CN103234700A - Method for quickly measuring rotational inertia of measured object - Google Patents

Abstract

The invention discloses a method for quickly measuring the moment of inertia of a measured object. It includes the following steps: (a) Adjustment of the fixed-axis moment of inertia measurement device; (b) Measuring the shading time of the loading platform without load; (c) Measuring the shading time of the loading platform being put into the object to be measured; (d) ) to determine the formula for the moment of inertia of the measured object. The process of the present invention is simple, and solves the key technical problems in the prior art that the actual measurement of the moment of inertia of a fixed-axis rotating rigid body is slow, the measurement period is long, and the repeatability of the measurement is poor; the measurement method of the present invention can be used Effectively reduce the adverse effects brought by the friction torque, greatly improve the accuracy of measurement, and meet the needs of users to the greatest extent.

Description

Measure the method for testee moment of inertia fast

Technical field

The present invention relates to a kind of measuring method of moment of inertia, relate in particular to a kind of method of quick measurement testee moment of inertia.Belong to mechanical field.

Background technology

Measurement for solid moment of inertia usually runs in the middle of the human being's production practice.Such as considering it in a lot of fields such as the research of Machine Design manufacturing, article for rotation, the derivation of kinematical theory.Many parts of producing in the factory also need their moment of inertia is measured, and whether meet standard with some rotating property of determining them.

There is the moment of inertia of the dead axle rotary rigid body of certain rule to try to achieve with theoretical Calculation Method for some regular shape, mass distribution, but do not have the moment of inertia of the governed dead axle rotary rigid body of certain rule for complex-shaped or mass distribution, just can only obtain with the method for experiment measuring.

The moment of inertia of dead axle rotary rigid body is carried out actual measurement, and method commonly used at present mainly contains: three string pendulum mensurations, rock mensuration, Experiment of Moment of Inertia instrument mensuration.When but the method for utilizing these measurements is measured, their measuring speed is all slower, and the cycle of measurement is also longer, and the repeatability of measurement neither be fine, the measurement number of times of Shi Shiing much maybe needs the object measured a lot of if desired, will demonstrate the deficiency of above-mentioned those measuring methods more.

Summary of the invention

The present invention is directed to above-mentioned problems of the prior art, through developing meticulously and doing painstaking research, a kind of measuring method that can measure the moment of inertia of article for rotation simply effectively, rapidly and accurately is provided, solved effectively in the prior art, the moment of inertia of dead axle rotary rigid body has been carried out that the speed of actual measurement is slow, measuring period is long and the problem of the repeatability difference measured.

Technical scheme of the present invention comprises the steps:

(a) to the adjustment of dead axle rotation inerttia device: reverse article carrying platform with external force, make article carrying platform turn over an angle around vertical axes, and make anti-dazzling screen through the photoelectricity door, torsion spring is twisted and has put aside energy simultaneously, utilizes locking plate that article carrying platform is pinned;

(b) measure shading time of article carrying platform zero load: separate unlock chip, the shading time when measuring unloaded article carrying platform anti-dazzling screen is through the photoelectricity door during to the position revolution of balance under the effect of torsion spring;

(c) measure the shading time that article carrying platform is put into testee: after repeating above-mentioned steps (a), the shading time when anti-dazzling screen is through the photoelectricity door when adopting step (b) to measure article carrying platform to be loaded with testee;

(d) determine the moment of inertia formula of testee: establish: the moment of inertia when article carrying platform is unloaded is J; Total moment of inertia that article carrying platform loads behind the testee is J ₁Anti-dazzling screen is r to the distance of vertical axes; The width of anti-dazzling screen is △ l, and the shading time during disk zero load revolution is △ t; The shading time when turning round behind the disk loading measured object is △ t ₁

According to conservation of mechanical energy:

$\frac{1}{2}\·J\·{\left(\frac{\mathrm{\Δl}}{\mathrm{\Δt}\·r}\right)}^2=\frac{1}{2}\·J_1\·{\left(\frac{\mathrm{\Δl}}{{\mathrm{\Δt}}_1\·r}\right)}^2$

Equation gets above separating:

$J_1={\left(\frac{\mathrm{\Δ}{t}_1}{\mathrm{\Δt}}\right)}^2\·J$

So moment of inertia of measured object:

The structure of described measurement mechanism is as follows: article carrying platform is installed on the vertical axes that base is connected by bearing, and article carrying platform links to each other with torsion spring on being fixed in vertical axes, is provided with anti-dazzling screen at the adapting position of the lower surface edge of article carrying platform; Link to each other with vertical axes and can be provided with and the corresponding photoelectricity door of anti-dazzling screen around the upper end of the sway brace of vertical axes rotation, in order to measure in the article carrying platform turning course anti-dazzling screen through the shading time of photoelectricity door.

Be fixed with support on the described base, the adapting position of this support be provided with the article carrying platform excircle on the locking plate that is complementary of locked groove, in order to lock, put article carrying platform.

A done determinator all should have a definite value (constant) for the shading time △ t of disk after decontroling unloaded garden dish of some fore shaft lockings; The known moment of inertia J of unloaded rotary disk also has certain value, they is placed operational formula (), so the moment of inertia J of testee _{To be measured}Just only by variable △ t ₁Unique definite.If make a corresponding operational software, top input △ t ₁Measured value signal, and utilize operational software to carry out computing according to formula (), terminal output function value J _{To be measured}Institute is signal accordingly, and it is shown, and is the readable measured value that gets the moment of inertia of testee by display finally.

Advantageous effect of the present invention is as follows:

Technology of the present invention is simple, has solved in the prior art, and the moment of inertia of dead axle rotary rigid body is carried out that the speed of actual measurement is slow, measuring period is long and the key technical problem of the repeatability difference measured; Utilize measuring method of the present invention can reduce effectively by the moment of friction adverse effect, improve the degree of accuracy of measuring greatly.Particularly because measured data are few, operational formula is simple relatively, the good reproducibility of measurement data, and can set out corresponding simple program, and utilize computer to carry out computing, show final measurement rapidly.Measurement mechanism of the present invention has simple and reasonable for structure, and measuring speed is exceedingly fast, measurement range wide and the high advantage of measurement result accuracy.Therefore, measurement mechanism of the present invention is used in batch that the rotation inerttia of workpiece is to be easy to, and the testee of measuring also can be very big workpiece.The present invention has satisfied user's needs to greatest extent, has favorable economic benefit and social benefit.

Description of drawings

Fig. 1 is the perspective view of measurement mechanism of the present invention;

Critical part among the figure: article carrying platform 1, photoelectricity door 2, anti-dazzling screen 3, sway brace 4, base 5, support 6, locking plate 7, torsion spring 8, vertical axes 9.

Embodiment

Below, with reference to accompanying drawing, in conjunction with the embodiments the present invention is described in more detail.

Embodiment 1

The perspective view of measurement mechanism of the present invention as shown in Figure 1, the structure of its measurement mechanism is as follows: article carrying platform 1 is installed on the vertical axes 9 that base 5 is connected by bearing, and below the article carrying platform 1 be fixed in vertical axes 9 on torsion spring 8 link to each other, be provided with anti-dazzling screen 3 at the adapting position of the lower surface edge of article carrying platform 1; Link to each other with vertical axes 9 and can be provided with and anti-dazzling screen 3 corresponding photoelectricity doors around the upper end of the sway brace 4 of vertical axes 9 rotations, in order to measure the shading time that anti-dazzling screen passes through the photoelectricity door in article carrying platform 1 turning course.Be fixed with support 6 on the above-mentioned base 5, the adapting position of this support 6 be provided with article carrying platform 1 excircle on the locking plate 7 that is complementary of locked groove, in order to lock, put article carrying platform 1.

The present invention utilize mass distribution evenly, have the thin plate of certain rigidity to make article carrying platform 1, the article carrying platform 1 after carrying out can calculate exactly with respect to the moment of inertia J of vertical axes 9, if measured object is bigger, can suitably add the yardstick of big loading platform 1.Be the irony annulus below with the testee, its external diameter is 20.00cm, and internal diameter is 17.80cm, and quality is that 585.0g rotates the method for carrying out rotation inerttia for example around vertical axes 9, comprises the steps:

(a) to the adjustment of dead axle rotation inerttia device: reverse article carrying platform 1 with external force, make article carrying platform 1 turn over an angle around vertical axes 9, and making anti-dazzling screen 3 through photoelectricity door 2, torsion spring 8 is twisted and has put aside energy simultaneously, utilizes locking plate 7 that article carrying platform 1 is pinned;

(b) measure shading time of article carrying platform zero load: separate unlock chip 7, the shading time △ t when measuring unloaded article carrying platform 1 anti-dazzling screen 3 is through photoelectricity doors 2 during to the position revolution of balance under the effect of torsion spring 8, measurement data sees Table one;

(c) measure the shading time that article carrying platform is put into testee: how much axle center of irony annulus are overlapped with vertical axes 9, after repeating above-mentioned steps (a), the shading time △ t when anti-dazzling screen 3 is through photoelectricity doors 2 when adopting step (b) to measure article carrying platform to be loaded with testee irony annulus ₁, measurement data sees Table one;

(d) determine the moment of inertia formula of testee and ask the result: known: the quality of article carrying platform is 680.0g; Total moment of inertia that article carrying platform loads behind the testee is J ₁The article carrying platform radius is 15.00cm; Moment of inertia when article carrying platform is unloaded for the J theoretical value is:

$J_1=\frac{1}{2}\×0.680\×{0.1500}^2=7.650\×{10}^{-3}(K_g\·m^2)$

The moment of inertia of measured object:

The data of utilizing table one to survey:

The torsion angle of article carrying platform is increased by 30 degree carry out similar measurement, measurement data sees Table two:

Utilize the measured data of table two:

J _Annulus=5.2423 * 1O ^-3(K _gM ²)

And the calculated value of tested annulus moment of inertia:

The annulus rotation inerttia value of utilizing table one, the measured data computation of table two to go out goes respectively relatively to obtain relative error with theoretical value:

$E_1=\frac{(5.2420+5.2229)\×{10}^{-3}}{5.2420\×{10}^{-3}}\×100\%=0.36\%$

$E_2=\frac{(5.2423+5.2420)\×{10}^{-3}}{5.2420\×{10}^{-3}}\×100\%=0.0057\%$

Protection scope of the present invention is as the criterion with claims, is not subjected to the restriction of specific embodiment.

Table one:

Measure number of times	1	2	3	4	5	6	On average
								△t(ms)	18.22	18.25	18.22	18.21	18.22	18.20	18.220
△t 1(ms)	23.64	23.64	23.63	23.65	23.60	23.65	23.635

Table two:

Measure number of times	1	2	3	4	5	6	On average
								△t(ms)	13.48	13.45	13.51	13.52	13.48	13.51	13.492
△t 1(ms)	17.53	17.50	17.50	17.51	17.54	17.51	17.515

Claims (2)

1. The method for quickly measuring the moment of inertia of the measured object is characterized in that it comprises the following steps: (a) Adjustment of the fixed-axis moment of inertia measurement device: twist the loading platform (1) with external force, make the loading platform (1) turn around the vertical axis (9) at an angle, and make the shading sheet (3) pass through The photoelectric door (2), meanwhile, the torsion spring (8) is twisted to accumulate energy, and the loading platform (1) is locked by the locking piece (7); (b) Measure the shading time of the unloaded loading platform: Unlock the locking piece (7), and measure when the unloaded loading platform (1) rotates to the balanced position under the action of the torsion spring (8) and the shading piece (3) passes through the photoelectric The shading time of the door (2); (c) Measure the shading time of the object under test on the loading platform: after repeating the above step (a), use step (b) to measure the shading sheet (3) passing through the photogate (2 ) shading time; (d) Determine the moment of inertia formula of the measured object: Suppose: the moment of inertia when the loading platform is empty is J; the total moment of inertia after loading the measured object on the loading platform is J ₁ ; is r; the width of the shading sheet is △l, and the shading time of the disc when it rotates without load is △ _t ; According to the conservation of mechanical energy: $\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;l</span>}}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;l</span>}}{{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ Solve the above equation to get: ${\mathrm{<span\; class="notranslate">\; J</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; t</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&Delta;t</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; J</span>}$ So the moment of inertia of the measured object is:

The structure of the measuring device is as follows: the loading platform (1) is installed on the vertical shaft (9) fixed to the base (5) through bearings, and the loading platform (1) is fixed on the vertical shaft (9) The upper torsion spring (8) is connected, and a shading sheet (3) is provided on the matching position of the lower surface edge of the loading platform (1); it is connected with the vertical axis (9) and can be wound around the vertical axis (9) ) The upper end of the rotating support arm (4) is provided with a photogate (2) corresponding to the shading sheet (3), which is used to measure the shading time when the shading sheet passes through the photogate during the rotation process of the loading platform (1). 2. The method for quickly measuring the moment of inertia of the measured object according to claim 1, characterized in that: the base (5) is fixedly connected with a bracket (6), and the fitting position of the bracket (6) is set There is a lock piece (7) matching the lock groove on the outer circumference of the loading platform (1) for locking and placing the loading platform (1).

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