Contacting Stability of Sliding Electrical Contacts

It is stated that the operation of the sliding contact unit is accompanied by vibrations of the brushes that occur as a result of internal and external mechanical influences. The resulting violations of the sliding contact (SC) and the instability of contacting lead to a deterioration in the quality of current transmission, increased sparking, accelerated wear of the SC. The article is devoted to the derivation and verification of universal formulas for calculating the relative instability factor (RIF) of the SC. Derived formulas allow calculating the RIF of any SC compounds. Mathematical expressions are obtained to determine the distributions of instability in the tangential and axial directions of the transition layer of the SC. An experimental stand for studying the instability of various SC compounds at idle and in the rated load mode is described. The contacting cycle, which establishes a correspondence between the instantaneous value of the length of the measuring platform and the movement of the collector is described. Expressions for determining the equivalent length of the measuring area for different cases of placing the measuring brush relative to the zone of the main sliding contact are derived. These formulas allow us to find the RIF of various SC regions on experimental data based.


Introduction
Sliding electrical contacts are used widely in electrical machines of various types as part of sliding contact unit (SCU). We will further consider the operation of SCU with slip rings, which are equipped, for example, with turbogenerators (TG). Nowadays despite the use of contactless current transmission SCU, consisting of slip rings and brushes sliding along them, are widely used. Such nodes are used [1]: -in turbo-and hydrogenerators, -in synchronous motors and DC motors, -in asynchronous motors with a wound rotor; -in urban railway transport (electric locomotives, electric rolling stock of the subway, electric trains); -in the anti-icing system of helicopter rotor blades; -in power plants of sea vessels. In synchronous turbo-and hydrogenerators, SCU are used to supply direct current to the field winding, as well as for other purposes. The current supply system to the exciting winding of the turbogenerator is carried out through a sliding contact formed by brushes located on a stationary brush crosshead and two slip rings fixed on a rotating rotor [2]. The rings operate at high angular speeds, so the material for them is high-strength structural steel. For modern turbogenerators with excitation currents of 3500-5000 A the permissible current density under the brushes is 8-9 A/cm2. The dimensions of the slip rings are 450-500 mm in diameter and 150-200 mm in width [3], the number of SCU of TG brushes can reach several hundred.
The work of the SCU is accompanied by mechanical vibrations of the brushes arising from their interaction with the moving irregularities of the contact surface. This causes dynamic efforts reaching values at which contact disturbances with short-term no-current pauses are observed [4][5][6][7]. The quality contacting of SC is evaluated by measuring of RIF [2,8]. As a result of unstable contacting short-term violations of electrical contact occur. It breaks the power electrical circuit of SCU. This leads to sparking in the transition layer of SC, especially at the running edge of the brush. Sparking causes increased wear of the contacting surfaces, overheating of the SC, in some cases it can lead to an allround fire in the SCU and the failure of the entire electrical machine. For collector electric machines, the main cause of sparking is the commutation process. For brush apparatus with slip rings (SR) the reasons for sparking have not been satisfactorily explained until recently. At present it is established that the main cause of sparking in the SCU with SR is the mechanical instability of the contact. As a result breaks of the power current of the brushes lead to the occurrence of parametric electromagnetic oscillations of high amplitude and frequency in the resonant electromagnetic circuits of SCU.
Analysing processes in the SCU of turbogenerators there is no problem of ensuring sparkless commutation of windings, however the problem of ensuring reliable current collection on slip rings of turbo generators is no less complicated than the problem of providing sparkless commutation of DC machines. It is much more difficult to ensure the mechanical stability of the brush contact when working with turbogenerators. The main material of the collectors is copper or its alloys, while for the slip rings it is necessary to use steel, which has the worst contact properties. The peripheral speed on the working surface of slip rings due to the large diameters of the rings is 70-90 m/s. Therefore, ensuring the stability of current transmission in the SCU of turbogenerators is a very important and difficult task. This implies the relevance of work on the research of the mechanics of contact interaction in the SCU.

Relative instability factor
The work of sliding contact unit is accompanied by mechanical vibrations of the brushes resulting from their interaction with the contact surface. The presence of irregularities on the surface causes dynamic forces reaching values at which disturbance of contact with short pauses, during which there is no current, are observed [9][10][11][12][13][14][15]. This causes parametric instability of the brush-contact. In this case, there is a parametric instability of the brush-contact device [4,9,[16][17][18][19][20].
The quality of contacting is evaluated traditionally by measuring of relative instability factor [7,14]: We introduce the random event A , which consists in the disturbance of contact during an infinitely small interval of time  d , then where n is the number of elementary disturbances of contact; m n N + = is the total number of elementary acts of contacting; m is the number of acts of successful contacting.
Thus we represent the relative instability factor as the probability of disturbances of contact during the electrofrictional interaction [20] ( ) We define by the methods of the probability theory of the RIF of various connections of sliding electrical contacts under the condition of mutual independence of random events j A consisting in an elementary disturbances of the j -th sliding contact. In parallel connection, the break of the electrical circuit occurs when the contact is disturbed in all parallel branches. Therefore, the RIF of the group M of parallel connected contacts DIZ K is defined as follows: where j K is the relative instability factor of the j -th sliding contact; M is the number of sliding contact. For the serial connection of sliding contact we get Equations (5, 7) allow to get the formulas for any combined connections of the sliding contacts. However, more often there is a need to determine the individual RIF indirectly through the instability of readily available combined connections. This corresponds to the solution of the inverse problem. To do this, we compose the following system of linear equations where j K is the sought for RIF; 1 K is the measured RIF of the 1st sliding contact; j K , 1 is the RIF of the serial connection of the 1st and j -th sliding contact.
In parallel connection of contacts, we take the probability of simultaneous occurrence of events j A for the number of brushes N S  as a generalized criterion of instability of contacting of the whole set of brushes.
The probability of the event B consisting in synchronous separation of S brushes from N : where k is the average value of RIF of the contacting of the individual brush.
The probability S P of a contact disturbance of at least S brushes from N we find by determining the sum of the probabilities ( ) We call the value of ( ) B P sectional instability factor (SIF), and the value S P is operational instability factor (OIF) of contacting of the sliding contact unit. We We represent the (12) where N S S = * is the relative number of brushes in the group with disturbance contact.
In the process of experimental studies two more practically valuable quality factors of brush contacting were identified [14].
1) Current transmission instability factor (CIF) Δτ is the period of the termination of the power current flow through the sliding contact.
Similarly to RIF, CIF is the probability of the termination of the power current flow through the sliding contact for where =  I I , is variable and constant brush current components.
These indicators make it possible to evaluate the quality of the sliding contact by the stability criterion in real operating modes of the sliding contact block. This distinguishes CIF K and CRF K from RIF, SIF and OIF which have been introduced for evaluating the mechanical stability of brush contacting without taking into account the processes of forming the contact layer conductivity. Since different brushes contact with different degree of instability it may be said that there is a distribution of instability in the SCU in tangential and axial directions. The tangential distribution is caused mainly by the different settings of the brush holders and the variation in the mechanical properties of the brushes, and therefore it is random. The axial distribution is caused also by the different quality of the contact surface and may be regular.

Dynamics and topology of contact instability
According to the experimental studies the instability of contacting is different in the different sections of the sliding contact. Consequently there is a distribution of RIF under the brush surface, and this distribution is twodimensional and continuous.
Let the sliding contact surface consists of m equally small sections, provided that the instability is equally distributed over the contact area. Accepting RIF of the sections given Δ K equal, one may present the sliding contact of sections 1 S and 2 S as a parallel connection of 1 n and 2 n elementary contacts accordingly. For the sections given in accordance with (5): , , As the sizes of the sections ΔS are small enough, one may turn to considering the surface areas 1 S and 2 S instead of considering the number of sections: . , Thus mathematical expressions for determining the main indicators by calculation have been derived. The indicators given describe the stability of contacting and current transmission in the sliding contact unit. Brief comments for the formulas are given in the table 1.
For general estimating quality of parallel brushes contact 5. The instability of the contact interaction of brushes leads to the electromagnetic transient processes in the electrodynamic system of "brush-contact surface", as well as in the power circuits of the group sliding contact. These processes can take a resonant behavior, intensifying the arcing and being the cause of the "breakdown of commutation" on the contact rings of turbogenerators.

Experimental studies of electrical brushes contact instability
The aim of the experiments was to test the theory based on the concept of the statistical nature of RIF, as well as to study the distribution of instability over the brush width and the influence of various factors on RIF.
The experiments were carried out on a stand containing two power units with DC generators ( nom I = 90 and 450 A) and a pilot plant designed and manufactured at "AO Electrosila" (now "Power Machines"). The unit is a collector (diameter 500 mm) with electrically unbound segments, placed on bearings in a steel housing. In the body is fixed insulated brush traverse with brush holders. The collector shaft is connected to the DC motor, which is connected to the generator by the Ward-Leonard drive system. The stand allows smoothly adjust the engine speed and power current through the brushes of the pilot plant.  Fig. 1. Experimental studies of the contact stability. Fig. 1a shows the scheme of experimental studies. On the brush traverse of the plant, four isolated brush holders are fixed, in which the test brushes 1, 2 and measuring brushes 3, 4 with a reduced contact pad are placed, pressed against the collector 5. There are two sets of measuring brushes (Fig. 1b): a pair of brushes with a contact pad on the leading edge of the test brush and two other pairs with contact pads on the trailing edge and in the middle. For a specific test, the brush holders are equipped with a pair of identical brushes 3, 4, which allows to measure the CRI in a given zone of sliding contact of the tested brushes. The DC generator G is connected to the brushes by a QF switch. The SA1 switch is intended for connection of the PICON device (for measuring of the relative instability factor of brushes) either to one, or to other tested brushes, and also to measuring. The SA2 switch is designed to connect the instrument to different measuring brushes. The SA3 switch allows the measuring brushes to be connected in parallel.
Before carrying out the main measurements, we check the RIF of the serial connection of the brushes 3, 4, achieving stable (continuous) operation in the full frequency range of the collector (SA1 in position 3, SA2 in position 2). Then SA1 is switched to position 1 or 2 and SA3 is closed, which further reduces the probability of accidental contact losses of the SC.
Using the oscillograph, we control the signal waveform of the voltage on the brushes and the packets of filling pulses at the output of the logic block of the PIKON device. Using the frequency meter we control the correctness of the decimal counter and produce a refined determination of the number of pulses filling the clock generator at the output of the logic block. Using the voltmeter, we adjust the device to a given value of the comparator offset voltage and the voltage of the internal source.
Commutator 1 with electrically unbound commutator segments ( Fig. 1) and measuring brushes are used in experimental investigation of relative instability factor RIF in different zones of sliding contact. Measuring brushes should be installed on the side of diagnosable brush 2, first of all, on the leading edge, then under the middle, and only then on the trailing edge. On Fig. 1 measuring brush 3 is situated on the side of leading edge of the diagnosable brush 2.
To calculate RIF of local zones of sliding contact one should define equivalent length of measuring square per contacting cycle. Let us assume that contact between measuring brush and commutator is stable ( 0 = K ). At start connection between main brush and measuring brush is carried out by commutator segment 1, so RIF of square of commutator segment 1 with length L l and contact surface of brush 2 should be calculated. Then commutator segment 2 starts to contact with brushes 2 and 3, and while commutator move over a distance of L l increasing of commutator segment's length, enveloped with measurement from L l to 2 l l L + takes place. Then commutator segment 1 is losing it's contact with measuring brush and square's length decreasing to 2 l step-wise. After this moment length of measuring square linearly increasing to L l while commutator segment 2 is moving under the leading edge of the brushes, and then it remains constant while commutator is moving over a distance of P l . This process has a cyclical pattern, where X is the commutator shift, l is the tangential size of measuring square.
Equivalent length of measuring square in a single cycle: ( ) Let's deduce mathematical expression for measuring square's equivalent length calculation when measuring brush installed symmetrically in the middle of contact zone.
Main diagnosable brush 1 and measuring brush 2, which pinned to commutator 3, that moves with velocity V are schematically illustrated on Fig. 2. Typical positions of commutator, that register borders of the basic phases of contacting cycle between main brush and measuring brush through commutator segments are shown on this picture.
Contacting cycle that set up correspondence between instantaneous length of measuring square l and commutator shift X is illustrated in Fig. 3. Let's deduce mathematical expression for measuring square's equivalent length  Formulas (21) and (24) helps to calculate CRI of different zones of sliding contact with the use of experimental data. They were used for experimental testing of theoretical expressions, that link space and time relationship of contacting instability.

Conclusions
Maksym, as a national Kyrgyz and Kazakh drink, is Formulas for determining the relative instability factor of contact of various compounds and areas of sliding electrical contact are derived from experimental data. Experimental verification established the validity of theoretical expressions establishing the spatial and temporal relationship of contact instabilities.
Practical methods for determining the relative instability factor of contact of various connections and areas of sliding electrical contact, designed for use in the diagnosis of sliding contact units of electrical machines and apparatus.