Spur gear design theory questions and answers part 1
Spur gear design terminology
Spur gear design nomenclature of various parts of gears and important definitions are given below.
(1) Pinion : A pinion is the smaller of the pair of two gears.
(2) Gear : A gear is the larger of the pair of two mating gears.
(3)Velocity ratio is the ratio of angular velocity of the driving gear to th the driven gear. It is also called the speed ratio.
(4) The pitch circle is the curve of intersection of the pitch surface of revolution with the plane of rotation. It is an imaginary circle that rolls without slipping with the pitch circle of a mating gears. The pitch circles of a pair of mating gears are always tangent to each other. Diameter of this circle is called P.C.D(Pitch circle diameter).It is denoted by d'.
(5) Addendum circle and Addendum circle : The addendum circle is an imaginary circle that borders the tops of gear teeth in the cross section. The addendum (ha) is the radial distance between the pitch and addendum circles. Addendum shows the height of the tooth above the pitch circle.
(6) Dedendum circle and Dedendum: The dedendum circle is an imaginary circle that borders the bottom of spaces between teeth in the cross section. It is also called root circle. The dedendum (h f ) is the radial distance between pitch and the dedendum circles. The dedendum indicates the depth of the tooth below the pitch circle.
(7) Clearance (c) The clearance is the amount by which the dedendum of a given gear exceeds the addendum of its mating tooth.
(8) The pressure angle is the angle which the line of action makes with the common tangent to the pitch circles. The pressure angle is also called the angle of obliquity. It is denoted by a.
(9) The circular pitch (p) is the distance measured along the pitch circle between two similar points on adjacent teeth.
(10) The diametral pitch (P) is the ratio of the number of teeth to the pitch circle diameter.
(11) The module (m) is defined as the inverse of the diametral pitch or the ratio of pitch circle diameter to the no of teeth.
Module is very important parameter in the gear design. Two meshing gears must have same module otherwise they will not mesh with each other. Secondly module of gear gives idea about the strength and size of the tooth. More module value more stronges and bigger gear tooth.
Diagram below gives the module values for same diameter gear.
Q.1. What are the various causes of gear tooth Failure? Also state remedies for each failure.
Causes of gear Tooth Failure in Spur gear design
The different modes of failure of gear teeth and their possible remedies to avoid the failure, are as follows:
1. Bending failure. Every gear tooth acts as a cantilever. If the whole repetitive dynamic load acting on the gear tooth is bigger than the beam strength of the gear tooth, then the gear tooth with fail in bending, i.e. the gear tooth with break. so as to avoid such failure, the module and face width of the gear is adjusted in order that the beam strength is larger than the dynamic load.
2. Pitting. it is the surface fatigue failure which occurs because of many repetitions of Hertz contact stresses. The failure occurs when the surface contact stresses are more than the endurance limit of the material. The failure starts with the formation of pits which continue to grow leading to the rupture of the tooth surface. in order to avoid the pitting, the dynamic load between the gear tooth should be less than the wear strength of the gear tooth.
3. Scoring. The excessive heat is generated when there's an excessive surface pressure, high speed or supply of lubricant fails. it is a stick-slip phenomenon within which alternate shearing and welding takes place rapidly at high spots. this kind of failure may be avoided by properly designing the parameters like speed, pressure and proper flow of the lubricant, in order that the temperature at the rubbing faces is within the permissible limits.
4. Abrasive wear. The foreign particles within the lubricants like dirt, dust or burr enter between the tooth and damage the form of tooth. This kind of failure may be avoided by providing filters for the oil or by using high viscosity lubricant oil which enables the formation of thicker oil film and hence permits easy passage of such particles without damaging the gear surface.
5. Corrosive wear. The corrosion of the tooth surfaces is especially caused thanks to the presence of corrosive elements like additives present within the lubricating oils. so as to avoid this sort of wear and tear , proper anti-corrosive additives should be used.
Q.2. What are the desirable properties of gear material? State the different materials used for gear manufacturing. Specify their field of application.
The desirable properties of gear material for spur gear design are as follows:
(i) Beam Strength :The load carrying capacity of the gear tooth depends upon the ultimate tensile strength or the yield strength of the material of gear. When the gear tooth is subjected to fluctuating stresses, the endurance limit of the tooth is the deciding factor. The gear material must have sufficient strength to resist failure due to breakage of the tooth.
(ii) Wear Strength : In most cases, it is ‘wear rating’ rather than ‘strength rating’ which decides the dimensions of the gear . The resistance to wear depends upon alloying elements in metal, grain size of material, percentage of carbon present, and surface hardness. The gear material should have sufficient surface endurance strength to avoid failure due to pitting.
(iii)Coefficient of friction : For high-speed power transmission, the sliding velocities are very high and the material should have low coefficient of friction to avoid failure due to scoring.
(iv) Thermal Stability : The amount of thermal distortion or warping during the heat treatment process is a major problem in gear applications. Due to warping, the load gets concentrated at one corner of the gear tooth. Alloy steels are superior to plain carbon steels in this respect, due to consistent thermal distortion.
Following are the different material used for Gears,
1. Cast iron, 2. Steel, 3. Bronze, 4.Non-metallic material
Area of Application of different gear material
1. Cast iron : Large size gears are usually made up of grey cast iron of Grades FG 200, FG 260 or FG 350. Main advantage of cast iron is that, it is cheap and generate less noise compared with steel gears. They have very good wear resistance. Their main drawback is poor beam strength, since cast iron is strong in compression but weak in tension.
2. Steel : This is more widely used material .Case-hardened steel gears offer the perfect combination of a wear- resisting hard surface together with a ductile and shock- absorbing soft core.
The plain carbon steels used for medium duty applications are 50C8, 45C8, 50C4 and 55C8.
For heavy duty applications, alloy steels 4OCrl, 30Ni4Cr1 and 4ONi3Cr65Mo55 are used.
For planetary gear trains, alloy steel 35NilCr60 is recommended. steel gears are costly, still they have higher load carrying capacity.
3. Bronze : Bronze is an alloy of copper and tin. it is mainly used for worm wheels due to its low coefficient of friction and excellent conformability. It is also suitable where resistance to corrosion is an important consideration in applications like water pumps. Their main drawback is excessive cost generated during the working.
4. Non-metallic materials : Non-metallic gears such as plastic are used under the following conditions:
(i) When the load is light and the pitch line velocity is of lower magnitude.
(ii) A long life is desired.
(iii) It is required to have quiet noiseless operation free from vibrations.
(iv) The gears are likely to be subjected to water and oil.
In non-metallic gear drives, mostly only the pinions are made of non-metals such as laminated phenolic's like Bakelite or Celoron, molded nylon,. The non- metallic pinions generally run in pair with cast iron gears. Gears made of phenolic resins have low modulus of elasticity and work on minimum lubrication. They can tolerate errors in the tooth profile. Also where the weight of gearing system is important non metallic gears are the choice like drone and other flying machines.
Q.3. Explain the Term Dynamic Load on the gear tooth. Describe various parameters which contribute dynamic load in spur gear design.
When gears are rotating at very low speed, almost at zero velocity, the transmitted load (Pt ) may be considered to be the actual force present between two meshing teeth. But in most of the cases, the gears rotate at considerable speed and it becomes necessary to consider the dynamic force resulting from the impact between mating teeth. The dynamic force is induced in gears due to the following factors:
(i) inaccuracies of the tooth profile during manufacturing
(ii) errors in spacing between tooth
(iii) misalignment between bearings and shafts
(iv) elasticity of parts and gears themselves
(v) inertia of rotating parts.
There are two methods to account for the dynamic load—
1) approximate estimation by the velocity factor in the preliminary stages of gear design and
2) precise calculation by Buckingham’s equation in the final stages of gear design.
It is difficult to calculate the exact magnitude of dynamic load in the preliminary stages of gear
design. To overcome this difficulty, a velocity factor Cv is used.
The effective load between two meshing teeth is given by,
The velocity factor is an empirical relationship used in design
For more accurate calculation of the incremental load M F Spott's equation is used for finding the effective load by taking into account the dynamic load.
where the incremental dynamic load is calculated by Buckingham’s equation,
where,
Pd = dynamic load or incremental dynamic load (N)
v = pitch line velocity (m/s)
C = deformation factor N/mm2
e = (ep+eg) sum of errors between two meshing teeth (mm) calculated from grade of gears
b = face width of tooth (mm)
Pt = tangential force due to torque (N)
The deformation factor C depends upon the modulus of elasticity of materials for pinion and gear.
Q.4. Write a note on gear lubrication.
Proper lubrication means adequate quality and quantity of lubricant with proper mode of lubrication. As the gears are in continuous engagement, lubrication plays very important role in the life of gears. Lac of lubrication causes the more heat to develop, faster wear of gears and ultimately may lead to failure of the gears. Also the lack of lubrication causes more noise and vibrations.
Purpose of Gear lubrication :
1. To reduce the power loss due to friction and wear of gear teeth.
2. To carry away the worn out particles and other dust.
3. to act like a coolant by dissipating the heat generated due to friction.
4. To minimize noise and vibration.
Types of lubricants used in gears : The type of lubricant used in gears should have sufficient viscosity to develop a suitable oil film between the tooth surfaces. It is necessary to ensure that the lubricant has sufficient oilness property. The various types of lubricants used in gears are as follows. 1. Greases : These are semisolid substances which are used for lubrication.
2. Mineral Oils 3. Extreme pressure (EP) Oils 4. Motor oils.
Q.5. Write a note on Gear Manufacturing methods.
The following are the most commonly used methods of manufacturing gears: 1. Casting 2. Hot-Rolling 3. Stamping 4. Powder-Metallurgy 5. Extruding 6. Stamping 7. Machining.
1) Casting : Gears are cast in sand moulds, permanent moulds, shell moulds, plastic mould dies and lost-wax moulds. The characteristics of gears produced by casting are same as those of other products made by these processes. Sand casting is particularly used for making heavy gears of cast-iron and steel. Gears made by this process have poor accuracy. These are mostly used for slow speed drive and are also not very efficient in power-transmission. Die casted gears are used where light loads are to be transmitted.
2) Hot rolling : Gears are made by forcing a master gear into a hot blank and the two are then rolled together until the teeth of the master have penetrated far enough to form a complete gear. The teeth are then machined.
3. Stamping : Stamped gears are made from sheet metals. Materials upto 3 mm thickness are practical for this process. These gears may be shaved after stamping to improve the accuracy and finish. These gears are used in watches, clocks, toys and house-hold gadgets.
4. Powder-Metallurgy : Gears made by the powder metallurgy process provide a cost effective alternative to conventional steel or cast iron gears that are machine finished. The powder metallurgy (P/M) process yields net-shape, or near-net-shape parts, so that little or no machining is required to obtain a finished part in many cases.
5. Extruding :In this process the brass or aluminium bar is extruded through several block dies with the final die having the shape of the desired tooth element and thus the material can finally be extruded to obtain gear form on its surfaces, and the extruded gear bar is then hack- sawed. At present only spur gears are manufactured by this method.
6. Stamping : Gears are stamped from blanks in a hydraulic press or forging hammer. Gears manufactured by this process require a light machining or may be used as such.
7. Machining : This one is the most common method of gear manufacturing. Gears can be simply made on Milling machine also when the quantity required is not large. For mass production Gear hobbing machines are used. CNC machines can also be used for making of the gears.
Q. Derive an expression for the beam strength of gear, State Assumptions made.
OR
Derive Lewis equation for the beam strength of spur gear.
Answer : The analysis of bending stresses in gear tooth was done by Wilfred Lewis.
The Lewis equation is based on the following assumptions for spur gear design:
(i) The effect of the radial component (P r ), which induces compressive stresses, is neglected.
(ii) It is assumed that the tangential component (P t ) is uniformly distributed over the face width of the gear. This is possible when the gears are rigid and accurately machined.
(iii) The effect of stress concentration is neglected.
(iv) It is assumed that at any time, only one pair of teeth is in contact and takes the total load.
LINKS to other pages related to spur gear design
Bevel Gear Design
Worm and worm gear design.