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**Chapter 9 Spur Gear Design**

Pinion Gear

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**Lecture Steps: Quick review, gear geometry (Chapter 8)**

Transmitted loads (overhead) Review bending stress, bending stress number, St, allowable bending stress number, Sat and adjusted allowable bending stress number, S’at. Review contact stress number, Sc, allowable contact stress number, Sac and adjusted allowable contact stress number S’ac. Overview gear design steps. Example(s) gear design!! handout

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**Quick review: Bending Stress No: Required Allowable Bending Stress No:**

Contact Stress No: n in rpm, vt in ft/min Required Allowable Contact Stress No:

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**Steps for Gear Drive Design:**

From design requirements, identify speed of pinion, nP, desired output speed of gear, nG, and power to be transmitted, P. Choose type of material for the gears (steel, cast iron, bronze, etc.) Determine overload factor, Ko, using table 9-5 Calculated Pdes = KoP and calculate a trial value for the diametral pitch, Pd (for steel use Figure 9-27). Note diametral pitch must be a standard size (see Table 8-2). Note, as Pd decreases, tooth size increases thus bringing down St and Sc. But….. As Pd increases, # teeth increases and gear train runs smoother and quiter and the drive gets smaller as well!

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**Steps for Gear Drive Design:**

Specify Np and NG to meet VR requirement. Calculate center distance, D, OD to make sure there aren’t any interference issues. Specify face width using recommended range: 8/Pd < F < 16/Pd. Remember, increasing face width reduces St and Sc but consider alignment factor. Face width is normally less than 2X Dp. Compute transmitted load, Wt, pitch line speed, vt, quality number, Qv, and other factors required for calculating bending stress and contact stress. Calculate St and required Sat. Does material in 2 meet Sat #? No – then select new material or define new geometry (step 4). If yes, continue to 9. Calculate Sc and required Sac. Does material in 2 meet Sac? No – then select new material to meet Sac and Sat or define new geometry (step 4). If yes, continue to 10. Summarize design

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Problem # 9.61 A gear pair is to be a part of the drive for a milling machine requiring 20 hp with the pinion speed at 550 rpm and the gear speed to be between 180 and 190 rpm. Given: Driven = Milling Machine Power = 20 hp Pinion Speed = 550 rpm Output Speed = rpm ≈ 185 rpm Continuous Use = 30,000 hours Find: Compact Gear Design

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**Solution: Design Power:**

Assume: Light Shock Driver and Moderate Shock Driven Ko = 1.75 (Table 9-5, page 389) PDesign = (Ko)(PInput) = (1.75)(20hp) = 35hp

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**Trial Size Pick Sizes Pd = 5 T/in Dp = 4.80 in DG = 14.2 in**

Np = 24 teeth NG = 71 teeth Check physical size!!

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**Center Distance Pitch Line Speed Tangential Load Face Width**

Note: Use Input Power Here as Ko is applied Later! Face Width

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**Assumptions: Design Decisions**

Quality Number, Qv = 6 (Table 9-2, Page 378) Steel Pinion Steel Gear More precision, higher quality number! Cp = (Table 9-9, Page 400) Softer material, more relative deformation, therefore contact area increases and stress decreases

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**Geometry Factors Pinion: JP = .36 Gear: JG = .415**

What is it? Fucntion of stress concentration, tooth geometry, number of teeth, etc. As J decreases, St increases. Don’t really need to calculate Jg really this and KB only difference between pinion and gear. Pinion: JP = .36 Gear: JG = .415 Figure 9-17, Page 387

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**Geometry Factors Cont…**

Page 402 I = .108

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**Load Distribution Factor**

Equation 9-16, Page 390; Equation is solved on next slide Page What is it? Alignment factor, takes into account misalighnment of meshing teeth which impacts load transfer – worst case vibration or loaded like helical tooth.. Note as F/D increases, Cpf increases because further away more difficult to control perpendicularity.

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**Load Distribution Factor Cont…**

Size Factor Page 389 As diametral pitch decreases, tooth size increases and therefore size factor increases. ks = 1.0 since Pd ≥ 5

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**Rim Thickness Factor Page**

Draw FBD of tooth with rim. Really only need to calculate this if not solid. Since M = F*d, where d will increase if flexible ring gear. For this problem, specify a solid gear blank KB = 1.00 KB = for mB = 1.2 or larger

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**Rim Thickness Factor Cont…**

We are assuming a solid gear blank for this problem, but if not then use: Min Rim Thickness = (1.2)(.45 in) = .54 in Min back-up ratio

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**Safety Factor Hardness Ratio Reliability SF = 1.25 (Mid-Range)**

CH =1.00 for early trials until materials have been specified. Then adjust CH if significant differences exist in the hardness of the pinion and the gear. Reliability Page 396 KR = 1.5 (for 1 in 10,000 failures)

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Dynamic Factor Kv Page 393 What is it? Accounts for quality of gear manufacture which leads to tolerance which impact how load is transferred to tooth = impact + Wt = total force. If Qc decreases, tolerance increases and gears will vibrate, not smooth X of torque, aggravated at high pitch line speeds. In other words, Kv increases with increasing pitch line speed and increases as Qv gets worse!

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**Dynamic Factor Cont… Kv**

Qv comes from Figure 9-21 Kv can be calculated like in above equations or taken from Figure 9-21. Equations are more accurate.

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**Design Life Ncp = (60)(L)(n)(q) L = 30,000 hours from Table 9-7**

n = 550 rpm q = 1 contacts Ncp = (60)(30,000 hours)(550 rpm)(1 contact) = 9.9x108 cycles NcG = (60)(30,000 hours)( rpm)(1 contact) = x108 cycles

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Stress Cycle Factors Page 395

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**Stress Cycle Factors Cont…**

Page 403

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**Bending Stress Numbers**

Pinion: Gear:

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**Required Bending Stress Allowable:**

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Contact Stress Number

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**Required Contact Stress Allowable:**

Pinion: Gear:

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**Hardness Numbers BENDING (Grade 1)**

Page 379 Pinion Bending Satp = 34,324.5 psi = HB 270 Gear Bending These stresses are OK SatG = 28,741.9 psi = HB 215 Go to appendix A3 or A4 and spec out material that meets this hardness requirement! Example AISI 1040, Temper at 900 F

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**Hardness Numbers CONTACT (Grade 1)**

Page 380 Pinion Contact Sacp = 261,178 psi Gear Contact These Stresses are WAY too HIGH! Values are off table! SacG = 245,609 psi

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Summary of Problem Contact stresses are too High. Must iterate until stress are low enough until a usable material can be found. NOTE: Contact Stress generally controls. If material cannot be found for bending, contact stress is too high! Iterate! Decrease Pd and increase F Excel is a GREAT tool to use for these Iterations. This problem solved after third iteration using Excel

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**Guidelines for Adjustments in Successive Iterations.**

Decreasing the numerical value of the diametral pitch results in larger teeth and generally lower stresses. Also, the lower value of the pitch usually means a larger face width, which decreases stress and increases surface durability. Increase the diameter of the pinion decreases the transmitted load, generally lowers the stresses and improves surface durability. Increase the face width lowers the stress and improves surface durability but less impact than either the pitch or pitch diameter. Gears with more and smaller teeth tend to run more smoothly and quietly than gears with fewer and larger teeth. Standard values of diametral pitch should be used for ease of manufacture and lower cost (See table 8-2). Use high alloy steels with high surface hardness – results in the most compact system but the cost is higher. Use gears with high quality number, Qv – adds cost but lowers load distribution factor, Km. The number of teeth in the pinion should be as small as possible to make the system compact. But the possibility of interference is greater with fewer teeth. Check Table 8-6 to ensure no interference will occur.

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