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Design of Spur Gears

Design of Spur Gears Using Profile Modification 741 TABLE 2—RATIO T1C T 1B AND T 2C T 2 D AT s MAX POINT FOR 20 AND 25 PRESSURE ANGLES For f D 20 For f D 25 Altered tooth-sum X 1 T 1 C/T 1 B X 1 T 2 C/T 2 D X 1 T 1 C/T 1 B X 1 T 2 C/T 2 D Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015 96 1.6 1.014 0.3 0.984 1.6 1.012 0.4 0.988 1.7 0.996 0.4 1.001 1.7 0.998 0.5 1.002 97 1.2 1.019 0.2 0.991 1.3 1.011 0.3 0.994 1.3 0.999 0.3 1.01 1.4 0.996 0.4 1.01 98 0.8 1.013 0.1 0.998 0.9 1.011 0 0.998 0.9 0.992 0.2 1.02 1 0.995 0.1 1.004 99 0.5 1.006 0 0.984 0.7 1 ¡0.1 0.995 0.6 0.985 0 1.008 0.8 0.983 0 1.012 100 0.1 1.015 ¡0.2 0.989 0.3 1.005 ¡0.4 0.987 0.2 0.989 ¡0.1 1.015 0.4 0.987 ¡0.3 1.005 101 ¡0.2 1.027 ¡0.3 0.998 0 1.018 ¡0.5 0.994 ¡0.1 0.996 ¡0.2 1.03 0.1 0.998 ¡0.4 1.015 102 ¡0.4 1.028 ¡0.5 0.998 ¡0.3 1.015 ¡0.8 0.982 ¡0.3 0.999 ¡0.4 1.036 ¡0.2 0.993 ¡0.7 1.004 103 ¡0.5 1.031 ¡0.9 0.966 ¡0.5 1.015 ¡0.9 0.999 ¡0.4 0.985 ¡0.8 1.009 ¡0.4 0.991 ¡0.8 1.015 104 ¡0.4 1.019 ¡1.4 0.993 ¡0.8 1.025 ¡1.1 0.997 ¡0.3 0.961 ¡1.3 1.005 ¡0.7 0.996 ¡1 1.025 C is 191.02 MPa for profile shift X 1 D 0.3 and lies in between point B and point D. However, the magnitude of s max was lower in the 25 pressure angle compared to the 20 pressure angle. For f D 20 , X 1 D¡0.4, and tooth-sum of 104 teeth, it has been noted that the s max at point C is 150.21 MPa. In this case, the length of T 1 C is smaller compared to T 1 B (10.60 mm < 13.32 mm). Point C is in between point A and point B and falls in a two-pair mesh. In this case, the contact stress is lower because the contact ratio is 2.01 (two pairs of teeth are lifting the load). However, for the same tooth-sum the s max is high for a TABLE 3—MAGNITUDE AND POINT OF s MAX FOR ALTERED TOOTH-SUM GEARING Altered s max at Tooth-sum X 1 B 1 (Mpa) For f D 20 s max at B 2 (Mpa) 25 pressure angle compared to a 20 pressure angle. This is due to fact that the pitch point C lies in between point B and point D and falls in a single-pair mesh with a contact ratio of 1.68. From Table 3 it is observed that the value of contact stress at point B 1 and point B 2 increases up to a tooth-sum of 102 for a 20 pressure angle as the tooth-sum increases. Further, the observed increased tooth-sum (103 and 104) decreased the magnitude of the contact stress. This is due to the reduction in length of T 1 C.Fora25 pressure angle it is seen that the value of contact stress at point B 1 and point B 2 continuously increases from s max at s max at C (Mpa) X 1 B 1 (Mpa) For f D 25 s max at B 2 (Mpa) s max at C (Mpa) 96 1.6 133.81 189.24 189.48 1.6 127.46 180.25 180.52 B 1.7 133.81 189.24 133.98 1.7 127.67 180.55 127.64 C 97 1.2 136.44 192.65 193.25 1.3 129.23 182.62 182.83 B 1.3 136.44 192.65 136.65 1.4 129.35 182.93 129.3 C 98 0.8 139.39 197.13 197.32 0.9 130.74 184.84 185.06 B 0.9 139.39 197.13 139.52 1 130.91 185.14 130.85 C 99 0.5 143.14 202.43 202.52 0.7 132.94 188.01 188.01 B 0.6 143.14 202.43 143.2 0.8 133.19 188.36 132.94 C 100 0.1 147.34 208.37 208.53 0.3 135 190.93 191.02 B 0.2 147.34 208.37 147.45 0.4 135.24 191.26 135.07 C 101 ¡0.2 152.81 216.1 216.31 0 137.69 194.63 194.89 B ¡0.1 152.81 216.1 152.96 0.1 137.83 194.12 137.81 C 102 ¡0.4 159.78 225.96 159.9 ¡0.3 140.65 198.91 199.11 B ¡0.3 159.78 225.96 226.36 ¡0.2 140.86 199.21 140.79 C 103 ¡0.5 138.33 169.42 138.4 ¡0.5 144.44 204.27 204.46 B ¡0.4 138.33 169.42 169.65 ¡0.4 144.66 204.58 144.57 C 104 ¡0.4 149.91 183.61 150.21 ¡0.8 148.81 210.46 210.68 B ¡0.3 149.91 183.61 183.97 ¡0.7 149 210.72 148.97 C Point of s max

Downloaded by [Manipal University], [sachidananda H K] at 21:24 26 May 2015 742 H. K. SACHIDANANDA ET AL. Fig. 4—Gear tooth surface morphology: (a) 96 tooth-sum (point B), (b) 96 tooth-sum (point D), (c) 100 tooth-sum (point B), (d) 100 tooth-sum (point D), (e) 104 tooth-sum (point B), and (f) 104 tooth-sum (point D). 96 teeth to 104 teeth due to a continuous decrease in the radius of curvature from negative alteration to positive alteration in tooth-sum. The s max for negative alteration in tooth-sum is lower compared to standard tooth-sum for both 20 and 25 pressure angles. Similarly, for a tooth-sum of 103 the contact stress induced is lower compared to a standard tooth-sum for f D 20 even though the length of T 1 T 2 is smaller compared to a standard tooth-sum. This is due to a negative profile shift for both pinion and gear compared to a positive shift in standard gearing. The s max for negative alteration in tooth-sum is lower compared to a standard tooth-sum. This is due to the longer length of T 1 T 2 . However, the magnitudes of contact stresses were higher for positive alteration in tooth-sum compared to a standard tooth-sum. From Table 3 it is seen that negative alteration in tooth-sum performed better compared to a standard tooth-sum from a contact stress point of view and the stresses are much

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