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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

Design of a Gear Reduction System

Abstract:

The Gear reduction system presented above has been analyzed and designed. Because the gears are very important components and determine a lot of the parameters, they were the first to be analyzed. The power to be transmitted was chosen to be 100 Hp, and so from strengths considerations the material chosen was steel grade 1 hardened. This material provides the system with a great safety factor on both gears for bending and wear. The shaft diameter was then determined to be 2.17 in. from bearing bore diameter analysis. To make the assembly and order easier, both bearings were selected equal, although considerations show that for one of the bearings a smaller size could have been chosen. Strength and fatigue analysis of the shaft yielded high moments created and a very strong material, steel 1144 CDSR had to be chosen. This allowed for a comfortable safety factor on fatigue, and a huge factor for static loading. The system will not fail under the prescribed conditions, and careful engineering considerations and analysis have been developed in order to achieve the most efficient design.

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

Table of Contents:

Content Introduction Description and Discussion of Design Analysis · Gears · Bearings · Keys · Shaft Conclusion and Recommendations Bibliography Appendix A: Tabulated Design Results Appendix B: Raw Calculations Page # 3 4 4 6 7 7 9 10 11 12

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

Introduction:

The purpose of a gear reduction system is to convert input an speed and torque into a different output speed and torque. The design at hand requires the use of two gears whose diameters are specified at 24 and 12 inches each. These gears are attached to a shaft whose diameter is specified at two inches, and the bearings, keys, gears, speeds, safety factors, etc need to be determined from statics, strengths, fatigue, and various other design considerations. The gears are crucial elements of this system. They transmit the power and act as the reducers of velocity to the other parts. They need to be carefully engineered and considered if the design is to be successful. The Bearings need to provide the smoothness to the motion, while still withstanding the loads to which the system is subjected. The keys hold the shaft and the gears together. The shaft holds everything and provides uniform rotation to all the parts. It is, therefore, key to design these elements so that they can interact with one another in perfect harmony and still achieve their goal.

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

Description and Discussion of Design Analysis

This system consists of two gears supported by a shaft. The bearings, the gears, the shaft, and the keys need to be designed and analyzed. The first component analyzed was the big gear (gear number 3). The reason behind this is that there's more information from which to attain, and this speeds up the design process. 1. Gear Design: From the figure, it is apparent that the loading on the gear is split into two components, and so the axial loading is neglected. The transmitted or transversal loading is determined by multiplying the force times the cosine of the angle it makes with the horizontal. From there, the radial force was determined too, this time multiplying by the sine of the angle. Using the formula to calculate torque, a torque transmitted to the shaft was also calculated. Before proceeding any further, various decisions and assumptions must be made. 1.1 Assumptions and design decisions:

The power, reliability, life, number of teeth, and reduction ratio had to be assumed or decided upon. A power of 100 Hp seemed reasonable for any application, so it was chosen. We want a high reliability, therefore 95% reliability was chosen. A normal life cycle of one million cycles also seemed reasonable to assume for the system. The gear was decided to have 72 teeth and a gear reduction ratio of 4:1. 1.2 Calculations:

After assuming the aforementioned parameters, the properties of the pinion were calculated using the formulas to relate gears. From the power and torque relationships, an important parameter, the speed of rotation was also determined. A speed of 2329 rpm was

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang determined. After looking at various tables [1], all the parameters that determine the strength of the gears were found. 1.3 Gear tooth Bending: Using the formula p = Wt K o K v K s

Pd K m K B , the stress on the pinion was found. From F J

there, we related this stress with the stress at the gear teeth by multiplying by the ratio of their face widths. Hardened steel grade 1 was chosen, and a factor of safety of 44 was determined. This factor of safety is extremely large. However, we still decided to keep this material because it is not very expensive, and the wear resistance would show later that it will do its job perfectly fine. 1.4 Gear tooth wear:

For the wear of the teeth, the compressive stress was calculated. The following formula was used in order to do so: C = Wt K o K v K s

C f Km dpF I

In the end, a safety factor of 2.9 was calculated, which is very good. In this case, the wear on the teeth dictates the material to be used.

1.5 Gear 4:

The calculations for this gear follow the same basic principles delineated above. The dimensions change, and thus the numbers turn out to be different. The material chosen was the same as above, hardened steel grade 1. The safety factor for bending was calculated at 9, and for wear 2. This means that the selection of this material fits this gear a lot better. A factor of safety of 9 is still very high, but as explained before, this is not a big issue because

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang the gear is safe, and the costs are not high. Additionally, because wear dictates the material selection for this design, a high factor of safety for bending is acceptable. 2. Bearing Design: The bearings are critical components that allow the system to move smoothly. They should also withstand loading in the radial direction and thrust in the axial direction. However, for this project, the axial loading is so small that it will be neglected, and we will assume it is all going to be absorbed or felt by the shaft only.

2.1 Bearing type:

A quick look at the tables provided by the book [1] show that roller bearings are able to withstand higher loadings than ball bearings. Therefore, we will base our design around roller bearings.

2.2 Statics:

A statics analysis had to be performed in order to find the reactions and determine the loads on the bearings. Two different planes had to be evaluated in order to do so. The system should be steady and not move in any direction, so the forces must cancel out. From a simple summation of forces, however, two parameters remain unknown. Therefore, a summation of the moments must be performed in order to solve the system.

2.3 Assumptions:

We assume that the K design parameters are all equal to 1 in order to make our calculations easier. Also, we want at least 98% combined reliability, so a 99% individual reliability is required. The design parameters are also assumed.

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

2.4 Calculations/Tables:

For the roller bearings, assuming no thrust load, the selection and design is very easy. By

XD using the relationship C10 = a f FD 1/ b X 0 + ( - X 0 )(1 - R)

1/ a

we obtain the Load rating

for the bearings at which 10 percent of the samples will fail. By looking at the tables, the values can be determined, and the bearing chosen. Though different bearings were chosen for both parts, we only choose to stay with the larger and more load resistant bearing in order to make the assembly easier. So, 03-55mm series bearing was chosen.

2.5 Bore diameter:

The bore diameter for the bearing was found at 55mm, which is approximately 2.17 inches. Therefore, in order to make the design better, the dimension on the shaft was changed to 2.17 inches, so that the bearing and the shaft fit in tightly. 3 Key Design: The keys are the mechanical devices that keep the gears in contact with the shaft. Their analysis is very simple, and using the torque, length and diameter from previous calculations, and shaft analysis, then we are able to determine the keys. The keys chosen will be made of 1020 CD steel, and with a factor of safety of 3, their length was approximated at 0.63 inches. They will also be of ½ in. width with a height of 3/8 in. 4 Shaft Analysis: The shaft holds everything together and it withstands most of the loads. Therefore, a thorough statics analysis is required in order to design this component.

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

4.1 Statics:

Borrowing the statics analysis already performed on the bearings, the shafts were analyzed. Shear Force and Bending Moment diagrams were developed in order to determine the maximum points.

4.2 Fatigue:

Once the statics were defined, a fatigue analysis had to take place. For this analysis, the von misses stresses were calculated. Once these stresses had been obtained, using Goodman criterion produced our safety factor based on the highest bending moment. The safety factor for our first trial was 1.4. Our target is at least 1.5, so a second try was performed with a new material. The final safety factor was determined at 1.6. The material selected was 1144 CDSR Steel.

4.3 Static Loading

After defining the fatigue loads, a static loading analysis was performed. This analysis used the simple stress calculation, and from there a safety factor for the material selected was determined at 8.2. This is a little bit high, but changing the material would hinder the fatigue safety, so we decide to keep this material.

4.4 Axial Stress

Axial stress analysis was also performed. As predicted before, the 4 KN force is very insignificant to the strength of the material, as can be noted by the huge safety factor of 1744.

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

Conclusion and recommendations:

The critical features involved in the design of the gear reduction system have been determined through the use of statics, strength, and fatigue analyses. The calculation of the safety factor under various conditions and loadings has made it clear that the system will not fail. The gears have very large safety factors under bending, which indicates that our selection of materials is extremely safe and conservative. For wear, the safety factor was smaller, on the average safety factor range, indicating that our selection is good. The bearings were carefully decided upon to be very safe as well, and to withstand the loads to which the system is subjected. The shaft is made of a very strong material that can withstand a lot of fatigue and stress. The determination of our safety factor under fatigue proves that the shaft will not fail and our selection is good. For static and tensile loading, our shaft is very strong, and the safety factors were big, meaning that our selection is safe and conservative. During the analysis of this system, one of the most important things that were considered was the reliability. Under the assumption that the design of our reduction gear system was critical and needed to be as safe as possible, very high reliabilities were chosen. This, along with the high safety factors make our design a very safe one, ready for high tech or space applications if the power produced and the velocity ratios match the requirements.

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Alciades Velasquez ME 4244--Project Prof: Dr. Pang

Bibliography

[1] Budynas, Richard and Nisbett, Keith. Shigley's Mechanical Engineering Design. McGraw Hill eigth edition. New York, New York, 2007.

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