Spur Gear: A Comprehensive Guide PDF

SPUR GEAR GEARS The function of a gear is to transmit motion from one rotating shaft to another. Gears are often used to increase or reduce speed or change the direction of motion from one shaft to the other. SPUR GEARS 1. Spur gears are simplest and, hence ,the most common type of...

SPUR GEAR GEARS The function of a gear is to transmit motion from one rotating shaft to another. Gears are often used to increase or reduce speed or change the direction of motion from one shaft to the other. SPUR GEARS 1. Spur gears are simplest and, hence ,the most common type of gear. The teeth of a spur gear are parallel to the axis of rotation. Spur gears are used to transmit motion between parallel shafts, which encompasses most applications. GEAR TERMINOLOGIES PITCH CIRCLES DRIVEN DRIVER  DRIVEN DRIVER DEDENDUM CIRCLE  DRIVEN DRIVER ADDENDUM CIRCLE  PITCH CIRCLES DRIVEN DRIVER ADDENDUM CIRCLE DEDENDUM CIRCLE GEAR TERMINOLOGIES The pitch circle of a gear is Pitch circles the circle that represents the size of the corresponding friction roller that could FOLLOWER replace the gear. DRIVER The pitch point is the point of contact of the two pitch circles. GEAR TERMINOLOGIES The pitch diameter d, of a Pitch circles gear is simply the diameter of the pitch circle. FOLLOWER DRIVER d1 d2 GEAR TERMINOLOGIES The addendum, a, is the radial distance from the pitch circle to the top of a gear tooth. Addendum The dedendum, b, is the Addendum circle radial distance from the pitch circle to the bottom of a gear tooth. Dedendum The whole depth, hT , is the height of a gear tooth Whole depth Dedendum circle and is the sum of the addendum and dedendum. GEAR TERMINOLOGIES Clearance, c, is the amount that the dedendum exceeds the addendum, this is the room between the top of a gear tooth and the bottom of Addendum the mating gear tooth. Addendum circle Working depth. It is the radial distance from the addendum circle to the Dedendum clearance circle. It is equal to the sum of the addendum of Dedendum circle the two meshing gears. Clearance Clearance circle Working depth GEAR TERMINOLOGIES The face width, F, is the length of the gear tooth parallel with the shaft axis. GEAR TERMINOLOGIES Face of tooth. It is the surface of the gear tooth above the pitch surface. Flank of tooth. It is the surface of the gear tooth below the pitch surface. The circular pitch, p, is the distance measured along the pitch circle from a point on one tooth to the corresponding point on the adjacent tooth of the gear. GEAR TERMINOLOGIES The base circle of a gear is the circle from which the curved shape of the gear tooth is constructed. The base diameter, db , is the diameter of the circle from which the gear tooth profile is derived. GEAR TERMINOLOGIES The clearance, c, is the amount that the dedendum exceeds the addendum. This is the room between the top of a gear tooth and the bottom of the mating gear tooth. The backlash, B, is the amount that the width of a tooth space exceeds the thickness of a gear tooth, measured on the pitch circle. GEAR TERMINOLOGIES Top land. It is the surface of the top of the tooth. Fillet radius. It is the radius that connects the root circle to the profile of the tooth. The number of teeth, N, is simply the total number of teeth on the gear. GEAR TERMINOLOGIES Tooth thickness. It is the width of the tooth measured along the pitch circle. Tooth space. It is the width of space between the two adjacent teeth measured along the pitch GEAR TERMINOLOGIES Arc of contact. It is the path traced by a point on the pitch circle from the beginning to the end of engagement of a given pair of teeth. Arc of approach. It is the portion of the path of contact from the beginning of the engagement to the pitch point. Arc of recess. It is the portion of the path of contact from the pitch point to the end of the engagement of a pair of teeth. GEAR TERMINOLOGIES The diametral pitch, Pd , refers to the tooth size and has become a standard for tooth size specifications. Formally, the diametral pitch is the number of teeth per inch of pitch diameter. GEAR TERMINOLOGIES GEAR TERMINOLOGIES Although mating gears can have different diameters and number of teeth, mating gears must have the same diametral pitch. The diametral pitch cannot be measured directly from a gear; yet, it is an extremely common referenced value. American Gear Manufacturer’s Association (AGMA) designated preferred diametral pitches The units of diametral pitch are the reciprocal of inches (in.-1 ); yet it is not customary to specify units when expressing numerical values. GEAR TERMINOLOGIES The module, m, is a commonly referenced gear parameter in the SI unit system. The module is also a relative measure of tooth size. It is defined as the ratio of pitch diameter to the number of teeth in a gear. GEAR TERMINOLOGIES GEAR TERMINOLOGIES The pressure angle, φ, is the angle between a line tangent to both pitch circles of mating gears and a line perpendicular to the surfaces of the teeth at the contact point. The line tangent to the pitch circles is termed the pitch line. GEAR TERMINOLOGIES The line perpendicular to the surfaces of the teeth at the contact point is termed the pressure line or line of contact. Therefore, the pressure angle is measured between the pitch line and the pressure line. GEAR TERMINOLOGIES The pressure angle affects the relative shape of a gear most gears are standardized at 20° and 25°. Gears with 14.5° pressure angles were widely used but are now considered obsolete. Because the pressure angle affects the shape of a tooth, two mating gears must also have the same pressure angle. GEAR TERMINOLOGIES Gears with smaller pressure angles efficiently transfer torque and apply lower radial loads onto the shaft and supporting bearings. However, as the pressure angles are reduced, a greater tendency exists for gear teeth to interfere as they engage. INVOLUTE TOOTH PROFILES The involute of a circle has become standard for most gear applications. An involute shape is constructed by unwinding a taut wire from a base circle with diameter db. The path traced by the end of the wire is termed the involute curve of a circle. A segment of this involute curve is then used to form a gear tooth profile. INVOLUTE TOOTH INOLUTE TOOTH PROFILES PROFILES Pressure angle increases as the distance between the base circle and the pitch circle increases. Any portion of tooth profile inside the base circle is not an involute. It is common to machine this portion as a radial line and a fillet to the dedendum circle. The portion of the tooth inside the base circle is not designed to be contacted by a mating gear tooth. Such contact would result in interference. A 20° full-depth, involute spur gear with 35 teeth has a diametral pitch of 10. Determine the diameter of the pitch circle, the circular pitch, and the base circle. 𝑵 = 𝟑𝟓 ϴ = 𝟐𝟎𝒐 𝑷𝒅 = 𝟏𝟎 𝑵 𝑷𝒅 = 𝒅 𝟑𝟓 𝒅= = 𝟑. 𝟓 𝒊𝒏. 𝟏𝟎 π𝒅 π(𝟑. 𝟓) 𝒑= = = 𝟎. 𝟑𝟏𝟒 𝒊𝒏. 𝑵 𝟑𝟓 𝒅𝒃 = 𝒅𝒄𝒐𝒔ϴ = 𝟑. 𝟓 𝒊𝒏. 𝒄𝒐𝒔 𝟐𝟎 = 𝟑. 𝟐𝟖𝟗 𝒊𝒏. STANDARD GEARS The AGMA is the primary organization that oversees this standardization scheme. Any two involute gears with the same diametral pitch and pressure angle will mate. Therefore, gear teeth have been standardized based on the diametral pitch and pressure angle. Consider the 20°full-depth,involute spur gear, with 35 teeth and a diametral pitch of 10. Determine the diameter of the addendum circle, dedendum circle, and the clearance. 𝑵 = 𝟑𝟓 𝟏 𝟏 𝒂= = = 𝟎. 𝟏𝟎𝟎 𝒊𝒏. 𝑷𝒅 𝟏𝟎 ϴ = 𝟐𝟎𝒐 𝟏. 𝟐𝟓𝟎 𝟏. 𝟐𝟓𝟎 𝑷𝒅 = 𝟏𝟎 𝒃= = = 𝟎. 𝟏𝟐𝟓 𝒊𝒏. 𝑵 𝑷𝒅 𝟏𝟎 𝑷𝒅 = 𝒅 𝟎. 𝟐𝟓𝟎 𝟎. 𝟐𝟓𝟎 𝒄= = = 𝟎. 𝟎𝟐𝟓 𝒊𝒏. 𝟑𝟓 𝑷𝒅 𝟏𝟎 𝒅= = 𝟑. 𝟓 𝒊𝒏. 𝟏𝟎 𝒅𝒂 = 𝒅 + 𝟐𝒂 = 𝟑. 𝟓 + 𝟐 𝟎. 𝟏 = 𝟑. 𝟕 𝒊𝒏. 𝒅𝒅 = 𝒅 − 𝟐𝒃 = 𝟑. 𝟓 − 𝟐 𝟎. 𝟏𝟐𝟓 = 𝟑. 𝟐𝟓 𝒊𝒏. RELATIONSHIPS OF GEARS IN MESH The smaller gear is commonly termed the pinion and the larger is referred to as the bull gear or simply the gear. Recall that in order for two gears to mate, they must have the same diametral pitch and pressure angle. CENTER DISTANCE Center Distance Defined as the center-to-center distance between two mating gears This is also the distance between the shafts that are carrying the gears  Two 5-pitch ,20° full-depth gears are used on a small construction site concrete mixer. The gears transmit power from a small engine to the mixing drum. This machine is shown. The pinion has 15 teeth and the gear has 30 teeth. Determine the center distance. 𝟏𝟓 + 𝟑𝟎 𝒊𝒏. 𝑪= = 𝟒. 𝟓 𝒊𝒏. 𝟐(𝟓) CONTACT RATIO Contact Ratio The contact ratio, mp ,is the average number of teeth that are in contact at any instant. Obviously, the contact ratio must exceed 1 because contact between gears must not be lost. In practice, contact ratios should be greater than 1.2. Robust designs have contact ratios of 1.4 or 1.5. A contact ratio of 1.2 indicates that one pair of teeth is always in contact and a second pair of teeth is in contact 20 percent of the time. Numerically, contact ratio can be expressed as the length of the path of contact divided by the base pitch, pb.  The base pitch, in turn, is defined as the distance between corresponding points of adjacent teeth, measured on the base circle. The length of this contact path, Z, is derived by the intersections of the respective addendum circles and the contact line. Two 5-pitch, 20° full-depth gears are used on a small construction site concrete mixer. The gears transmit power from a small engine to the mixing drum. The pinion has 15 teeth and the gear has 30 teeth. Determine the determine the contact ratio.  Two 5-pitch, 20° full-depth gears are used on a small construction site concrete mixer. The gears transmit power from a small engine to the mixing drum. The pinion has 15 teeth and the gear has 30 teeth. Determine the determine the contact ratio. = 𝟎. 𝟓𝟗 𝒊𝒏. 𝟏𝟓 𝟑𝟎 𝒅𝟏 = = 𝟑 𝒊𝒏. 𝒅𝟐 = = 𝟔 𝒊𝒏. 𝟓 𝟓 π 𝟑 𝒊𝒏 𝒄𝒐𝒔(𝟐𝟎) 𝟏 𝟏 𝒑𝒃 = = 𝟎. 𝟓𝟗 𝒂𝟏 = 𝒂𝟐 = = = 𝟎. 𝟐 𝒊𝒏. 𝟏𝟓 𝑷𝒅 𝟓 𝟑 𝟔 𝒓𝟏 = = 𝟏. 𝟓 𝒊𝒏. 𝒓𝟐 = 𝟐 = 𝟑 𝒊𝒏. 𝟐 𝒁 = 𝟎. 𝟗𝟐𝟓𝟓. 𝒎 = 𝟎. 𝟗𝟐𝟓𝟓 = 𝟏. 𝟓𝟔𝟖𝟔 𝒑 𝟎. 𝟓𝟗 INTERFERENCE Interference commonly occurs when a small gear mates with a much larger one. The largest number of teeth in the gear to ensure no interference is given by The relationship is given as a function of the number of teeth in the mating pinion, along with the pressure angle and addendum size. where k is defined from the addendum relation INTERFERENCE Interference  Two 5-pitch ,20° full-depth gears are used on a small construction site concrete mixer. The gears transmit power from a small engine to the mixing drum. This machine is shown. The pinion has 15 teeth and the gear has 30 teeth. determine whether interference is a concern.  Two 5-pitch ,20° full-depth gears are used on a small construction site concrete mixer. The gears transmit power from a small engine to the mixing drum. This machine is shown. The pinion has 15 teeth and the gear has 30 teeth. determine whether interference is a concern. 𝟑𝟎 < 𝟒𝟓. 𝟒𝟖𝟗 UNDERCUTTING Undercutting Interference can also be avoided by removing the material on the gear tooth between the base circle and dedendum circle. This is the portion of the gear tooth that is not an involute and would interfere with the mating tooth. Undercutting obviously reduces the strength of the gear, thus reducing the power that can be safely transmitted. BACKLASH Backlash Backlash is the amount that the width of a tooth space exceeds the thickness of a gear tooth, measured on the pitch circle. It is the amount that a gear can turn without its mating gear turning. Some backlash is necessary to provide for lubrication on the gear teeth. Gears that run continuously in one direction can actually have considerable backlash. Gears that frequently start/stop or reverse direction should have closely controlled backlash. BACKLASH Backlash General power-transmitting gears have recommended backlash values of For commercially available stock gears, backlash values are considerably higher to allow for greater flexibility in applications. BACKLASH Backlash Backlash values are strongly influenced by any variation in the center distance of the gears. The backlash variation ΔB that will be encountered with a variation in the center distance ΔC can be approximated by the following relationship: Reducing the center distance reduces the backlash, and vice versa. The gears for the concrete mixer with a center distance and diametral pitch of 4.5in and 5. are catalog items with a designed backlash of 0.4/Pd. Specify a center distance that reduces the backlash to an AGMA-recommended value of 0.1/Pd 𝟎. 𝟒 𝟎. 𝟏 Δ𝑩 = − = 𝟎. 𝟎𝟔 𝟓 𝟓 0. 𝟎𝟔 = 𝟐 Δ𝑪 𝒕𝒂𝒏(𝟐𝟎) Δ𝑪 = 𝟎. 𝟎𝟖 𝒊𝒏. = 𝑪𝟏 − 𝑪𝟐 𝑪𝟐 = 𝟒. 𝟓 − 𝟎. 𝟎𝟖 𝒊𝒏 = 𝟒. 𝟒𝟏𝟕𝟔 𝒊𝒏. OPERATING O PRESSURE ANGLE The actual pressure angle during operation differs from the designated value. In other words, two 20° gears may actually have a greater pressure angle during operation by increasing the center distance from the nominal value. The relationship that can be used to determine the amount of variance is