Detection of Tire Lateral Force Based on a Resolver Mechanism

Transcription

1 4 Special Issue Esimaion and Conrol of Vehicle Dynamics for Acive Safey Research Repor Deecion of Tire Laeral Force Based on a Resolver Mechanism Takaji Umeno To observe he fricional sae of a ire and improve he acive safey conrol sysem of a vehicle, i is necessary o sense he ire-generaed forces. This paper presens a echnique for deecing a laeral ire-force. This is based on he resolver mechanism ha is used as a roaional speed sensor for a wheel. I is realized simply by replacing a convenional wheel speed sensor, and can deec ire laeral force by magneically Absrac sensing he posiional offse of he roaing shaf ha occurs due o he siffness of he shaf and axle hub bearing. Therefore, here is no need for complex machining and he sysem can accommodae variaions in he ire characerisics caused by changes in emperaure, inner pressure, aspec raio, and so on. The principle of he echnique has been confirmed by experimens on a ire es machine and on a es vehicle. Keywords Resolver, Laeral force, Differenial phase shif, Siffness, Momen R&D Review of Toyoa CRDL Vol. 4 No. 4

2 5. Inroducion To observe he fricional sae of a ire and improve he acive safey conrol sysem ) of a vehicle, i is a necessary o sense ire-generaed forces such as he longiudinal force, self-aligning orque, and laeral force. Of hese force componens, he longiudinal force and self-aligning orque can be sensed by vehicle conrol equipmen, such as he ABS hydraulic pressure sensor and he EPS orque sensor. The ire laeral force, however, has always been assumed o be difficul o deec using convenional sensors. Many mehods of deecing ire-generaed forces have been proposed. One ypical mehod involves deecing he ire-generaed forces by embedding a srain gauge in a suspension knuckle, 2) while anoher mehod uses a magneic marker on he surface of he ire o deec ire deformaion. 3) Unforunaely, boh of hese mehods require complex machining of he knuckle or ire, and lack wide applicabiliy. Also, he deecion accuracy is poor and hey canno be regarded as being reliable. This paper presens a ire laeral force deecion echnique ha is based on he resolver mechanism ha is used as a roaional speed sensor for a wheel. I can be realized simply by replacing a convenional wheel speed sensor, and deecs ire laeral forces by magneically sensing he posiional offse of he roaing shaf ha occurs due o he siffness of he shaf and axle hub bearing. Therefore, i needs no complex machining and can accommodae variaions in he ire characerisics resuling from changes in emperaure, inner pressure, aspec raio, and so on. The validiy of his mehod has been confirmed by experimens on a ire es machine and on a es vehicle. E sin he saor coils by elecromagneic inducion. Ec = KE cos θ sin ω, () Es = KE sin θ sin ω where, K is a coupling coefficien. The magniudes of he induced volages vary in accordance wih he roaional angle θ of he roor. The R/D converer shown in Fig. 2 deermines and hen oupus he angular posiion of he roor from Es and Ec. I has wo mulipliers and a subracer ha generae a signal, as follows: KE sin ω sin (θ - φ). (2) Then, he synchronous commuaor removes he sin ω from he above signal. The volage conrol oscillaor (VCO) oupus couner up-down pulses corresponding o he magniude of he volage KE sin (θ - φ), and adjuss he value of φ such ha i coincides wih he roaional angle θ, namely, θ = φ. As a resul, digial oupu angle φ becomes equal o he acual angle posiion θ of he roor Differenial phase shif (DPS) To deec he laeral force of a ire, he roary ransformer is mouned on a drive shaf and he saor coils are fixed o he knuckle. When he laeral force Fy occurs as shown in Fig. 3, a momen Mx, which is a produc of Fy and he ire radius R, is Roary Transformer Fig. Roor Elecromagneic Inducion Change in ampliude in accordance wih roaional angle Saor Configuraion of resolver. Ec = KE cos sin Es = KE sin sin 2. Deecion mechanism 2. Principle of he resolver Figure shows he configuraion of a roary ransformer resolver. I feaures a roary ransformer on he roor and muliple coils on he saor ha are laid ou such ha he phase difference in he oupu signals is π/2. When a high frequency AC volage E sin ω is applied o he roary ransformer, volages expressed by he following equaions are induced in Resolver E sin Es Ec cos sin Couner Oupu Fig. 2 E sin KE sin (sin cos - cos sin = KE sin sin( - VCO R/D Converer. ) Synchronous Commuaor KE sin( - ) ) R&D Review of Toyoa CRDL Vol. 4 No. 4

3 6 applied o he roaing shaf and bearing. Then, he posiion of he shaf is offse by γ due o he siffness of he shaf and bearing. In his case, he volages induced in he resolver, Ec and Es, are as follows: Ec = KE cos (θ + δ c )sin ω Es = KE sin (θ + δ s )sin ω. (3) Then, VCO and he couner of he R/D converer deermine he digial oupu angle φ, such ha sin(θ - δ s )cosφ cos(θ + δ c )sinφ (4) Equaion (4) derives sin ( θ δ ) s sin φ an, cos( θ + δ ) = c which can be approximaed o φ = θ + {( δ (5) c δs) ( δc + δs) cos 2θ} 2 by assuming ha δ c, δ s <<. Here, he speed change rae is obained by differeniaing Eq. (5), as follows: v^ v = ( δ, (6) c + δ s ) sin 2θ v where v^ is he deeced speed and ν is he rue speed. Since ν canno be measured, he average speed during one roaion is used insead of ν. This equaion indicaes ha if a laeral force is generaed, he rae of change of he speed flucuaes periodically in he magniude of (δ c + δ s ) and a a frequency equal o wice he roaional speed of he wheel. Generally, given ha he number of magneic poles is P, he period of he speed change rae is P imes he number of roaions of he wheel: v^ v = ( δ P. (7) c + δ s ) sin θ v Since (δ c + δ s ) indicaes he difference beween he phase shif in he volage induced in he wo coils, i is defined as he "Difference Phase Shif (DPS)" in his paper. The laeral force can be deeced from Eq. (7), provided he characerisic relaionship beween DPS and he laeral force, namely he siffness of he shaf and bearing, has been deermined in advance. 3. Experimen using a ire es machine To confirm he laeral force deecion principle, we performed an experimen using a ire es machine. 3. Experimenal sysem A general view of he ire es machine and he resolver insalled on he axle hub is shown in Fig. 4. To sense he acual forces, we used a six-axis force sensor. The resolver used in his experimen has eigh poles and is of he variable relucance ype. This has he same characerisics o he roary ransformer ype shown in Fig Deecion of DPS The algorihm used o deec he laeral force using DPS is shown in Fig. 5. According o Eq. (7), DPS can be deeced as he magniude of he speed Bearing Resolver Fy Momen Mx = R Fy Fz Fig. 3 R Roaing shaf is offse by due o he momen Saor coil Ec = KE cos( + c )sin Es = KE sin( - s )sin Momen and phase shif of resolver. s c Roaing shaf Saor coil 6-axis force sensor Knuckle Saor coil Roor drum ( m ) Fig. 4 Tire es machine and resolver. R&D Review of Toyoa CRDL Vol. 4 No. 4

4 change rae. The roaional speed is obained as follows: Normally, he R/D converer is designed so as o have an angular resoluion of 6 bis per roaion by using a 6-bi regiser in he couner. If we look a he ime series signal of each bi of he regiser, we see ha a signal of one pulse rises a MSB wihin a single roaion, and ha 2 5 pulses rise a LSB. In his experimen, he bi posiion o be measured is seleced so ha 256 pulses rise in one roaion. By measuring he inerval beween he rising or falling edges (he period of he pulse), he roaional speed v^ in Eq. (7) can be obained. Figure 6 shows he resuls of measuring he wheel speed for a case in which he laeral force is almos zero (slip angle deg) and a case in which a laeral force is generaed (slip angle 4 deg). We can show ha he flucuaion of he wheel speed clearly appears o have eigh periods in one roaion when a laeral force is generaed. DPS δ(ν), which is he value a he Nh pulse in one roaion, is calculaed by using he following equaions: N Re ( N) = α( i)sin( 2πPi/ 256) 28 i= N 255 N Im( N) = α( i)cos( 2π Pi/ 256) (8) 28 i= N δ( N) = δc( N) + δs( N) = Re ( N) + Im ( N) δ ( N) = K δ ( N ) + ( K ) δ ( N), < K < f f f f f where, N vn ^( ) vn ( ) vn ( ) = vi ^ ( ), α( N) = vn ( ) 256 i= N 255 and δ f (Ν) is he oupu from he lowpass filer. The lowpass filer suppresses noise from he load surface. A simple Fourier ransform is applied in he above seps o exrac he periodic componen from he speed change rae α(ν) Resuls Figure 7 shows he resuls of an experimen in which he vehicle weigh Fz and he wheel speed were varied and he laeral force was se o zero. In his figure, we can see ha DPS has a cerain offse Wheel speed (rad/s) Wheel speed (rad/s) Slip angle: deg, Fy : 3 N roaion roaion Slip angle: 4 deg, Fy : 67 N (Wheel load: 2 N, Speed: 4 km/h) 7 Fig. 6 Wheel speed signal from resolver. Measure period of pulse from resolver Deec rae of speed change wih respec o he average over one roaion for each pulse period Apply Fourier ransform o rae of change of each pulse period wih respec o roaional angle Calculae of DPS Differenial phase shif (rad) Slip angle: deg Offse Fz = 5 N Fz = 2 N Fz = 3 N Fz = 4 N Conver momen Mx and compue ire laeral force Fy Roaional speed (rad/s) Fig. 5 Laeral force deecion algorihm. Fig. 7 Offse of resolver. R&D Review of Toyoa CRDL Vol. 4 No. 4

5 8 value, bu i is no affeced by eiher Fz or he wheel speed. I is believed ha his offse is derived from he alignmen accuracy and elecrical imbalance beween he wo coils in he saor. Since his offse is fixed regardless of he change in Fz and he wheel speed, a correced DPS can be obained by subracing he offse from he acual DPS. Figure 8 shows he resuls obained from an experimen ha uses he correced DPS wih respec o he momen Mx(=FyR) which is applied o he bearing cener. In his case, he vehicle weighs Fz are 2N and 3N, and each wheel speed is se o 2, 4, and 6 km/h. This figure indicaes ha he correced DPS depends on Mx or Fy and is no affeced by any oher parameers. Therefore, if he relaionship beween Mx(or Fy) and he correced DPS are known in advance, he laeral force can be deeced from DPS. 4. Experimen using a es vehicle The es vehicle was a rear-drive car wih he resolver insalled on he axle hub of he righ-fron Correced differenial phase shif (rad) Fz = 2N Fz = 3N Slip angle:,, 2, 4 deg Speed: 2, 4, 6 km/h. Deermined by shaf and bearing siffness Momen Mx (Nm) Fig. 8 Momen vs. correced DPS. wheel. For his experimen, we used a roary ransformer resolver. Figure 9 shows he wheel speed deeced by he resolver when he es vehicle was run hrough a slalom. We can see ha he flucuaion in he deeced speed increased as he laeral acceleraion increased. This flucuaion appears o be caused by he previously menioned differenial phase shif. Figure shows he relaionship, experimenally deermined in advance, beween he DPS and momen Mx applied o he bearing cener of he axle hub. The esimaed values of Mx and Fy obained from filered DPS δ f by using he characerisic shown in Fig. are depiced in Fig.. In his figure, Fy is compued by simply dividing he esimaed momen Mx by he ire radius R. To Correced differenial phase shif (rad) Measured Deermined Momen Mx (Nm) Fig. Relaionship beween Mx and DPS of es vehicle. Momen Mx (Nm) Measured Esimaed Inner wheel Ouer wheel Wheel speed (rad/s) 45 Acual speed Resolver oupu Laeral acceleraion Laeral acceleraion (G) Laeral force Fy (N) Measured Esimaed Fig. 9 Resolver oupu during slaloming. Fig. Resuls of esimaion. R&D Review of Toyoa CRDL Vol. 4 No. 4

6 9 compare his wih he measured value, he filered absolue values of Mx and Fy as sensed by he 6-axis force sensor are shown in his figure. The highly accurae deecion can clearly be seen, especially in ha area when he righ-fron wheel is he ouer wheel in a urn. 5. Conclusion This paper has presened a ire laeral force deecion echnique ha is based on a resolver mechanism. I can be realized simply by replacing a convenional wheel speed sensor, and deecs he ire laeral force by magneically sensing he posiional offse of he roaing shaf ha occurs as a resul of he siffness of he shaf and he axle hub bearing. Therefore, i needs no complex machining and can accommodae variaions in he ire characerisics due o he change in he emperaure, inner pressure, aspec raio, and so on. The mehod has been confirmed by experimens in a ire es machine and on a es vehicle. Currenly, his mehod is sofware-based and can only deec he absolue value of he laeral force. In he fuure, we aim o develop a hardware-based mehod ha can direcly deec signed forces. Takaji Umeno Research fields : Vehicle sae esimaion and conrol Academic degree : Dr. Eng. Academic sociey : Ins. Elecr. Eng. Jpn., Soc. Insrum. Conrol Eng., IEEE, Soc. Auomo. Eng. Jpn. Awards : IEEE/IES Ousanding Paper Award, 994 Robomec'94 Bes Poser Award, 995 R&D Award, 997 SICE Chubu Chaper Award for Ousanding Technology, 22 Paper Award of AVEC'2, 22 References ) Haori, Y., e al. : "Force and Momen Conrol wih Nonlinear Opimum Disribuion for Vehicle Dynamics'', Proc. AVEC'2, (22), 595, JSAE 2) Miyazaki, N. : Examined Paen Pub. H (in Japanese) 3) Giusino, J. : US Paen No. US B (Repor received on Sep. 22, 25) R&D Review of Toyoa CRDL Vol. 4 No. 4