CN104792460A - Horizontal test method for revolve-body polar moment of inertia - Google Patents

Abstract

The invention relates to a horizontal test method for revolve-body polar moment of inertia. During horizontal test of polar moment of inertia, a revolve body is tightly held through a steel ring; in a state of equilibrium, a product torsionally vibrates freely along the rotary axis direction of the product when an instantaneous driving moment is exerted to the steel ring. The moment of inertia, namely the size of the polar moment of inertia of the product along a rotary axis can be calculated out by measuring the torsional vibration cycle of the product. With the method, the revolve-body polar moment of inertia can be effectively tested, convenience in test is achieved, and the method is small in test error and high in precision.

Description

The horizontal method of testing of a kind of solid of revolution polar moment of inertia

Technical field

The present invention relates to the horizontal method of testing of a kind of solid of revolution polar moment of inertia, belong to moment of inertia technical field of measurement and test.

Background technology

Suppose two points at the two ends of an object, and 2 company's being aligneds are through object, object is with this line for rotation center, and its each part rotates to when fixing a position is when rotated the same shape, and this is standard solid of revolution.At present, the moment of inertia test needs for solid of revolution are improved, to obtain the higher method of testing of precision.

Summary of the invention

The object of the present invention is to provide the horizontal method of testing of a kind of solid of revolution polar moment of inertia, to test polar moment of inertia of turning better; When equilibrium state, as applied an instantaneous driving moment to steel loop, product just can along its free torsional oscillation in revolving shaft direction.By measuring its torsional oscillation cycle, the size of product along the moment of inertia (i.e. polar moment of inertia) of axis of rotation can be calculated.Polar moment of inertia measuring instrument adopts roll mode to measure polar moment of inertia.

To achieve these goals, technical scheme of the present invention is as follows.

The horizontal method of testing of a kind of solid of revolution polar moment of inertia, when horizontal polar moment of inertia test, solid of revolution is held tightly by steel loop; When equilibrium state, as applied an instantaneous driving moment to steel loop, product just can along its free torsional oscillation in revolving shaft direction.By measuring its torsional oscillation cycle, the moment of inertia of product along axis of rotation and the size of polar moment of inertia can be calculated;

According to law of rotation, formed by frock, rotating shaft and object under test, Equation of Motion is:

Jφ′+Kφ+M＝0 (1)

In formula, J is moment of inertia; K is the drawing coefficient of extension spring; M is damping torque; φ is angular displacement.If the impact ignoring damping has:

φ′+ω ²φ＝0 (2)

In formula: ${\mathrm{\ω}}^2=\frac{K}{J};$

Because: ${\mathrm{\ω}}^2=\left(\frac{2\mathrm{\π}}{T}\right)=\frac{K}{J};$

So: $J=\frac{K}{4{\mathrm{\π}}^2}{T}^2$

Wherein J:

J＝J ₀+J _d＝AT ²(3)

J ₀for the moment of inertia of the system of rocking itself; J _dfor object under test moment of inertia; T is the hunting period of pallet and determinand, so formula (3) can be written as:

$J_d=\frac{K}{4{\mathrm{\π}}^2}{T}^2-J_0={\mathrm{AT}}^2-J_0---\left(4\right)$

In formula: it is a constant, is determined by torsion-bar spring.

Formula (4) is exactly measure the computing formula of moment of inertia, from formula (4), if A and J ₀given, if measure pallet add determinand after T hunting period, just can calculate the moment of inertia J of object under test _d.Discuss below and how to measure A and J ₀.

First, testing apparatus is placed the first standard body, the first standard body measures T hunting period _b1, have according to above formula:

$J_{b_1}={\mathrm{AT}}_{b_1}^2-J_0---\left(5\right)$

Then, testing apparatus is placed the second standard body, the second standard body measures T hunting period _b2, have according to above formula:

$J_{b_2}={\mathrm{AT}}_{b_2}^2-J_0---\left(6\right)$

Can be obtained by (5) and (6) two formulas:

$A=\frac{J_{b_1}-J_{b_2}}{T_{b_1}^2-T_{b_2}^2}---\left(7\right)$

$J_0=\frac{J_{b_1}-J_{b2}}{T_{b_1}^2-T_{b_2}^2}{T}_{b_2}^2-J_{b_1}---\left(8\right)$

In formula: J _b1it is the theoretical value of the first standard body moment of inertia; J _b2it is the theoretical value of the second standard body moment of inertia; T _b1hunting period is rocked after adding the first standard body; T _b2hunting period is rocked after adding the second standard body.

In above-mentioned computing method,

(1) analysis of measurement errors: Δ J _d=2AT Δ T, omits J ₀after can obtain:

${\mathrm{\μ}}_{\mathrm{Jd}}=\frac{\mathrm{\Δ}{J}_d}{J_d}\≈\frac{2\mathrm{AT\ΔT}}{{\mathrm{AT}}^2}\≈2\frac{\mathrm{\ΔT}}{T}=2{\mathrm{\μ}}_T---\left(8\right)$

From (8), the relative error of rotation inerttia, is only the twice of time test relative error, is very little.

(2) site error:

1. the skew of solid of revolution longitudinal axis position is to polar moment of inertia Accuracy:

The impact of rotating shaft skew on polar moment of inertia, if bias is e, rotating shaft and solid of revolution centre of form axle deviation distance are △, and solid of revolution to centre of form axle polar moment of inertia is:

J _{pole (centre of form)}=J _{pole (barycenter)}+ Me ²(9)

Solid of revolution to the polar moment of inertia of the rotating shaft departed from is:

J _{pole (bias)}=J _{pole (barycenter)}+ (e ²+ Δ ²-2e Δ cos θ) M

J _{pole (bias)}=J _{pole (centre of form)}+ Δ ²m-2e Δ cos θ M

Δ J _pole ^max=J _{pole (bias)} ^max-J _{pole (centre of form)}=M Δ ²+ 2e Δ M (10)

The relative error (maximum) of polar moment of inertia:

Relative error size, relevant with bias.

2. the impact of rotating shaft skew on equator moment of inertia:

If y-axis is by centroidal axis, so solid of revolution is (J to the moment of inertia of y-axis _y); Due to positioning error cause with y' axle for rotating shaft, so J _y'with J _ydifference is exactly error.

From parallel axis theorem:

J _y'＝J _y+d ²M (12)

3. axes of rotation skew is on the impact of pole and equator moment of inertia:

Apply rotation axis formula to obtain when tilt alpha angle:

$J_x={\cos }^2\mathrm{\α}\·J_{x_1}+J_{y_1}{\sin }^2\mathrm{\α}+2J_{x_1{y}_1}\cos \mathrm{\α}\·\sin \mathrm{\α}$

$J_y={\sin }^2\mathrm{\α}\·J_{x_1}+J_{y_1}{\cos }^2\mathrm{\α}-2J_{x_1{y}_1}\cos \mathrm{\α}\·\sin \mathrm{\α}---\left(13\right)$

When α angle is very little, and J _xyalso, time very little, above formula can be reduced to:

$J_x={\cos }^2\mathrm{\α}\·J_{x_1}+J_{y_1}{\sin }^2\mathrm{\α}$

$J_y={\sin }^2\mathrm{\α}\·J_{x_1}+J_{y_1}{\cos }^2\mathrm{\α}---\left(14\right)$

When during α≤0.5 °, inclined angle alpha is to polar moment of inertia J _xthe impact of relative error is no more than 2 × 10 ^-3, just less on the impact of equator moment of inertia.

4. the impact on moment of inertia simultaneously when axes of rotation skew and skew exist:

When axes of rotation skew and skew exist simultaneously, can be superposed by above-mentioned analysis result and obtain.

(3) damping is on the impact of moment of inertia test result:

1) impact of damping

If solid of revolution to be measured is very long, and diameter is comparatively large, although rotating speed is comparatively slow, air resistance must be considered.Before analysis damps torsional vibrations, first analyze the process that undamped oscillation surveys moment of inertia.

1. undamped surveys equator moment of inertia J _d:

The first step: T hunting period measuring idle running platform ₀(now turntable not putting anything);

Second step: measure the hunting period T of turntable together with standard component _s;

3rd step: measure the hunting period T of turntable together with solid of revolution to be measured _d;

Record three known number T ₀, T _s, T _d, according to the relation between vibration frequency and moment of inertia, three equations can be listed, solve three unknown quantitys: idle running platform moment of inertia J _o, solid of revolution rigidity k and solid of revolution moment of inertia J to be measured _d.

System of equations by following:

$\left\{\begin{array}{c}{T_o}^2=4{\mathrm{\π}}^2\frac{J_o}{k}\\ {T_s}^2=4{\mathrm{\π}}^2\frac{J_s+J_0}{k}\\ {T_d}^2=4{\mathrm{\π}}^2\frac{J_d+J_0}{k}\end{array}\right.$ (J _sstandard component moment of inertia)

Can obtain:

$k=\frac{4{\mathrm{\π}}^2{J}_0}{{T_0}^2},J_s=\frac{{T_o}^2}{{T_s}^2-{T_d}^2}{J}_0,J_d=\frac{{T_d}^2-{T_o}^2}{{T_s}^2-{T_o}^2}{J}_s$

2. the equator moment of inertia recorded during damping is had:

Be directly proportional assuming that swing the moment of resistance to pivot angle speed first power.At this moment swing equation is:

In formula: k is torsion spring stiffness

Above formula can turn to:

In formula:

ratio of damping and undamped frequency respectively;

As n < P, the solution of the differential equation is:

Damped frequency: ${\stackrel{\&OverBar;}{p}}^2=p^2-n^2$

Damping period:

$\stackrel{\&OverBar;}{T}=\frac{2\mathrm{\&pi;}}{\stackrel{\&OverBar;}{p}}=\frac{2\mathrm{\&pi;}}{\sqrt{p^2-n^2}}---\left(17\right)$

Again by measuring damped oscillation cycle T, calculate the moment of inertia J of solid of revolution to be measured.

2) the practical measuring method of damping:

The vibration equation of damping is:

Its general solution is:

The ratio of two amplitudes is in succession:

be the cycle recorded under having damping situation, n is ratio of damping.

For improving measuring accuracy, the ratio of two amplitudes of desirable m all after date of being separated by.That is:

As long as record amplitude and the cycle in the amplitude in i-th cycle and the i-th+m cycle, just ratio of damping n can be obtained.

Such as: t _d=0.8642 "

Then ratio of damping: $n=\frac{-1.470+1.560}{10\&times;0.8642}=0.0104$

Through 10 cycles, because air damping amplitude reduces 1 °, damping is quite large, but result of calculation shows that it still can omit the impact in cycle, sees formula (17).

(4) rotation inerttia precision analysis:

In moment of inertia computing formula, A and J ₀can accurately measure in advance.The main source of such error is the measuring error of T hunting period, and cycle T source of error has two: one to be time determination error, and two is ignore the error that damping torque causes.

Time determination error can be obtained by error analysis below the impact that moment of inertia is tested, and the computing formula of moment of inertia is:

J＝AT ²(18)

So according to formula of error transmission:

$\begin{array}{c}\mathrm{\&delta;J}=2\mathrm{AT\&delta;T}\\ \mathrm{\&eta;}=\frac{\mathrm{\&delta;J}}{J}=\frac{2\mathrm{AT\&delta;T}}{{\mathrm{AT}}^2}=2\frac{\mathrm{\&delta;T}}{T}\end{array}---\left(19\right)$

Due to, the response frequency of moment of inertia testing apparatus period measurement sensor is 1000HZ, and the response time, therefore assert that time difference method is very high, time determination error can be ignored at below 1ms.

Moment of inertia computing formula releases when ignoring damping action, according to theory of oscillation, considers damping effect to rotation inerttia device, has been at this moment cycle stretch-out.If T ' is for there being the cycle of damping, vibration damping is exponential damping, has according to torsional oscillation principle:

$J\frac{d_{\mathrm{\&theta;}}^2}{d_t^2}+c\frac{d_{\mathrm{\&theta;}}}{d_t}+\mathrm{k\&theta;}=0---\left(20\right)$

Further conversion has:

$\frac{d_{\mathrm{\&theta;}}^2}{d_t^2}+2n{\mathrm{\&theta;}}^{\&prime;}+P^2\mathrm{\&theta;}=0---\left(21\right)$

In formula:

$n=\frac{c}{2J},$

$p=\sqrt{\frac{k}{J}}$

Torsional oscillation non trivial solution is:

${\mathrm{\&theta;}}_{n+1}=A_0{e}^{-{\mathrm{nt}}_{n+1}}\cos (p_d{t}_{n+1}-{\mathrm{\&alpha;}}_0)---\left(22\right)$

${\mathrm{\&theta;}}_n=A_0{e}^{-{\mathrm{nt}}_n}\cos (p_d{t}_n-{\mathrm{\&alpha;}}_0)---\left(23\right)$

So:

$\frac{{\mathrm{\&theta;}}_{n+1}}{{\mathrm{\&theta;}}_n}{e}^{-n(t_{n+1}-t_n)}\frac{\cos (p_d{t}_{n+1}-{\mathrm{\&alpha;}}_0)}{\cos (p_d{t}_n-{\mathrm{\&alpha;}}_0)}---\left(24\right)$

Again because:

t _n+1＝t _n+T _α

p _αt _n+1＝p _αt _n+p _αT _α＝p _αt _n+2π (25)

So:

$\frac{{\mathrm{\&theta;}}_{n+1}}{{\mathrm{\&theta;}}_n}=e^{-n(t_{n+1}-t_n)}=e^{-T_{\mathrm{\&alpha;}}n}---\left(26\right)$

$L_n\frac{{\mathrm{\&theta;}}_{n+1}}{{\mathrm{\&theta;}}_n}=\mathrm{\&beta;}=-T_{\mathrm{\&alpha;}}n---\left(27\right)$

So have:

$n^2=\frac{{\mathrm{\&beta;}}^2}{T_{\mathrm{\&alpha;}}^2}=\frac{{\mathrm{\&beta;}}^2}{{\left(2\mathrm{\&pi;}\right)}^2\&CenterDot;p_{\mathrm{\&alpha;}}^{-2}}\&ap;\frac{{\mathrm{\&beta;}}^2}{4{\mathrm{\&pi;}}^2\&CenterDot;p_0^{-2}}---\left(28\right)$

By $p_d^2=p_0^2-n^2$ Can obtain:

$p_d=p_0\sqrt{1-\frac{n^2}{p_0^2}}---\left(29\right)$

By $T_0=\frac{2\mathrm{\&pi;}}{p_0},T_d=\frac{2\mathrm{\&pi;}}{p_d}$ Can obtain:

${T_d}^2=\frac{T_0^2}{(1-\frac{n^2}{p_0^2})}=T_0^2(1+\frac{n^2}{p_0^2})---\left(30\right)$

Formula (29) this formula is substituted into formula (30) can obtain:

$T_d^2\&ap;T_0^2(1+\frac{{\mathrm{\&beta;}}^2}{4{\mathrm{\&pi;}}^2\&CenterDot;\frac{p_0^2}{p_0^2}})\&ap;T_0^2(1+\frac{0.25{\mathrm{\&beta;}}^2}{{\mathrm{\&pi;}}^2})---\left(31\right)$

That is:

$\begin{array}{c}{T}^{\&prime;2}=T^2[1+0.25{\left(\frac{\mathrm{\&beta;}}{\mathrm{\&pi;}}\right)}^2]\\ \mathrm{\&beta;}=\ln \left(\frac{{\mathrm{\&theta;}}_n}{{\mathrm{\&theta;}}_{n+1}}\right)\end{array}---\left(32\right)$

In the method, period measuring utilizes photoelectric sensor to realize, and it is using photovalve as detecting element, first measured change is converted to the change of light signal, then converts light signal to electric signal further by photovalve.Cycle is measured by sampling time sequence, adopts photo-electricity calculagraph, with high speed monocycle C8051F series monolithic timer composition timing circuit.Photoelectrical coupler a kind ofly infrared light emission device and infrared light are accepted device and signal processing circuit etc. is encapsulated in device in same base.When input electrical signal is added on input end luminescent device LED, LED is luminous, and optical receiving set part accepts light signal and converts electric signal to, is then directly exported by electric signal, or electric signal is amplified and is processed into the output of standard digital level, realize conversion and the transmission of " electrical-optical-electricity ".Period measuring device is formed primarily of photoelectric sensor and balancing point, and be arranged on base interior, photoelectricity, to Shoot type sensor and external cabling socket, can be connected with industrial computer by cable.

In order to avoid ambient light interference, the photoelectrical coupler execution cycle is adopted to gather, in the signal processing, moment timer being started to timing is needed to measure accurately, in order to anti-interference in circuit, have employed the broadening shaping circuit of level reference and the certain time-delay with certain thresholding, but now must there be a stochastic error timing start time, in like manner also inevitable when next count pulse arrives exist a stochastic error on exact time, measurement as a complete cycle characterizes periodic quantity with the time between two pulses and obviously can not reach requirement, in order to reduce this error to greatest extent, according to the condition that hunting period is substantially constant, measure multiple cycle and take the mean as the measured value in cycle.At this moment, if vibration continuously, then each cycle pendulum end is by twice through reflection spot, and in one-period, form two count pulses, can know that the time often between adjacent three pulses should be one-period, namely adjacent two time period sums are one-period.Final disposal route is: remove the several cycles the most initially having outer force-disturbance, two often adjacent time periods are adopted to be one-period number, timing from effective count pulse, every two count pulses are a cycle data, and remove the complete cycle number (every two pulses) obtained and then the periodic quantity obtaining this moment with total timing time.Because system is only responsive to the exact time of first pulse, pulse is afterwards only relevant to meter number of cycles, insensitive to concrete due in, will obtain periodic quantity comparatively accurately after such multiple averaging.

By torsional oscillation equation periodic solution can rock the moment of inertia of system itself:

$J_0=\frac{K}{4{\mathrm{\&pi;}}^2}{T}_0^2---\left(33\right)$

T ₀for the torsional oscillation cycle of the system of rocking itself; K is the torsion spring stiffness rocked.

For measuring K value, available standards part is demarcated, cycle T when measurement standard part is shimmy together with fixture _sso, have:

$J_S+J_0=\frac{K}{4{\mathrm{\&pi;}}^2}{T_S}^2---\left(34\right)$

Cancellation K, can obtain:

$J_0=J_S\frac{{T_0}^2}{{T_S}^2-{T_0}^2}---\left(35\right)$

Wherein:

$K=\frac{4{\mathrm{\&pi;}}^2{J}_S}{{T_S}^2-{T_0}^2}.$

At this, just can turn the survey time after demarcation.If the cycle that solid of revolution records is T _d, then tested moment of inertia is:

$J_d=\frac{{T_d}^2-{T_0}^2}{T_{S}2-{T_0}^2}{J}_S---\left(36\right)$

Present analysis T _derror, by the J in (4.31) formula _s, T ₀, T _s, T _dbe considered as independent variable, after differential:

$\mathrm{\&Delta;}{J}_d=J_d\frac{\mathrm{\&Delta;}{J}_S}{J_S}+2[\frac{T_d\&CenterDot;\mathrm{\&Delta;}{T}_d}{{T_d}^2-{T_0}^2}-\frac{T_0\&CenterDot;\mathrm{\&Delta;T}}{{T_d}^2-{T_0}^2}-\frac{T_S\&CenterDot;\mathrm{\&Delta;}{T}_S}{{T_S}^2-{T_0}^2}+\frac{T_0\&CenterDot;\mathrm{\&Delta;}{T}_0}{{T_S}^2-{T_0}^2}]J_d---\left(37\right)$

Absolute error Δ J can be obtained thus _d, at this moment above formula is every all gets positive sign:

$\mathrm{\&Delta;}{J}_d=\{\frac{\mathrm{\&Delta;}{J}_S}{J_S}+2[\frac{T_d\mathrm{\&Delta;}{T}_d}{{T_d}^2-{T_0}^2}+\frac{T^S\&CenterDot;{\mathrm{\&Delta;T}}^S}{{T_S}^2-{T_0}^2}+\frac{({T_d}^2-{T_S}^2)(T_0\&CenterDot;\mathrm{\&Delta;}{T}_0)}{({T_d}^2-{T_0}^2)({T_0}^2-{T_S}^2)}\left]\right\}\mathrm{Jd}---\left(38\right)$

Variance Δ J can be obtained further _d:

$\mathrm{\&Delta;}{J}_d=\{{{\mathrm{\&mu;}}_{J1}}^2+4{[\frac{{T_d}^2\&CenterDot;\mathrm{\&Delta;}{T_d}^2}{{({T_d}^2-{T_0}^2)}^2}+\frac{{T_S}^2\&CenterDot;\mathrm{\&Delta;}{T_S}^2}{{({T_S}^2-{T_0}^2)}^2}+\frac{({T_d}^2-{T_S}^2){T_0}^2\mathrm{\&Delta;}{T_0}^2}{{({T_d}^2-{T_0}^2)}^2{({T_S}^2-{T_0}^2)}^2}]}^{\frac{1}{2}}\}{J}_d---\left(39\right)$

If equal precision measurement, then:

ΔT ₀＝ΔT _S＝ΔT _d(40)

Make again:

$\frac{J_S}{J_0}=\frac{{T_S}^2-{T_0}^2}{{T_0}^2}=K_1---\left(41\right)$

$\frac{J_d}{J_0}=\frac{{T_d}^2-{T_0}^2}{{T_0}^2}=K_2---\left(42\right)$

Substitute in above formula, after arranging, can obtain:

${\mathrm{\&mu;}}_J={\{{{\mathrm{\&mu;}}_{J_1}}^2+4[{(1-\frac{K_1}{K_2})}^2\frac{1}{{K_1}^2}+\frac{{(1+\frac{1}{K_1})}^2}{(1+K_1)}+\frac{{(1+\frac{1}{K_2})}^2}{(1+K_2)}\left]{{\mathrm{\&mu;}}_{T_0}}^2\right\}}^{1/2}---\left(43\right)$

In formula:

${\mathrm{\&mu;}}_{T_0}=\frac{\mathrm{\&Delta;}{T}_0}{T_0}$

μ _jfor the relative error of testee moment of inertia; for the relative error of standard component moment of inertia; the relative error of hunting period during for only having frock clamp; J ₀for the moment of inertia of frock clamp; J ₁for the moment of inertia of standard component; J ₁=K ₁j ₀; J is the moment of inertia of measured piece; J=K ₂j ₀.K ₁for the ratio of standard component moment of inertia and frock clamp moment of inertia; K ₂for the moment of inertia of measured piece and the ratio of frock clamp moment of inertia;

Require as basic norm to meet measuring accuracy, adopt the method for error analysis to carry out stepping, if T ₀measuring accuracy be 1 × 10 ^-5second, and (T ₀>=0.5 second), at this moment K ₁, K ₂desirable K ₁>=0.3, K ₂>=0.3, can μ be ensured _j< 1 × 10 ^-3.K ₂>=0.3 mean the moment of inertia of testee minimum be the fixture inertia of 0.3 times, or on the contrary: the moment of inertia maximal value of fixture is 3.3 times of measured piece moment of inertia, if exceed the measuring accuracy that this scope will affect measured piece.

This beneficial effect of the invention is: the method can test solid of revolution polar moment of inertia, convenient test effectively, and test error is little, and precision is high.

Embodiment

Below in conjunction with embodiment, the specific embodiment of the present invention is described, better to understand the present invention.

Embodiment

The horizontal method of testing of solid of revolution polar moment of inertia in the present embodiment, when horizontal polar moment of inertia test, solid of revolution is held tightly by steel loop; When equilibrium state, as applied an instantaneous driving moment to steel loop, product just can along its free torsional oscillation in revolving shaft direction.By measuring its torsional oscillation cycle, the moment of inertia of product along axis of rotation and the size of polar moment of inertia can be calculated;

According to law of rotation, formed by frock, rotating shaft and object under test, Equation of Motion is:

Jφ′+Kφ+M＝0 (1)

In formula, J is moment of inertia; K is the drawing coefficient of extension spring; M is damping torque; φ is angular displacement.If the impact ignoring damping has:

φ′+ω ²φ＝0 (2)

In formula: ${\mathrm{\&omega;}}^2=\frac{K}{J};$

Because: ${\mathrm{\&omega;}}^2=\left(\frac{2\mathrm{\&pi;}}{T}\right)=\frac{K}{J};$

So: $J=\frac{K}{4{\mathrm{\&pi;}}^2}{T}^2$

Wherein J:

J＝J ₀+J _d＝AT ²(3)

J ₀for the moment of inertia of the system of rocking itself; J _dfor object under test moment of inertia; T is the hunting period of pallet and determinand, so formula (3) can be written as:

$J_d=\frac{K}{4{\mathrm{\&pi;}}^2}{T}^2-J_0={\mathrm{AT}}^2-J_0---\left(4\right)$

In formula: it is a constant, is determined by torsion-bar spring.

Formula (4) is exactly measure the computing formula of moment of inertia, from formula (4), if A and J ₀given, if measure pallet add determinand after T hunting period, just can calculate the moment of inertia J of object under test _d.Discuss below and how to measure A and J ₀.

First, testing apparatus is placed the first standard body, the first standard body measures T hunting period _b1, have according to above formula:

$J_{b_1}={\mathrm{AT}}_{b_1}^2-J_0---\left(5\right)$

Then, testing apparatus is placed the second standard body, the second standard body measures T hunting period _b2, have according to above formula:

$J_{b_2}={\mathrm{AT}}_{b_2}^2-J_0---\left(6\right)$

Can be obtained by (5) and (6) two formulas:

$A=\frac{J_{b_1}-J_{b_2}}{T_{b_1}^2-T_{b_2}^2}---\left(7\right)$

$J_0=\frac{J_{b_1}-J_{b2}}{T_{b_1}^2-T_{b_2}^2}{T}_{b_2}^2-J_{b_1}---\left(8\right)$

In formula: J _b1it is the theoretical value of the first standard body moment of inertia; J _b2it is the theoretical value of the second standard body moment of inertia; T _b1hunting period is rocked after adding the first standard body; T _b2hunting period is rocked after adding the second standard body.

In the method, period measuring utilizes photoelectric sensor to realize, and it is using photovalve as detecting element, first measured change is converted to the change of light signal, then converts light signal to electric signal further by photovalve.Cycle is measured by sampling time sequence, adopts photo-electricity calculagraph, with high speed monocycle C8051F series monolithic timer composition timing circuit.Photoelectrical coupler a kind ofly infrared light emission device and infrared light are accepted device and signal processing circuit etc. is encapsulated in device in same base.When input electrical signal is added on input end luminescent device LED, LED is luminous, and optical receiving set part accepts light signal and converts electric signal to, is then directly exported by electric signal, or electric signal is amplified and is processed into the output of standard digital level, realize conversion and the transmission of " electrical-optical-electricity ".Period measuring device is formed primarily of photoelectric sensor and balancing point, and be arranged on base interior, photoelectricity, to Shoot type sensor and external cabling socket, can be connected with industrial computer by cable.

In order to avoid ambient light interference, the photoelectrical coupler execution cycle is adopted to gather, in the signal processing, moment timer being started to timing is needed to measure accurately, in order to anti-interference in circuit, have employed the broadening shaping circuit of level reference and the certain time-delay with certain thresholding, but now must there be a stochastic error timing start time, in like manner also inevitable when next count pulse arrives exist a stochastic error on exact time, measurement as a complete cycle characterizes periodic quantity with the time between two pulses and obviously can not reach requirement, in order to reduce this error to greatest extent, according to the condition that hunting period is substantially constant, measure multiple cycle and take the mean as the measured value in cycle.At this moment, if vibration continuously, then each cycle pendulum end is by twice through reflection spot, and in one-period, form two count pulses, can know that the time often between adjacent three pulses should be one-period, namely adjacent two time period sums are one-period.Final disposal route is: remove the several cycles the most initially having outer force-disturbance, two often adjacent time periods are adopted to be one-period number, timing from effective count pulse, every two count pulses are a cycle data, and remove the complete cycle number (every two pulses) obtained and then the periodic quantity obtaining this moment with total timing time.Because system is only responsive to the exact time of first pulse, pulse is afterwards only relevant to meter number of cycles, insensitive to concrete due in, will obtain periodic quantity comparatively accurately after such multiple averaging.

The above is the preferred embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.

Claims (2)

1. the horizontal method of testing of solid of revolution polar moment of inertia, is characterized in that: when horizontal polar moment of inertia test, solid of revolution is held tightly by steel loop; When equilibrium state, as applied an instantaneous driving moment to steel loop, product just can along its free torsional oscillation in revolving shaft direction; By measuring its torsional oscillation cycle, the moment of inertia of product along axis of rotation and the size of polar moment of inertia can be calculated;

According to law of rotation, formed by frock, rotating shaft and object under test, Equation of Motion is:

Jφ′+Kφ+M＝0 (1)；

In formula, J is moment of inertia; K is the drawing coefficient of extension spring; M is damping torque; φ is angular displacement; If the impact ignoring damping has:

φ′+ω ²φ＝0 (2)

In formula: ${\mathrm{\&omega;}}^2=\frac{K}{J};$

Because: ${\mathrm{\&omega;}}^2=\left(\frac{2\mathrm{\&pi;}}{T}\right)=\frac{K}{J};$

So: $J=\frac{K}{{4\mathrm{\&pi;}}^2}{T}^2$

Wherein J:

J＝J ₀+J _d＝AT ²(3)

J ₀for the moment of inertia of the system of rocking itself; J _dfor object under test moment of inertia; T is the hunting period of pallet and determinand, so formula (3) can be written as:

$J_d=\frac{K}{{4\mathrm{\&pi;}}^2}{T}^2-J_0={\mathrm{AT}}^2-J_0---\left(4\right)$

In formula: it is a constant, is determined by torsion-bar spring;

Formula (4) is exactly measure the computing formula of moment of inertia, from formula (4), if A and J ₀given, if measure pallet add determinand after T hunting period, just can calculate the moment of inertia J of object under test _d; Discuss below and how to measure A and J ₀;

First, testing apparatus is placed the first standard body, the first standard body measures T hunting period _b1, have according to above formula:

$J_{b1}={\mathrm{AT}}_{b1}^2-J_0---\left(5\right)$

Then, testing apparatus is placed the second standard body, the second standard body measures T hunting period _b2, have according to above formula:

$J_{b_2}={\mathrm{AT}}_{b_2}^2-J_0---\left(6\right)$

Can be obtained by (5) and (6) two formulas:

$A=\frac{J_{b_1}-J_{b_2}}{T_{b_1}^2-T_{b_2}^2}---\left(7\right)$

$J_0=\frac{J_{b_1}-J_{b_2}}{T_{b_1}^2-T_{b_2}^2}{T}_{b_2}^2-J_{b_1}---\left(8\right)$

In formula: J _b1it is the theoretical value of the first standard body moment of inertia; J _b2it is the theoretical value of the second standard body moment of inertia; T _b1hunting period is rocked after adding the first standard body; T _b2hunting period is rocked after adding the second standard body.

2. the horizontal method of testing of solid of revolution polar moment of inertia according to claim 1, it is characterized in that: in the method, period measuring utilizes photoelectric sensor to realize, it is using photovalve as detecting element, first measured change is converted to the change of light signal, then convert light signal to electric signal further by photovalve, cycle is measured by sampling time sequence, adopts photo-electricity calculagraph, with high speed monocycle C8051F series monolithic timer composition timing circuit, photoelectrical coupler a kind ofly infrared light emission device and infrared light are accepted device and signal processing circuit etc. is encapsulated in device in same base, when input electrical signal is added on input end luminescent device LED, LED is luminous, and optical receiving set part accepts light signal and converts electric signal to, is then directly exported by electric signal, or electric signal is amplified and is processed into the output of standard digital level, realize conversion and the transmission of " electrical-optical-electricity ", period measuring device is formed primarily of photoelectric sensor and balancing point, and be arranged on base interior, photoelectricity, to Shoot type sensor and external cabling socket, can be connected with industrial computer by cable, in order to avoid ambient light interference, the photoelectrical coupler execution cycle is adopted to gather, in the signal processing, moment timer being started to timing is needed to measure accurately, in order to anti-interference in circuit, have employed the broadening shaping circuit of level reference and the certain time-delay with certain thresholding, but now must there be a stochastic error timing start time, in like manner also inevitable when next count pulse arrives exist a stochastic error on exact time, measurement as a complete cycle characterizes periodic quantity with the time between two pulses and obviously can not reach requirement, in order to reduce this error to greatest extent, according to the condition that hunting period is substantially constant, measure multiple cycle and take the mean as the measured value in cycle, at this moment, if vibration continuously, then each cycle pendulum end is by twice through reflection spot, and in one-period, form two count pulses, can know that the time often between adjacent three pulses should be one-period, namely adjacent two time period sums are one-period, final disposal route is: remove the several cycles the most initially having outer force-disturbance, two often adjacent time periods are adopted to be one-period number, timing from effective count pulse, every two count pulses are a cycle data, and remove the complete cycle number (every two pulses) obtained and then the periodic quantity obtaining this moment with total timing time, because system is only responsive to the exact time of first pulse, pulse is afterwards only relevant to meter number of cycles, insensitive to concrete due in, will obtain periodic quantity comparatively accurately after such multiple averaging.