Swinburne University of Technology (Sarawak Campus) Faculty of Engineering and Science
HES5310 Machine Dynamics 2 Lab 2 Report: Epicyclical Gear Train System Lecturer: Dr. Samer Yahya
Group Members: Aminu Ismaila Ibrahim (4216997) Ammar Baig (4218930)
EPICYCLIC GEAR SYSTEM Objective: 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. To calculate gear ratio of the epicyclic gear system. 4.
1. 2. 3. 4. 5.
Experiment 2: To determine the input power and output power of the epicyclic gear system. To determine the power loss of the epicyclic gear system. To measure the different stage epicyclic gear ge ar systems speed output. To measure the output torque generated by the epicyclic gear system. To calculate the epicyclic gear system efficiency. Theory: Epicyclic gearing also called as planetary gearing. It is a gear system that consists of one or more outer gear (planet gear) rotating about a central (sun gear). The planet gear are mounted on a moveable arm (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.
Figure 1 show an example of epicyclic gearing. It is used 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. Gear ratio: The gear ratio in an epicyclic gearing system can be different by the design of the gear teeth and the ways of input rotation to the gear. The three basic components of the epicyclic gear are:
1. 2.
Sun: The central gear Planet carrier: Holds one or more peripheral planet gears, of the same size, meshed with the sun gear 3. Annulus: An outer ring with inward-facing teeth that mesh with the planet gear or gears In many epicyclic gearing systems, among the three basic components, one component is held stationary; one component is input, provide power to the system and last component is output, receive the 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. This rotation of the planet gears can inturn drive the annulus, in a corresponding ratio. If the annulus has P teeth, then the annulus will rotate by P/A turns for each turn of the planet gears. In summarize: 1. One turn of the sun gear results in - S / P turns of the planets 2. One turn of a planet gear g ear results in P / A turns of the annulus a nnulus 3. One turn of the sun gear gea r results in –S / A turns of the annulus an nulus One situation is when 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 ge ar ratio, equal to 1+A/S. These are all described by the equation: (2+n)!a + 2!s – 2(1+n) !c = 0 Where n is the form factor of the planetary p lanetary gear, defined by: n = Ns/N p
For the case where the annulus is held stationary while the sun gear is used as an input and the planet carrier as an output, the gear ratio in this case will be 1/(1+A/S). This is the lowest ratio obtainable with an epicyclic gear train. This type of gearing is normally used in tractors and construction equipment in order to have a higher torque provided 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.
A
A Spring scale
B
Pulley & belt
C
3rd stage epicyclic gear train
D
2nd stage epicyclic gear train
E
1st stage epicyclic gear train
F
Inductive sensor
G
Main power switch
H
Motor speed controller
I
Digital torque meter
J
Motor speed meter
K
1st stage speed meter
L
Loading nut
Equipment & Accessories: 1. LS - 12097 Motorized Epicyclic Gear Train. Stop Watch. 2. Safety & Precaution: 1. Keep body parts and all a ll objects away from the moving parts in the system. 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. Stop the apparatus immediately if the gear system does not move when the motor is running. Experimental Procedure: 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. 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 epicyc lic gear system is stated. 7. From the data given, calculate the gear ratio for the following: NSun / NPlanetary NSun / NRing NPlanetary / NRing 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 appa ratus 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. 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.
7. 8.
9.
10.
11. 12.
The time taken to complete the total number of cycle is state down by using a stop watch. ( Reminder: Reminder: Take few set of reading to achieve better average time). time). Step 6 is repeated for the 3rd stage ring gear output speed (C). 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. From the spring scale (A), the force generated is measured. Take the different between the maximum and minimum value as the force reading. The reading is recorded to the table provided. Step 5 to 11 are repeated by using different type of input speed (i.e 45, 55, 65 rpm). ( Note: Note: Please reset the maximum value for the torque meter by pressing the max/min button for 3 seconds.) All the tables provided are computed. The input and output torque of the system as well as the input and output power of the system is compared.
Results: Calculation of power input to the epicyclic gear system
Motor Speed Torque (rpm) Input (Nm) 35 0.8 44 0.8 56 0.8 65 0.72
1st Stage Ring Load Output Motor Angular Power Gear Speed (rpm) (kg) Speed (rad/s) Input 10 10.5 3.6652 2.93216 13 10.5 4.6077 3.686 17 10.75 5.8643 4.691 20 11 6.8068 4.901
Sample calculation FOR 35 rpm:
Motor Angular Speed = = Power Input = = = Sample calculation for 44 rpm: Motor Angular Speed = = Power Input = = =
3.6652 Torque Input 0.8 * 3.6652 2.93216 W
4.6077 rad/s Torque Input 0.8 * 4.6077 3.686 W
Motor Angular Speed
Motor Angular Speed
Sample calculation for 56 rpm:
Motor Angular Speed = = Power Input = = = Sample calculation FOR 65 rpm:
5.8643 rad/s Torque Input 0.8 * 5.8643 4.691 W
Motor Angular Speed
Motor Angular Speed
= = 6.8068 Power Input = Torque Input Motor Angular Speed = 0.72 * 6.8068 = 4.901 W nd Calculation for the 2 stage ring gear speed (rpm) n Motor Speed Number of Time (s) 2 Stage Ring Gear Angular Speed (rpm) Cycle Speed (rps) (rad/s) 35 1 64 0.0156 0.09817 44 1 50 0.02 0.1257 56 65
1 1
40 33
Sample calculation for 35 rpm: nd 2 Stage Ring Gear Speed
Angular Speed
Sample calculation for 44 rpm: nd 2 Stage Ring Gear Speed
Angular Speed
Sample calculation for 56: nd 2 Stage Ring Gear Speed
0.025 0.0303
0.157 0.1904
= = = = = =
Number of Cycle / Total Time Taken 1/64s 0.015625 rps nd 2 stage gear speed 0.015625 rps * 2" 0.09817 rad/s
= = = = = =
Number of Cycle / Total Time Taken 1/50s 0.02 rps nd 2 stage gear speed 0.02 rps * 2" 0.1257 rad/s
= =
Number of Cycle / Total Time Taken 1/40s
Angular Speed
Sample calculation for 65rpm: 2nd Stage Ring Gear Speed
Angular Speed
= = = =
0.025 rps nd 2 stage gear speed 0.025rps * 2" 0.157 rad/s
= = = = = =
Number of Cycle / Total Time Taken 1/33s 0.0303 rps nd 2 stage gear speed 0.0303rps * 2" 0.1904 rad/s
rd
Calculation for the 3 stage ring gear speed (rpm)
Motor Speed Number (rpm) Cycle 35 1 44 1 56 1 65
of Time (s)
1
62.5. 50.7 39.6 34
0.0294
Sample calculation for 35 rpm: rd 3 Stage Ring Gear Speed
Angular Speed
Sample calculation for 44 rpm : rd 3 Stage Ring Gear Speed
Angular Speed
Sample calculation for 56 rpm: 3rd Stage Ring Gear Speed
Angular Speed
r
3 Stage Ring Gear Angular Speed Speed (rps) (rad/s) 0.016 0.1005 0.0197 0.1239 0.02525 0.1587 0.1848
= = = = = =
Number of Cycle / Total Time Taken 1/62.5.00s 0.016 rps rd 3 stage ring gear speed * 2" 0.016rps * 2" 0.1005 rad/s
= = = = = =
Number of Cycle / Total Time Taken 1/50.7 s 0.0197 rps rd 3 stage ring gear speed * 2" 0.0197rps * 2" 0.1239 rad/s
= = = =
Number of Cycle / Total Time Taken 1/39.6s 0.02525 rps rd 3 stage ring gear speed * 2"
Sample calculation for 65 rpm: rd 3 Stage Ring Gear Speed
Angular Speed
= =
0.02525rps * 2" 0.1587 rad/s
= = = = = =
Number of Cycle / Total Time Taken 1/34.00s 0.0294 rps rd 3 stage ring gear speed * 2" 0.0294rps * 2" 0.1848 rad/s rd
Calculation for torque & power generated at the 3 stage of epicyclical gear Motor Speed Load Output Load Output Torque Output Power Output (rpm) (kg) (N) (Nm) (W) 35 10.5 103.005 4.635 0.4658
44 56 65
10.5 10.75 11
103.005 105.458 107.91
4.635 4.74558 4.85591
0.5743 0.75312 0.8973
Radius of the Pulley = 0.045m Sample calculation for 35 rpm: 2 Load Output (N) = Load Output (kg) 9.81m/s 2 = 10.5 kg 9.81m/s = 103.005 N Torque Output = Load Output (N) Radius of the pulley = 103.005 N 0.045m = 4.635 Nm rd Power Output = Torque Output Angular Speed of 3 Stage Ring Gear = 4.635 m * 0.1005 rad/s = 0.4658 W Sample calculation for 44 rpm : 2 Load Output (N) = Load Output (kg) 9.81m/s 2 = 10.5 kg 9.81m/s = 103.005 N Torque Output = Load Output (N) Radius of the pulley = 103.005 N 0.045m = 4.635 Nm Power Output = Torque Output Angular Speed of 3rd Stage Ring Gear = 4.635 m * 0.1239 rad/s = 0.5743 W Sample calculation for 56 rpm :
2
Load Output (N)
= Load Output (kg) 9.81m/s 2 = 10.75 kg 9.81m/s = 105.4575 N Torque Output = Load Output (N) Radius of the pulley = 105.4575 N 0.045m = 4.74558 Nm rd Power Output = Torque Output Angular Speed of 3 Stage Ring Gear = 4.74558 m * 0.1587 rad/s = 0.75312 W Sample calculation for 65 rpm: 2 Load Output (N) = Load Output (kg) 9.81m/s 2 = 11 kg 9.81m/s = 107.91 N Torque Output = Load Output (N) Radius of the pulley = 107.91 N 0.045m = 4.85591 Nm rd Power Output = Torque Output Angular Speed of 3 Stage Ring Gear = 4.85591 m * 0.1848 rad/s = 0.8973 W Calculation of power loss and overall efficiency
Motor Speed Power Input Power Output Power Loss Overall (rpm) (W) (W) (W) Efficiency, # 35 2.93216 0.4658 2.46636 0.1588 44 3.686 0.5743 3.1117 0.15580 56 4.691 0.75312 3.93788 0.1605 65
4.901
0.8973
4.0037
Sample calculation for 35 rpm: Power Loss = Power Input – Power Output = 2.93216 W – 0.4658 W = 2.46636 W Efficiency = Power Output / Power Input = 0.4658/2.93216 = 0.1588 Sample calculation for 44 rpm Power Loss = Power Input – Power Output = 3.686 W – 0.5743W = 3.1117 W Efficiency = Power Output / Power Input
0.18308
= 0.5743/3.686 = 0.15580 Sample calculation for 56 rpm Power Loss = Power Input – Power Output = 4.691 W – 0.75312W = 3.93788 W Efficiency = Power Output / Power Input = 0.75312/4.691 = 0.1605 Sample calculation for 65 rpm Power Loss = Power Input – Power Output = 4.901 W – 0.8973 W = 4.0037 W Efficiency = Power Output / Power Input = 0.8973/4.901 = 0.18308 Calculation of speed ratio of the epicyclical gear system st
n
r
Motor Angular 1 Stage Ring Gear 2 Stage Ring Gear 3 Stage Ring Gear Speed (rad/s), R 1 Speed (rad/s), R 2 Speed (rad/s), R 3 Speed (rad/s), R 4 3.6652 4.6077 5.8643 6.8068
1.047 1.3613 1.7802 2.094
Motor Speed R 1/R 2 (rpm) 35 3.5006 44 3.384 56 3.294 65 3.2506
0.09817 0.1257 0.157 0.1904
0.1005 0.1239 0.1587 0.1848
R 1/R 3
R 1/R 4
R 2/R 3
R 2/R 4
R 3/R 4
37.335 36.65 37.352 35.75
36.469 37.1888 36.952 36.833
10.665 10.829 11.338 11.0
10.4149 10.987 11.217 11.331
.9768 1.0145 0.989 1.0303
Comparison between the torque input and output of the system Motor Speed Torque Ouput Torque Input Input (Nm) Torque Output (Nm) (rpm) Torque Input
35
0.8
4.635
5.7937
44 56 65
0.8 0.8 0.72
4.635 4.74558 4.85591
5.7937 5.9319 6.7443
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From the above two graphs we can see that the gear speed is directly proportional to the power which goes in line with the theory. Observing the experiment we can see that the output torque isn’t affected by the power input however the power output lost increases when the power input is increased. Useful data No of Teeth Pitch Diameter (mm) Pitch Size (mm) Sun Gear 18 36 7 21 44 7 Planetary Gear 60 120 7 Ring Gear Gear Ratio Gear Ratio Gear Ratio Gear Ratio Gear Ratio Gear Ratio
= = = = = = = = =
Nsun / N Planetary 18/21 0.86 Nsun/N Ring 18 / 60 0.30 N Planetary / N Ring 21 / 60 0.35
Advantages & Disadvantages of the epicyclic gear system The planetary gear box offers 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 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. 2.
From the tables we can that the relationship between powers input and output is linear. 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
3.
Energy loss in the form of heat 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
Conclusion 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 0.8Nm in 4.635Nm 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 44rpm motor speed a power loss of 3.1117 W was observed.
