Experimental stand with automation for gears grinding process.

Carabas, Iosif ; Sticlaru, Carmen

1. INTRODUCTION

Grinding can be defined as the rapid removal of material from a sample either to reduce it to a suitable size or to remove large irregularities from the surface.The quality of a grinding operation depends on the behaviour of the grinding wheel in the grinding process. Understanding the performance of a grinding wheel is required for control of the grinding process (Bogdan, 1998). To judge the future of grinding the process and machine developments have to be taken into account. Actually the industrial experimental stands for gears are equipped so that allows the grinding process and measuring of the gears efficiency in the same time (Xun&Brian, 1996). The grinding process is organized in such a matter so that this process depends on the desired efficiency value for the gears. Typically grinding is applied to hard metals such as high carbon steels where rapid removal is essential and subsurface damage is not a critical parameter.

Gear lapping is the process of imparting a very fine finish and high degree of accuracy to gear teeth. Lapping typically improves the wear properties of gear teeth. To ensure smooth and quiet running, the Gears and Pinions are lapped after hardening. Lapping is accomplished by running mating pairs together in a gear lapping machine and feeding a liquid abrasive compound under pressure into the gear pair. The compound removes small amounts of metal as the gears rotate, thus refining the tooth surface and achive desired contact pattern.

Some of the grinding equipments are functioning so that are simulating the real working conditions. The most of the experimental stands have facilities to modify the values of some factors that are influening the resistance and durability of tested gears (Xun, 1998).

The experimental stand was designed for testing gears in closed circuit (Carabas, 1998). The kinematics scheme is presented in figure 1. The components are:

1. electrical three-phase motor with: --rotational speed n = 1500 [rev/min], power P = 7.5 [kW];

2. various speed duo with a range of 800--2000 [rev/min];

3. gear for closing the circuit with transmission report i = 1;

4. measuring instrument for loading moment for tested gear;

5. gear for closing the circuit--transmission ratio i = 1;

6. inertial loading system (figure 2).

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The device design and the calculation of the relationship for loading moment is done according to (Carabas, 1998), figure 2.

Between the two parts of the device must be a mechanical connection. This connection is made by two parts of a coupling --that attaches two aligned shafts (the gears 1 and 1' are flow constriction mounted on the shafts).

Unbalanced masses m is rigidly connected with the gears 2 and 2'. The distance between the gravity and gears centres is l. In order to obtain an equilibrate static rotor, the numbers of mass m are n > 1, so the loads that are acting upon the fixed element are at lower values.

2. THEORETICAL ASPECTS

If the device is rotating with angular velocity co, upon the mass m acts the inertial load Fc,:

[F.sub.c] = m x [[omega].sup.2] x [rho] (1)

The torsion moment has the expression (2) (n--number of masses m; i--transmission ratio between 1 (1') and 2 (2') gears; [lambda] = r/1 - notation for geometrical dimensions).

[M.sub.t] = n x i x m x [[omega].sup.2] x [r.sup.2] x sin [alpha] x(cos [alpha] + 1/[lambda] x [square root of 1 - [[lambda].sup.2] x [sin.sup.2] [alpha]]) (2)

The torsion moment M0 of the device depends only on the geometry of the equipment and it is calculated for n = 1, m = 1, [omega] = 1, r = 1, i = 1 in expression (3).

[M.sub.0] = sin [alpha] x (cos [alpha] + 1/[lambda] x [square root of 1 - [[lambda].sup.2] x [sin.sup.2] [alpha]]) (3)

Between the axial displacements of the speed variating device mobil disc there is a direct relation; [s.sub.x] represents the axial displacement between a minimum and maximum values, the expression for [s.sub.x] is given by relation (4).

[s.sub.x] = [D.sub.p min] x ([D.sub.px / [D.sub.p min] - 1) (4)

The angular velocity of the driven shaft has the (5) expression:

[[omega].sub.2x] = [[omega].sub.2min] x (1 + [s.sub.x] / [D.sub.p min] x tg [alpha]/2) (5)

The loading moment is a function [M.sub.t] = [M.sub.t] ([[omega].sup.2.sub.2x]) that can have a general expression (6):

[M.sub.t] = A x [[omega].sup.2.sub.2x] + B x [[omega].sub.2x] + C (6)

where: A, B and C are inertial loading system constants.

For the device presented in figure 2 the relation (6) is:

[M.sub.t] = A x [[omega].sup.2.sub.2x] (7)

In this case, the torsional moment gets the (2') expression.

[M.sub.t] = n x m x i x [r.sup.2] x [M.sub.0d] x [[omega].sup.2.sub.2min] x (1 + [s.sub.x] / [D.sub.p min] x tg [alpha] /2) (2')

Using the notations:

E = n x m x i x [r.sup.2] x [M.sub.0d] x [[omega].sup.2.sub.min] = ct, (8)

F = 2 x D/[D.sub.p min] x tg [alpha]/2 = ct; G = E/[([D.sub.p min] x tg [alpha]/2).sup.2] = ct (9)

the relation (7) has a general form (10)

[M.sub.t] = G x [s.sup.2.sub.x] + F x [s.sub.x] + E (10)

This is the relationship between the torsion moment [M.sub.t] and the axial displacement of the speed variating device mobile disc and it is a quadratic equation with the unknown [s.sub.x]. When the values for torsional moment in time are known, that can be calculate the displacement [s.sub.x i] = [s.sub.xi] ([t.sub.i]), i = 1 ... n, where n is the number of [M.sub.t] values. These values [s.sub.xi] are the entrance dimensions for a hydraulic drive system that realize the displacement of the mobile disc.

3. THE HYDRO DRIVE SYSTEM

The hydraulic driving system can be designed in classical way that means a hydraulic engine power or a rotative hydraulic engine with a classical hydraulic distributor. This method doesn't allow a continuous and quick track of the driven element only a sequential track.

The system proposed by this paper contains a proportional control--in this case the system has a proportional driven element such as electrohydraulic driven valve.

[FIGURE 3 OMITTED]

The command of the driven valve is given by an electrical signal that acts a magnetic system. This system establishes the displacement of a central plunge. The reduced values for inertia and nonliniarity are very important for the quick response of the system. The driving system is correlated with the mechanical part, the driven and control systems. When the system is equipped with position and load sensors results a complex system with position and load reaction in closed circuit for all degree of freedom. The hydraulic scheme is presented in fig. 3.

The notation used in fig. 3 are: P--hydraulic pump with constant volume; SP--pressure safety valve, AC--hydraulic accumulator, SV--driven valve, MHL--linear hydraulic engine, DM--mobil disc, TM--mechanical transmission, TP--position transducer, CP--program reader, A--amplifier, [C.sub.1,2]--comparator.

The drivenvalve transforms a command current into a flow Q that means a displacement of the linear hydraulic engine piston (MHL) and also of the mobile disc (DM) with [s.sub.x]. The assembly driven valve--hydraulic engine is in figure 3. The instantaneous position [s.sub.x] is detected by the position transducer (TP) and transformed in a tension voltage [U.sub.p] that is totalized in the comparator [C.sub.1] with the tension voltage [U.sub.M] given by the load transducer. The obtained value for the voltage tension is U. The comparator [C.sub.1] compares the imposed value [U.sub.PR] with U ([U.sub.SV]=[U.sub.PR]-U), so the value for amplified tensiun for the amplifier A it is obtained. From this value results the command current I for the driven valve.

4. CONCLUSION

The use of the described equipment allows the complete automation of the actioning system and automatic emphasize of the experimental measuring results. The equipment is simply and doesn't need special components. The dynamic analyze of such an element is given by the dynamic analyze of the assembly driven valve-engine. The designed equipment can be used in small test laboratories. This equipment will be used in working with students, it will be improwed to obtain a grinding maschine at low costs.

5. REFERENCES

Baron, T. (1988) Quality and reliability, Manual practice, Editura Tehnica Bucuresti, 1988

Bogdan W., Kruszynski, Stanislaw M. and Jan Kaczmarek (1998) Forces in Generating Gear Grinding-Theoretical and Experimental Approach, Manufacturing Technology Volume 47, Issue 1, 1998, Pages 287-290

Carabas I. (1998) Experimental stand for testing gears, COMEFIM 5, The National Conference of Precision Mechanics and Mechatronics Timisoara Romania 22-24 oct. 1998 The Romanian Review of Precision Mechanics&Optics, supliment 2/1998 ISSN 1220-6830

Xun, C, Brian R. W.,(1996) Analysis and simulation of the grinding process. Part III: Comparison with experiment, International Journal of Machine Tools and Manufacture, Volume 36, Issue 8, August 1996, Pages 897906

Xun, C., Allanson D. R. and Rowe W. B. (1998), Life cycle model of the grinding process, Computers in Industry Volume 36, Issues 1-2, 30 April 1998, Pages 5-11