External Spur Gear Nomenclature Quiz
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Questions and Answers

What is the formula for the addendum in standard gear tooth proportions using 200 Full Depth?

  • 0.8/Pd
  • 1.5708/Pd
  • 1/Pd (correct)
  • 1.157/Pd

    • Which law governs the shape of teeth on gears?

  • The tangent law for curves
  • The common normal law of teeth contact (correct)
  • The stress law of materials
  • The law of pitch contact

    • What is the total depth formula for 200 Stub gears?

  • 1.8/Pd (correct)
  • 2.25/P2
  • 2.157/Pd
  • 2/Pd

    • In the gear tooth nomenclature, what does 'Pd' represent?

    <p>Pitch Diameter</p> Signup and view all the answers

    What is the clearance formula for 200 Fellows gears?

    <p>0.2/Pd</p> Signup and view all the answers

    What is the primary requirement when drawing lines through the contact points of gear teeth?

    <p>They must be tangent to the curves</p> Signup and view all the answers

    In the context of gear nomenclature, which of these statements is true about tooth thickness?

    <p>It is expressed as 1.5708/Pd</p> Signup and view all the answers

    Which term describes the maximum extent of a gear tooth measured from the pitch circle to the top of the tooth?

    <p>Addendum</p> Signup and view all the answers

    What is the relationship between diametral pitch and pitch diameter?

    <p>Diametral pitch is the number of teeth divided by pitch diameter.</p> Signup and view all the answers

    Which term describes the angle subtended by an arc on the pitch circle?

    <p>Pitch Angle</p> Signup and view all the answers

    What does tooth thickness measure?

    <p>The width of the tooth at the pitch circle.</p> Signup and view all the answers

    What is the formula for calculating backlash?

    <p>b = Ts - Tt</p> Signup and view all the answers

    Which statement is true about circular pitch?

    <p>Circular pitch is the distance along the pitch circle between similar points on adjacent teeth.</p> Signup and view all the answers

    What is the significance of the pitch point?

    <p>It is the point on the pitch circle where two pitch circles tangentially contact.</p> Signup and view all the answers

    How is gear ratio defined?

    <p>The number of teeth in the gear divided by the number of teeth in the pinion.</p> Signup and view all the answers

    What does the face width of a gear indicate?

    <p>The length of the teeth measured in the axial plane.</p> Signup and view all the answers

    What does the Pitch Circle (D) represent in gear nomenclature?

    <p>The diameter of the cylinder if gears are treated like rolling cylinders</p> Signup and view all the answers

    Which of the following accurately defines the Addendum in gear terminology?

    <p>The height of the tooth above the pitch circle</p> Signup and view all the answers

    How is the Dedendum Circle (Dd) calculated?

    <p>Dd = D - 2(a + c)</p> Signup and view all the answers

    What purpose does Clearance (c) serve in gear design?

    <p>It allows the teeth to mesh without interference</p> Signup and view all the answers

    What does the Working Depth (WR) refer to in the context of gear teeth?

    <p>The depth of engagement between two gears</p> Signup and view all the answers

    Which statement about the Base Circle (Db) is true?

    <p>It is the circle from which the involute of a gear is drawn</p> Signup and view all the answers

    What is the Whole Depth (WL) of a gear tooth space?

    <p>Addendum plus Dedendum</p> Signup and view all the answers

    In gear design, what does the formula $d = a + c$ define?

    <p>The relationship between addendum, dedendum, and clearance</p> Signup and view all the answers

    What must the tangent line ST do in relation to the line drawn from point a to point P?

    <p>It must be perpendicular to the line from a to P.</p> Signup and view all the answers

    How should the spacing for the dividers be set when starting to draw the involute?

    <p>At about one-eighth the diameter of the circle.</p> Signup and view all the answers

    What should be done at each point after spacing along the circumference?

    <p>Draw radial lines and then perpendicular lines to these radii.</p> Signup and view all the answers

    What distance should be laid off from point n on the tangent line?

    <p>Twice the distance used for spacing.</p> Signup and view all the answers

    What is the final step in approximating the true involute after finding points on the tangents?

    <p>Draw a smooth curve using a French curve.</p> Signup and view all the answers

    What will each constructed perpendicular line represent?

    <p>A tangent to the circle at a point.</p> Signup and view all the answers

    How far out should points be found when constructing the involute?

    <p>As far out as desired.</p> Signup and view all the answers

    If the dividers are not changed, what should be marked off from point r?

    <p>The distance three times that from point p.</p> Signup and view all the answers

    What is the correct formula to find the center distance between two gears?

    <p>$C = \frac{D_1 + D_2}{2}$</p> Signup and view all the answers

    If a gear has a 40-tooth count and a diametral pitch of 2, what is its pitch diameter?

    <p>20 in</p> Signup and view all the answers

    What is the effective RPM of the 40-tooth gear if the speed of another connected gear is 150 RPM?

    <p>75 RPM</p> Signup and view all the answers

    In a gearset with a 16-tooth pinion driving a 40-tooth gear, what is the circular pitch if the diametral pitch is 2?

    <p>1.57 in</p> Signup and view all the answers

    What is the dedendum of a gear with a diametral pitch of 2?

    <p>1.25 in</p> Signup and view all the answers

    How do you calculate the radius of the base circle of a gear if the pitch diameter is 20 in and the pressure angle is 20°?

    <p>Use $R_B = D_B \times cos(\theta)$</p> Signup and view all the answers

    If two shafts are 15 in on centers and one carries a gear with 40 teeth, what is the corresponding radius of the other gear if its tooth count is 10?

    <p>10 in</p> Signup and view all the answers

    For a gear with 12 teeth and a diametral pitch of 7, what is the diameter of the first gear?

    <p>1.714 in</p> Signup and view all the answers

    Study Notes

    External Spur Gear Nomenclature

    • Pitch Circle (D) is the circle with a radius equal to the distance from the gear axis to the pitch point. It represents the diameter of a cylinder if the gear pair is replaced by rolling cylinders
    • Addendum (a): The height of the tooth above the pitch circle
    • Dedendum (d): The radial distance from the pitch circle to the root circle (bottom of the tooth space). The formula for dedendum is: 𝑑 = 𝑎 + 𝑐
    • Clearance (c): The distance separating the outside diameter of a gear and the root diameter of its mating gear, preventing tooth interference
    • Addendum Circle (Da): The circle that bounds the outer ends of the teeth. The formula is: 𝐷𝑎 = 𝐷 + 2𝑎 (where D is the pitch circle diameter)
    • Dedendum Circle (Dd): The circle coinciding with or tangent to the bottoms of the tooth spaces. Formula: 𝐷𝑑 = 𝐷 − 2𝑑 or 𝐷𝑑 = 𝐷 − 2(𝑎 + 𝑐)
    • Root Diameter: Diameter of the dedendum circle
    • Base Circle (Db): The circle from which the involute of a gear is drawn. Formula: 𝐷𝐵 = 𝐷cos 𝜃 (where 𝜃 is the pressure angle)
    • Working Depth (WR): The depth of engagement of two gears, calculated by summing their addenda. Formula: 𝑊𝑅 = 2𝑎
    • Whole Depth (WL): The total depth of a tooth space, equal to the addendum plus the dedendum. Alternatively, it is equal to working depth plus clearance. Formula: 𝑊𝐿 = 2𝑎 + 𝑐 or 𝑊𝐿 = 𝑎 + 𝑑
    • Diametral Pitch (PD): Ratio of the number of teeth (T) to the pitch diameter (D): 𝑃𝐷 = 𝑇/𝐷
    • Circular Pitch (PC): Distance measured along the pitch circle between corresponding points on adjacent teeth. Formula: 𝑃𝐶 = 𝜋𝐷/𝑇. Important relationship: 𝑃𝐶 𝑥 𝑃𝐷 = 𝜋. Gears in mesh must have the same circular pitch. The term "pitch" typically refers to diametral pitch unless otherwise specified.
    • Pitch Point: Point of tangency between two pitch circles, located on the line of centers
    • Pitch Angle (α): Angle subtended by an arc on the pitch circle equal in length to the circular pitch. Formula: 𝛼° = 360/𝑇
    • Pitch Line: Line passing through the pitch point, perpendicular to the line of centers
    • Tooth Flank: Surface of the tooth between the pitch circle and the root
    • Tooth Face: Surface of the tooth between the pitch circle and the addendum circle
    • Face Width: Length of the teeth in the axial plane
    • Tooth Thickness (Tt): Width of the tooth measured along the pitch circle
    • Tooth Space (Ts): Space between teeth measured along the pitch circle
    • Backlash (b): Excess thickness of the tooth space over the thickness of the mating tooth. Formula: 𝑏 = 𝑇𝑠 − 𝑇𝑡. Relationship: 𝑃𝑐 = 𝑇𝑡 + 𝑇𝑠
    • Chordal Thickness: Tooth width measured along the chord at the pitch point
    • Gear Ratio: Number of teeth on the gear divided by the number of teeth on the pinion
    • Speed Ratio: Angular speed of the driver divided by the angular speed of the driven gear

    Standard Gear Tooth Proportions

    • System: 14 1/2°, Brown and Sharpe, 14 1/2°, Composite, Cycloidal, Full-Depth, 200 Full Depth, 200 Stub, 200 Fellows
    • Addendum: 1/Pd, 1/Pd, 1/Pd, 0.8/Pd, 1/P2
    • Dedendum: 1.157/Pd, 1.157/Pd, 1.157/Pd, 1/Pd, 1.25/P2
    • Clearance: 0.157/Pd, 0.157/Pd, 0.157/Pd, 0.2/Pd, 0.25/P2
    • Working Depth: 2/Pd, 2/Pd, 2/Pd, 1.6/Pd, 2/P2
    • Total Depth: 2.157/Pd, 2.157/Pd, 2.157/Pd, 1.8/Pd, 2.25/P2
    • Outside Diameter: T + 2 / Pd, T + 2 / Pd, T + 2 / Pd, T + 1.6 / Pd, T/P1 + 2/P2
    • Tooth Thickness: 1.5708/Pd, 1.5708/Pd, 1.5708/Pd, 1.5708/Pd, 1.5708/P1
    • Tooth Space: 1.5708/Pd, 1.5708/Pd, 1.5708/Pd, 1.5708/Pd, 1.5708/P1
    • Fillet Radius: 0.209/Pd, 0.209/Pd, 0.236/Pd, 0.3/Pd, 0.25/P1

    Law Governing the Shape of Teeth

    • The shape of gear teeth must follow a fundamental law ensuring smooth operation: The line drawn from the pitch point to the point of contact between teeth must be perpendicular to the tangent line drawn through the point of contact

    The Involute of a Circle

    • The involute is a curve generated by a point on a taut string unwinding from a circle, creating the tooth profile.
    • To draw an involute:
      • Start with a circle and a point on its circumference.
      • Use dividers to mark equal distances along the circle's circumference.
      • Draw radial lines from the center of the circle through each mark.
      • Construct perpendicular lines to these radial lines at each mark.
      • Lay off equal distances from the marked point along the perpendicular lines, increasing the number of spaces for each consecutive perpendicular line.
      • A smooth curve drawn through these points approximates the involute.

    Example 1: Finding the Center Distance between Gears

    • Given: T1 (number of teeth on gear 1) = 12, T2 (number of teeth on gear 2) = 37, PD (diametral pitch) = 7
    • Required: Center distance (C)
    • Solution: 𝐷1 (pitch diameter of gear 1) = 𝑇1/𝑃𝐷 = 12/7 = 1.714 in, 𝐷2 (pitch diameter of gear 2) = 𝑇2/𝑃𝐷 = 37/7 = 5.286 in
    • Final Answer: 𝐶 = (𝐷1 + 𝐷2)/2 = (1.714 + 5.286)/2 = 3.5 in

    Example 2: Finding the Speed of a Gear

    • Given: Center distance (C) = 15 in, T1 (number of teeth of gear 1) = 40, PD (diametral pitch) = 2, N2 (speed of gear 2) = 150 rpm
    • Required: N1 (speed of gear 1)
    • Solution: 𝐷1 (pitch diameter of gear 1) = 𝑇1/𝑃𝐷 = 40/2 = 20 in, 𝐷2 (pitch diameter of gear 2) = 2C - D1 = 2(15) - 20 = 10 in
    • Final Answer: N1 (speed of gear 1) = N2 * 𝐷2/𝐷1 = 150 * 10 / 20 = 75 rpm

    Example 3: Gearset Calculations

    • Given: T1 (number of teeth on pinion) = 16, T2 (number of teeth on gear) = 40, PD (diametral pitch) = 2, addendum = 1/P, dedendum = 1.25/P, pressure angle (𝜃) = 20°
    • Required: Circular pitch (PC), center distance (C), radii of base circles (Db)
    • Solution:
      • PC (Circular Pitch) = π/PD = π/2 = 1.571 in
      • D1 (pitch diameter of pinion) = T1/PD = 16/2 = 8 in
      • D2 (pitch diameter of gear) = T2/PD = 40/2 = 20 in
      • C (center distance) = (D1 + D2)/2 = (8 + 20)/2 = 14 in
      • Db1 (base circle radius of pinion) = D1 * cos 𝜃 = 8 * cos 20° = 7.52 in
      • Db2 (base circle radius of gear) = D2 * cos 𝜃 = 20 * cos 20° = 18.79 in

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    Description

    Test your knowledge on the key terms and formulas related to external spur gears. This quiz covers definitions like pitch circle, addendum, dedendum, and more, essential for understanding gear functionality. Perfect for engineering students and professionals looking to refresh their gear design knowledge.

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