JPH0543045B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION Field of Industrial Application The present invention relates to an improvement of a non-circular gear in a positive displacement flowmeter in which the non-circular gear is the main moving part.

BACKGROUND ART FIG. 5 is a diagram showing an example of a non-circular gear type flowmeter. As is well known, the non-circular gear type flowmeter is an oval gear type flowmeter and is the mainstream of positive displacement flowmeters. As shown in Fig. 5, this non-circular gear type flowmeter has rotation centers O ₁ and O _{2 as fixed points in an outer cylinder 3 that integrally constitutes an inlet 1 and an outlet 2} , and the rotation angle is determined from each fixed point. At the distances of γ ₁ and γ _{2 obtained as functions of θ 1 and θ 2 , the} condition for rolling contact is γ ₁ + γ ₂ = constant...(1) γ ₁ dθ ₁ = γ ₂ dθ ₂ ...(2 ) Pitch curve that satisfies: γ=a/1±b _cps 2θ _i ...(3) (a: similarity coefficient, b flatness, i=1, 2) Rotors 4 and 5 of non-circular gears It is configured to rotatably support and contain the

The non-circular gear type flowmeter rotates due to the torque difference caused by the pressure difference between the inflow pressure P ₁ and the outflow pressure P ₂ acting on the rotors 4 and 5, respectively.

When a fluid with a constant flow rate passes through the non-circular gear, the non-circular gear rotates with a constant areal velocity. In this condition, (1) above,
If we calculate the rotational angular velocity ωi of a non-circular gear using Equation (2) as a representative, we get ωi = (1+b-√1-b/√1+b) × (1±b _cps 2θ _i )(1± b _cps 2θ _i +b ² )/(1±(
b _cps 2θ _i ) {(1+b) (1±b _cps 2θ _i )−2(1−b
)}+(1-b) ² (1+b)...(4) It is given as a sine function.

Furthermore, calculating the angular acceleration from equation (4), rotors 4 and 5
The angular accelerations ω・₁ and ω・₂ are as shown by the dotted lines in Figure 6,
The relative angular acceleration ω・=ω・
₁ -ω・₂ has positive and negative polarities every 1/4 period, as shown by the solid line. This is non-circular gears 4 and 5 are 1/4
This shows that the torque changes in the driving and driving forces every cycle.If the moment of inertia of the rotor is I, the inertia force Iω is maximum at the midpoint of the pitch curve γi = γi (θ), γ ₁ = γ ₂ . Become.

Means for Solving the Problems The present invention provides a pitch curve for a non-circular gear in which relative angular acceleration ω, which causes tooth profile wear, is constant, and its outline will first be explained. Now, assuming the condition that the relative angular acceleration ω is constant ω・=ω・₁ −ω・₂ =α=const...(5), let the angular accelerations ω・₁ and ω・₂ be functions of time t, When ω 1 −ω ₂ is calculated by determining the integral constant with t=to at the intermediate point γ ₁ =γ ₂ , the following is obtained: _{ω 1 −ω 2} =−α(to−t) (6).

If the pitch curve γ=γ(t), θ=θ(t), and RA is the major axis, the areal velocity dA/dt is expressed by equation (7).

2 (dA/dt) = (RA ² − γ ² ₁ ) ω ₁ + (RA ² −
γ ² ₂ ) ω ₂ = CA = const...(7) Substituting the rolling contact conditions (1) and (2) for the pitch curve
Rearranging equation (7), ω ₁ =CA/K ² ×1−γ ₁ /K/(RA/K) ² −γ ₁ /K(1
−γ ₁ /K)……(8) ω ₂ =CA/K ² ×1−γ ₂ /K/(RA/K) ² −γ ₂ /K(1
-γ ₂ /K)...(9) From this, (ω ₁ -ω ₂ ) is given by the following equation.

ω ₁ −ω ₂ =CA/K ² ×1−2γ ₂ /K/(RA/K) ² −γ ₂
/K(1-γ ₂ /K)...(10) In equations (6) and (10) and at t=0, finding γ ₁ and γ ₂ as the condition of γ ₁ =RA, Also, from equation (2), γ ₁ ω ₁ = γ ₂ ω ₂ , and (6), (11),
From equation (12), Derive equation (3), further integrate this, insert the condition θ ₁ = θ ₂ = 0 at t = 0, find the relationship between the argument angles θ ₁ and θ ₂ of the pitch curve, and further calculate the n-lobe shape. In the case of the pitch curve, γ and θ are determined by setting θ ₁ +θ ₂ =π/2 at t=to, is obtained.

Here, 0≦t≦to, and α is It is.

As described above, a non-circular gear with pitch curves expressed by equations (14), (15), and (16) is obtained, which satisfies the condition ω・=α=cost.

Embodiment FIG. 1 shows the bilobal (n=2) pitch curve according to the present invention expressed by the above equations (14), (15), and (16) as a solid line A, and the conventional example equation (3) The oval pitch curve represented is shown by a dotted line B. In the embodiment shown by the solid line A in FIG. 1, if ω·=const, the pitch curve becomes discontinuous at the major axis and minor axis positions, and has a so-called salient point.

Figure 3 shows the angular acceleration in the 1/2 rotation section when a constant flow rate fluid passes through the pitch curve of the non-circular gear according to the present invention. Acceleration remains constant. 0, respectively, for the time lapse T of one rotation.
At the salient points of T/4 and T/2, there is a discontinuous change from ω to -ω, but this is because a pair of non-circular gears rotating at a constant angular velocity converts to driving or driven. This shows that.

In the above embodiment, the pitch curve has a peak, but in this case, a second tooth profile such as a tocolloid curve is used as the tooth profile. It should be noted that it has a continuous pitch curve with no salient points and realizes ω = const of the present invention, and a continuous curve that is continuously connected to the pitch curve of the present invention is connected in a minute section near the salient point. , ω・= in the range of time tm≦t≦to
const, in the range 0≦t≦tm, ω・=αt/tm
A pitch curve as shown by the solid line A in Figure 2, which gives the curve of Shown below.

Effects As described above, according to the present invention, a non-circular gear having a pitch curve with a constant relative angular acceleration is realized, so that the inertial force acting mutually on the non-circular gear becomes constant. As a result, the tooth profile is not worn locally as in the conventional case, which not only increases durability, but also eliminates the increase in friction torque caused by increased tooth contact pressure, improving the accuracy of the flowmeter. It is possible to realize a volumetric flowmeter with extremely excellent characteristics such as improved and stable operation and reduced noise during operation.

[Brief explanation of the drawing]

1 and 2 are views showing the profiles of the non-circular gears according to the present invention, respectively, and FIGS. 3 and 4 are views showing the 1/2 rotation section when using the non-circular gears according to the present invention, respectively. Diagram showing angular acceleration, fifth
This figure is a diagram for explaining an example of a positive displacement flowmeter using a conventional non-circular gear, and FIG. 6 is a diagram showing angular acceleration when a conventional gear is used. 1... Inlet, 2... Outlet, 3... Outer cylinder,
4, 5...Rotor (non-circular gear).

Claims (1)

[Scope of Claims] 1. A positive displacement flowmeter having a pair of non-circular gears as a main moving part that mesh and rotate in accordance with the flow rate, wherein the pair of non-circular gears have a constant area velocity and a constant relative angular acceleration. A non-circular gear for a positive displacement flowmeter characterized by having a curved line. 2. A non-circular positive displacement flowmeter according to claim 1, characterized in that portions near the major axis and minor axis of the pitch curve are joined by a continuous curve to form a pitch curve without discontinuities. gear.