RU2148744C1 - Opposite crank-and-slider mechanism - Google Patents

Abstract

FIELD: balancing of machines on foundations; avoidance of vibrations transmitted to foundation from member of opposite crank-and-slider mechanism included in machine unit. SUBSTANCE: opposite crank-and-slider mechanism has strut with curvilinear guide, two identical sliders mounted in guide, double-arm crank made in form of hollow shaft with fixed pivot axle secured on strut and two identical connecting rods; each connecting rod is articulated to respective slider and arm of crank. Longitudinal axis of slider guide intersects axis of rotation of crank at acute angle in center point of crank. Hinges connecting the ends of connecting rods with respective arms of crank are spherical in shape; they are mounted on inner surface of hollow shaft at diametrically opposite points. Outer surface of hollow shaft of crank is engageable with balancing member having fixed pivot axle parallel to axis of rotation of crank. Angular velocity of balancing member is proportional in magnitude and opposite in direction relative to direction of angular velocity of crank. Parameters of geometry of mass of mechanism members are determined according to dependences. EFFECT: reduced vibration activity of machine unit; improved conditions for operating personnel; increased productivity. 1 dwg

Description

 The invention relates to balancing machines on a foundation and can be used to exclude vibrations transmitted to the foundation from the links of the opposed crank-slide mechanism included in the machine assembly.

 Known opposed crank-slide mechanism with a forked connecting rod [1], containing a rack with a straight guide, two identical sliders installed in the guide, a crank in the form of a three-cranked shaft with a rotation axis fixed on the rack, a straight rod and a fork rod. A straight connecting rod is pivotally connected to the middle crank and the first slider. The forked connecting rod is connected by two lateral hinges to the extreme knees of the crank, and the middle hinge - to the second slider. The center point of the crank coincides with the intersection of the axis of rotation of the crank and the longitudinal axis of the slide guide.

 With continuous rotation of the crank, identical sliders make reciprocating motion along the guide in mutually opposite directions. The inertia forces of the sliders are equal in magnitude and opposite in direction; when the mechanism is in operation, they balance each other. Thus, the sliders are excluded from the number of sources of vibration of the foundation of the machine.

 At any angle of rotation of the crank, the longitudinal axes of the straight and forked connecting rods remain mutually parallel, the angular speeds and angular accelerations of the connecting rods are the same in magnitude and direction. The inertia forces of the connecting rods and crank are mutually not compensated. They are reduced to the main vector and the main moment of the inertia forces, which determine the static and momentary imbalance of the mechanism.

 Thus, the drawback of the opposed crank-slide mechanism with a forked rod is its static and momentary imbalance. As a consequence of this, a periodically changing dynamic load causing vibration is transmitted to the foundation of the machine from the mechanism; vibration worsens the working conditions of staff, reduces labor productivity, the quality of the process.

 The second drawback of this mechanism is associated with the presence of excess communication. Such a connection is one of the two side joints of the forked connecting rod. Excessive coupling makes the mechanism more sensitive to changes in the dimensions of the links that occur during the manufacture of parts during assembly. These deviations lead to a significant increase in resistance to movement, to intensive wear of the contacting surfaces. The gaps in the joints of the links increase, periodically acting shock forces arise, which cause elastic deformation of the links and, as a result, the vibration of the machine unit.

 The closest technical solution for the totality of features is the opposite crank-slide mechanism according to patent N 2085791 [2]. It contains a rack with a straight guide, two identical sliders installed in the guide, a two-arm crank with a rotation axis fixed on the rack, two identical connecting rods, each of which is pivotally connected to a corresponding slide and a crank arm. The center point of the crank coincides with the intersection of the axis of rotation of the crank and the longitudinal axis of the slide guide. The crank is made in the form of a hollow shaft. The hinges connecting the ends of the connecting rods with the corresponding crank arms are spherical and mounted on diametrically opposite points on the inner surface of the hollow shaft. The longitudinal axis of the slide guide crosses the axis of rotation of the crank at an acute angle.

 In this mechanism, there are no excessive connections, therefore, in comparison with the crank-slide mechanism with a forked connecting rod, its articulated joints of the links are more wear-resistant; this mechanism has a less pronounced tendency to the occurrence of shock interactions and elastic deformations of the contacting surfaces of the links. As a consequence of this, the hollow shaft crank-slide mechanism has less vibration activity.

 The identity of the sliders, the identity of the connecting rods and the geometric symmetry of the mechanism relative to the center point of the crank provide an important condition for balancing: when the mechanism moves, its center of mass is constantly at a fixed central point of the crank, the acceleration of the center of mass is zero. This means that the main vector of the inertial forces of the mechanism is always zero, - the crank-slider mechanism with a hollow shaft is a statically balanced mechanism.

 But this mechanism has momentary imbalance, which is characterized by the main moment of inertia forces of all parts of the mechanism.

 The main influence on the magnitude of the main moment of the inertia forces of the mechanism is exerted by the inertia forces of the connecting rods. This is due to the following. During the rotation of the crank, the rods remain parallel to each other, the accelerations of the centers of mass of the rods are equal in magnitude, but opposite in direction. The inertia forces of each connecting rod are reduced to the main vector and the main moment, which are applied in the center of mass of the connecting rod (the main vector of inertia forces of the connecting rod is the product of its mass and the acceleration of the center of mass; the main moment is the time derivative of the kinetic moment calculated relative to the center of mass of the connecting rod). The main vectors of the inertia forces of two identical connecting rods of the mechanism form a pair of forces, the moment of which has variable components in the projections of the main moment of the inertia forces of the entire mechanism on three mutually perpendicular fixed coordinate axes. These projections include components from the main moments of the inertia forces of the connecting rods. In addition, one of these projections, namely the projection onto the axis parallel to the axis of rotation of the crank, includes variable components from the inertia of the crank during its uneven rotation.

 Thus, the main moment of inertia of the crank-slider mechanism with a full shaft, characterizing its momentary imbalance, has variable projections onto three mutually perpendicular fixed coordinate axes. These projections have a complex algebraic structure.

 The presence of this momentary imbalance is a drawback of this mechanism. Unbalanced moments of inertia are transmitted from the mechanism to the fixed base of the machine, causing rotary vibrations of the machine unit in three mutually perpendicular planes.

 The basis of the invention is the task of creating an opposed crank-slide mechanism without excessive connections, in which the static and momentary imbalances are completely eliminated by installing one balancing link and selecting the appropriate parameters of the geometry of the masses of the links.

 In the prior art there are no mechanisms in which such momentary imbalance is eliminated by the installation of one balancing link.

 The solution to this problem will completely eliminate the vibrations transmitted to the foundation of the machine from the inertia forces of the links of the opposing crank-slide mechanism.

The problem is solved in that in the known opposite crank-slide mechanism containing a rack with a straight guide, two identical sliders installed in the guide, a two-arm crank in the form of a hollow shaft with a rotation axis fixed on the rack, two identical connecting rods, each of which is pivotally connected to the corresponding slider and the crank arm, while the longitudinal axis of the slide guide intersects the axis of rotation of the crank at an acute angle at the center point of the crank, and the hinges connecting the ends of the crank new with corresponding crank shoulders, made spherical and mounted on diametrically opposite points on the inner surface of the hollow shaft, an additional balancing link with a rotation axis fixed on the strut parallel to the crank axis of rotation, in contact with the external surface of the hollow crank shaft, the angular velocity of the balancing link proportional in magnitude and opposite in direction of the angular velocity of the crank, and the parameters of the geometry of the mass of the links of the mechanism are determined dependencies:
S _xy1 = S _xz1 = S _yz1 = S _xy2 = S _xz2 = S _xy3 = S _xz3 = S _yz3 = 0; (1)
I _xy1 = I _xz1 = I _xy2 = I _xz2 = I _yz2 = I _xy3 = I _xz3 = 0; (2)
I _x2 = 0; I _y2 = I _z2 = l • S _yz2 ;
I _x1 + 2r ² (m ₂ - l ^-1 • S _yz2 ) - kI _x3 = 0, (3)
where S _xyi , S _xzi , S _yzi are the static moments of mass of the ith link relative to the planes of the Cartesian coordinate system (Axyz) _i associated with the ith link; i - link number: 1 - crank, 2 - connecting rod, 3 - balancing link; A _i is the link pole: A ₁ and A ₃ are the central points of the crank and the balancing link, respectively, A ₂ is the center of the hinge connecting the connecting rod to the crank; the axes A ₁ x ₁ and A ₃ x ₃ coincide with the rotation axes of the crank and balancing link, respectively, the axis A ₂ x ₂ coincides with the longitudinal axis of the connecting rod; I _xi , I _yi , I _zi , I _xyi , I _xzi , I _yzi - axial and centrifugal moments of inertia of mass of the i-th link in the coordinate system (Axyz) _i ; m ₂ is the mass of the connecting rod, r is the length of the crank arm, l is the length of the crank, k is the ratio of the angular velocity of the balancing link to the angular velocity of the crank.

The drawing shows a diagram of the opposite crank-slide mechanism in the Cartesian coordinate system A ₁ xyz.

Opposite crank-slide mechanism comprises a rack 1 with a straight guide 2, a two-arm crank 3 with a rotation axis 4 fixed on the rack, two identical sliders 5 and 6 installed in the guide 2, two identical connecting rods 7 and 8, a balancing link 9 with an axis fixed relative to the rack rotation 10. Two-armed crank 3 is made in the form of a hollow shaft (the front part of the hollow shaft is not shown in the figure). The central point of the crank 3 coincides with the intersection of the axis 4 and the longitudinal axis of the guide 2. The crank 3, the sliders 5 and 6, the connecting rods 7 and 8 are interconnected by hinges 11, 12, 13, 14, and the hinges 11 and 12 are mounted on the inner surface of the hollow shaft (crank 3) at diametrically opposite points. The balancing link 9 is in contact without slipping with the outer surface of the hollow shaft 3, the movable connection of these links is the highest kinematic pair. The axis of rotation of the crank 4 coincides with the axis A ₁ x of the Cartesian coordinate system A ₁ xyz associated with the strut 1. The axis 10 of rotation of the balancing link 9 is parallel to the axis of rotation of the crank, the center point A _{3 of the} balancing link coincides with the intersection point of the axis 10 with the plane A ₁ yz . The longitudinal axis of the guide 2 is located in the plane A ₁ xy. The circle described by the hinges 11 and 12 is in the plane A ₁ yz. The longitudinal axis of the guide 2 intersects the axis of rotation of the crank 4 at an acute angle α.
The parameters of the mass geometry of the mechanism are determined by the following relationships:
S _xy1 = S _xz1 = S _yz1 = S _xy2 = S _xz2 = S _xy3 = S _xz3 = S _yz3 = 0; (1)
I _xy1 = I _xz1 = I _xy2 = I _xz2 = I _yz2 = I _xy3 = I _xz3 = 0; (2)
I _x2 = 0; I _y2 = I _z2 = l • S _yz2 ;
I _x1 + 2r ² (m ₂ - l ^-1 • S _yz2 ) - kI _x3 = 0, (3)
where S _xyi , S _xzi , S _yzi are the static moments of mass of the ith link relative to the planes of the Cartesian coordinate system (Axyz) _i associated with the ith link; i - link number: 1 - crank, 2 - connecting rod, 3 - balancing link; A _i is the link pole: A ₁ and A ₃ are the central points of the crank and the balancing link, respectively, A ₂ is the center of the hinge connecting the connecting rod to the crank; the axes A ₁ x ₁ and A ₃ x ₃ coincide with the rotation axes of the crank and balancing link, respectively, the axis A ₂ x ₂ coincides with the longitudinal axis of the connecting rod; I _xi , I _yi , I _zi , I _xyi , I _xzi , I _yzi - axial and centrifugal moments of inertia of mass of the i-th link in the coordinate system (Axyz) _i ; m ₂ is the mass of the connecting rod, r is the length of the crank arm, l is the length of the crank, k is the ratio of the angular velocity of the balancing link to the angular velocity of the crank.

 Mass geometry parameters not included in dependencies (1), (2), (3) are assigned for structural reasons.

Opposite crank-slide mechanism works as follows. When the crank 3 is rotated around axis 4, the hinges 11 and 12 move along a circle lying in the plane A ₁ yz. The sliders 5 and 6 move along the guide 2, and the balancing link 9 rotates around the axis 10. For a full revolution of the crank 3, the sliders 5 and 6 will make a direct and reverse stroke along the guide 2, the link 9 will make k revolutions around the axis 10. With continuous rotation of the crank 3 the sliders 5 and 6 will reciprocate along the guide 2 in mutually opposite directions, and the link 9 will rotate around the axis 10 in the direction opposite to the rotation of the crank.

The fulfillment of dependences (1), the identity of the connecting rods, the identity of the sliders and the geometric symmetry of the opposite crank-slide mechanism with respect to the center A ₁ , ensure the translation of the common center of mass of its links to a fixed point located on the segment A ₁ A ₃ . In this regard, the main vector of all inertial forces of the mechanism is zero at any position of the mechanism, that is, the mechanism is statically balanced.

To prove the condition that the principal moment of the inertia forces of the mechanism equal to zero, we replace the set of inertia forces of all points of each connecting rod with the inertia forces of two replacement points. From dependences (1) and (2) related to the connecting rod, it follows that each connecting rod can be considered as a straight thin rod. The conditions for the dynamic location of the link mass for such a connecting rod model will be satisfied if the first replacement point with mass l ^-1 • S _{yz2 is} placed in the center of the hinge connecting the connecting rod and the slider, and the second point with mass (m ₂ - l ^-1 • S _yz2 ) - in the center of the hinge connecting the connecting rod to the crank. After this arrangement of the masses of each connecting rod, the determination of the main moment of inertia of the mechanism can be made under the following assumptions: the connecting rods have no mass, the mass of each slide is increased by the mass of the first replacement point, the mass of the crank is increased by twice the mass of the second replacement point, and the center of mass of the crank is still at the center point, and the crank moment of inertia relative to the axis of rotation is
I _x1 + 2r ² (m ₂ - l ^-1 • S _yz2 ).

M $\genfrac{}{}{0ex}{}{\text{ин}}{\text{y}}$ = 0, M $\genfrac{}{}{0ex}{}{\text{ин}}{\text{z}}$ = 0.
где ε₁ и ε₃ - угловые ускорения соответственно кривошипа и уравновешивающего звена; остальные величины в этих формулах взяты без изменения из (3).The inertia forces of the sliders remain mutually balanced even after the addition of masses of replacement points. Therefore, the magnitude of the main moment of the inertia forces of the mechanism will be determined only by the inertia forces of the balancing link 9 and the crank 3 with increased inertia. The projections of the main moment of the inertial forces of the mechanism on the axis of the fixed coordinate system A ₁ xyz are expressed by the formulas

M $\genfrac{}{}{0ex}{}{\text{in}}{\text{y}}$ = 0, M $\genfrac{}{}{0ex}{}{\text{in}}{\text{z}}$ = 0.
where ε ₁ and ε ₃ are the angular accelerations of the crank and balancing link, respectively; the remaining quantities in these formulas are taken without change from (3).

Given the dependence (3), as well as the dependence between the angular accelerations of the balancing link and the crank (ε ₃ = -kε ₁ ), we obtain M $\genfrac{}{}{0ex}{}{\text{in}}{\text{x}}$ = 0. This result in combination with the above formulas (M $\genfrac{}{}{0ex}{}{\text{in}}{\text{y}}$ = 0, M $\genfrac{}{}{0ex}{}{\text{in}}{\text{z}}$ = 0) allows us to conclude: the main moment of inertia of the mechanism in question is zero, that is, the mechanism satisfies the condition of momentary equilibrium. (On the static balance of the mechanism mentioned above).

 Thus, the opposite crank-slider mechanism, the mass geometry of which satisfies the dependencies (1), (2), (3), is completely balanced. The inertia forces of the links of this mechanism are mutually compensated. The mechanism is excluded from the number of vibration sources transmitted to the foundation of the machine.

 Using the proposed solution allows to reduce the vibration activity of the machine unit, improve the working conditions of the maintenance personnel, and increase labor productivity.

Sources of information
1. Vidyakin Yu. A., Dobrosklonsky Ye. B., Kondratyeva T.F. Box compressors. - L.: Engineering (Leningrad. Department), 1979, p. 279.

 2. RF patent N 2085791, 6 F 16 H 21/16, 1997.

 3. Artobolevsky I.I. Theory of mechanisms. - M .: Nauka, 1965, p. 776.

Claims (1)

Opposite crank-slide mechanism, comprising a rack with a guide, two identical sliders installed in the guide, a two-shoulder crank in the form of a hollow shaft with a rotation axis fixed on the rack, two identical connecting rods, each of which is pivotally connected to the corresponding slide and the crank arm, while the axis of the slide guide intersects the axis of rotation of the crank at an acute angle at the center point of the crank, and the hinges connecting the ends of the connecting rods to the corresponding shoulders of the crank are made spherical and and are installed on diametrically opposite points on the inner surface of the hollow shaft, characterized in that the balancing link is contacted with the external surface of the crank shaft with a rotation axis fixed on the column parallel to the axis of rotation of the crank, while the angular velocity of the balancing link is proportional in magnitude and opposite in magnitude the direction of the angular velocity of the crank, and the parameters of the geometry of the masses of the links of the mechanism are determined by the dependencies:
S _xy1 = S _xz1 = S _yz1 = S _xy2 = S _xz2 = S _xy3 = S _xz3 = S _yz3 = 0; (1)
J _xy1 = J _xz1 = J _xy2 = J _xz2 = J _yz2 = J _xy3 = J _xz3 = 0; (2)
J _x2 = 0; J _y2 = J _z2 = l • S _yz2 ;
J _x1 + 2r ² (m ₂ - l ^-1 • S _yz2 ) - k • J _x3 = 0, (3)
where S _xyi , S _xzi , S _yzi are the static moments of mass of the ith link relative to the planes of the Cartesian coordinate system (Axyz) _i associated with the ith link;
i - link number: 1 - crank, 2 - connecting rod, 3 - balancing link;
A _i is the link pole: A ₁ and A ₃ are the central points of the crank and the balancing link, respectively, A ₂ is the center of the hinge connecting the connecting rod to the crank; the axes A ₁ x ₁ and A ₃ x ₃ coincide with the rotation axes of the crank and balancing link, respectively, the axis A ₂ x ₂ coincides with the longitudinal axis of the connecting rod;
J _xi , J _yi , J _zi , J _xyi , J _xzi , J _yzi - axial and centrifugal moments of inertia of mass of the i-th link in the coordinate system (Axyz) _i ;
m ₂ is the mass of the connecting rod;
r is the crank arm length;
l is the length of the connecting rod;
k is the ratio of the angular velocity of the balancing link to the angular velocity of the crank.