Swinburne University of Technology (Sarawak Campus) Faculty of Engineering, Computing and Science HES 5310 Machine Dynamics 2
Epicyclical Gear Train System Lab Report
Author: Ibrahim Hussaini (4241606)
May 2, 2016
Supervisor: Dr. Ha How Ung
Contents 1 Objective 1.1 Experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2 Theory 2.1 Introduction . . . . . . . . . . 2.2 Epicyclic Gearing . . . . . . . 2.3 Gear ratio . . . . . . . . . . . 2.4 A simpler way to calculate the
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Apparatus 3.1 Safety & Precaution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4 Experimental Procedure 4.1 Experiment 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Experiment 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Results
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6 Discussion 12 6.1 Advantages of the epicyclic gear system . . . . . . . . . . . . . . . . . . . . . . . 13 6.2 Disadvantages of planetary gear systems . . . . . . . . . . . . . . . . . . . . . . 13 7 Conclusion
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Objective
1.1
Experiment 1
1. To understand the gear system. 2. To understand the epicyclic gear system. 3. To understand the working principle of epicyclic gear system. 4. To calculate gear ratio of the epicyclic gear system.
1.2
Experiment 2
1. To determine the input power and output power of the epicyclic gear system. 2. To determine the power loss of the epicyclic gear system. 3. To measure the di↵erent stage epicyclic gear systems speed output. 4. To measure the output torque generated by the epicyclic gear system. 5. To calculate the epicyclic gear system efficiency.
2 2.1
Theory Introduction
A gear train is two or more gear working together by meshing their teeth and turning each other in a system to generate power and speed. It reduces speed and increases torque. To create large gear ratio, gears are connected together to form gear trains. They often consist of multiple gears in the train. The smaller gears are one-fifth of the size of the larger gear. Electric motors are used with the gear systems to reduce the speed and increase the torque. Electric motor is connected to the driving end of each train and is mounted on the test platform. The output end output end of the gear train is connected to a large magnetic particle brake that is used to measure the output torque (Universiti-Tunku-Abdul-Rahman 2012). Simple Gear Train - The most common of the gear train is the gear pair connecting parallel shafts. The teeth of this type can be spur, helical or herringbone. The angular velocity is simply the reverse of the tooth ratio. The main limitation of a simple gear train is that the maximum speed change ratio is 10:1. For larger ratio, large size of gear trains are required; this may result in an imbalance of strength and wear capacities of the end gears. The sprockets and chain in the bicycle is an example of simple gear train. When the paddle is pushed, the front gear is turned and that meshes with the links in the chain. The chain moves and meshes with the links in the rear gear that is attached to the rear wheel. This enables the bicycle to move. Compound Gear Train - For large velocities, compound arrangement is preferred. Two keys are keyed to a single shaft. A double reduction train can be arranged to have its input and output shafts in a line, by choosing equal center distance for gears and pinions. Epicyclic or Planetary Gear Train - It is made of few components, a small gear at the center called the sun, several medium sized gears called the planets and a large external gear called the ring gear. The planet gears rolls and revolves about the sun gear and the ring gear rolls on the planet gear. Planetary gear trains have several advantages. They have higher gear ratios. They are popular for automatic transmissions in automobiles. They are also used in bicycles 2
for controlling power of pedaling automatically or manually. They are also used for power train between internal combustion engine and an electric motor.
2.2
Epicyclic Gearing
Epicyclic or planetary gearing is a gear system that consists of one or more outer gears, or planet gears, rotating about a central, or sun gear. Typically, the planet gears are mounted on a movable arm or carrier which itself may rotate relative to the sun gear. Epicyclic gearing systems may also incorporate the use of an outer ring gear or annulus, which meshes with the planet gears.
The epicyclic gearing shown in Figure 1 is to increase output speed. The planet gear carrier is driven by an input torque. The sun gear provides the output torque, while the ring gear is fixed. Note both the marks (A) on the planet carrier and (B) on the sun gear before and after the input drive have rotated 45 degrees clockwise.
2.3
Gear ratio
The gear ratio in an epicyclic gearing system is somewhat non-intuitive, particularly because there are several ways in which an input rotation can be converted into an output rotation. The three basic components of the epicyclic gear are: • Sun - The central gear. • Planet carrier - Holds one or more peripheral planet gears, same size, meshed with the sun gear. • Annulus - An outer ring with inward-facing teeth that mesh with the planet gear or gears. Figure 2 shows the carrier is held stationary while the sun gear is used as input. The planet gears turn in a ratio determined by the number of teeth in each gear. Here, the ratio is -24/16, or -3/2; each planet gear turns at 3/2 the rate of the sun gear, in the opposite direction. In many epicyclic gearing systems, one of these three basic components is held stationary; one of the two remaining components is an input, providing power to the system, while the last component is an output, receiving power from the system. The ratio of input rotation to output rotation is dependent upon the number of teeth in each gear, and upon which component is held stationary. One situation is when the planetary carrier is held stationary, and the sun gear is used as input. In this case, the planetary gears simply rotate about their own axes at a rate determined by the number of teeth in each gear. If the sun gear has S teeth, and each planet gear has P teeth, then the ratio is equal to -S/P. For instance, if the sun gear has 24 teeth, and each planet 3
has 16 teeth, then the ratio is -24/16, or -3/2; this means that one clockwise turn of the sun gear produces 1.5 counterclockwise turns of the planet gears. This rotation of the planet gears can in turn drive the annulus, in a corresponding ratio. If the annulus has A teeth, then the annulus will rotate by P/A turns for each turn of the planet gears. For instance, if the annulus has 64 teeth, and the planets 16, one clockwise turn of a planet gear results in 16/64, or 1/4 clockwise turns of the annulus. Extending this case from the one above: • One turn of the sun gear results in - S / P turns of the planets • One turn of a planet gear results in P / A turns of the annulus So, with the planetary carrier locked, one turn of the sun gear results in - S / A turns of the annulus. The annulus may also be held fixed, with input provided to the planetary gear carrier; output rotation is then produced from the sun gear. This configuration will produce an increase in gear ratio, equal to 1 + A/S. If the annulus is held stationary and the sun gear is used as the input, the planet carrier will be the output. The gear ratio in this case will be 1 / (1 + A/S). This is the lowest gear ratio attainable with an epicyclic gear train. This type of gearing is sometimes used in tractors and construction equipment to provide high torque to the drive wheels. More planet and sun gear units can be placed in series in the same ring gear housing (where the output shaft of the first stage becomes the input shaft of the next stage) providing a larger (or smaller) gear ratio. This is the way some automatic transmission work.
2.4
A simpler way to calculate the output RPM from the input RPM
It is first drawn simplified as the sun, a single planet, the annulus, and an arm holding the planet. Any gear can be the input or output, including the arm. Now, simply plug in the known values and solve for !out : Nin !out !in = (1) Nout !in !arm where N is the number of teeth, w is rpm. NOTE: If the arm is the input or output, say the ring is the output/input instead and reverse the direction (since if the arm moves a certain speed relative to the ring, the ring moves
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that same speed the other way relative to the arm, and obviously the arm does not have a tooth count to plug in). To derive this, just imagine the arm is locked, and calculate the gear ratio !out : !in = Nin : Nout , then unlock the arm. From the arms reference frame the ratio is always Nin /Nout , but from your frame all the speeds are increased by the angular velocity of the arm. So to write this relative relationship, you arrive at the equation from above. Also, make sure Nsun + 2Nplanet = Nring where N is the number of teeth. This simply says that the gears will fit, since N is directly proportional to diameter.
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Apparatus 1. Motorized Epicyclic Gear Train which consists of: A = Spring scale B = Pulley and belt C = 3rd stage epicyclic gear train D = 2nd stage epicyclic gear train E = 1st stage epicyclic gear train F = Inductive sensor G = Main On/O↵ H = Motor speed controller and digital speed display I = Digital torque meter J = Digital speed meter (for annulas of the 1st stage) K = Geared motor 2. Stop watch
3.1
Safety & Precaution
1. No body part should touch any rotating object. 2. Do not attempt to change any setting of the digital meters. 3. Do not impact the load cell. 4. Ensure the belt if properly sit on the pulley and tighten to the spring scales. 5. Do not run the motor for more than 70rpm 6. Stop the apparatus immediately if the gear system does not move when the motor is running.
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Experimental Procedure
4.1
Experiment 1
1. The apparatus is placed on a level table. The adjustable leveling feet is adjusted if necessary. 2. The epicyclic gear system is observed and the components required to compute an epicyclic gear system is identified.
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Figure 1: Epicyclic gear train apparatus. 3. Identify which is sun gear, which is planetary gear and which is annulus (ring gear). 4. A brief sketch of an epicyclic gear system is sketched. 5. The advantages and disadvantage of the epicyclic gear system is stated in the discussion. And, the reason why sometimes multistage epicyclic gear system is needed is being discussed. 6. The application of an epicyclic gear system is stated. 7. From the data given, calculate the gear ratio for the following: NSun /NP lanetary , NSun /NRing and NP lanetary /NRing
4.2
Experiment 2
1. Ensure the belt is sat properly on the pulley (B) and tighten to the spring scales (A). 15 kg is applied to each of the spring load by turning the loading nut (L) provided. 2. The main switch (G) of the apparatus at the control panel. 3. Ensure all the digital meters are working in order. The UP button is pressed to tare zero the speed and torque digital meter (I, J, K). All the maximum and minimum value of the meters is cleared by pressing the max/min button for 3 second. 4. The geared motor is switched ON and the speed of the motor is slowly increased to the 35rpm by turning the speed knob of the motor speed controller (H). The motor speed is shown on the motor speed meter (J). The reading is stated down. 6
5. Also, the stage 1st ring gear speed is stated down by taking the reading from the speed meter (K). 6. The total number of cycle of the 2nd stage ring gear output speed (D) is calculated. The time taken to complete the total number of cycle is state down by using a stop watch. (Reminder: Take few set of reading to achieve better average time). 7. Step 6 is repeated for the 3rd stage ring gear output speed (C). 8. The torque reading from the digital torque meter (I) is stated down. The torque reading will be fluctuated. The max/min button is pressed to obtain the maximum torque reading. The reading is stated down to the table provided. 9. From the spring scale (A), the force generated is measured. Take the di↵erent between the maximum and minimum value as the force reading. The reading is recorded to the table provided. 10. Step 5 to 11 are repeated by using di↵erent type of input speed (i.e 45, 55, 65 rpm). (Note: Please reset the maximum value for the torque meter by pressing the max/min button for 3 seconds.) 11. All the tables provided are computed. 12. The input and output torque of the system as well as the input and output power of the system is compared.
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Results Table 1: Calculation of power input to the epicyclic gear system. Motor Motor 1st stage ring Load Power Tmax Tmin Tavg angular speed gear speed output input [Nm] [Nm] [Nm] speed [rpm] [rpm] [kg] [W] [rad/s] 35 0.81 0.34 0.58 11 7 3.6652 2.1075 45 0.65 0.37 0.51 14 7 4.7124 2.4033 55 0.81 0.33 0.57 17 7 5.7596 3.2830 65 0.81 0.33 0.57 19 7 6.8068 3.8799
Motor angular speed (rad/s) =
2⇡ ⇥ Motor speed 60
Power input (W) = Torque input (Nm) ⇥ Motor angular speed (rad/s)
Motor speed [rpm] 35 45 55 65
(3)
Table 2: Calculation for the 2nd stage ring gear speed. 2nd Stage Ring Angular T1 T2 Tavg Gear Speed speed Number of cycle [s] [s] [s] [rps] [rad/s] 1 18.50 18.70 18.60 0.0538 0.3378 1 14.52 14.63 14.58 0.0686 0.4311 1 11.91 11.92 11.92 0.0839 0.5273 1 10.26 10.22 10.24 0.0977 0.6136
2nd stage ring gear speed =
Number of cycle Total time taken (s)
Angular speed (rad/s) = 2nd stage gear speed (s 1 ) ⇥ 2⇡
Motor speed [rpm] 35 44 56 65
(2)
(4) (5)
Table 3: Calculation for the 3rd stage ring gear speed. 3rd stage ring Angular T1 T2 Tavg gear speed speed Number of cycle [s] [s] [s] [rps] [rad/s] 1 62.00 62.00 62.00 0.0161 0.1013 1 48.73 48.96 48.85 0.0205 0.1286 1 40.04 39.84 39.94 0.0250 0.1573 1 34.44 34.27 34.36 0.0291 0.1829
3rd stage ring gear speed =
Number of cycle Total time taken (s)
Angular speed (rad/s) = 3rd stage gear speed (s 1 ) ⇥ 2⇡ 8
(6) (7)
Table 4: Calculation for torque & power generated at the 3rd stage of epicyclic gear. Motor speed Load output [kg] Load output [N] Torque output [Nm] Power output [W] [rpm] 35 7 70 3.15 0.3192 45 7 70 3.15 0.4052 55 7 70 3.15 0.4955 65 7 70 3.15 0.5761
Load output (N) = Load output (kg) ⇥ 9.81 m/s2
(8)
Torque output (Nm) = Load output (N) ⇥ Radius of the pulley (m)
(9)
Power output (W) = Torque output (Nm) ⇥ Angular speed of 3rd stage ring gear (rad/s) (10) Table 5: Calculation of power loss and overall efficiency. Motor Power Power Power Overall speed input output loss efficiency [rpm] [W] [W] [W] ⌘ [%] 35 2.1075 0.3192 1.7883 15.1473 45 2.4033 0.4052 1.9981 16.8601 55 3.2830 0.4955 2.7874 15.0944 65 3.8799 0.5761 3.3038 14.8485
Power loss (W) = Power Input (W) ⌘=
Power Output (W)
Power Output (W) ⇥ 100% Power Input (W)
Table 6: Calculation of R1 [rad/s] 3.6652 4.7124 5.7596 6.8068
speed ratio of the epicyclic gear system. R2 R3 R4 [rad/s] [rad/s] [rad/s] 1.1519 0.3378 2.1225 1.4661 0.4311 2.7086 1.7802 0.5273 3.3133 1.9897 0.6136 3.8553
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(11) (12)
Table 7: Motor speed [rpm] 35 45 55 65
Calculation of speed ratio of the epicyclic gear system. R1/R2
R1/R3
R1/R4
R2/R3
R2/R4
R3/R4
3.1818 3.2143 3.2353 3.4211
10.8500 10.9313 10.9221 11.0933
1.7268 1.7398 1.7383 1.7656
3.4100 3.4008 3.3759 3.2427
0.5427 0.5413 0.5373 0.5161
0.1592 0.1592 0.1592 0.1592
Table 8: Summary of Motor Torque speed input [rpm] [Nm] 35 0.575 45 0.51 55 0.57 65 0.57
the input and output torque. Torque Torque output output Torque input [Nm] 3.15 5.4783 3.15 6.1765 3.15 5.5263 3.15 5.5263
Power output (W)
3.5 3 2.5 2 0.3
0.35 0.4 0.45 0.5 0.55 0.6 3rd Stage Ring gear (R4 rad/s)
Figure 2: Plot of the experimental Power output (W) versus 3rd Stage Ring gear (R4 rad/s).
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Power output (W)
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4 0.3
0.35 0.4 0.45 0.5 0.55 Motor Speed (R1 rad/s)
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Figure 3: Plot of the experimental Power output (W) versus Motor Speed (R1 rad/s).
Overall Efficiency ⌘ (%)
17 16.5 16 15.5 15 4 5 6 Motor Speed (R1 rad/s)
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Figure 4: Plot of the experimental Overall Efficiency ⌘ (%) versus Motor Speed (R1 rad/s).
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Discussion
From the above table of torque it can be seen that the output torque is much higher than the input torque which proves the theory that the epicyclic gear system increases or improves the torque value. Observing the experiment we can see that the output torque isnt a↵ected by the power input however the power output lost increases when the power input is increased. When the motor speed was increased, input power was also increased which results an increase in output power. Even though there are some power loss which occurred due to friction between gears, vibration and also other form of energy loss to the surrounding. It is very important to know that in any individual gear, the efficiency is always maximum and reaches up to 95% but when it comes to a gear system such as this epicylcic gear train, the efficiency drops significantly to around 15%. This mainly occurs due to the transformation from one gear to another where energy is continuously lost. From the Figures 2 and 3, we can see that the gear speed is directly proportional to the power which goes in line with the theory. From table 8, we can see that the output torque is not a↵ected by the power input however from table 5, the power loss increases as the power input is increased. From Figure 4, it can be observed that as the motor speed is increased, the overall efficiency also increases an reaches a maximum value of 16.8601% at 45 rpm thereafter its starts to decrease and reaches a minimum value of 14.8485% at 65 rpm. This just goes to show that the overall efficiency and motor speed are not directly proportional.
Sun Gear Planetary Gear Ring Gear
Table 9: Useful data. No of teeth Pitch diameter [mm] 18 36 21 44 60 120
N sun N Planetary 18 = 21 = 0.86
Gear Ratio =
N sun N ring 18 = 60 = 0.30
Gear Ratio =
N Planetary N ring 21 = 60 = 0.35
Gear Ratio =
12
Pitch size [mm] 7 7 7
6.1
Advantages of the epicyclic gear system
The planetary gear box o↵ers a set of distinct advantages which makes it an interesting alternative to traditional gear types such as helical and parallel shaft gear boxes in applications requiring: • High reduction ratios • Compact and lightweight with high torque transmission • High radial loads on output shaft
6.2
Disadvantages of planetary gear systems
• Complexity • Assembly of gears is limited to specific teeth per gear ratios • Efficiency calculations are difficult • Driver and driven equipment must be in line to avoid additional gearing A good example of the everyday application of a planetary gear system is the automatic transmission of a car. 1. From the tables we can that the relationship between powers input and output is linear. 2. From the calculation we can see that there is power loss from the input to the output this can be attributed to the following reasons: • Frictional for between the teeth of the gears • Energy loss in the form of sound • Energy loss in the form of heat
3. Errors associated with the experiment include: • Parallax Errors Unparalleled reading of angular values by the observer.
• Accuracy Error The stopwatch is not pressed immediately after the time is up. The digital Vernier calliper is not perpendicular to the pulley during the measurement of the pulley diameter. • Systematic Errors
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Conclusion
The efficiency of this type of gear system can be increased if proper lubrication can be used which will reduce friction between gears and in return will reduce the power loss. The aim and objectives for experiment 1 and 2 which were to understand the terminologies of epicylic gear train and their gear ratios, input and output torque and efficiency which has been analysed and understood. Hence the experiment that was conducted on epicyclic gear system was a success. By increasing the motor speed the torque is increased as well. There is a liner relationship between input and output power. There was a power loss due to friction between the gears or 13
heat. The efficiency of all four cases is almost the same and it is in the range of 15% which is quite low. In conclusion we say that the in this experiment we have seen how we can increase the torque input to a higher value using an epicyclic gear train system. For example for a motor speed of 35rpm we can see how we were able to turn the 0.81 Nm in 3.15 Nm in a much smaller setting than using a compound train system. We have also seen the significant power losses that occur due to this increase in torque. For the 45 rpm motor speed a power loss of 3.1117 W and 16.8601% overall efficiency were observed.
References Universiti-Tunku-Abdul-Rahman (2012). Epicyclic Gear Train Experiment. url: https : / / www.scribd.com/doc/55002880/1-Epicyclic-Gear-Train-Experiment.
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