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presentation on CENTRE DISTANCE VARIATION,MINIMUM NUMBER OF TEETH,CONTACT RATIO,SPUR,HELICAL GEARS AND PROBLEMS
- 1. TOPIC: CENTRE DISTANCE VARIATION,MINIMUM NUMBER OF TEETH,CONTACT RATIO,SPUR,HELICAL GEARS AND PROBLEMS ROLL NUMBERS : 63,66,72,79,81 Kinematics of machine
- 2. CENTER DISTANCE VARIATION IN GEARS • Backlash is a play between tooth surfaces of paired gears in mesh. Mating gears also have a clearance (play) vertical to tooth depth. This is called Tip and Root Clearance (c), the distance between tooth root and the tooth tip of mating gears. • Gear centre distance variation is one of the most common defects of gear transmission systems. The changes in the gear center distance as well as other faults have a direct influence on the Time Varying Mesh Stiffness (TVMS) which further modifies gear vibration behaviors. Accurately estimating gear TVMS under fault conditions is crucial in gear vibration dynamic simulation. Common methods used to evaluate TVMS are generally based on the assumption that the gear pair is perfectly mounted and that all mesh points are at their theoretical positions. This assumption prevents these methods from modeling deviations in gear center distance.
- 3. • To address this shortcoming, this paper proposes a new gear mesh kinematic model that can evaluate the actual contact positions of tooth engagement with time varying gear mesh centre distance. With the proposed kinematic model, the actual TVMS of both healthy and cracked gear teeth are computed under conditions of perfect mounting, constant gear center distance deviation, and also time- varying gear center distance. Numerical simulations indicate that gear center distance variation has a significant effect on gear TVMS. Comparison between the effect of multiple faults and summed individual effects on TVMS indicates that the TVMS modification due to multiple-faults do not appear to combine in a linear manner. The proposed model for actual TVMS enables gear system dynamic models to be used to study the effects of assembly errors, gear run- out errors, shaft bending, and bearing deformation on the vibration behavior of gear transmission systems.
- 4. MINIMUM NO. OF TEETH • the minimum number of teeth (z) is: For pressure angle 20 degrees, the minimum number of teeth free of undercutting is 17. However, gears with 16 teeth or less can be usable if their strength and contact ratio pose any ill effect. 1. Start with a two-gear train. To be able to determine a gear ratio, you must have at least two gears engaged with each other — this is called a "gear train." ... 2. Count the number of teeth on the drive gear. ... 3. Count the number of teeth on the driven gear. ... 4. Divide one teeth count by the other.
- 5. To avoid interference without undercutting, the addendum circles of both the pinion and the gear should intersect the common tangent AB to the base circles within the points of tangency A and B. When the addenda are equal, obviously, then the interference will always occur first at number of teeth on the pinion (for a given speed ratio) for this situation can be determined as now explained. The addendum length a = O2A – O2P. From ΔO2AP, we can write, with α as the pressure angle,
- 6. CONTACT RATIO • The contact ratio is defined as the ratio of the length of arc of contact (from lowest point to the highest point at contact exit) to the circular pitch. In other words ,contact ratio is the average number of teeth in mesh during a contact cycle; its value usually can span from 1.30–140. • In a simple way, it can be defined as a measure of the average number of teeth in contact during the period during which a tooth comes and goes out of contact with the mating gear. Transverse contact ratio, mp, εα The contact ratio in a transverse plane. It is the ratio of the angle of action to the angular pitch.
- 7. • For machine tool components, addressing this question is more related to the end-purpose of the gears involved, e.g. (1) are the gear train be used for precision driving of a turret or linear worktable. • If the gears involved are used in precision-positioning devices, the contact ratio must be high, e.g. 1.30–1.40, as this guarantees a more uniform motion (more teeth involved), more sliding action and a greater load capacity at the expense of little efficiency if helical gearing is involved. On the other side, if the gears are to be used for a spindle transmission drive, the contact ratio can range below 1.35, as the requirements for precision in rotation can be addressed more through the bearing precision and their preload (use of spur or low helix-angle helical pairs).
- 8. SPUR GEARS • Spur gears are a type of cylindrical gear, with shafts that are parallel and coplanar, and teeth that are straight and oriented parallel to the shafts. They’re arguably the simplest and most common type of gear – easy to manufacture and suitable for a wide range of applications. • The teeth of a spur gear have an involute profile and mesh one tooth at a time. The involute form means that spur gears only produce radial forces (no axial forces), but the method of tooth meshing causes high stress on the gear teeth and high noise production. Because of this, spur gears are typically used for lower speed applications, although they can be used at almost any speed.
- 9. HELICAL GEARS • Helical is the most commonly used gear in transmissions. They also generate large amounts of thrust and use bearings to help support the thrust load. Helical gears can be used to adjust the rotation angle by 90 deg. when mounted on perpendicular shafts. • Helical or "dry fixed" gears offer a refinement over spur gears. The leading edges of the teeth are not parallel to the axis of rotation, but are set at an angle. Since the gear is curved, this angling makes the tooth shape a segment of a helix. Helical gears can be meshed in parallel or crossed orientations.
- 10. • Another advantage of helical gears over spur gears is in torque capacity. Spur gears, by design, are weaker than helical gears because loads are transmitted over fewer teeth. Helical gearing is machined with angled teeth, then hardened and ground, which is complex but necessary to achieve a high-efficiency gear mesh.
- 11. PROBLEMS