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Dual-Impulse Response Model by a Spall and the Size Evaluation in Rolling Element Bearings

Dual-Impulse Response Model  by a Spall and the Size Evaluation in Rolling Element Bearings
Dual-Impulse Response Model  by a Spall and the Size Evaluation in Rolling Element Bearings

6606IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.62,NO.10,OCTOBER

2015

Dual-Impulse Response Model for the Acoustic Emission Produced by a Spall and the Size

Evaluation in Rolling Element Bearings

An-bo Ming,Wei Zhang,Zhao-ye Qin,and Fu-lei Chu

Abstract—The size of the spalling area has a signi?cant in?uence on the operation performance and the remaining useful life of rolling element bearings.Therefore,spall size estimation is of great importance to the bearing perfor-mance degradation assessment and the life prediction.In this paper,the acoustic emission(AE)signal is used to evaluate the size of a single spall,considering the sensi-tivity of the AE signal to the incipient fault detection.First, based on the hypothesis that the AE signal is composed of two events for each passage of the rolling element across the spall,an analytical model,named as dual-impulse re sponse model,is developed to describe the AE signal.Then, an averaged dual-impulse interval determining method is proposed to evaluate the spall size.Finally,simulations and experiments are carried out to validate the proposed model and method.It is indicated that the proposed model de-scribes the collected AE signals more satisfactorily than the traditional vibration model involving only a single-impulse https://www.wendangku.net/doc/8b2763107.html,pared with the method performed by averaging real cepstra of the dual-impulse segments,the proposed method is more powerful in the inner and outer spall size estimation tests.

Index Terms—Acoustic emission(AE),rolling ele-ment bearings,size evaluation,spall,squared envelope spectrum.

I.I NTRODUCTION

R OLLING element bearings are critical and fragile com-ponents in a majority of rotating machines.Their failure is one of the most common causes of mechanical breakdowns in engineering applications.For example,the main support bearing is one of the most fragile components of a wind turbine [1]–[4].Therefore,bearing condition monitoring techniques have attracted great attention in the past decades[5]–[15].Many

Manuscript received October6,2014;revised March11,2015and May14,2015;accepted June19,2015.Date of publication August3, 2015;date of current version September9,2015.This work was supported in part by the National Natural Science Foundation of China under Grant51335006,in part by the Beijing Natural Science Foun-dation under Grant3131002,and in part by the Y outh Foundation of University under Grant2015QNJJ032.

A.Ming and W.Zhang are with the Xi’an High-Tech Institute, Xi’an710025,China(e-mail:79607672@https://www.wendangku.net/doc/8b2763107.html,;zhangweihuaiyu@ https://www.wendangku.net/doc/8b2763107.html,).

Z.Qin and F.Chu are with the State Key Laboratory of Tribology, Department of Mechanical Engineering,Tsinghua University,Beijing 100084,China(e-mail:qinzy@https://www.wendangku.net/doc/8b2763107.html,;chu?@mail. https://www.wendangku.net/doc/8b2763107.html,).

Color versions of one or more of the?gures in this paper are available online at https://www.wendangku.net/doc/8b2763107.html,.

Digital Object Identi?er10.1109/TIE.2015.2463767signal processing methods such as(squared)envelope analysis [16]–[18],cyclostationary analysis[19],and modulation inten-sity density[20]are introduced to detect the occurrence of a fault,such as pitting and spalling.However,the appearance of the?rst spall does not mean the end of the useful life.When the faulty bearing should be replaced,it is a more interesting and meaningful issue since a premature removal of the bearing from service may be very expensive,whereas chances cannot be taken with the safety of machines and/or personnel.In this instance,it is greatly helpful for the correct maintenance decision if the spall size can be exactly and promptly tracked. An accurate description of the fault-induced signal is the basis of the spall size evaluation.Much research has been performed based on vibration information due to its noninva-sive nature and major economic bene?t.In1984,McFadden and Smith[21]proposed an analytical model to describe the vibration produced by a single point defect on the inner race of a rolling element bearing under constant radial load.This model could satisfactorily explain the pattern of spectral lines observed and the manner in which these lines were in?uenced by the bearing parameters.Subsequently,involving the slippage between the rolling element and the inner/outer race,Antoni and Randall[22]developed the model into a stochastic form. Modeling the arrival time of the impulses induced by a spall as an independent increment process,the stochastic model could describe the in?uence of the random slippage of the rolling element on the races and reveal the smearing of the defect harmonics at higher frequencies.However,these investigations modeled the vibration as a single-impulse response of the bearing system and were dif?cult to quantify the spall size.In 1994,Epps and McCallion[23]discovered that the signature of the vibration signal originating from the passage of a rolling element over a?aking area was composed of two impulse responses.The?rst impulse response was originated from the entry of the rolling element into the fault,and the second part was induced by the departure of the rolling element from the fault.Naming the two points as the point of entry and the point of impact,the two scholars implied that the size of the fault was measurable if each event was visible in the time series.On this basis,Sawalhi and Randall[24]indicated that the acceleration signals resulting from the entry of the rolling element into the spall and exit from it were of different nature and the amplitudes of the two events were always greatly different.Furthermore, they developed an analytical model involving the two events to describe the observed phenomena.The entry event into the fault was modeled as a step response with mainly a low-frequency

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MING et al.:MODEL FOR AE PRODUCED BY SPALL AND SIZE EVALUATION IN ROLLING ELEMENT BEARINGS6607

content,whereas the departure event was modeled as an im-pulse response containing a much higher frequency component. Unfortunately,the spectral characteristics of the vibration sig-nal involving the two events were not further investigated.

A proper size evaluation index is another important element for the spall size evaluation.It is known that statistic indicators such as root mean squares(RMSs),kurtosis,and impulse energy are widely used to evaluate the bearing performance. However,these indicators are indirect index,and the relation-ship between those indicators and the spall size is complicated [9].In2011,Sawalhi and Randall[24]developed a direct spall size estimation method based on the estimation of the average interval between the entry and departure events in the vibration signal.Two approaches were proposed to enhance the entry event while keeping the impulse response.By averaging the power spectra of the windowed dual-impulse segments,the real cepstrum was used to quantify the interval between the two events.Since the amplitude of the de-stress response is often much smaller than that of the re-stress response and the fre-quency contents of the two events are different,the processing procedure,balancing both the amplitude and frequency con-tents of the two events,needs much expertise and is not conve-nient for real-time https://www.wendangku.net/doc/8b2763107.html,pared with the vibration, acoustic emission(AE)is more sensitive in detecting incipi-ent damage because the AE parameters such as RMS,maxi-mum amplitude,and kurtosis are more sensitive to the onset and growth of defects than vibration measurements[25]–[28]. Al-Ghamd and Mba[25]discovered that the duration of the impulse response was proportional to the circumferential fault size and the amplitude of the burst to the background noise was positively correlated to the fault size.They proposed a fault size estimation method by observing the associated AE burst duration in the time domain.However,the duration of the impulse response was determined by the load distribution, the rotating speed,the parameters of the AE transducer,and the distance between the fault and the transducer in a complicated manner.Hence,the proposed fault size estimation method is not suitable for the cases with only one single spall.

In order to evaluate the spalls more exactly,we have in-vestigated the spall size evaluation method by the AE signal. However,no proper analytical model could accurately describe the AE signal produced by the spall and explain the spectrum satisfactorily.Therefore,based on a carefully investigation on the characteristic of the AE signal induced by a single spall, an analytical model is developed and a fault size evaluation method is proposed in this paper.

II.P RESENTATION OF THE AE S IGNAL

A.Generation Mechanism of AE Events

Induced by a Spall

Without loss of generality,Fig.1(a)illustrates a sketch of a radial loaded bearing with a groove in the center of the load area.Suppose that the inner race rotates with a constant angular frequency ofωr and the diameter of the outer race is D o.Considering a tiny area[see AE in Fig.1(b)],which is a little larger than the groove,the radial load is assumed

to Fig.1.Sketch of the passing process of the rolling element across the spall.(a)Whole view sketch.(b)Zoomed-in view of the?aking area.

(c)Counterforce F(t)between the rolling element and the outer race.

(d)Differential of F(t).(e)Typical burst-type AE signal.

be invariable when the rolling element is passing across with a constant speed of v c if there is no fault.However,when a spall[see BD in Fig.1(b)]with the circumferential length of L occurs,the counterforce between the rolling element and the race changes adaptively.When a rolling element enters into the spall,a de-stress process happens for the loss of the material on the race.Consequently,an impulse or re-stress process occurs when the rolling element arrives at the middle point of the fault (point C).Fig.1(c)illustrates the corresponding counterforce between the rolling element and the race.It is shown that the force sharply changes at the points of entry and exit[see Fig.1(d)].Generally,burst-type AE is de?ned as the generation of transient elastic waves produced by a sudden redistribution of energy from localized sources within a material[29].In this case,with the sharp change of the force,energy redistribution will happen and generate transient elastic waves.Therefore, burst-type AE events will be produced at the points of entry and exit when a rolling element passes across a localized fault.As the shaft rotates,these two events,named as the dual-impulse response for simpli?cation,will cyclically appear in the series of the collected AE signals and the cyclical period of the dual-impulse response is dependent on the location of the spall[30].

B.Analytical Model

It is known that the AE transducer is produced on the basis of the resonance principle and the collected AE signal is actually the resonant vibration of the AE transducer.Based on the above analysis,the dual impulse is cyclically produced when the shaft rotates with a determined speed(see Fig.2).Therefore,the temporal waveform of the AE signal produced by a spall can be expressed as

x(t)=

+∞

k=?∞

[A1,k h(t?T k)+A2,k h(t?T k?T L,k)](1)ΔT k=T k?T k?1,?∞

6608IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.62,NO.10,OCTOBER

2015 Fig.2.Collected AE signal caused by a spall on the outer race of the

rolling element bearing.

where A1,k and A2,k denote the k th amplitudes of the dual-

impulse responses caused by the entry into and departure from

the spall of the rolling element,respectively;T k denotes the

arrival time of the k th dual-impulse responses;T L,k denotes

the interval of the k th dual-impulse responses;and h(t)is the

unit impulse response function of the AE transducer.

For the sake of simplicity,it is assumed that{T k}k∈Z is an

independent increment process with probability density func-

tionφT(T k),i.e.,{ΔT k}k∈Z is a delta-correlated point process

with probability density functionφT(ΔT k)and{T L,k}k∈Z is

a delta-correlated point process with probability density func-

tionψT

L (T L,k),and that both{A1,k}k∈Z and{A2,k}k∈Z are

periodically delta-correlated point https://www.wendangku.net/doc/8b2763107.html,ly,

E{T k}=k E{ΔT k}=kT(3)

E{T L,k}=T L=βT(4) where T is the averaged interval consumed by the adjacent rolling elements passing across the spall,T L is the averaged interval of the dual-impulse response,andβ=T L/T is the ratio of the averaged dual-impulse interval to the averaged repetitive interval.Moreover,both{A1,k}k∈Z and{A2,k}k∈Z

are assumed to be periodically correlated with a period Q strictly longer than T in order to encompass amplitude modula-tion.In this instance,the proposed model can describe an inner race fault or a rolling element fault.Although these assumptions are idealized from a physical standpoint,they will allow us to gain suf?cient insight into the analyzed phenomenon from simple calculation.It is worth noting that the proposed model should be carefully used in applications since it may not be suitable for the AE signal produced by multiple spall points.

III.F AULT S IZE E STIMATION M ETHOD

A.Geometrical Relationship Analysis

As stated above,if the dual-impulse phenomenon is visible in the collected AE signal,the spall size is measurable[23]. Suppose that the rolling elements experience pure rolling on the outer/inner race and the cage speed is invariant no matter whether the fault exists or not when the shaft rotates with a determined speed.The interval of the dual-impulse response corresponds to the half-width of the spall since the impact event takes place when the center of the rolling element arrives at the middle point of the spall.Then,the fault size can be theoretically determined based on the geometrical structure of the bearing.When the fault is located on the outer race,the relationship between the fault size and the dual-impulse interval can be expressed as follows[24]:

L o

2

πD o

Z

=

T L

T o

=T L f o(5)

L i

2

πD i

Z

=

T L

T in

=T L f i(6)

where Z denotes the number of the rolling element,T L denotes the interval between the entry and exit AE events,f o denotes the ball-passing frequency on the outer race,T o=1/f o,f i denotes the ball-passing frequency on the inner race,and T i=1/f i. Denotingβ=T L/T o orβ=T L/T i,fault size estimation can be carried out by

?L

o

=

2πD o

Z

?T

L

?T

o

=

2πD o

Z

?β(7)

?L

i

=

2πD i

Z

?T

L

?T

i

=

2πD i

Z

?β(8)

where?T L,?T o,and?βdenote the estimation of T L,T o,andβ, respectively.

B.Determination Method of the Dual-Impulse Interval Because of the randomness of the series{T L,k}k∈Z,an averaged estimation of the dual-impulse interval will be more meaningful.However,it is very dif?cult to estimate the dual-impulse interval directly from the temporal waveform.By considering that the envelope signal carries generous fault fea-tures and the autocorrelation function can ef?ciently protrude the self-similarity of the signal,therefore,the autocorrelation function of the envelope signal of the dual-impulse responses is calculated here as follows:

R x

e

(τ)=

+∞

u=?∞

r11,u R?

h e11

(uT+τ)+r22,u R?

h e22

(uT+τ)

+r12,u R?

h e12

((u+β)T+τ)+r21,u R?

h e21

((u?β)T+τ)

(9) where

r11,u=E

+∞

r=?∞

ˉA

1,r

ˉA

1,r+u

=

+∞

k=?∞

?r11,q exp

j2πkT

q

Q

(10)

r22,u=E

+∞

r=?∞

ˉA

2,r

ˉA

2,r+u

=

+∞

k=?∞

?r22,q exp

j2πkT

q

Q

(11)

r12,u=E

+∞

r=?∞

ˉA

1,r

ˉA

2,r+u

=

+∞

k=?∞

?r12,q exp

j2πkT

q

Q

(12)

MING et al.:MODEL FOR AE PRODUCED BY SPALL AND SIZE EVALUATION IN ROLLING ELEMENT BEARINGS6609

r21,u=E

+∞

r=?∞

ˉA

2,r

ˉA

1,r+u

=

+∞

k=?∞

?r21,q exp

j2πkT

q

Q

(13)

?h

e1

=h e(t)?φT(t)(14)

?h e2=h e(t)?φT(t)?ψT

L

(t).(15)

In(9),R{·}denotes the correlation operator,subscript“e”denotes the envelope signal,and{R?

h eij

,i,j=1,2}denotes the cross-correlation function of{?h ei,i=1,2}and{?h ej,j= 1,2}.From(10)–(13),{?r ij,q,i,j=1,2}denotes the q th Fourier coef?cient of{r ij,u,i,j=1,2}.Let

P1=

+∞

u=?∞

r11,u R?

h e11

(uT+τ)+r22,u R?

h e22

(uT+τ)

(16)

P2=

+∞

u=?∞

r12,u R?

h e12

((u+β)T+τ)

+r21,u R?

h e21

((u?β)T+τ).(17)

It is shown that P1is the summation of two repetitive impulse components sharing the same repetitive period of T,whereas P2is the companying“sidebands”,which carries the informa-tion of the dual-impulse interval.It is shown that the value of r11,u+r22,u is generally larger than that of r12,u+r21,u,the amplitude of the central impulse is usually bigger than those of the“sidebands”.Only when A1,r=A2,l,r∈Z,l∈Z,the “sidebands”are the most obvious.It means that the interval of the dual impulse is most measurable when the two amplitudes of the dual-impulse response are equivalent.

From above analysis,it can be seen that the averaged dual-impulse interval of the impulses can be estimated by evalu-ating the location of“sidebands”.However,the dual-impulse responses of incipient faults are very weak and usually buried in the noise.A powerful noise elimination operation is needed before the envelope calculation.Since the AE signal is the resonance of the AE transducer,a bandpass?lter whose center frequency is located around the resonance frequency will sat-isfy the demand of the noise elimination.Moreover,when the signal-to-noise ratio is bigger than unity in the envelope signal, the impulse feature can be further enhanced by a squaring oper-ation.Therefore,a novel method for the estimation of the dual-impulse interval is proposed by calculating the autocorrelation function of the squared envelope here.The main processing program is summarized as follows.

Step1:Filter the raw AE signal using a bandpass?lter whose center frequency is located around the resonance frequency of the AE transducer.For the convenience of application,an optimal complex Morlet?lterφ(f)= exp((?π2/σ2)×(f?f c)2)suggested in[31]is used here.The kurtosis measured from the squared envelope signal of the?ltered signal is employed to construct the objective function of the genetic algorithm.The optimal combination of both the center frequency f c and the bandwidthσof the bandpass?lter is determined by the

candidate solution with the largest kurtosis.The range of the center frequency is[0.1,0.4]×f s,whereas the range of the bandwidth is[0.01,0.49]×f s,where f s denotes the sampling frequency.

Step2:Calculate the squared envelope of the?ltered signal x(t).The squared envelope is given by x e(t)2=x(t)2+?x(t)2,where?x(t)is the Hilbert transform of x(t).It is worth noting that x e(t)is the envelope of the signal here and cannot be confused with the analytical form of the signal.

Step3:Calculate the autocorrelation function of the squared envelope of the?ltered signal.

Step4:Read the estimation value of the averaged dual-impulse interval and the averaged period of rolling element passing across the spall in the inner/outer race,namely,?T L,?T

o

,or?T i.Generally,the squared envelope spectrum is used to diagnose the occurrence and the location of the bearing fault.Therefore,the estimation of the ball-pass frequency ?f

o

or?f i is inevitable and can be helpful for the spall size evaluation.

Once the averaged dual-impulse interval and the fault char-acteristic frequency or its reciprocal are obtained,the spall size can be estimated based on(7)and(8).

IV.S IMULATIONS

Simulations were performed in this section to validate the proposed model and method.Because approximately90%of the bearing failure is caused by the defects on either outer race or inner race[32],only the outer and inner race faults are involved here.For simplicity,the AE transducer is assumed to be a single-degree-of-freedom system,whose unit impulse response function is determined by

h(t)=exp(?2πζf n t)sin(2πf n t),0≤t<+∞(18) whereζdenotes the relative damping ratio,and f n denotes the resonant frequency of the AE transducer.Sampled at20kHz, the AE waveforms and corresponding squared envelope spectra (SES),including both outer race fault and inner race fault signals,are produced and illustrated in Fig.3.In both cases, the corresponding parameter settings are listed as follows:f n is equal to3kHz,ζis equal to0.05,{ˉA1}k∈Z is equal to1, {ˉA2}k∈Z is equal to2,and T is equal to0.1s.{A1}k∈Z follows a normal distribution of N(ˉA1,0.0025ˉA1),{A2}k∈Z follows a normal distribution of N(ˉA2,0.0025ˉA2),and{ΔT k}k∈Z follows a normal distribution of N(T,0.0025T).However,in order to illustrate the in?uence of the different dual-impulse intervals,βof the inner race fault is0.15,whereas that of the outer race fault is set to be0.10.In the inner race fault signal simulation,the amplitudes of the dual-impulse responses share the same amplitude modulation component of a(t)=cos(2π×2t)+1.It can be seen that all discrete spectral lines on the SES are amplitude modulated by an oscillatory component,and the modulation periods are different from each other,for the reason that the two signals are produced with different dual-impulse intervals.Such phenomenon is different from that of the traditional model involving only a single-impulse response.

6610IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.62,NO.10,OCTOBER

2015 Fig.3.Simulations added with white noise of0dB.(a)Waveform of the

outer race fault,i.e.,β=0.10.(b)SES of(a).(c)Waveform of the inner

race fault,i.e.,β=0.15.(d)SES of

(c).

Fig.4.Spectra and STFT of the simulations added with white noise

of?18dB.(a)Spectrum of the outer race fault signal and the corre-

sponding optimal complex Morlet?lter(red line).(b)STFT of the outer

race fault signal.(c)Spectrum of the inner race fault signal and the

corresponding optimal complex Morlet?lter(red line).(d)STFT of the

inner race fault signal.

Furthermore,both outer and inner race fault simulated sig-

nals,added with white noise of?18dB,are used to illustrate

the performance of the proposed dual-impulse interval estima-

tion method.Fig.4illustrates spectra,short-time Fourier trans-

form(STFT)distributions,and corresponding optimal complex

Morlet?lters of both outer and inner race fault simulated

signals.It can be seen that no fault information can be noticed

in the spectra owing to the heavy noise.Moreover,the impulses

induced by the fault are very weak near the resonance frequency

(3kHz)on the time–frequency plane,and no dual impulse is

visible.The optimal complex Morlet?lter adaptively designed

for the outer race fault signal is located at the frequency of

2.98kHz with the width of1.176kHz,whereas the inner

race fault signal is located at the frequency of2.987kHz with

the width https://www.wendangku.net/doc/8b2763107.html,ly,the carrier frequencies of

the impulse responses are estimated with very high accuracy,

although the signals are seriously disturbed by the noise.

The averaged real cepstrum of dual-impulse response seg-

ments proposed in[24]is also applied on the simulations

to validate the ef?cacy of the proposed method.The

results

https://www.wendangku.net/doc/8b2763107.html,parisons between different methods on simulations added

with white noise of?18dB.(a)and(b)Autocorrelation functions of the

squared envelope of raw signals.(c)and(d)Autocorrelation functions

of the squared envelope obtained by corresponding optimal complex

Morlet?lters.(e)and(f)Averaged real cepstra of the dual-impulse

segments?ltered by corresponding optimal complex Morlet?lters.

obtained by different methods are shown in Fig.5for conve-

nience of comparison.The bandpass?lters used in the averaged

real cepstrum calculation are identical with those used in the

proposed method.Fig.5(a)and(b)illustrates the autocorrela-

tion functions of squared envelopes of both outer and inner race

fault signals added with white noise of?18dB.It is shown

that the results are heavily disturbed by the noise and no dual-

impulse interval information,even no fault information,can be

noticed when the noise is not eliminated.In comparison,the

“sidebands”of0.01and0.015s are visible in Fig.5(c)and(d),

i.e.,the autocorrelation functions of squared envelopes of the

outer and inner race fault simulated signals,respectively,when

both signals are?ltered by corresponding optimal complex

Morlet?lters.It is indicated that adaptive?ltering of the

bandpass?lter plays an important role in the dual-impulse

interval estimation when the dual-impulse responses are buried

by heavy noises.Fig.5(e)and(f)illustrates the averaged real

cepstra of the dual-impulse segments obtained in the outer

and inner race fault https://www.wendangku.net/doc/8b2763107.html,pared with the autocorrela-

tion functions of the?ltered signals,the dual-impulse interval

information is very weak in both outer and inner race fault

cases,although the dual-impulse segments are obtained based

on the identical optimal complex Morlet?lters.It is indicated

that the proposed method is more powerful than the averaged

real cepstrum of dual-impulse response segments on the dual-

impulse interval estimation.It is worth noting that the?rst

“sideband”close to zero is usually used to estimate the averaged

dual-impulse interval because it is the most protrudent owing to

the?nite length of the collected signal in applications.

V.C ASE S TUDY

Several experimental investigations,involving an inner race

fault and two outer race faults,are carried out in the Machine

Fault Diagnostics Laboratory at Tsinghua University.

MING et al.:MODEL FOR AE PRODUCED BY SPALL AND SIZE EVALUATION IN ROLLING ELEMENT BEARINGS

6611

Fig.6.Experimental apparatus and the faults.(a)Test bearing rig.

(b)Measurement apparatus.(c)Inner race fault with1-mm width.(d) Spalls with different sizes in the outer race.

A.Test Equipments and Measurements

The corresponding experimental apparatus,used to investi-gate the running condition of the main support bearing in a wind turbine gear box with the type of FZXR1500,are shown in Fig.6.The shaft is driven by a three-phase asynchronous elec-tromotor via V-belt.Two taper roller bearings,mounted face to face,are used as supports of the test end,whereas a cylinder roller bearing supports at the driven end.With the ball diameter of25.4mm,the pitch circle diameter of140mm and ten rolling elements in total,the test bearing of type6220is located at the counter end of the motor.The load of11.76kN is applied vertically downhill by a two-stage lever.A groove with a width of1mm(3.94%of the rolling element)is planted in the inner race,whereas two spalls with the circumferential widths of 1.36mm(5.35%of the rolling element)and3.14mm(12.4%of the rolling element)are introduced by the electrodischarge ma-chine on the outer race,respectively.An AE transducer with the type ofα30is attached to the outside of the outer ring against the spall in order to catch details of the AE signals induced by the spall.Measurements are carried out at different speeds (297.4,368.4,442.1,515.7,and589.4r/min).Sampled at the frequency of2MHz,the AE signals are ampli?ed at40dB and collected with the length of5s.In order to eliminate the storage and calculation burden,the AE signals are decimated by20and the?nal sampling frequency of the signal is100kHz in the experimental tests.It is worth noting that all rotating speeds of the experiment tests are much higher than the truth speed in the wind turbine since the bearing rig is just designed for the vibration test of the main support bearing of the wind turbine and cannot work with very low speeds.Furthermore, the typeα30is marked on the AE transducer and indicates that the resonance frequency of the transducer is almost30kHz. B.Inner Race Fault Case

Fig.7illustrates the temporal waveform,spectrum,and STFT distribution of the AE signal collected at the speed

of Fig.7.STFT of the AE signal induced by the inner race fault at the speed of589.4r/min.(a)Spectrum and corresponding optimal complex Morlet?lter.(b)STFT distribution.(c)Raw waveform.

589.4r/min.It is shown that repetitive impulses are produced and the impulse amplitudes are modulated in the temporal waveform.On the time–frequency distribution plane,the dual-impulse response phenomena are noticed in many repetitive impulses and the energy of both parts is mainly concentrated at the frequency band of[10,30]kHz.Different from those of the vibration investigated in[24],such phenomena validate the hypothesis proposed in Section https://www.wendangku.net/doc/8b2763107.html,ly,two burst-type AE events are substantially produced at the points of entry and exit when a rolling element passes across a localized fault and the carrier frequencies of both parts are located around the resonance frequency of the AE transducer.Moreover,the spectrum is continuous in the resonance frequency band,which indicates that some random?uctuations exist.The optimal complex Morlet?lter adaptively designed by the proposed method is located at the frequency of17.947kHz with the width of16.429kHz.

Fig.8illustrates the raw waveforms,autocorrelation func-tions of the squared envelopes,and averaged real cepstra of the dual-impulse segments at speeds of294.7and589.4r/min.It is shown that the autocorrelation function of the squared envelope is dominated by the repetitive impulses with the interval of ball-pass period on the inner race.Moreover,the amplitudes of these impulses are also amplitude modulated.The“sidebands,”originated from the dual-impulse interval,are very close to the dominant impulses.However,the one located near zero is still protrudent enough for the dual-impulse interval determination. On the other hand,the averaged real cepstra are dominated by damping oscillation waveforms in both speed conditions,and little dual-impulse interval information can be obtained.It is worth noting that the autocorrelation function of the squared envelope of the?ltered signal is very similar to that of the original signal in both speed cases because the collected signals are mainly dominated by repetitive impulse responses and the optimal complex Morlet?lter catches the most energy of the dual-impulse responses.

The fault size evaluation results carried out at various speeds are listed in Table I.?f i and?T L are respectively obtained from the squared envelope spectrum and the autocorrelation function of the squared envelope.The estimation results obtained by

6612IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.62,NO.10,OCTOBER

2015

Fig.8.Estimation results of the inner race fault at different speeds.(a)and (b)Raw waveforms.(c)and (d)Autocorrelation functions of the squared envelope of raw signals.(e)and (f)Autocorrelation functions of the squared envelope of the ?ltered signals.(g)and (h)Averaged real cepstra of the dual-impulse segments.

TABLE I

E STIMATIONS O

F THE

G ROOVE IN THE I NNER R

ACE

the proposed method are denoted by “ACF”(autocorrelation function),whereas those obtained by the method in [24]are denoted by “ARC”(averaged real cepstrum).It is shown that the estimation values of the proposed method are much better than those of the method in [24]at all test speed conditions.The biggest error of 9.21%is at the speed of 294.7-r/min condition,whereas the smallest error of 0.70%is at the speed of 368.4r/min.

C.Outer Race Fault Case

Fig.9illustrates the temporal waveform,spectrum,and STFT distribution of the AE signal induced by the spall of 3.14mm at the speed of 589.4r/min.Similar to the inner fault case,the dual-impulse phenomena of the cyclical responses are visible when the rolling elements pass by the spall.Different from that of the vibration,of which the two events caused by the passage of the rolling element are different in the fre-quency content [24],the energy of both AE events of the dual-impulse response concentrates around the frequency of 35kHz.Moreover,the spectrum is continuous,and the optimal

complex

Fig.9.STFT of the AE signal induced by the outer race spall of 3.14mm at the speed of 589.4r/min.(a)Spectrum and corresponding optimal complex Morlet ?lter.(b)STFT distribution.(c)Temporal

waveform.

Fig.10.Estimation results of the 1.36-mm outer race fault with different speeds.(a)and (b)Raw waveforms.(c)and (d)Autocorrelation functions of the squared envelope of the original signals.(e)and (f)Autocorrela-tion functions of the squared envelope of the ?ltered signals.(g)and (h)Averaged real cepstra of the dual-impulse segments.

Morlet ?lter adaptively designed by the proposed method is located at the frequency of 35.545kHz with the width of 13.710kHz.It can be included that the proposed model is also suitable for the AE signal produced by an outer race fault.Because of the similar frequency content of the two events of the dual-impulse response,the feature extraction program using the AE signal may be more easier than the one using vibrations.Fig.10illustrates the raw waveforms,autocorrelation func-tions of the squared envelopes,and the averaged real cepstra of the AE signal produced by the 1.36-mm outer race fault at speeds of 294.7and 368.4r/min.It is shown that the dual-impulse responses can hardly be noticed in the raw waveform in both speed conditions.However,the sideband located near zero is still visible in the autocorrelation function of the squared

MING et al.:MODEL FOR AE PRODUCED BY SPALL AND SIZE EVALUATION IN ROLLING ELEMENT BEARINGS

6613

Fig.11.Estimation results of the 3.14-mm outer race fault with different speeds.(a)and (b)Raw waveforms.(c)and (d)Autocorrelation functions of the squared envelope of the original signals.(e)and (f)Autocorrela-tion functions of the squared envelope of the ?ltered signals.(g)and (h)Averaged real cepstra of the dual-impulse segments.

https://www.wendangku.net/doc/8b2763107.html,pared with Fig.10(c)and (d),i.e.,autocorrela-tion functions of squared envelopes of raw signals,Fig.10(e)and (f),i.e.,autocorrelation functions of squared envelopes of the ?ltered signals contain less noise and are more suitable for the dual-impulse interval https://www.wendangku.net/doc/8b2763107.html,paratively,the dual-impulse interval information is very weak on the averaged real cepstra.Fig.11illustrates the raw waveforms,autocorrelation functions of the squared envelopes,and the averaged real cepstra of the AE signal produced by the 3.14-mm outer race fault at speeds of 442.1and 515.7r/min.It is shown that the dual-impulse responses are more visible than those of the case with the fault size of 1.36mm.Both autocorrelation functions of the squared envelope and the averaged real cepstrum work well for the dual-impulse information https://www.wendangku.net/doc/8b2763107.html,bining Figs.10and 11,it can be concluded that the proposed method is more powerful than the averaged real cepstrum on the dual-impulse interval information extraction.However,the ?ltering program of the proposed method can be left out when the raw signal is dominated by dual-impulse responses or not seriously contaminated by noises.

The estimation results for the different spall sizes at various

speeds are listed in Tables II and III .?f o and ?T L are respectively

obtained from the SES and the autocorrelation functions of the squared envelopes or the averaged real cepstra.It is shown that the relative errors of the proposed method are smaller than 10%at all test speed conditions.In the evaluation of the 1.36-mm outer race fault,the proposed method is much better than the one in [24]for the reason that the relative errors of the proposed method are much smaller than those obtained by the method in [24]at all test speed conditions.Although the accuracy of the method in [24]greatly improves in the evaluation of the outer

TABLE II

E STIMATIONS O

F THE S PALL W ITH THE W IDTH OF 1.36

mm

TABLE III

E STIMATIONS O

F THE S PALL W ITH THE W IDTH OF 3.14

mm

race fault with 3.14mm,the proposed method has presented better accuracy at most tests.It is worth noting that the proposed method gives an average estimation of the impulse period and the dual-impulse interval since the Fourier transform is global.However,the rotating speed seems to have an effect on the size evaluation,which cannot be explained in this paper and further investigation is needed.

VI.C ONCLUSION

In this paper,the generation mechanism of the AE signal has been investigated,and an analytical model was developed to describe the AE signal produced by a single spall on the inner or outer race of a rolling element bearing under the radial load at ?rst.Then,an averaged dual-impulse interval determining method,used to evaluate the spall size,was carried out by cal-culating the autocorrelation function of the squared envelope.Finally,simulations and experiments were used to validate the model and the performance of the spall size estimation method.The investigation showed that two burst-type AE events were consequently produced when the rolling element entered into and departed from the spall and that both events could excite the resonant response of the AE transducer.With the capability of describing the dual-impulse response phenomena,the proposed analytical model was the extension form of the traditional model with only one single-impulse response and could explain some frequency characteristics,which the traditional model could not reveal satisfactorily.The dual-impulse response in-terval was presented as sidebands around the dominating repet-itive impulses in the autocorrelation function of the squared envelope.The incidental sidebands were most obvious when the amplitudes of every dual-impulse response were equivalent.Adaptively,?ltering the raw signal with an optimal complex Morlet ?lter around the resonance frequency of the AE trans-ducer,the proposed dual-impulse interval determining method can still work well even when the signals were contaminated by heavy https://www.wendangku.net/doc/8b2763107.html,pared with the method performed by the

6614IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,VOL.62,NO.10,OCTOBER2015

averaged real cepstrum of the dual-impulse segments,the method proposed in this paper is more powerful because the dual-impulse feature is more visible on the autocorrelation function of the squared envelope than the averaged real cep-strum and the estimation results of the spall sizes at various speed conditions are more accurate.

What should be emphasized here is that the rolling ele-ment faults were not involved because our existing condition cannot satisfy corresponding test demands and the rotating speed seemed to have an effect on the estimation of the spall size.Further investigation and improved experimental tests are required.

A CKNOWLEDGMENT

The authors would like to thank Z.Li,an Experiment Assis-tant in the Machine Fault Diagnostics Laboratory at Tsinghua University,for the apparatus preparation and data acquisition works in the experimental validation,as well as the Associate Editor and the reviewers for improving the quality of this paper.

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1988.

An-bo Ming received the B.S.degree in aircraft

power engineering,the M.S.degree in aircraft

design,and the Ph.D.degree in aeronautical

science and technology from the Xi’an High-

Tech Institute,Xi’an,China,in2007,2010,and

2014,respectively.

From2010to2014,he was a visiting Ph.D.

candidate in mechanical engineering with

Tsinghua University,Beijing,China.He is cur-

rently a Research Assistant with the Xi’an High-

Tech Institute.His research interests include rolling element bearing fault diagnosis,signal processing,and bearing fault dynamics.

MING et al.:MODEL FOR AE PRODUCED BY SPALL AND SIZE EVALUATION IN ROLLING ELEMENT BEARINGS

6615

Wei Zhang received the B.S.degree in power (generating)machines from the Xi’an High-Tech Institute,Xi’an,China,in1985,the specialized M.S.degree in mechanics from Xi’an Jiaotong University,Xi’an,in1995,and the Ph.D.degree in ordnance science and technology from the Xi’an High-Tech Institute in2003.

He is currently a Professor of aeronautical science and technology with the Xi’an High-Tech Institute.His research interests include non-destructive testing for liquid rocket motors,

condition monitoring,and fault

diagnosis.

Zhao-ye Qin received the B.S.and M.S.de-

grees in mechanical engineering and automa-

tion from Northeastern University,Shenyang,

China,in2003and2006,respectively,and the

Ph.D.degree in mechanical design and the-

ory from Tsinghua University,Beijing,China,

in2010.

He is currently a Research Fellow with

the Department of Mechanical Engineering,

Tsinghua University.His research interests in-

clude rotor dynamics,aerospace engineering, structural vibration and control,and nonlinear

systems.

Fu-lei Chu received the B.S.degree in me-

chanical engineering from Jiangxi University

of Science and Technology,Ganzhou,China,

in1982,the M.S.degree in applied mechan-

ics from Tianjin University,Tianjin,China,in

1985,and the Ph.D.degree in mechanical en-

gineering from the University of Southampton,

Southampton,U.K.,in1994.

He is currently a Professor of vibration engi-

neering with the Department of Mechanical En-

gineering,Tsinghua University,Beijing,China. His research interests include rotating machinery dynamics,machine condition monitoring and fault detection,nonlinear vibration,and vibra-tion control.

bs期权定价与二叉树期权定价学习资料

b s期权定价与二叉树 期权定价

第三节 Black-Scholes期权定价模型 一与期权定价有关的基本假设: (一).关于金融市场的基本假设 假设一:市场不存在摩擦.这就是说金融市场没有交易成本(包括佣金费用,买卖价差,税赋,市场冲击等),没有保证金要求,也没有买空的限制.提出市场无摩擦的假设在于简化金融资产定价的分析过程,其主要理由有以下两点:第一,对于大的金融机构来说,这一假设是一个较好的近似,因为他们的交易成本很低,他们在保证金要求和卖空方面受的约束很少,他们能够以买卖差的中间价进行交易等.由于金融机构是市场价格的制定者,所以从描述性角度出发,上述假设是一个较为现实的假设.第二,对于小的市场参与者来说,他们首先需要了解的是无摩擦条件下金融市场将如何运作.在此基础上,才能对复杂场合下的市场规律进行进一步深入分析.因此,从规范性角度出发,上述假设也是绝对必要的. 假设二:市场参与者不承担对家风险.这就是说,对于市场参与者所涉及的任何一个金融合同交易,合同对家不存在违约的可能. 假设三:市场是完全竞争的这就是说,金融市场上任何一位参与者都是价格的承受者,而不是价格的制定者.此假设被现代财务金融学普遍采纳,相当于一条标准的公理.任何参与者都可以根据自己的愿望买入和卖出任何数量的证券,而不至于影响该证券的市场价格.显然市场规模越大,竞争性市场假设就越接近于现实.

假设四:市场参与者厌恶风险,而且希望财富越多越好. 假设五:市场不存在套利机会.如果市场上存在套利的机会,价格会迅速准确的进行调整,使得这种套利机会很快消失. (二).关于股利的假设 股利是影响期权价值的一个重要因素.不过,在研究期权定价问题时,股利是一个广义概念.首先,这一概念包含了通常意义上的股利,即发行标的股票公司向其股东定期支付的现金股利,我们称之为离散股利对于标的资产为股票的合同其大小一般用D 表示.一般来说,离散股利的支付发生在期权有效期内某些特定的时刻,它们往往是可以预先知道的.例如,公司将在每个季度末或每隔半年发放一定的股利.另一方面,对于标的资产为货币,股票指数,期货等的非股票期权来讲,所谓的的股利是指标的资产所有者在一段时间内,按一定的收益率所得到的报酬,如利息收入,因此它是一种连续的支付,我们称之为连续股利,其大小通常用股利支付率 二 模型假设与概述 (一)模型假设 Black 和Scholes 在推导B-S 模型时做了以下假设: (1)无风险利率r 已知,且为一个常数,不随时间变化. (2)标的资产为股票,其价格t s 的变化为一几何布朗运动,即 t t t t ds s dt s dz μσ=+ 或者说, t s 服从正态分布 21/20exp{(0.5)},0t t s s t t e t T μσσ=-+<<……… 由(18)式容易得到

Tesla Model S底盘全透视..

水平对置、后置后驱、低重心、前双横臂后多连杆、全铝合金车架、5门5座,你以为笔者说的是保时捷新车型吗?那笔者再补充多几个关键词好了,后置的水平对置双电刷电动机、0油耗、藏在地板下的笔记本电池组,同时拥有这些标签的,便是Tesla第二款车型Model S。Model S是五门五座纯电动豪华轿车,布局设计及车身体积与保时捷Panamera相当,并且是目前电动车续航里程的纪录保持者(480公里)。虽然现在纯电动在我国远未至于普及,但是在香港地区却是已经有Tesla的展厅,在该展厅内更是摆放了一台没有车身和内饰,只有整个底盘部分的Model S供人直观了解Model S的技术核心。 图:Tesla Model S。

图:拆除车壳之后,Model S的骨架一目了然。

图:这套是Model S的个性化定制系统,可以让买家选择自己喜爱的车身颜色、内饰配色和轮圈款式,然后预览一下效果。可以看到Model S共分为普通版、Sign at ure版和Performance版,后面两个型号标配的是中间的21寸轮圈,而普通版则是两边的19寸款式。Signature版是限量型号,在美国已全部售罄,香港也只有少量配额。 图:笔者也尝试一下拼出自己心目中的Model S,碳纤维饰条当然是最爱啦。

图:参观了一下工作车间,不少Roadster在等着检查保养呢,据代理介绍,不同于传统的汽车,电动车的保养项目要少很多,至少不用更换机油和火花塞嘛,换言之电动车的维护成本要比燃油汽车要低。 Tesla于2010年5月进军香港市场,并于翌年2011年9月成立服务中心。由于香港政府对新能源车的高度支持,香港的电动车市场发展比起大陆地区要好得多。例如Tesla的第一款车型Roadster(详见《无声的革命者——Tesla Roadster Sport 》),在香港获得豁免资格,让车主可以节省将近100万港元的税款。在这样的优惠政策之下,Tesla Roadster尽管净车价达100万港元,但50台的配额已经基本售罄。而Model S目前在香港已经开始接受报名预定,确定车型颜色和配置之后约两个月左右可以交车。

美式期权定价.doc

美式期权定价 由于美式期权提前执行的可能,使得解决最优执行决策成为美式期权定价和套期保值的关键。由第三章的内容我们知道,如果标的股票在期权的到期日之前不分红,则美式看涨期权不会提前执行,因为在到期日之前执行将损失执行价格的利息。但是,如果标的股票在期权到期日以前支付红利,则提前执行美式看涨期权可能是最优的。提前执行可以获得股票支付的红利,而红利的收入超过利息损失。事实上,我们将证明,投资者总是在股票分红前执行美式看涨期权。 对于美式看跌期权而言,问题变的更复杂。看跌期权的支付以执行价格为上界,这限制了等待的价值,所以对于美式看跌期权而言,即使标的股票不支付红利,也可能提前执行。提前执行可以获得执行价格的利息收入。 许多金融证券都暗含着美式期权的特性,例如可回购债券(called bond ),可转换债券(convertible bond ), 假设: 1.市场无摩擦 2.无违约风险 3.竞争的市场 4.无套利机会 1.带息价格和除息价格 每股股票在时间t 支付红利t d 元。当股票支付红利后,我们假设股价将下降,下降的规模为红利的大小。可以证明,当市场无套利且在资本收益和红利收入之间没有税收差别时,这个假设是成立的。 ()()t e c d t S t S += 这里()t S c 表示股票在时间t 的带息价格,()t S e 表示股票在时间t 的除息价格。 这个假设的证明是非常直接的。如果上述关系不成立,即()()t e c d t S t S +≠,则存在套利机会。 首先,如果()()t e c d t S t S +>,则以带息价格卖出股票,在股票分红后马上以除息价格买回股票。因为我们卖空股票,所以红利由卖空者支付,从而这个策略的利润为()()()t e c d t S t S +-。因为红利是确定知道的,所以只要()()() t S t S e c -var =0,则利润是没有风险的。 其次,如果()()t e c d t S t S +<,则以带息价格买入股票,获得红利后以除息价格卖 出,获得利润为()()t S d t S c t e -+。

SCOR模型-供应链运作参考模型

SCOR模型 SCOR模型,即供应链运作参考模型。SCOR (Supply-Chain Operations Reference-model) 是由国际供应链协会 (Supply-Chain Council) 开发支持,适合于不同工业领域的供应链运作参考模型。1996年春,两个位于美国波士顿的咨询公司——Pittiglio Rabin Todd & McGrath (PRTM) 和 AMR Research (AMR) 为了帮助企业更好地实施有效的供应链,实现从基于职能管理到基于流程管理的转变,牵头成立了供应链协会 (SCC) ,并于当年底发布了供应链运作参考模型(SCOR)。 什么是SCOR模型? 供应链运作参考模型(Supply-Chain Operations Reference model,简称SCOR模型) SCOR是第一个标准的供应链流程参考模型,是供应链的诊断工具,它涵盖了所有行业。SCOR使企业间能够准确地交流供应链问题,客观地评测其性能,确定性能改进的目标,并影响今后供应链管理软件的开发。流程参考模型通常包括一整套流程定义、测量指标和比较基准,以帮助企业开发流程改进的策略。SCOR不是第一个流程参考模型,但却是第一个标准的供应链参考模型。SCOR模型主要由四个部分组成:供应链管理流程的一般定义、对应于流程性能的指标基准,供应链 “最佳实施” (best practices) 的描述以及选择供应链软件产品的信息。 SCOR(供应链运作参考)模型把业务流程重组、标杆比较和流程评测等著名的概念集成到一个跨功能的框架之中。SCOR是一个为供应链伙伴之间有效沟通而设计的流程参考模型,是一个帮助管理者聚焦管理问题的标准语言。作为行业标准,SCOR帮助管理者关注企业内部供应链。 SCOR用于描述、量度、评价供应链配置:规范的SCOR流程定义实际上允许任何供应链配置;量度;规范的SCOR尺度能使供应链绩效本衡量和标杆比较;供应链配置可以被评估以支持连续的改进和战略计划编制。 SCOR的涵盖范围 SCOR包括

(战略管理)战略咨询工具模型

战略咨询工具模型 图4-14描述了战略咨询项目的总体思路。一般而言,企业战略需涉及从愿景设计到管理实施的七个阶段,将战略分解为公司战略、业务战略、职能战略三大层次。 图4-15给出了战略咨询项目的框架结构。一个标准的战略咨询项目需要从内外部环境的分析入手,在战略方案制定的过程中,将其分解成业务组合与发展、资本运营、资源整合、IT、品牌和人力资源等局部战略。

图4-16描述了战略咨询项目的详细步骤。总体来说,战略咨询分为内部能力分析、外部环境分析、战略目标制定和战略方案制定四大步骤。 图4-17展示了一个系统化的战略管理体系。在这里,战略从制定到实施的每一个环节均得以完整地体现。值得注意的是,一个科学、合理的战略管理体系必须具备完善的沟通、反馈机制,以保证战略目标准确到位的贯彻与执行。

图4-18描绘了企业进行战略决策的三个层面:既定方针、重点需做出的决策和可推迟的决策。位于这三个层面中的企业战略决策构成了一个决策阶梯。通过阶梯的形式,读者可以清晰地看到不同战略对企业而言的重要性与紧迫性程度。

图4-19给出了一张根据决策阶梯制定的战略决策表。从决策表中可以看出,企业的真实战略往往就是市场决策的有机组合。 图4-20说明,一个企业的最终战略,极有可能是各种草案的综合体。通过最大化地吸收各种方案的优势,尽可能地规避其各自的风险,保证最终实施方案的完备性与可操作性。

图4-21展现了战略从制定到实施的整体流程。从中可见,一个科学的战略需要评估者、实施者和制定者三方共同的努力,也只有从这三方角度出发而出台的战略方案,在执行的过程中,才能保证将推行的阻力降到最低,方案的成功几率也就相对较高。 图4-22说明,一个战略实施的基本思路就是要形成从实施到结果反馈的循环。 图4-23描述了战略实施的四个基本步骤。这是一个从诠释战略和规划、反馈调整、建立各级规划到交流和挂钩的过程。同样也是一个循环的过程。

特斯拉整体介绍

Tesla Model S 特斯拉Model S是一款纯电动车型,外观造型方面,该车定位一款四门Coupe车型,动感的车身线条使人过目不忘。此外在前脸造型方面,该车也采用了自己的设计语言。另值得一提的是,特斯拉Model S的镀铬门把手在触摸之后可以自动弹出,充满科技感的设计从拉开车门时便开始体现。该车在2011年年中正式进入量产阶段,预计在2012年年内将有5000台量产车投放市场。 目录 1概述 2售价 3内饰 4动力 5车型 6技术规格 7性能表现 8荣誉 9对比测试 10车型参数 1概述

Tesla Model S是一款由Tesla汽车公司制造的全尺寸高性能电动轿车,预计于2012年年中投入销售,而它的竞争对手则直指宝马5系。该款车的设计者Franz von Holzhausen,曾在马自达北美分公司担任设计师。在Tesla汽车公司中,Model S拥有独一无二的底盘、车身、发动机以及能量储备系统。Model S的第一次亮相是在2009年四月的一期《大卫深夜秀》节目中 4 Tesla Model S 。 2售价 Model S的电池规格分为三种,分别可以驱动车辆行驶260公里、370公里和480公里。而配备这三种电池的Model S的售价则分别为57400美元、67400美元和77400美元。下线的首批1000辆签名款车型将配有可以行驶480公里的蓄电池。尽管官方尚未公布该签名款车型的具体售价,但据推测,价格将会保持在50000美元左右。 Tesla汽车公司称其将会对市场出租可以提供480公里行驶距离的电池。而从Model S中取得的收益将为第三代汽车的发展提供资金保障。 3内饰

第七章_美式期权定价(金融衍生品定价理论讲义)

第七章 美式期权定价 由于美式期权提前执行的可能,使得解决最优执行决策成为美式期权定价和套期保值的关键。由第三章的内容我们知道,如果标的股票在期权的到期日之前不分红,则美式看涨期权不会提前执行,因为在到期日之前执行将损失执行价格的利息。但是,如果标的股票在期权到期日以前支付红利,则提前执行美式看涨期权可能是最优的。提前执行可以获得股票支付的红利,而红利的收入超过利息损失。事实上,我们将证明,投资者总是在股票分红前执行美式看涨期权。 对于美式看跌期权而言,问题变的更复杂。看跌期权的支付以执行价格为上界,这限制了等待的价值,所以对于美式看跌期权而言,即使标的股票不支付红利,也可能提前执行。提前执行可以获得执行价格的利息收入。 许多金融证券都暗含着美式期权的特性,例如可回购债券(called bond ),可转换债券(convertible bond ), 假设: 1.市场无摩擦 2.无违约风险 3.竞争的市场 4.无套利机会 1.带息价格和除息价格 每股股票在时间t 支付红利t d 元。当股票支付红利后,我们假设股价将下降,下降的规模为红利的大小。可以证明,当市场无套利且在资本收益和红利收入之间没有税收差别时,这个假设是成立的。 ()()t e c d t S t S += 这里()t S c 表示股票在时间t 的带息价格,()t S e 表示股票在时间t 的除息价格。 这个假设的证明是非常直接的。如果上述关系不成立,即()()t e c d t S t S +1,则存在套利机会。 首先,如果()()t e c d t S t S +>,则以带息价格卖出股票,在股票分红后马上以除息价格买回股票。因为我们卖空股票,所以红利由卖空者支付,从而这个策略的利润为()()()t e c d t S t S +-。因为红利是确定知道的,所以只要()()()t S t S e c -var =0,则利润是没有风险的。 其次,如果()()t e c d t S t S +<,则以带息价格买入股票,获得红利后以除息价格卖出,获得利润为()()t S d t S c t e -+。

供应链运作参考模型(简称SCOR模型)

供应链运作参考模型(Supply-Chain Operations Reference model,简称SCOR模型) 什么是SCOR模型? SCOR (Supply-Chain Operations Reference-model) 是由国际供应链协会(Supply-Chain Council) 开发支持,适合于不同工业领域的供应链运作参考模型。1996年春,两个位于美国波士顿的咨询公司——Pittiglio Rabin Todd & McGrath (PRTM) 和AMR Research (AMR) 为了帮助企业更好地实施有效的供应链,实现从基于职能管理到基于流程管理的转变,牵头成立了供应链协会(SCC) ,并于当年底发布了供应链运作参考模型(SCOR)。 SCOR是第一个标准的供应链流程参考模型,是供应链的诊断工具,它涵盖了所有行业。SCOR使企业间能够准确地交流供应链问题,客观地评测其性能,确定性能改进的目标,并影响今后供应链管理软件的开发。流程参考模型通常包括一整套流程定义、测量指标和比较基准,以帮助企业开发流程改进的策略。SCOR不是第一个流程参考模型,但却是第一个标准的供应链参考模型。SCOR模型主要由四个部分组成:供应链管理流程的一般定义、对应于流程性能的指标基准,供应链“最佳实施” (best practices) 的描述以及选择供应链软件产品的信息。 SCOR(供应链运作参考)模型把业务流程重组、标杆比较和流程评测等著名的概念集成到一个跨功能的框架之中。SCOR是一个为供应链伙伴之间有效沟通而设计的流程参考模型,是一个帮助管理者聚焦管理问题的标准语言。作为行业标准,SCOR帮助管理者关注企业内部供应链。SCOR用于描述、量度、评价供应链配置:规范的SCOR流程定义实际上允许任何供应链配置;量度;规范的SCOR尺度能使供应链绩效本衡量和标杆比较;供应链配置可以被评估以支持连续的改进和战略计划编制。 [编辑] SCOR的涵盖范围 SCOR包括: ?所有与客户之间的相互往来,从定单输入到货款支付 ?所有产品(物料实体和服务)的传送,从你的供应商 的供应商到你的客户的客户,包括设备、原材料、配 件、大批产品、软件等。 ?所有与市场之间的相互影响,从对累计总需求的理解 到每项定单的完成。 SCOR不试图描述以下每一个商业流程或活动:

BS期权定价模型

Black-Scholes期权定价模型 (重定向自Black—Scholes公式) Black-Scholes期权定价模型(Black-Scholes Option Pricing Model),布莱克-肖尔斯期权定价模型 Black-Scholes 期权定价模型概述 1997年10月10日,第二十九届诺贝尔经济学奖授予了两位美国学者,哈佛商学院教授罗伯特·默顿(RoBert Merton)和斯坦福大学教授迈伦·斯克尔斯(Myron Scholes)。他们创立和发展的布莱克——斯克尔斯期权定价模型(Black Scholes Option Pricing Model)为包括股票、债券、货币、商品在内的新兴衍生金融市场的各种以市价价格变动定价的衍生金融工具的合理定价奠定了基础。 斯克尔斯与他的同事、已故数学家费雪·布莱克(Fischer Black)在70年代初合作研究出了一个期权定价的复杂公式。与此同时,默顿也发现了同样的公式及许多其它有关期权的有用结论。结果,两篇论文几乎同时在不同刊物上发表。所以,布莱克—斯克尔斯定价模型亦可称为布莱克—斯克尔斯—默顿定价模型。默顿扩展了原模型的内涵,使之同样运用于许多其它形式的金融交易。瑞典皇家科学协会(The Royal Swedish Academyof Sciencese)赞誉他们在期权定价方面的研究成果是今后25年经济科学中的最杰出贡献。 [编辑] B-S期权定价模型(以下简称B-S模型)及其假设条件 [编辑] (一)B-S模型有7个重要的假设 1、股票价格行为服从对数正态分布模式; 2、在期权有效期内,无风险利率和金融资产收益变量是恒定的; 3、市场无摩擦,即不存在税收和交易成本,所有证券完全可分割; 4、金融资产在期权有效期内无红利及其它所得(该假设后被放弃); 5、该期权是欧式期权,即在期权到期前不可实施。 6、不存在无风险套利机会;

详解特斯拉Model S

详解特斯拉Model S 1、Model S的核心技术是什么? 核心技术是软件,主要包括电池管理软件,电机以及车载设备的电控技术。最重要的是电池控制技术。 Model S的加速性能,续航里程、操控性能的基础都是电池控制技术,没有电池控制技术,一切都就没有了。 2、Model S的电池控制技术有什么特色? 顶配的Model S使用了接近7000块松下NCR 18650 3100mah电池,对电池两次分组,做串并联。设置传感器,感知每块电池的工作状态和温度情况,由电池控制系统进行控制。防止出现过热短路温度差异等危险情况。 在日常使用中,保证电池在大电流冲放电下的安全性。 其他厂商都采用大电池,最多只有几百块,也没有精确到每块电池的控制系统。 3、为什么要搞这么复杂的电池控制系统? 为了能够使用高性能的18650钴锂电池。高性能电池带来高性能车。因为18650钴锂电池的高危性,没有一套靠谱的系统,安全性就不能保证。这也是大多数厂商无论电力车,插电车,混合动力车都不太敢用钴锂电池,特别是大容量钴锂电池的原因。 松下NCR 18650 3100mah,除了测试一致性最好,充放电次数多,安全性相对较好以外,最重要的是能量大,重量轻,价格也不高。 由于能量大,重量轻,在轿车2吨以内的车重限制下,可以塞进去更多的电池,从而保证更长的续航里程。因为电池输出电流有限制,电池越多,输出电流越大,功率越大,可以使用的电机功率也就越大。电机功率越大,相当于发动机功率大,车就有更快的加速性能,而且可以保持较长的一段时间。 4、作为一辆车,Model S有哪些优点?这些优点是电动车带来的吗? 作为一辆车,Model S主要具有以下几个优点 (1)起步加速快,顶配版本0-100公里加速4秒多,能战宝马M5

管理咨询常用模型Word

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TESLA特斯拉解析

TESLA 硅谷工程师、资深车迷、创业家马丁·艾伯哈德(Martin Eberhard)在寻找创业项目时发现,美国很多停放丰田混合动力汽车普锐斯的私家车道上经常还会出现些超级跑车的身影。他认为,这些人不是为了省油才买普锐斯,普锐斯只是这群人表达对环境问题的方式。于是,他有了将跑车和新能源结合的想法,而客户群就是这群有环保意识的高收入人士和社会名流。 2003年7月1日,马丁·艾伯哈德与长期商业伙伴马克·塔彭宁(Marc Tarpenning)合伙成立特斯拉(TESLA)汽车公司,并将总部设在美国加州的硅谷地区。成立后,特斯拉开始寻找高效电动跑车所需投资和材料。

由于马丁·艾伯哈德毫无这方面的制造经验,最终找到AC Propulsion公司。当时,对AC Propulsion公司电动汽车技术产生兴趣的还有艾龙·穆思科(Elon Musk)。在AC Propulsion公司CEO汤姆·盖奇(Tom Gage)的引见下,穆思科认识了艾伯哈德的团队。2004年2月会面之后,穆思科向TESLA投资630万美元,但条件是出任公司董事长、拥有所有事务的最终决定权,而艾伯哈德作为创始人任TESLA的CEO。 在有了技术方案、启动资金后,TESLA开始开发高端电动汽车,他们选择英国莲花汽车的Elise作为开发的基础。没有别的原因,只是因为莲花是唯一一家把TESLA放在眼里的跑车生产商。

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SCOR模型

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管理咨询工具模型

咨询管理工具模型 李为明 0769-******* 139******** llwmemail@https://www.wendangku.net/doc/8b2763107.html, 1

1.波特五种竞争力分析模型 ?波特的五种竞争力分析模型被广泛应用于很多行业的战略制定。 ?波特认为在任何行业中,无论是国内还是国际,无论是提供产品还是提供服务,竞争的规则都包括在五种竞争力量内。 ?这五种竞争力就是 –企业间的竞争、 –潜在新竞争者的进入、 –潜在替代品的开发、 –供应商的议价能力、 –购买者的议价能力。 ?这五种竞争力量决定了企业的盈利能力和水平。 3

新进入者新进入者行业竞争对手企业 之间的竞争 行业竞争对手企业之间的竞争供应商 供应商顾客 顾客替代品 替代品

?竞争对手 ?企业间的竞争是五种力量中最主要的一种。只有那些比竞争对手的战略更具优势的战略才可能获得成功。为此,公司必须在市场、价格、质量、产量、功能、服务、研发等方面建立自己的核心竞争优势。?影响行业内企业竞争的因素有:产业增加、固定(存储)成本/附加价值周期性生产过剩、产品差异、商标专有、转换成本、集中与平衡、信息复杂性、竞争者的多样性、公司的风险、退出壁垒等。 ?新进入者 ?企业必须对新的市场进入者保持足够的警惕,他们的存在将使企业做出相应的反应,而这样又不可避免地需要公司投入相应的资源。 ?影响潜在新竞争者进入的因素有:经济规模、专卖产品的差别、商标专有、资本需求、分销渠道、绝对成本优势、政府政策、行业内企业的预期反击等。 5

?购买者 ?当用户分布集中、规模较大或大批量购货时,他们的议价能力将成为影响产业竞争强度的一个主要因素。 ?决定购买者力量的因素又:买方的集中程度相对于企业的集中程度、买方的数量、买方转换成本相对企业转换成本、买方信息、后向整合能力、替代品、克服危机的能力、价格/购买总量、产品差异、品牌专有、质量/性能影响、买方利润、决策者的激励。 ?替代产品 ?在很多产业,企业会与其他产业生产替代品的公司开展直接或间接的斗争。替代品的存在为产品的价格设置了上限,当产品价格超过这一上限时,用户将转向其他替代产品。?决定替代威胁的因素有:替代品的相对价格表现、转换成本、客户对替代品的使用倾向。 ?供应商 ?供应商的议价力量会影响产业的竞争程度,尤其是当供应商垄断程度比较高、原材料替代品比较少,或者改用其他原材料的转换成本比较高时更是如此。 ?决定供应商力量的因素有:投入的差异、产业中供方和企业的转换成本、替代品投入的现状、供方的集中程度、批量大小对供方的重要性、与产业总购买量的相关成本、投入对成本和特色的影响、产业中企业前向整合相对于后向整合的威胁等。 6

Tesla Model S电池组设计全面解析

Tesla Model S电池组设计全面解析 对Tesla来说最近可谓是祸不单行;连续发生了3起起火事故,市值狂跌40亿,刚刚又有3名工人受伤送医。Elon Musk就一直忙着到处“灭火”,时而还跟公开表不对Tesla“不感冒”的乔治·克鲁尼隔空喊话。在经历了首次盈利、电池更换技术·穿越美国、水陆两栖车等头条新闻后,Elon Musk最近总以各种负面消息重返头条。这位"钢铁侠。CE0在201 3年真是遭遇各种大起大落。 其中最为人关注的莫过于Model S的起火事故,而在起火事故中最核心的问题就是电池技术。可以说,牵动Tesla股价起起落落的核心元素就是其电池技术,这也是投资者最关心的问题。在美国发生的两起火事故有着相似的情节Model S 撞击到金属物体后,导致电池起火,但火势都被很好地控制在车头部分。在墨西哥的事故中,主要的燃烧体也是电池;而且在3起事故中,如何把着火的电池扑灭对消防员来说都是个难题。 这让很多人产生一个疑问:Model S的电池就这么不禁撞吗?在之前的一篇文章中,我跟大家简单讨论了一下这个问题,但只是停留在表面。读者普遍了解的是,Model S的电池位于车辆底部,采用的是松下提供的18650钴酸锂电池,整个电池组包含约8000块电池单元;钴酸锂电池能量密度大,但稳定性较差,为此Tesla研发了3级电源管理体系来确保电池组正常运作。现在,我们找到了Tesla的一份电池技术专利,借此来透彻地了解下Model S电池的结构设计和技术特征。 电池的布局与形体

FIG3 如专利图所示,Model S的电池组位于车辆的底盘,与轮距同宽,长度略短于轴距。电池组的实际物理尺寸是:长2.7m,宽1.5m,厚度为0.1 m至0.1 8m。其中0.1 8m较厚的部分是由于2个电池模块叠加而成。这个物理尺寸指的是电池组整体的大小,包括上下、左右、前后的包裹面板。这个电池组的结构是一个通用设计,除了18650电池外,其他符合条件的电池也可以安装。此外,电池组采用密封设计,与空气隔绝,大部分用料为铝或铝合金。可以说,电池不仅是一个能源中心,同时也是Model S底盘的一部分,其坚固的外壳能对车辆起到很好的支撑作用。 由于与轮距等宽,电池组的两侧分别与车辆两侧的车门槛板对接,用螺丝固定。电池组的横断面低于车门槛板。从正面看,相当于车门槛板"挂着。电池组。其连接部分如下图所示。 FIG, 4

管理咨询工具SWOT分析模型

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(2)优势与劣势分析(SW) 识别环境中有吸引力的机会是一回事,拥有在机会中成功所必需的竞争能力是另一回事。每个企业都要定期检查自己的优势与劣势,这可通过“企业经营管理检核表”的方式进行。企业或企业外的咨询机构都可利用这一格式检查企业的营销、财务、制造和组织能力。每一要素都要按照特强、稍强、中等、稍弱或特弱划分等级。 当两个企业处在同一市场或者说它们都有能力向同一顾客群体提供产品和服务时,如果其中一个企业有更高的赢利率或赢利潜力,那么,我们就认为这个企业比另外一个企业更具有竞争优势。换句话说,所谓竞争优势是指一个企业超越其竞争对手的能力,这种能力有助于实现企业的主要目标——赢利。但值得注意的是:竞争优势并不一定完全体现在较高的赢利率上,因为有时企业更希望增加市场份额,或者多奖励管理人员或雇员。 竞争优势可以指消费者眼中一个企业或它的产品有别于其竞争对手的任何优越的东西,它可以是产品线的宽度、产品的大小、质量、可靠性、适用性、风格和形象以及服务的及时、态度的热情等。虽然竞争优势实际上指的是一个企业比其竞争对手有较强的综合优势,但是明确企业究竟在哪一个方面具有优势更有意义,因为只有这样,才可以扬长避短,或者以实击虚。 由于企业是一个整体,并且由于竞争优势来源的广泛性,所以,在做优劣势分析时必须从整个价值链的每个环节上,将企业与竞争对手做详细的对比。如产品是否新颖,制造工艺是否复杂,销售渠道是否畅通,以及价格是否具有竞争性等。如果一个企业在某一方面或几个方面的优势正是该行业企业应具备的关键成功要素,那么,该企业的综合竞争优势也许就强一些。需要指出的是,衡量一个企业及其产品是否具有竞争优势,只能站在现有潜在用户角度上,而不是站在企业的角度上。 企业在维持竞争优势过程中,必须深刻认识自身的资源和能力,采取适当的措施。因为一个企业一旦在某一方面具有了竞争优势,势必会吸引到竞争对手的注意。一般地说,企业经过一段时期的努力,建立起某种竞争优势;然后就处于维持这种竞争优势的态势,竞争对手开始逐渐做出反应;而后,如果竞争对手直接进攻企业的优势所在,或采取其它更为有力的策略,就会使这种优势受到削弱。

特斯拉Model S电动汽车性能介绍

特斯拉Model S 特斯拉Model S并非小尺寸、动力不足的短程汽车——这是某些人对电动车的预期。作为特斯拉三款电动车中体积最大的车型,根据美国环保署认证,这款快捷、迷人的运动型轿车一次充电能够行驶265英里(426公里),不过特斯拉声称可以达到300英里。不管哪种情况,这肯定是电动车行业的新高。Model S Performance版本的入门级价格为94,900美元,我测试的版本价格为101,600美元(按照美国联邦税收抵免,可以在此基础上扣减7,500美元)。 在一次开放驾驶上,这款特斯拉汽车硕大的85千瓦时电池的确可以至少行驶426公里。电流来自于车底的电池组,里面有大约7,000颗松下锂电池,重量约为590公斤(1,300磅). 试驾的第二天是前往威斯康辛州,在行驶了320公里后电几乎用光,不过其中包括了在芝加哥的一场交通拥堵中无奈爬行的两个小时。这天的测试充满野心,更多是针对性能而非行驶里程,包括这款特斯拉汽车迅速地用4.4秒时间从0加速到时速97公里(0至60英里每小时),此外测试达到的最高时速为210公里。 我有没有提到,在0到时速100英里的加速时间方面,这款310千瓦(416马力)的特斯拉汽车将击败威力巨大、使用汽油的413千瓦(554马力)宝马M5?部分原因在于这款特斯拉汽车的同步交流电发动机能够即时提供600牛·米(443英尺磅)的扭矩。像电灯开关一样轻点特斯拉的油门,最大的扭矩已经准备就绪,一分钟内能够实现从0到5,100转。后悬挂、液冷式发动机可以保持1.6万转每分钟,通过一个单速变速箱将动力传导至后轮。 它就像一头冷酷的猛兽,在出奇安静之中让内燃机这个猎物消失于无形——安静到何种程度呢?来自轮胎和风阻的声音比在其他大部分豪华车中感受到的更加明显。安装于车底的电池让特斯拉获得与很多超级车相当的重心,这非常有利于稳定操控。Model S经过弯道的时候也能很好地保持贴地感。 尽管这款特斯拉汽车看起来并不笨重,但其重量达到2,108公斤;随着速度和重力的提升,这些多余的重量表露无遗。加大油门后,沉重的尾部会产生震动。在操控手感的愉悦性方面,特斯拉无法与宝马相提并论,甚至连马自达都赶不上。 美妙的试驾体验在你进入车内之前就开始了,你靠近汽车时,可伸缩的车门把手自动弹出。接着看到的是特斯拉标志性的驾驶室特色内容,一个43厘米(17英寸)电容触摸屏,看起来就像一对相互配合的iPad. 在其用铝合金加强的底盘和车身内,Model S可以容纳5人。一个可爱但是奇怪的按钮可以在车门位置增加脸朝车后的儿童座椅,从而实现最多承载7人。将第二排座椅向下折,可以扩展后座载货空间,可用于家得宝(Home Depot)采购之旅。由于引擎盖下面没有发动机,这些空间可以作为有用的前置行李箱,特斯拉将其称为“前备箱”(“frunk”),就像保时捷911一样。

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