIN DER 3	CYLIN DER 4	CYLIN DER 5
   Diameter (mm)	20	35	36	35	30
   Length (mm)	20	26.3	20	55	21
   Surface roughness (µm)	8	8	8	8	8
   Keyway (mm)	–	20	–	42	–

   TABLE.XVII INTERMEDIATE SHAFT FORCES PARAMETERS

   PARAMETERS	GEAR 2	GEAR 3
   Position on shaft (mm)	35.5750	89.35
   Position in global system (mm)	35.5750	89.35
   Operating pitch diameter (mm)	136.5	47.888
   Helix angle (°)	19.8380 right	20.0430 right
   Working pressure angle at normal section (°)	18.7270	20.3320
   Position of contact (°)	0.0000	0.0000
   Length of load application (mm)	21.5500	45.900
   Power (kW)	7.5000 driving (Input)	7.5000 driven (Output)
   Torque (Nm)	179.049	-179.049
   Axial force (N)	-946.460	2728.067
   Shearing force X (N)	945.459	-2949.520
   Shearing force Z (N)	-2623.43	7477.83
   Bending moment X (Nm)	0.0000	-0.0000
   Bending moment Z (Nm)	-64.5959	65.3205

   TABLE.XVIII INTERMEDIATE SHAFT BEARINGS

   PARAMETERS	BEARING 1	BEARING 2
   Bearing type	SKF *22205/20E Spherical roller bearings	SKF *22206E Spherical roller bearings
   Bearing position (mm)	9.000	132.350
   Attachment of external ring	Fixed bearing	Fixed bearing
   Inner diameter (mm)	20.000	30.000
   External diameter (mm)	52.000	62.000
   Width (mm)	18.000	20.000
   Corner radius (mm)	1.000	1.000
   Basic static load rating	44.000	60.000
   Basic dynamic load rating	49.000	64.000
   Fatigue load rating	4.750	6.400
   Basic dynamic load rating (kN)	0.000	0.000
   Basic static load rating (kN)	0.000	0.000

   Fig.19 Load application

   Fig. 20 Force Diagram

   Fig.21 Torque Diagram TABLE.XIX OUTPUT SHAFT PARAMETERS

   PARAMETERS	GEAR 4	COUPLING
   Position on shaft (mm)	125.8	10.0
   Position in global system (mm)	125.8	10.0
   Operating pitch diameter (mm)	151.645	0.0000
   Helix angle (°)	20.0430	0.0000
   Working pressure angle at normal section (°)	20.3220	0.0000
   Position of contact (°)	180.000	0.0000
   Length of load application (mm)	44.4000	0.0000
   Power (kW)	7.5000 driving (Input)	7.5000 driven (Output)
   Torque (Nm)	-572.95	572.95
   Axial force (N)	-2756.8	0.0000
   Shearing force X (N)	2978.98	0.0000
   Shearing force Z (N)	-7556.5	0.0000
   Bending moment X (Nm)	0.0000	0.0000
   Bending moment Z (Nm)	209.026	0.0000

   TABLE.XX OUTPUT SHAFT FORCES PARAMETERS

   PARAMETERS	CYLINDER 1	CYLINDER 2	CYLINDER 3
   Diameter (mm)	45	50	52
   Length (mm)	60	88	35
   Surface roughness (µm)	8	8	8
   Keyway (mm)	–	43	–
   Splines (mm)	44.60	–	–

   PARAMETERS	BEARING 1	BEARING 2
   Bearing type	SKF *22209E Spherical roller bearings	SKF *22211E Spherical roller bearings
   Bearing position (mm)	48.500	170.000
   Attachment of external ring	Fixed bearing	Fixed bearing
   Inner diameter (mm)	45.000	55.000
   External diameter (mm)	85.000	100.00
   Width (mm)	23.000	25.000
   Corner radius (mm)	1.100	1.500
   Basic static load rating	98.000	127.000
   Basic dynamic load rating	102.000	125.000
   Fatigue load rating	10.800	13.700
   Basic dynamic load rating (kN)	0.000	0.000
   Basic static load rating (kN)	0.000	0.000

   PARAMETERS	BEARING 1	BEARING 2
   Bearing type	SKF *22209E Spherical roller bearings	SKF *22211E Spherical roller bearings
   Bearing position (mm)	48.500	170.000
   Attachment of external ring	Fixed bearing	Fixed bearing
   Inner diameter (mm)	45.000	55.000
   External diameter (mm)	85.000	100.00
   Width (mm)	23.000	25.000
   Corner radius (mm)	1.100	1.500
   Basic static load rating	98.000	127.000
   Basic dynamic load rating	102.000	125.000
   Fatigue load rating	10.800	13.700
   Basic dynamic load rating (kN)	0.000	0.000
   Basic static load rating (kN)	0.000	0.000

   TABLE.XXI OUTPUT SHAFT BEARINGS PARAMETERS

   Fig.22 Load application

   Fig.23 Force diagram

   Fig.24 Torque diagram

6. FACTORS OF GENERAL INFLUENCE

   PARAMETERS	GEAR 1	GEAR 2
   Axial force (N)	945.8	945.8
   Radial force (N)	944.8	944.8
   Pitch line velocity (ft/min)	563.13	563.13
   Mesh alignment factor	0.140	0.140
   Mesh alignment correction factor	0.800	0.800
   Lead correction factor	1.000	1.000
   Pinion proportion factor	0.025	0.025
   Face load distribution factor	1.138	1.138
   Load distribution factor	1.138	1.138
   Dynamic factor	1.250	1.250
   Number of load cycles (in mio.)	153.471	48.464
   Rim thickness factor	1.00	1.00
   Size factor	1.00	1.00
   Load angle (°)	30.33	21.45

   PARAMETERS	GEAR 1	GEAR 2
   Axial force (N)	945.8	945.8
   Radial force (N)	944.8	944.8
   Pitch line velocity (ft/min)	563.13	563.13
   Mesh alignment factor	0.140	0.140
   Mesh alignment correction factor	0.800	0.800
   Lead correction factor	1.000	1.000
   Pinion proportion factor	0.025	0.025
   Face load distribution factor	1.138	1.138
   Load distribution factor	1.138	1.138
   Dynamic factor	1.250	1.250
   Number of load cycles (in mio.)	153.471	48.464
   Rim thickness factor	1.00	1.00
   Size factor	1.00	1.00
   Load angle (°)	30.33	21.45

   TABLE.XXII 1ST REDUCTION PARAMETERS

   Height of Lewis parabola(mm)	4.08	3.90
   Tooth thickness at critical section(mm)	4.31	4.29
   Helical factor	1.35	1.35
   Tooth form factor Y	0.512	0.469
   Stress correction factor	1.464	1.482
   Load sharing ratio	0.63	0.63
   Bending strength geometry factor J	0.557	0.505
   Bending stress number(N/mm2 )	259.23	286.26
   Stress cycle factor	0.969	0.989
   Temperature factor	1.000	1.000
   Reliability factor	1.000	1.000
   Required safety factor	1.400	1.400
   Size factor	1.000	1.000
   Load sharing ratio	0.627	0.627
   Geometry factor I	0.217	0.217
   Contact stress number	168021	1158.26
   Service factor for tooth root	3.22	2.97
   Service factor for pitting	2.96	3.12
   Service factor for gear set	2.96	2.96

   Height of Lewis parabola(mm)	4.08	3.90
   Tooth thickness at critical section(mm)	4.31	4.29
   Helical factor	1.35	1.35
   Tooth form factor Y	0.512	0.469
   Stress correction factor	1.464	1.482
   Load sharing ratio	0.63	0.63
   Bending strength geometry factor J	0.557	0.505
   Bending stress number(N/mm2 )	259.23	286.26
   Stress cycle factor	0.969	0.989
   Temperature factor	1.000	1.000
   Reliability factor	1.000	1.000
   Required safety factor	1.400	1.400
   Size factor	1.000	1.000
   Load sharing ratio	0.627	0.627
   Geometry factor I	0.217	0.217
   Contact stress number	168021	1158.26
   Service factor for tooth root	3.22	2.97
   Service factor for pitting	2.96	3.12
   Service factor for gear set	2.96	2.96

   TABLE.XXIII 2ND REDUCTION PARAMETERS

   PARAMETERS	GEAR 3	GEAR 4
   Axial force (N)	2721.0	2721.0
   Radial force (N)	2940.2	2940.2
   Pitch line velocity (ft/min)	197.95	197.95
   Mesh alignment factor	0.154	0.154
   Mesh alignment correction factor	0.800	0.800
   Lead correction factor	1.000	1.000
   Pinion proportion factor	0.077	0.077
   Face load distribution factor	1.200	1.200
   Load distribution factor	1.200	1.200
   Dynamic factor	1.091	1.091
   Number of load cycles (in mio.)	48.013	15.162
   Rim thickness factor	1.00	1.00
   Size factor	1.00	1.00
   Load angle (°)	30.33	21.45
   Height of Lewis parabola (mm)	4.60	4.52
   Tooth thickness at critical section(mm)	4.89	5.12
   Helical factor	1.35	1.35
   Tooth form factor Y	0.527	0.524
   Stress correction factor	1.475	1.525
   Load sharing ratio	0.65	0.65
   Bending strength geometry factor J	0.556	0.526
   Bending stress number(N/mm2 )	302.83	314.68
   Stress cycle factor	0.990	1.010
   Temperature factor	1.000	1.000
   Reliability factor	1.000	1.000
   Required safety factor	1.400	1.400
   Size factor	1.000	1.000
   Load sharing ratio	0.627	0.627
   Geometry factor I	0.217	0.217
   Contact stress number	168021	1158.26
   Service factor for tooth root	2.81	2.76
   Service factor for pitting	2.76	2.90
   Service factor for gear set	2.75	2.90

7. FORMULAE USED

   • Gear Wear Equations

     [1]

     • Gear Bending Equations

     [1]

8. RESULTS AND DISCUSSIONS

   TABLE.XXIV GEAR PARAMETERS

   PARAMETERS	1st Reduction		2nd Reduction
   Bending safety factor	Gear 1	Gear 2	Gear 3	Gear 4
   	1.61	1.49	1.41	1.38
   Pitting safety factor	1.22	1.25	1.17	1.20
   Probability of scuffing	<5%		<5%
   Meshing stiffness (N/mm/µm)	17.145		17.463
   Total weight (kg)	2.871		7.464
   Wear sliding coefficient by Niemann	0.986		0.868
   Gear power loss (kW)	0.113		0.126
   Meshing efficiency (%)	98.489		98.323
   Kinematic viscosity of oil (40C)	220		220
   Kinematic viscosity of oil (100C)	17.5		17.5
   Oil temperature (C)	70		70

   • FOR 1ST REDUCTION

     Fig.25 Hardening depth

     Fig.26 Oil viscosity

     Fig.27 Factor of safety

     Fig.28 Contact temperature

   • FOR 2ND REDUCTION

     Fig.29 Hardening depth

     Fig.30 Oil viscosity

     Fig.31 Factor of safety

     PARAMETER	INPUT SHAFT	INTERMEDIATE SHAFT	OUTPUT SHAFT
     Maximum deflection	0.019	0.028	0.029
     Mass centre of gravity (mm)	73.746	74.941	117.0
     Total axial load (N)	937.47	1781.604	-2756.7
     Torsion under torque()	0.105	-0.045	-0.096
     Minimum factor of safety for endurance	3.49	2.56	3.77
     Minimum factor of safety for yield point	4.92	6.45	3.69
     Eigen frequency (Hz)	4195.66	4116.53	4816.68
     Critical speed (1/min)	251739.33	246991.62	289000.64

     PARAMETER	INPUT SHAFT	INTERMEDIATE SHAFT	OUTPUT SHAFT
     Maximum deflection	0.019	0.028	0.029
     Mass centre of gravity (mm)	73.746	74.941	117.0
     Total axial load (N)	937.47	1781.604	-2756.7
     Torsion under torque()	0.105	-0.045	-0.096
     Minimum factor of safety for endurance	3.49	2.56	3.77
     Minimum factor of safety for yield point	4.92	6.45	3.69
     Eigen frequency (Hz)	4195.66	4116.53	4816.68
     Critical speed (1/min)	251739.33	246991.62	289000.64

     Fig.32 Contact temperature TABLE.XXV SHAFT PARAMETERS

   • FOR INPUT SHAFT

     Fig.33 Bending and torsion angle

     Fig.34 Displacement

     Fig.35 Equivalent stress

     Fig.36 Goodman diagram

     Fig.37 Strength diagram

   • FOR INTERMEDIATE SHAFT

     Fig.38 Bending and torsion angle

     Fig.39 Displacement

     Fig.40 Equivalent stress

     Fig.41 Strength

   • FOR OUTPUT SHAFT

Fig.42 Bending and torsion angle

Fig.43 Displacement

Fig.44 Equivalent stress

Fig.45 Goodman diagram

Fig.48 With Casing

1. GEAR PAIR ANALYSIS

   TABLE.XXVI ANALYSIS PARAMETERS

   PARAMETERS	VALUE
   Equivalent stress	2.5924e-6
   Maximum deformation	1.124e-10
   Minimum factor of safety	4.5

   1. GEARBOX DESIGN

      Fig.46 Strength

      Fig.47 Without Casing

      Fig.49 Equivalent stress

      Fig.50 Total deformation

2. TOOLS USED

SOLIDWORKS- It is used to create a complete 3D digital model of the component. The model consists of 2D and 3D solid model data which can also be used downstream in finite element analysis.

ANSYS- It is software which provides finite element analysis (FEA), in this methodology any component under consideration is discredited into small geometric shapes and the material properties are analyzed over these small elements.

KISSsoft- It is used for the design calculations involved in the designing of the various mechanical parts. KISSsoft have been incorporated with various calculation methods for the gear and shaft design separately.

1. CONCLUSION

This paper unveils the more sophisticated methodology of the gearbox designing using the modern designing softwares. By defining the load spectrum in the program more realistic driving conditions have been entered as an input to the software. And as a result designer can achieve more accurate results of strength, equivalent stress, deformation, safety factors and other such parameters .

REFERENCES

1. BudynasNisbett: Shigleys Mechanical Engineering Design,

   Eighth Edition, 2008; Pg. 746-47

2. Gitin M. Maitra: Handbook of gear design, 1994 Stephen P. Radzevich; Dudleys Handbook of Practical Gear Design and Manufacture, Second Edition, 2012

3. Kapelevich, A. and McNamara, T., "Direct Gear Design® for Automotive Applications, 2013

4. Milosav Ognjanovic1 Miroslav Milutinovic2, Design for Reliability Based Methodology For Automotive Gearbox Load Capacity Identification, 2012