Determination of the optimum variant of shaft-hub joint for gears.

Argesanu, Veronica ; Jula, Mihaela ; Carabas, Iosif 等

1. INTRODUCTION

The principle of relatively immobilization (joint) of some parts that form the specific cylindrical fits for gears may be of the type: with or without intermediate elements (Manea, 1970). (Gheorghiu, 1986; Sheng, 2008)

From the category of the ones with intermediate elements are mentioned:

--Shrink joints with cylindrical smooth surfaces with intermediate conic elements -rings--annular keys (fig. 1.a);

--Shrink joints with cylindrical smooth surfaces with intermediate elements elastic hub-hydropath (fig.1.b);

--Shrink joints with double conic intermediate elements (fig. 1.c);

--Key joints (fig.1.d).

Of the category of those without intermediate elements are mentioned:

--Shrink joints pushed or fretted (fig. 1.e).

According to the figure 1 it is observed the existence of a large number of modalities of relatively fixing the shaft and the hub, but the main request of choice of one of the alternatives is constituted by the ratio between the weight and the transmissible torque, that is that of a maximum carrying capacity.

In the choice of the fixing solution of the gear on the shaft, it always must be made a compromise between the economic requirement for a compact construction, of some low costs of fabrication and the technical condition of a great carrying capacity (Gheorghiu & Madaras, 1986).

The best accomplishment of some requirement like: high reliability, safety in exploitation, the minimum of tension concentrations, high qualities of the fabrication of joint surfaces etc., depends on the consideration of the following conditions:

a) The choice of a solution that best accomplishes the working requirements.

b) The compact construction and the right dimensioning_of all the joint elements.

c) The use of proper materials.

d) Mechanical working and thermal treatments as cheap as possible.

e) The easy assembling and disassembling.

f) Optimum servicing and working conditions for on all the load steps.

[FIGURE 1 OMITTED]

Each condition in part has a more or less influence on the carrying capacity, so at the question regarding "THE MOST FAVORABLE" choice of the joint it cannot be found an universal right/valid answer without a comparative analysis. (Zografos, 2008; Korakianitis, 2008)

2. COMPARATIVE ANALYSIS

Among the options of fixing the gear on the shaft (fig.1) are analyzed the alternatives c) and d) which are considered to be the most used in the machine construction.

The choice derives also by the fact that at an inadequate process of the joint surfaces, but also a inadequate thermal treatment or a defective assembling drives at unfavorable displacement of the contact spot which determine the occurrence of some extremely high normal forces (fig.2).

The consequences can be failures of the surface, bending breaking or displacements.

In such of these cases, errors of execution and assembling determine a real carrying capacity, which can be really different from the calculated one. (Guang, 2007; Gheorghiu, 1986)

The calculations were made for:

--d [member of] (25;400)mm--the shaft diameter;

--[beta]BG--the fatigue coefficient of concentration [v.2];

--[epsilon][delta]--dimensional coefficient [v.2];

--[gamma][delta]--the surface quality coefficient [v.2];

--Shaft material OL 50 STAS 500/2-80;

--The torsion of the shaft is after a pulsate cycle;

--c=1,5 the safety coefficient at the fatigue resistance;

It was determined:

--the weight of shaft included in hub (G);

--transmissible torques of joint (Mt);

--the ratio between the weight and the transmissible torque (G/[M.sub.t]);

--(G/[M.sub.t])/(G/[M.sub.t])standard.

The values of the mentioned parameters are shown in the table 1.

[FIGURE 2 OMITTED]

According to the obtained values the dependence [G/[M.sub.t]]/[[G/[M.sub.t]].sub.etalon] (d) that reflects the maximum carrying capacity of the joint, is represented graphically (fig.3).

[FIGURE 3 OMITTED]

3. CONCLUSION

The evolution of the constructive solutions of the joint that form the cylindrical fitting specific to the gears determined the occurrence of some typified families whose carrying capacity tend to equal the performances obtained by the joint by shrinking joints.

From figure 3 can be observed the advantage shown by the shrink joints with the double conics intermediate elements fig.1c, which allows the obtaining of high performance solutions.

The choice of one of the joint solution (fig.1) according to the analyzed parameters (G/[M.sub.t]); (G/[M.sub.t])/(G/[M.sub.t]) and (G/[M.sub.t])/ [(G/[M.sub.t])sub.e] = [absolute value of (G/[M.sub.t])/[(G/[M.sub.t]).sub.e]] (d)--(fig.3)--give the best accomplishment of the formulated requirements.

4. REFERENCES:

Gheorghiu N. & Madaras L. (1986). Considerations regarding the evolution of joint by shrinking of the conic surfaces, The fifth National Symposium of Mechanic Machineries and Transmissions, MTM'88, pg.361, Cuj Napoca

Guang M. & Wen-Ming Z. & Hai H. & Hong-Guang L. & Di C. (2007). "Micro-rotor dynamics for micro-electromechanical systems (MEMS)", State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China

Korakianitis T. & Boruta M. & Jerovsek J. & Meitner P. (2008). "Performance of a single nutating disk engine in the 2 to 500 kWpower range", School of Engineering and Materials Science, Queen Mary, University of London, London, UK

Manea Gh.--Machineries organs, Ed.Tehnica, 1970. Zografos A. & Dini D. & Olver A. (2008). ""Fretting fatigue and wear in bolted connections: A multi-level formulation for the computation of local contact stresses", Department of Mechanical Engineering, Imperial College London, South Kensington Campus, Exhibition Road, London SW7 2AZ, UK

Sheng X. (2008). "Model identification and order response prediction for bladed wheels", Applied Mechanics, Technical Centre, Cummins Turbo Technologies Co. Ltd., St Andrew's Road, Huddersfield, West Yorkshire HD1 6RA, UK

***BIKON TECHNDK GmbH company prospects

***OERLIKON company prospects

Tab. 1. The values of the mentioned parameters

 One key joint Two key joints
No. d
 [mm] (10- (10- G/[M.sub.t]/
 [sup.3]G)/ [sup.3]G)/ [(G/[M.sub.t])
 [M.sub.t] [M.sub.t] .sub.[epsilon]]

0. 1. 2. 3. 4. 5.

1 25 1,52 7,23 0,93 4,42
2 28 1,216 5,15 0,93 3,94
3 30 1,099 4,30 1,02 4,00
4 35 1,176 3,37 0,66 2,47
5 40 1,297 5,19 0,886 4,19
6 50 1,327 4,97 0,928 3,74
7 60 1,338 5,17 0,924 3,59
8 70 1,419 6,14 0,956 4,13
9 80 1,381 5,67 0,884 3,66
10 100 1,234 5,66 0,951 4,36
11 130 1,447 5,52 0,975 3,72
12 160 1,353 6,66 0,884 4,35
13 190 1,630 6,12 1,021 3,83
14 220 1,675 6,54 1,033 4,03
15 240 1,674 6,36 0,975 3,70
16 280 1,9 7,19 1,055 3,99
17 300 1,86 7,29 1,065 4,17
18 360 1,94 7,26 1,098 4,11
19 400 1,92 7,41 1,086 4,20

 DOBIKON (standard)
No. d
 [mm] (10- G/[M.sub.t]/
 [sup.3]G)/ [(G/[M.sub.t])
 [M.sub.t] .sub.[epsilon]]

0. 1. 6. 7.

1 25 0,210 1
2 28 0,236 1
3 30 0,255 1
4 35 0,348 1
5 40 0,211 1
6 50 0,267 1
7 60 0,257 1
8 70 0,231 1
9 80 0,244 1
10 100 0,218 1
11 130 0,262 1
12 160 0,203 1
13 190 0,266 1
14 220 0,266 1
15 240 0,263 1
16 280 0,264 1
17 300 0,255 1
18 360 0,267 1
19 400 0,259 1