Introduction: (Initial Observation)
Gears are among the most efficient and the most reliable methods for transmitting rotary motion and force. Gears are used in watches, clocks, cars, toys, and millions of other industrial and household equipment. Gears are strong, durable and reliable. In this project we will test the efficiency of a gear system and test the effect of lubricants on gears efficiency.
The gear wheel is a basic mechanism. Its purpose is to transmit rotary motion and force. A gear is a wheel with accurately machined teeth round its edge. A shaft passes through its center and the gear may be geared to the shaft. Gears are used in groups of two or more. A group of gears is called a gear train. The gears in a train are arranged so that their teeth closely interlock or mesh. The teeth on meshing gears are the same size so that they are of equal strength. Also, the spacing of the teeth is the same on each gear. An example of a gear train is shown below.
When two spur gears of different sizes mesh together, the larger gear is called a wheel, and the smaller gear is called a pinion. In a simple gear train of two spur gears, the input motion and force are applied to the driver gear. The output motion and force are transmitted by the driven gear. The driver gear rotates the driven gear without slipping.
The wheel or the pinion can be the driver gear. It depends on the exact function the designer wishes the mechanism to fulfill. When two spur gears are meshed the gears rotate in opposite directions, as shown in the figure below.
Wheel and pinion
The spur gear is the last gear we will look at and the most important as far as we are concerned. We will be looking at the gear terms and how to draw the gear teeth using Unwins construction. Firstly, we will discuss the spur gear itself.
A spur gear is one of the most important ways of transmitting a positive motion between two shafts lying parallel to each other. A gear of this class may be likened to a cylindrical blank which has a series of equally spaced grooves around its perimeter so that the projections on one blank may mesh in the grooves of the second. As the design should be such that the teeth in the respective gears are always in mesh the revolutions made by each is definite, regular and in the inverse ratio to the numbers of teeth in the respective gears. This ability of a pair of well made spur gears to give a smooth, regular, and positive drive is of the greatest importance in many engineering designs. An example of two spur gears in mesh are shown below.
Involute spur gear terms
The spur gear terms:
The pitch circle is the circle representing the original cylinder which transmitted motion by friction, and its diameter the pitch circle diameter.
The center distance of a pair of meshing spur gears is the sum of their pitch circle radii. One of the advantages of the involute system is that small variations in the center distance do not affect the correct working of the gears.
The addendum is the radial height of a tooth above the pitch circle.
The dedendum is the radial depth below the pitch circle.
The clearance is the difference between the addendum and the dedendum.
The whole depth of a tooth is the sum of the addendum and the dedendum.
The working depth of a tooth is the maximum depth that the tooth extends into the tooth space of a mating gear. It is the sum of the addenda of the gear.
The addendum circle is that which contains the tops of the teeth and its diameter is the outside or blank diameter.
The dedendum or root circle is that which contains the bottoms of the tooth spaces and its diameter is the root diameter.
Circular tooth thickness is measured on the tooth around the pitch circle, that is, it is the length of an arc.
Circular pitch is the distance from a point on one tooth to the corresponding point on the next tooth, measured around the pitch circle.
The module is the pitch circle diameter divided by the number of teeth.
The Diametrical pitch is the number of teeth per inch of pitch circle diameter. This is a ratio.
The pitch point is the point of contact between the pitch circles of two gears in mesh.
The line of action. Contact between the teeth of meshing gears takes place along a line tangential to the two base circles. This line passes through the pitch point and is called the line of action.
The pressure angle. The angle between the line of action and the common tangent to the pitch circles at the pitch point is the pressure angle.
The tooth face is the surface of a tooth above the pitch circle, parallel to the axis of the gear.
The tooth flank is the tooth surface below the pitch circle, parallel to the axis of the gear. If any part of the flank extends inside the base circle it cannot have involute form. It may have ant other form, which does not interfere with mating teeth, and is usually a straight radial line.
You will need to understand the terms load, effort, efficiency, mechanical advantage and velocity ratio to tackle the calculations you will find on this page.
You will need to know and be able to use the following formulae:
In any system of gears an pulleys, part of input force is being wasted by friction. Lubricants are being used to reduce the friction. The purpose of this project is to see how the efficiency of such system is being affected by lubricants.
The independent variable for this experiment is the lubricant (None, Oil, Grease).
The dependent variable is the efficiency of the system.
My hypothesis is that lubricants will greatly increase the efficiency of the gear system.
Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”
- Assemble a system of gears and use it to lift a heavy load with little effort. Do not use any lubricant for this test. Then we calculate the efficiency using this formula:
load x distance moved by load
effort x distance moved by effort
2. Apply some mineral oil such as motor oil to the gears and all other moving parts. Repeat the experiment and calculate the efficiency again.
3. Cleanup the mineral oil with paper towel or cotton cloth. If you are using plastic or metal gears, you may be able to wash away the mineral oil using warm water and detergent.Then dry it with a hair dryer.
4. Apply some synthetic oil such as grease to the gears and all other moving parts. Repeat the experiment and calculate the efficiency again.
5. Record your results in a table like this:
Efficiency is calculated as (Load x D1) / (Effort x D2)
|Mineral Oil Lube.|
To make your own wooden gears first make a drawing of the gear. Paste your drawing on a sheet of aspen wood or good quality plywood and when it is fully dry, start cutting over the lines. You can use a 3/8″ dowel as a shaft and use some glue to attach the shaft to the gear.
To draw the small gear draw a circle with 4 cm diameter. This circle will be the root circle. Using the same center draw another 6 cm diameter circle that will be addendum circle. Distance between these two circles will be one cm that is the height of each tooth. Use a protractor to divide the circumference of this circle to 12 pieces (use 30 degree angles) . In every other space created in this way, highlight a tooth.
To draw the large gear draw a circle with 12 cm diameter. This circle will be the root circle. Using the same center draw another 14 cm diameter circle that will be addendum circle. Distance between these two circles will be one cm that is the height of each tooth.
When you draw the individual gears, provide them with enough curve so the gears to not get locked in each other.
The right image is a sample drawing for small gear that has 6 teeth.
The following image is a sample drawing for the large gear with 18 teeth.
Make a 3/8″ hole in the center of each gear and insert a 2 inches long, 3/8″ wood dowel in them.
We will also make two circles with 3″ diameter each and a 3/8″ hole in the center to be used as pulleys”
Build up the machine:
When gears and pulleys are ready, we must mount them on another base board to build our test machine.
Based on the size of our gears, when they are engaged, the distance between the centers of two gears is 9 cm. To make the structure loose, we make two holes on the base board 9.3 cm apart (Center to center). These holes should be slightly larger so the wood dowel can spin inside them.
We cover our board with a thin layer of wood glue and then paste the drawing over the board. We will let it dry before cutting.
When fully dry, use a coping saw to cut the gears.
You may need to do this a few times until you come up with a good pair of gears. Sand the teeth before installing them.
Pulleys will be in one side of the board and gears will be on the other side of the board. One pulley is attached to the small gear and the other is attached to the large gear.
If we turn one of the pulley attached to large gear one full turn, the other will turn 3 times.
By hanging different weight objects we test the efficiency of our system.
If there be no friction, efficiency should be 100%. For example if we hang 1 lb weight to the pulley attached to small gear, then the pulley attached to the large gear must be balanced by a 3 lbs object. Also a small force in any direction should be able to move our pulleys and gear system. Because of friction this does not happen. In other words in order to lift a 3 Lbs object with pulley attached to the large gear, we may need 2, 3 or even 6 lbs force on the pulley attached to the small gear. **
After performing some tests and calculating the efficiency of your gear system, lubricate it and repeat your tests again.
Compare the efficiency before and after lubrication
** The soda can in the above picture is filled with sand so it will get heavy. The other item is a spring scale. When you pull a string using a spring scale, the scale shows how much force you are using. The spring scales often measure the force in Newtons and in grams.
Materials and Equipment:
For this experiment you can use plastic gears, metal gears or wooden gears. You may get them from a local mechanic or buy them from toy’s stores or hobby stores.
I prefer making wooden gears. That requires some hours of work, a drill, a coping saw, glue and some aspen wood.
To measure the load and effort, you may use spring scales and known weights. The good thing about spring scales is that you can use them to provide a specific force or use them to measure a force. At any time you can read the force in Newtons or grams on the graduated display of the spring scale.
Spring scales are available at www.klk.com
Results of Experiment (Observation):
Record your results in a table like this for each trial. What you enter in this table include:
load: is the heavy weight or mass you are trying to lift. In the above pictures the load is the soda can filled with water or sand to make it heavy.
D1: is the distance the load moves up when you do your experiment.
Effort: is the force you use to pull down the opposite end of the string. In the above pictures I have hanged a spring scale to that side. In this way when I pull down the string, the spring scale will show me how much force I am using.
D2: is the distance you pull down the effort string.
Efficiency is calculated as (Load x D1) / (Effort x D2)
|Mineral Oil Lube.|
Efficiency is a ratio; so it does not have a unit.
- Measure forces in grams (or convert them to grams).
- Measure distances in centimeters (or convert them to centimeters)
Example: Imagine my soda can (load) is 800 grams. I use 300 grams effort (as shown by my spring scale) to move the soda can up. While doing this my soda can moves up 5 centimeters while my effort (the hook of the spring scale) moves down 17 centimeters.
Efficiency= (800 x 5) / (300 x 17) = 0.78
Write your calculations in this section for your report.
If you decide to make your own gears, you will need to do more calculations while designing the gears.
Summary of Results:
Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.
It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.
Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did.
Related Questions & Answers:
What you have learned may allow you to answer other questions. Many questions are related. Several new questions may have occurred to you while doing experiments. You may now be able to understand or verify things that you discovered when gathering information for the project. Questions lead to more questions, which lead to additional hypothesis that need to be tested.
If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.
If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.
Visit your local library and review some books in general mechanics and simple machines.
Name those books as your references.
Also visit following web sites for more information
Efficiency = (Load x Distance Load Moves)/((Effort x Distance Effort Moves)
Velocity Ratio = (Number of teeth on driven wheel)/(Number of teeth on driving wheel)
Axle: a bar on which a wheel turns ball bearings: spheres placed between the surfaces of a wheel and axle to reduce friction.
Beveled gears: beveled gears like all gears, transfer the direction of rotation from clockwise to counterclockwise (or vise versa); at the same time, beveled gears transfer the motion from one plane of rotation to an opposing plane.
Counterweight: a weight that balances the weight of a load
Force: a push or a pull
Friction: invisible force that occurs when one object rubs against another; resistance to motion; reduces motion, produces heat, and causes wear and tear on machines
Fulcrum: The point upon which a lever balances.
Gear: wheel with teeth along the outer edge; a toothed wheel that interlocks with another toothed wheel
Gravity: the force that holds and pulls all objects to earth
Inclined plane: tilted up flat surface; The steeper the angle, the more effort is required; slanted surface or ramp
Lever: a rigid bar that pivots around a fixed point called a fulcrum.
Machine: any device that changes either the direction or the amount of force that you must apply to accomplish a task; any tool used to change either the magnitude, the direction, or the speed of a force.
Mechanical advantage: what you gain when a device allows you to work with less effort.; The number calculated as the mechanical advantage of a machines indicates how many times a machine multiplies the effort used.
Pitch: the distance between thread on a screw
Pulley: a grooved wheel that turns an axle and can change the direction of a pull; a wheel with a rope or cable running over it
Screw: a simple device with a grooved track on its shaft
Sheave: grooved wheel
Torque: the turning or rotational effect of a force
Wedge: inclined plane on end; a device placed between objects to split, tighten, or secure a hold
Wheel and Axle: A wheel and axle is a lever that rotates in a circle around a center point or fulcrum. The larger wheel (or outside) rotates around the smaller wheel (axle). Bicycle wheels and gears are all examples of a wheel and axle.
Work: a force acting on an object to move it across a distance (pushing, pulling, lifting); a push or a pull on an object causing movement.
Theory of Conservative Energy: “hard effort for a short distance” = “easy effort for a long distance”
Formula for Levers:
Effort X distance from the fulcrum = weight X its distance from the fulcrum
work = force X distance
Mechanical Advantage = distance from the fulcrum to the effort/distance from the fulcrum to the load
– The mechanical advantage of a lever is in:
1. Load – what is lifted or moved
2. Effort – the force used to move the load
3. Fulcrum – support or balance (pivot point)
– Levers are used to change force and motion
– First class levers – fulcrum is in the middle between the load and effort (example seesaw); a first-Class lever changes the direction of the force (one end of the lever moves up while the other goes down.); Less effort is required when the distance from the effort to the fulcrum is longer than the distance from the fulcrum to the load
– Second class levers – load is in the middle between the fulcrum and the effort (example wheelbarrow); A second class lever does not change the direction of the force. The load moves in the same direction as the force.
– Third class levers – effort is in the middle between the fulcrum and the load (example drawbridge on a castle; broom); third class levers do not change the direction of the force; It requires more effort because the distance from the effort to the fulcrum is always shorter that the distance from the load to the fulcrum.; Third class levers always have a mechanical advantage less than one (they require more effort to lift a load than it would require to lift it with your hands); the advantage to third class levers is that they can be used to handle delicate objects because they reduce the force you apply directly.
– Double levers – two levers joined together (example scissors)
– Could use animation to demonstrate how a shadow works (see Internet info)
– A fixed pulley gives the advantage of change in direction; a fixed pulley makes work easier by changing the direction of the effort force.; a moveable pulley makes work easier by decreasing the effort needed to move an object.
– Each supporting rope of a pulley increases the mechanical advantage.
– A pulley consists of a grooved wheel, and a rope, chain, or cable that passes around the rim.
– Pulleys make it easier to lift heavy loads by changing the direction of the lifting force. They can also reduce the effort required to lift the load, but increase the distance through which the force is applied (force X distance = work)
– The distance the rope or chain is pulled (with two pulleys) is always twice the height the load is lifted.
– A screw is an inclined plane wrapped around a cylinder to form spiraling edges. The distance between the ridges winding around the screw is called the pitch. Screws with less distance between the threads are easier to turn.
– A screw is a twisted inclined plane
WHEEL AND AXLE
– A load is easily moved by a wheel and axle when the radius of the wheel (effort) is longer than the radius of the axle (radius of axle)
– Every time the axle makes one complete turn, the load is raised a height equal to that of the axle’s circumference.
– As the radius of a wheel increases, the force required to turn it decreases
– An inclined plane reduces the force needed to raise an object to a specific height. The plane increases the distance the object must travel to reach that height. If the length of an inclined plane stays the same but its height increases, it will take more force to move a load the same distance. The angle of the ramp, the amount of gravity, the amount of friction, and the weight of the object affect how the object moves.
– The longer the slope the an inclined plane, the easier it is to pull or push the object up the inclined plane.
– Machines enable you to harness forces such as electricity, water power, wind power, or gravity in order to perform a task.
– The criterion for classifying an object as a scientific machine is that it must change the force required to do something. The energy required to do something will not be reduced by the use of a machine, in fact it will probably be increased because of the presence of friction.
– Archimedes Principle of the Lever – the longer the arm of the lever to which force is applied, the less that force need be.