Automation of the Transverse Feed of the Grinding Wheel on Groove-Grinding Machines

V. A. Beinarovich

(Presented by the scientific seminar of the Electromechanical Faculty)

The technical culture, precision, reliability, and durability of mechanical-engineering products depend to a great extent on the technology of metalworking. The size of the fleet of grinding machines is one of the indicators of the technical level of mechanical engineering. In this connection, the automation of grinding machines is becoming increasingly important, especially for the bearing industry, where grinding machines constitute the principal part of the equipment (50–60%).

One of the main tasks in the automation of groove-grinding machines is the automation of the transverse feed of the grinding wheel.

As a result of a whole series of technological studies [1, 2, 3], it has been established that the principal indicators of the grinding process (the cleanliness of the ground surface, the depth of burn, machining time, wear of the grinding wheel, elastic deformations of the machine–tool–workpiece system, and the cost of grinding) depend on the magnitude of the rate of removal of the metal allowance, i.e., on the rate of actual feed. Figures 1 and 2 give the dependences of the rate of linear wear of grinding wheels of grade E-100-STV and of the magnitude of elastic deformation (compression, tension) on the rate of actual feed [2]. Analysis of these dependences shows the necessity of taking into account the elastic deformations and wear of the grinding wheel that vary during the machining process. Consequently, feed automation can be carried out only by using a follow-up system that provides automatic regulation of the feed magnitude according to an optimal law during the grinding process. The grinding-wheel feed drive must operate in an automatic-control system (ACS).

Let us consider certain questions of feed automation as applied to the LZ-5 groove-grinding machine.

Selection of the Controlled Parameter

As shown in [1, 2, 4], automation of the transverse feed of grinding machines can in practice be carried out according to the magnitude of the rate of their actual feed and the grinding power.

Fig. 1.

Fig. 2.

The speed of the actual feed is easily measured, is conveniently standardized, and unambiguously determines the indices of the grinding process. However, when grinding wheels become dull or loaded, control of the speed of the actual feed does not make it possible to evaluate the depth of burn and the possible occurrence of defects.

Grinding power is measured with great difficulty and low accuracy, and characterizes the indices of the grinding process only for definite geometrical relationships between the dimensions of the part and the grinding wheel.

A comparison of these two paths of automation makes it possible to conclude that the most universal system will be a combined one, in which both parameters are monitored and feed regulation is carried out according to an optimal law. However, this considerably complicates the system.

In practice it is considered that a system for controlling the speed of the actual feed is rational to use when working with self-sharpening grinding wheels, and a system for controlling grinding power when working with non-self-sharpening grinding wheels, with periodic dressing.

On all groove-grinding machines, including model LZ-5, only self-sharpening grinding wheels are used. Consequently, for feed automation it is expedient to apply a system with regulation according to the speed of the actual feed.

Representation of the Machine Tool as an Element of an Automatic Control System

In the grinding process the mechanical (motor) feed, \(S_m\), is equal to the sum of the stock removed, \(S_d\), the radial wear of the grinding wheel, \(S_k\), and the magnitude of elastic deformation (deflection), \(S_y\),

\[ S_m = S_d + S_k + S_y. \tag{1} \]

Differentiating (1) with respect to time, we obtain

\[ V_m = V_d + V_k + V_y, \tag{2} \]

where \(V_m\) is the speed of the mechanical (motor) feed;
\(V_d\) is the speed of stock removal, or of the actual feed;
\(V_k\) is the wear rate of the grinding wheel;
\(V_y\) is the rate of change of elastic deformation (deflection, tension).

With a small error (about 10%), the dependences \(V_k = f(V_d)\) and \(S_y = f_1(V_d)\), presented in Figs. 1 and 2, may be replaced by linear ones [1, 2]:

\[ V_k = aV_d, \tag{3} \]

\[ S_y = bV_d. \tag{4} \]

Then the differential equation describing the relationship of the speeds in grinding, and representing the equation of the “machine tool” element in the automatic control system for transverse feed, is written as

\[ V_m = V_d + aV_d + b\,\frac{dV_d}{dt}. \tag{5} \]

The input quantity of the “machine tool” element is the speed of the motor feed \(V_m\); the output is the speed of the actual feed \(V_d\).

The transfer function of the “machine” element is

\[ K(p)=\frac{V_d}{V_m}=\frac{1}{1+a+pb}. \tag{6} \]

Such a function corresponds to an ordinary first-order aperiodic element. Let us determine the gain coefficient \(K_c\) and the time constant \(T_c\) of the “machine” element:

\[ K_c=\frac{1}{1+a}; \qquad T_c=\frac{b}{1+a}. \tag{7} \]

Physically, the gain coefficient of the “machine” element is the ratio of the rate of the actual feed to the sum of the rate of the actual feed and the rate of wear of the grinding wheel; that is, it expresses the decrease in the rate of the actual feed by a factor of \(K_c\) relative to the rate of displacement of the axis of rotation of the grinding wheel.

The time constant \(T_c\) of the “machine” element physically represents the time for the rate of the actual feed to increase from zero to \(0.632\) of the established value at a constant rate of motor feed.

Taking (7) into account, the transfer function of the “machine” element is written as

\[ K(p)=\frac{K_c}{1+pT_c}. \tag{8} \]

Selection of the structural system of automatic control

In developing a system of automatic control by the drive of the feed of the grinding wheel, three varieties of structural diagrams may occur: open-loop, closed-loop, and closed-open.

1) An open-loop automatic-control system (Fig. 3) cannot provide regulation according to a specified law, since the wear of the grinding wheel and elastic deformations change during the grinding process and cannot be allowed for in advance, owing to changes in a number of influencing factors, including random ones.

Fig. 3.

2) A closed-loop automatic control system (Fig. 4) can ensure the prescribed law of regulation. In this system the tracking feed, with a definite accuracy, maintains the controlled quantity equal to the specified one, independently of changes in other parameters (within certain limits).

For the regime of established elastic deformations of the machine tool, the velocity equation (2) is written (see Fig. 4) as

\[ K\left(V_{s}-V_{a}\right)=V_{a}(1+a), \tag{9} \]

where \(K\) is the mechanical amplification coefficient of the automatic control system;
\(V_{s}\) is the specified feed rate;
\(V_{a}\) is the rate of actual feed;
\(a\) is the coefficient of linear wear of the grinding wheel (3).

The regulation error is

\[ \delta=\frac{V_{s}-V_{a}}{V_{s}}=\frac{1+a}{1+a+K}. \tag{10} \]

Fig. 4.

3) A closed-open automatic control system (Fig. 5) can also ensure the prescribed law of regulation. Such a system is a combination of a programmed-control system and a tracking system. When the controlled quantity \(V_{a}\) is equal to the specified \(V_{s}\), the tracking system does not operate; the signal \(V_{s}-V_{a}=0\). This corresponds to an open-loop structure of the automatic control system. When the controlled quantity \(V_{a}\) deviates from the specified value \(V_{s}\), the tracking system comes into action, striving to eliminate the mismatch. This corresponds to a closed-loop structural diagram of the automatic control system.

The velocity equation (2) for the regime of established elastic deformations is written as

\[ V_{s}+K\left(V_{s}-V_{a}\right)=V_{a}(1+a). \tag{11} \]

The regulation error is

\[ \delta_{1}=\frac{V_{s}-V_{a}}{V_{s}}=\frac{a}{1+a+K}. \tag{12} \]

A comparison of expressions (10) and (12) shows that, with identical gain coefficients \(K\), the error in the closed-open automatic control system (12) is smaller than in the closed one (10). Consequently, the closed-open structural scheme of the automatic control system provides higher regulation accuracy and is the most appropriate for automating the feed.

Fig. 5.

Selection of the electric drive system for the feed

The feed drive must provide a sufficiently large range of stepless regulation of the feed rate. In works [2, 3, 4] it is shown that the rate of the actual feed must be regulated from \(1.5\text{–}1.8\ \mathrm{mm/min}\) to \(0.05\ \mathrm{mm/min}\), a regulation range of about \(30\text{–}40\). Taking into account the influence of elastic deformations and wear of the grinding wheel, the range is expanded still further. The most suitable drive for such a regulation range is an independently excited direct-current motor supplied from a source with controlled voltage. In view of its low power, it is expedient to use as the latter a controlled thyratron rectifier, which has greater speed of response, lower weight, cost, and dimensions in comparison with generator–motor and magnetic-amplifier–motor systems, and at present is cheaper than a rectifier–semiconductor-amplifier–motor system.

For controlling the speed of the feed motor it is convenient to use the method of pulse regulation. A feed system with pulse speed regulation was developed at the Department of EPP [5] and showed good results on the LZ-5M machine. In comparison with a continuous-action system, the pulse-regulation system is distinguished by simplicity, greater reliability, speed of response, the absence of phase-shifting and phase-regulating devices, better dynamic stability, and a large starting torque, which is of very great importance for the drive of the feed mechanism, belonging to mechanisms with a dry-friction type of load.

The disadvantages of drives with pulse regulation—overrated motor power due to conditions of greater heating and speed pulsations—are insignificant for the feed drive.

The motor of the feed drive on grinding machines always has a power rating overestimated by several times, owing to the difficulty of allowing for changes in load during operation as the parts wear, as well as for the quality and regularity of lubrication, adjustment of assemblies, etc. For example, according to calculations, the motor power of the feed mechanism of the LZ-5M machine is 15–30 W, while the manufacturer installs motors of 125 W. Evidently, such a measure is fully justified by the increase in reliability, and also by the low significance of the cost of such a motor in the total cost of the machine’s electrical equipment.

Pulsations in the speed of the feed-drive motor do not have a negative effect on the grinding process, owing to the presence of elastic deformations and the inertia of the machine’s kinematic units. For this reason, on most modern grinding machines, mechanical systems of intermittent feed are used (cam, ratchet, etc.).

In automated feed mechanisms, when the stiffness of the “machine–tool–workpiece” system is low, it is necessary to use reversible tracking drive systems. These systems ensure rapid creation of interference, removal of the main allowance at constant speed, removal of the interference by reversing the feed (retraction) at the end of machining, and completion of machining at very small feeds, ensuring a high machining frequency. In practice, the use of a reversible system may be considered necessary if the magnitude of the elastic deformation of the machine is equal to or greater than the allowance that is removed with a constantly decreasing feed rate under conditions preventing burns [2, 4]. The groove-grinding machines LZ-5 under consideration have high stiffness; the magnitude of the elastic deformations is much less than 0.1 mm—the allowance from which the feed rate is usually uniformly decreased. Consequently, for machines of the LZ-5 model it is possible to use a simpler nonreversible feed drive, as is confirmed by practice [4].

In view of the above considerations, for the feed drive of LZ-5 groove-grinding machines it is rational to use a nonreversible drive with a separately excited direct-current motor and pulse control of the rotational speed by means of a controlled thyratron rectifier.

On the basis of the above, the following conclusions may be drawn regarding automation of the transverse feed of LZ-5 groove-grinding machines:

1. As the controlled parameter, it is advisable to choose the speed of the actual feed.

2. The machine in the automatic-control system is represented as an aperiodic first-order element.

3. The automatic feed-control system should rationally be constructed according to a closed–open structural scheme.

4. It is recommended that the feed drive be made according to the nonreversible scheme: thyratron amplifier–motor with pulse control of the rotational speed.

REFERENCES

1. G. B. Lur’e. Main directions in the automation of the working cycle of cylindrical grinding. Collection Automation in Machine Building, MASHGIZ, 1957.

2. E. S. Zheleznov. Electric tracking feed for grinding grooves of bearing rings. Technology of the Bearing Industry, No. 10, 1956.

3. Kh. Kh. Batalov. Experimental investigation of spherical grinding of bearing rings by the rolling method. Machine Tools and Tooling, No. 1, 1956.

4. V. A. Beinarovich, A. I. Zaitsev. Automation of groove-grinding machines. Proceedings of Higher Educational Institutions, Machine Building, No. 3, 1962.

5. V. A. Beinarovich, A. I. Zaitsev. Author’s certificate No. 134746. Bulletin of Inventions, No. 1, 1961.

Received by the editors
in May 1962.