RU2581738C2 - Method for determining slowing of reciprocating systems - Google Patents

Abstract

FIELD: test equipment.

SUBSTANCE: present invention relates to testing of mechanical systems, which are assessed by slowing down at frequency drift of a rotating part, and can be used to determine negative acceleration of rotating parts or systems as a whole. Method of determining decelerations of progressively moving systems consists in that on rotating part of system is set a mark, signals from which are received by a sensor. Method comprises using only one mark, generating one signal during one revolution of rotating part, recording number of revolutions of rotating part in a function of time, approximating dependence of number of revolutions on time for continuous differentiable “path-time” function considering kinematic connection of a rotating part with speed of system. After that deceleration is obtained in form of a second derivative of said time function.

EFFECT: invention improves accuracy and efficiency of determining low value decelerations of mechanical systems.

1 cl, 7 dwg

Description

The invention relates to mechanical engineering. It relates to measuring the deceleration of progressively moving mechanical systems to determine the resistances to their movement in order to assess energy losses. The magnitude of these losses is judged on the energy perfection of systems and mechanisms. In this case, the motion resistance is defined as the product of the deceleration value and the reduced moments of inertia of the systems.

Known methods for determining the negative accelerations (decelerations) of mechanical systems by the coast method [1], [2], [3] in which a speed sensor is installed on the rotating parts of the system and its signals are used to record the time of receipt of each signal, after which the deceleration j is determined by the formula small increments of speed ΔV and time Δt (figure 1):

$$j=\frac{\Delta V}{\Delta t}=\frac{V_{\mathrm{one}}-{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">V</figure-callout>}}_2}{\Delta t},\left(\mathrm{one}\right)$$

where V ₁ is the speed of a point of a rotating part of radius R at the beginning of the interval Δt, V ₂ is the speed at the end of the interval Δt.

In turn, the speeds V ₁ and V _{2 are} determined by the formulas of small increments of the path Δl ₁ and Δl ₂ and the time Δt ₁ and Δt ₂ (figure 2):

; $$V_2=\frac{\Delta l_2}{\Delta t_2}$$

. $$V_{\mathrm{one}}=\frac{\Delta l_{\mathrm{one}}}{\Delta t_{\mathrm{one}}}$$

; $${\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">V</figure-callout>}}_2=\frac{\mathrm{<figure-callout\; id="2"\; label="\Delta \; l"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{l}_{}{}_2}{\mathrm{<figure-callout\; id="2"\; label="\Delta \; t"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{t}_{}{}_2}$$

.

As a result of measurements receive:

$$j=\frac{\frac{\Delta l_{\mathrm{one}}}{\Delta t_{\mathrm{one}}}-\frac{\mathrm{<figure-callout\; id="2"\; label="\Delta \; l"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{l}_{}{}_2}{\mathrm{<figure-callout\; id="2"\; label="\Delta \; t"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">\Delta \; </figure-callout>}{t}_{}{}_2}}{\Delta t},\left(2\right)$$

Thus, the deceleration measurement algorithm contains five error sources included in Formula 2, and an additional three error sources as a result of straightening of sections of the curves V ₁ -V ₂ (see Fig. 1) and l ₁ -l ₂ , l ₃ -l ₄ (see figure 2). This is the main disadvantage of these methods for determining the decelerations of rotating bodies.

There are also known methods for determining the deceleration of the shafts of internal combustion engines using a combination of special devices [4], [5]. However, in the description of these methods there is no information regarding computational actions for determining decelerations.

The problem to be solved is to achieve high accuracy and efficiency in determining the slowdowns of mechanical systems, in particular, slowdowns of small magnitude, the resistance to movement of which is described by a polynomial of the second degree of speed of the form:

P = a + bV + cV ² ,

where a , b and c are constants,

V is the translational speed of the system.

The specified problem is solved by:

- eliminating the need to measure values of indirect measurement, such as speed,

- the use of a special formula of the path-time function for approximating the measurement results, ensuring minimal discrepancies between the experimental and analytical data,

- giving the method universal applicability for measuring decelerations both over the entire speed range and for local speed values.

The rotating part of the translationally moving system is equipped with a revolution sensor with one mark, which eliminates the inaccuracy of the angular marking, which would appear with a large number of marks. The speed sensor responding to a single mark is connected to a recording device and a computer. For example, the dependence of the number of revolutions is recorded, for example, in discrete form, and for a known radius of the rotating part — the paths as a function of time over a certain period of the time interval, this dependence is approximated by a determinate, continuous, differentiable function that takes into account the kinematic relationship of the rotating part with the translational speed of the system. The second time derivative of the specified function is used to obtain the time deceleration of the system. Since the conversion of the path-time function to the deceleration-time function is performed on the basis of the provisions of the differential calculus of higher mathematics with absolute mathematical accuracy, the accuracy of determining the deceleration depends only on the accuracy of measurements of the rotation period and the motion parameter of the observed point and the quality of approximation of the experimental path -time". This achieves simplicity, high accuracy of the obtained results and reduction of time of each measurement.

The determination of the slowdowns of translationally moving systems with rotating elements is performed by establishing a kinematic relationship between the peripheral and translational speeds.

Figure 3 shows the principle of measuring the stick-out time as an incremental sum of periods of rotation of a body of radius R with a single label for the sensor.

Figure 4 shows a fragment of an example of a real record of the running time of a rotating body for each revolution. In this case, the serial number of the recording line is identical to the number of revolutions z made by the body.

Figure 5 shows a graphical dependence of the discrete values of the path-time run-out in the form of a function l (z) = f (t) based on data similar to those shown in figure 4.

Figure 6 shows the approximation of the experimental path-time dependence by a special function S = f (T). The same figure explains the relationship between current and retrospective run-out parameters.

Figure 7 shows the transition from the path-time relationship S = f (T) to the deceleration-time relationship j = f (T) according to the differential calculus rule.

The inventive method is implemented as follows: on a rotating body of the system, one mark is set, and on a base motionless relative to the rotating body, a sensor, for example, an inductive sensor, is used to detect the values of time t of each revolution with the accuracy of at least ± 50 μs bodies, as shown in FIGS. 4 and 5. As a result, a discrete expression "path-time" is obtained in the form of a dependence of the number of revolutions z and the path l = 2πRz on time t. This discrete dependence is transmitted to a computer and approximated (Fig.6) by the formula:

$$S=A\left[\ln \frac{\cos \beta }{\cos \left(BT+\beta \right)}-hT\right],\left(3\right)$$

where S and T are the retrospective path and time, respectively, i.e. the path and time to stop the rotating body;

A, B, β and h are constants, moreover:

, $$\beta =arctg\frac{h}{B}$$

,

, $$h=\frac{\mathrm{<figure-callout\; id="2"\; label="g\; b"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">g\; </figure-callout>}b}{2\delta }$$

,

where δ is the coefficient of the rotating masses of the system.

The constant b and the associated h and β are found by preliminary tests of a system node having resistance to movement P ₁ , described by the dependence:

P = a + bV + cV ² ,

For the relationship between the values of S and l use the ratio, which explains Fig.6:

S = S _∑ -l,

where S _∑ is the full coast path.

For the relationship between the values of T and t use the ratio (see Fig.6):

T = T _∑ -t,

where T _∑ is the total run-out time.

The constants A and B included in formula (3), as well as the parameters S _∑ and T _{∑ are} found from a system of 4 equations of the form:

, $$S_{\sum }-l_i=A\ln \frac{\mathrm{one}}{\cos B\left(T_{\sum }-t_i\right)}$$

,

where l _i and t _{i are the} coordinates of the selected i-th point of the function l = f (t). The values z = 1,2,3,4 are selected from the values of the number of revolutions z, for example, at the same intervals Δ:

Δ = z ₁ = z ₂ -z ₁ = z ₄ -z ₃ ,

For example, a car’s wheel, when coasting from a speed of 90 to 70 km / h, made 203 turns. Accept for z _{4 the} closest z value that is a multiple of the 4th, i.e. z ₄ = 200. Then Δ = z _4/4 = z ₁ = 50, z = ₂ 100, z = ₃ to 150.

The slowdown j is obtained by taking the second derivative of the function (3) (Fig. 7):

$$j=\frac{d^2\mathrm{<figure-callout\; id="2"\; label="S\; d\; T"\; filenames="00000016.png,00000017.png"\; state="\{\{state\}\}">S\; </figure-callout>}}{d{T}^{}}=A\frac{B^2}{{\cos }^2\left(BT+\beta \right)},\left(\mathrm{four}\right)$$

Numerous experiments have shown that the use of formula (3) for fitting the experimental data provides the standard deviation of curve fit that does not exceed 0.02%, and the correlation coefficient R _² exceeds 0.9999.

Thus, the method provides:

- obtaining data on the values of negative accelerations (decelerations) of a rotating body without the need to measure speed as a source of significant errors,

- minimal discrepancies between the experimental data and the analytical expression of their results,

- the versatility of the application of the method for measuring deceleration for various ranges of coasting speeds.

This solves the problem posed by the applicant.

The method can be used to measure the decelerations of mechanical systems with the aim of further determining:

- resistance to the movement of cars and road trains in road-polygon conditions,

- diagnostics of mechanisms and assemblies using rotating rotors (turbines, electric motors, etc.) as the main elements,

- the method is especially useful for high-precision measurements of decelerations of systems in which the resistance to motion is described by equations of the 2nd degree of speed for small values of j≤0.02g, where other methods are ineffective.

Information sources

1. A. Jant. The Mechanics of Car Movement, Part 1, Mashgiz, 1958. pp. 118-124.

2. B.S. Falkevich. Road tests of cars, Gostransizdat, 1936. Pages 19-20.

3. I.V. Novopolsky. Measurement of rolling losses - one of the types of laboratory tests of automobile tires, Proceedings of NIISHP, collection 3, Moscow, Goskhimizdat. 1957. pp. 122-138.

4. RF patent No. 2250469. Device for measuring the acceleration of the crankshaft of an internal combustion engine. IPC: G01P 15/00.

5. RF patent №2329510. A device for measuring the acceleration of the crankshaft of an internal combustion engine over the entire speed range. IPC: G01P 15/00.

Claims (1)

The method for determining the slowdowns of progressively moving systems, which consists in placing a mark on the rotating part of the system, the signals from which are received by the sensor, using only one mark creating one signal during one revolution of the rotating part, recording the number of revolutions of the rotating part in the function time, approximate the dependence of the number of revolutions on time by a continuous differentiable function "path-time", taking into account the kinematic relationship of the rotating part with the translational orostyu of the system:

,
where S and T are the retrospective path and time, respectively, i.e. the path and time to stop the rotating body;
A, B, β and h are constants, moreover:

,

,
where δ is the coefficient of rotating masses of the system, the constant b and the associated h and β are found by preliminary tests of the system node having resistance to motion P ₁ , described by the dependence:
P = a + bV + cV ² ,
after which the deceleration j is obtained in the form of the second time derivative of this function:

.

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