RU2020484C1 - Pendulous flexible compensation accelerometer - Google Patents

Abstract

FIELD: instrumentation engineering. SUBSTANCE: accelerometer includes pendulum connected to body by means of flexible suspension with mass center of pendulum located between two pairs of stops, device for measurement of displacement and balancing transducer. Stops are located relative to pendulum and end of flexible member at distances determined from condition given in invention description. Number of pairs of second stops may be equal to number of flexible members. In this case, they form together with first stops the support plane of pendulum. EFFECT: higher efficiency. 2 cl, 4 dwg

Description

 The invention relates to instrumentation, in particular to instruments for measuring acceleration, and can be used in navigation and orientation systems.

 Known pendulum compensation accelerometers with an elastic suspension, designed to determine the acceleration of an object (French patent N 2562254, CL G 01 P 15/08, 1986). Such accelerometers have a sensitive element (SE) in the form of a pendulum on an elastic suspension, a device for measuring the movement of the SE, the output of which through an amplifier is connected to the input of the balancing sensor.

 The disadvantage of such accelerometers is the possibility of linear displacement of the SE due to the flexibility of the elastic suspension under the action of peak accelerations, for example, shock, leading to plastic deformation of the elastic suspension, or to its destruction.

 Of the known accelerometers, the closest in technical essence is a pendulum compensation accelerometer with an elastic suspension (see French patent N 2562254, CL G 01 P 15/08, 1986), adopted as a prototype and comprising a housing, CE connected to the housing by means of an elastic suspension, a device for measuring the movement of CE, a balancing sensor and one stop on each side of the CE, limiting the movement of the CE and located in the center of the impact of the CE, due to which the load in the elastic suspension is zero (see Nikolai EA Theoretical mechanics. CH . II. M., 1958, p. 317).

 The disadvantage of the accelerometer is the need to place the stops with great accuracy in a strictly defined place, which is not always achievable, based on the given design requirements and structural features of the nodes and assemblies, as well as due to inevitable technological tolerances. In a real design, the contact point of the CE with the stop may not coincide with the center of impact, which will lead to unacceptable stresses in the elastic element under the action of external forces, to the appearance of plastic deformation of the elastic suspension, or to its destruction, which is practically a failure of the accelerometer and navigation system.

 The aim of the invention is to increase the reliability of the pendulum compensation accelerometer with an elastic suspension.

+

- σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{д}}$ _оп≅ 0 ,
(1) где С_у - угловая жесткость упругого элемента подвеса;
С_л - линейная жесткость упругого элемента подвеса;
W - момент сопротивления сечения упругого элемента;
S - площадь сечения упругого элемента подвеса;
h - расстояние от конца упругого элемента до первых упоров;
h₁ - расстояние от конца упругого элемента до вторых упоров;
Н - расстояние от плоскости ЧЭ до первых упоров;
Н₁ - расстояние от плоскости ЧЭ до вторых упоров;
σ_доп - допустимое напряжение в упругом элементе подвеса;
l - длина упругого элемента подвеса.The goal is achieved by the fact that in a pendulum compensation accelerometer with an elastic suspension containing a housing, a CE connected to the housing by means of an elastic suspension, a device for measuring the movement of the CE, a balancing sensor and one stop on each side restricting the angular movement of the CE are set additionally, the second stops, one on each side so that the center of mass of the SE is between the first and second stops located on one side of the pendulum, and the distances h and h ₁ from the end of the elastic suspension element CA (UP) to the first and second stops and the distance H and H ₁ from the plane of the CE to the first and second stops satisfied the condition

+

- σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{d}}$ _op ≅ 0,
(1) where C _y is the angular stiffness of the elastic element of the suspension;
With _l - linear stiffness of the elastic element of the suspension;
W is the moment of resistance of the cross section of the elastic element;
S is the cross-sectional area of the elastic element of the suspension;
h is the distance from the end of the elastic element to the first stops;
h ₁ is the distance from the end of the elastic element to the second stops;
H is the distance from the plane of the SE to the first stops;
H ₁ - the distance from the plane of the SE to the second stops;
σ _add - allowable stress in the elastic element of the suspension;
l is the length of the elastic element of the suspension.

 From the foregoing, we can conclude that the proposed technical solution meets the criterion of "novelty."

 Figure 1-4 shows the proposed accelerometer.

Disturbing force acts on the SE
P _in = m ˙a _x , where a _x is the acceleration applied to the center of mass of the SE;
m is the mass of the SE.

Using the lemma on parallel transfer of the line of action of a force, it is possible to replace this force with a force applied to the end of a unitary force and some coupled forces with a moment equal to the moment of a given force relative to a new point of its application (Fig. 1). Thus, the UP is loaded with a transverse force applied to its end
P = P _in and bending moment
M = P _in ˙ L, where L is the distance from the center of mass of the SE to its UP.

-

,
(2) где х_о и θ_o - соответственно прогиб и угол поворота в начале координат;
М_о и Р_о - изгибающий момент и поперечная сила, действующие в сечении, совпадающем с началом координат;
Е - модуль Юнга материала;
J - центральный момент инерции поперечного сечения УП.We depict the unit separately figure 2. To describe the movement of the UE, we use the universal equation of the elastic line (see G. Pisarenko and others. Resistance of materials / Kiev .: Vishcha school, 1979, p. 285)
X ′ (Z ′) = X _o + θ _o Z ′ + (EJ ^-1

-

,
(2) where x _o and θ _o are the deflection and angle of rotation at the origin, respectively;
M _o and P _o - bending moment and shear force acting in the section coinciding with the origin;
E - Young's modulus of the material;
J is the central moment of inertia of the cross section of the unitary enterprise.

M_oZ′-

(3)
Из условий статического равновесия

-

(4)
Поскольку для УП, имеющего заделку, прогиб и угол поворота сечения равны нулю, то
х_о= θ_o = 0 (5) (см. Писаренко Г.С. и др. Сопротивление материалов. Киев: Вища школа, 1979, с.273). Следовательно, (2) и (3) с учетом (4) и (5) для z=l можно записать в виде:

(6) где l - длина УП.Differentiating (2), we obtain the equation of angles of rotation of the UE sections
θ ′ (Z ′) = θ _o + (EJ)

M _o Z′-

(3)
From the conditions of static equilibrium

-

(4)
Since for a unitary enterprise with a seal, the deflection and the angle of rotation of the cross section are zero, then
x _o = θ _o = 0 (5) (see Pisarenko G.S. et al. Resistance of materials. Kiev: Vishka school, 1979, p.273). Therefore, (2) and (3) taking into account (4) and (5) for z = l can be written in the form:

(6) where l is the length of the unitary enterprise.

(7)
Для упругого элемента известно понятие центра жесткости. Особенность этой точки заключается в том, что для системы координат, начало которой совпадает с центром жесткости упругого элемента, диагональные элементы c_ij (i≠j) матрицы жесткостей с=ll c_ij ll обращаются в нуль (см. Вибрация в технике. Под ред. Болотина В.В. Т.1, М.: Машиностроение, 1978 с.74). Переходя в (7) к новой системе координат ОХZ с началом в центре жесткости (фиг.3), имеем

-l

(8) где l - расстояние между центром жесткости и заделкой УП.By definition, UE stiffness is the ratio of the load acting on the UE to the displacement caused by this load. Therefore, the coefficients c _ij , i, j = 1,2) in the expressions for P and M obtained from (6) are the stiffnesses of the elastic element under consideration

(7)
For an elastic element, the concept of a center of stiffness is known. The peculiarity of this point is that for a coordinate system whose origin coincides with the center of stiffness of the elastic element, the diagonal elements c _ij (i ≠ j) of the stiffness matrix c = ll c _ij ll vanish (see Vibration in Engineering. Ed. Bolotina V.V.T.1, M .: Mechanical Engineering, 1978 p.74). Passing in (7) to a new coordinate system OXZ with a beginning at the center of stiffness (Fig. 3), we have

-l

(8) where l is the distance between the center of stiffness and the termination of the unitary enterprise.

(9) где Р и М - поперечная сила и изгибающий момент, действующие на УП в системе координат ОХZ.From equations (7) and (8) we have

(9) where P and M are the transverse force and bending moment acting on the UP in the coordinate system OXZ.

=

, а уравнения (9) примут вид

(10) где С_л=С₁₁ - линейная жесткость УП;
С_у=С₂₂+С₂₁l₁ - угловая жесткость УП.Since the point O is the center of rigidity of the UP, from the condition that the diagonal terms of the stiffness matrix vanish, we find its position
l ₁ = -

=

, and equations (9) take the form

(10) where C _l = C ₁₁ - linear stiffness UP;
C _y = C ₂₂ + C ₂₁ l ₁ - angular stiffness UP.

(11)
где h₁, h - расстояние от конца УП до вторых и первых упоров соответственно;
Н₁, Н - расстояния от плоскости, определяемой осями подвеса Y и Z ЧЭ, до вторых и первых упоров соответственно.When position 3 of the SE on the first 1 and second 2 stops, placed in such a way that the center of mass 5 of the SE is between them, the end 4 of the unitary unit is rotated by an angle θ and shifted by x (Fig. 4). Wherein

(eleven)
where h ₁ , h is the distance from the end of the UP to the second and first stops, respectively;
H ₁ , N - the distance from the plane defined by the suspension axes Y and Z SE, to the second and first stops, respectively.

(12)
Очевидно, что независимо от величины нагрузки, приложенной к ЧЭ 3 (фиг. 4), момент и поперечная сила, приложенные к концу УП, будут определяться уравнениями (12), т.е. будут определяться только конструкцией прибора.Since, in view of the smallness of the angle θ tan θ≈θ, equations (10) take the form

(12)
Obviously, regardless of the magnitude of the load applied to the SE 3 (Fig. 4), the moment and shear force applied to the end of the UE will be determined by equations (12), i.e. will be determined only by the design of the device.

(13) где σ,τ,σ_экв - нормальные, касательные и эквивалентные напряжения соответственно.Since the UE is a beam, one end of which is sealed up, and the other is loaded with a transverse force P and moment M, the normal, tangential, and equivalent stresses are determined by the formulas (see V.I. Feodosiev. Resistance of materials. M .: Nauka, 1967, p. 135-139, 267)

(13) where σ, τ, σ _equiv are normal, tangent, and equivalent stresses, respectively.

The condition for the absence of deformation UP
σ _equiv ≅ σ _add , (14) where σ _add - permissible stresses in unitary enterprise.

+

- σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{д}}$ _оп≅ 0
(15)
Таким образом, расположение в акселерометре двух пар упоров, ограничивающих перемещение ЧЭ, на расстояниях h и h₁ от конца УП и Н и Н₁ от плоскости ЧЭ прибора, связанных между собой соотношением (15), ограничивает напряжения в УП заранее заданной величиной σ_доп, обеспечивающей отсутствие остаточных деформаций УП, что повышает надежность.Substituting expressions (12) and (13) in (14), we obtain

+

- σ $\genfrac{}{}{0ex}{}{\text{2}}{\text{d}}$ _op ≅ 0
(fifteen)
Thus, the location in the accelerometer of two pairs of stops restricting the movement of the SE at distances h and h ₁ from the end of the UE and N and N ₁ from the plane of the SE of the device, interconnected by relation (15), limits the stresses in the UE to a predetermined value σ _add , ensuring the absence of residual deformation of UP, which increases reliability.

 From the foregoing, we can conclude that the proposed technical solution meets the criterion of "Significant difference".

 Figure 1 presents the loading diagram of the SE; figure 2 - loading diagram UP; figure 3 is a diagram of loading UE in the coordinate system with the beginning in the center of stiffness of RE; figure 4 - pendulum compensation accelerometer, consisting of a housing 8, with which an elastic suspension 4 is connected to the sensing element 3, the center of mass 5 of which is located between the stops 1 and 2, the device 7 for measuring displacement, sensor 6 balancing 6 and amplifier 9.

Consider an accelerometer, which has the following characteristics:
C _l = 2.94 ˙10 ⁴ n / m;
With _y = 4˙10 ^-4 n ˙m / rad;
l = 1.5˙10 ^-4 m;
W = 5.4 · 10 ⁻¹⁴ m ³ ;
S = 1.8˙18 ^-8 m ² ; σ _add = 1˙10 ⁸ n / m ²
Let the first stops be arranged in such a way that h = 8.8˙10 ^-5 m, and Н = 5.1˙10 ^-5 m, and for the second, h ₁ = 1.1˙10 ^-3 m, then from the equation (15) we have H ₁₁ = 7.0˙10 ^-6 m and H ₁₂ = 4.8˙10 ^-6 m, i.e. at 4.8˙10 ^-6 ≅ Н ₁ ≅7.0˙10 ^-6 m the voltage in the unitary enterprise will be ≅σ _add . The case of H ₁ = 7.0 × 10 ⁻⁶ m is shown in FIG. 4, and with H ₁ = 4.8 × 10 ⁻⁶ m, the end of the UE will be to the right of the Z axis (FIG. 4).

 The use of two pairs of stops located in accordance with equation (15) distinguishes the proposed accelerometer from the prototype, as it ensures the reliability of the UE and does not require the location of the stops in a strictly defined place determined by the design.

Claims (2)

1. PENDULAR COMPENSATION ACCELEROMETER WITH AN ELASTIC SUSPENSION, comprising a housing, a sensing element connected to the housing by means of an elastic suspension, a device for measuring the movement of the sensitive element, a balancing sensor and two stops restricting the movement of the sensitive element, characterized in that, in order to increase reliability , the second two stops are set so that the center of mass of the sensor is between the first and second stops located on one side of the sensor ment, and the distance from the end of the elastic element to the first and second stops and from the plane of the sensing element to the first and second stops satisfied the condition:

+

- σ _d $\genfrac{}{}{0ex}{}{\text{2}}{\text{about}}$ _n ≅ 0,
where C _y , C _l - angular and linear stiffness of the elastic element;
W is the moment of resistance of the cross section of the elastic element;
S is the cross-sectional area of the elastic element;
l is the length of the elastic element;
σ _add - allowable stress in the elastic element;
h, h ₁ - the distance from the end of the elastic element to the first and second stops, respectively;
H, H ₁ - the distance from the plane of the sensing element to the first and second stops, respectively.  2. The accelerometer according to claim 1, characterized in that the second stops are installed at each elastic suspension element and form a plane with the first stop.

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