Abstract:
An electric power steering apparatus comprising a torque detector  6  for detecting a steering torque applied to a steering wheel (not shown) and a steering assist motor  8  which is driven under control based on a drive current corresponding to the steering torque detected by the torque detector  6 . By further comprising an angle detector  20  for detecting a turn angle of the steering wheel, angular velocity calculating means  23  for calculating an angular velocity of turn of the steering wheel from the turn angle detected by the angle detector  20 , friction compensating unit  24  for calculating an angular acceleration of turn of the steering wheel for friction compensation from the angular velocity of turn calculated by the angular velocity calculating means  23  and adding means  24   d   , 25  for adding a current related to the angular velocity of turn and a current related to the angular acceleration of turn calculated by the friction compensating unit  24  to the drive current, friction compensation is performed at the start of steering, more accurate friction compensation of a steering system is carried out, and an electric power steering apparatus having a good feel of steering is achieved.

Description:
BACKGROUND OF THE INVENTION 
     The present invention relates to an electric power steering apparatus for detecting a steering torque applied to a steering wheel and controlling driving of a steering assist motor according to the detected steering torque. 
     An electric power steering apparatus, which controls driving of a steering assist motor based on a result of detection of steering torque applied to a steering wheel and assists power required for steering an automobile by the torque of the motor so as to give a comfortable steering feel to a driver, has spread. 
     FIG. 1 is a block diagram showing an example of the constitution of “a power steering apparatus” proposed by the assignee of the present application in Japanese Patent No. 2694213. 
     In this power steering apparatus as an electric power steering apparatus, an output signal of a torque sensor  6  is inputted to a control unit  7 . The control unit  7  supplies a drive signal to a steering assist motor  8  based on this output signal. The steering assist motor  8  transmits its torque to the lower shaft of a steering shaft. 
     The torque sensor  6  detects, as the steering torque applied to a steering wheel, a relative displacement in a circumferential direction which is generated between the upper and lower shafts of the steering shaft turning about the axis of the steering wheel according to turn of the steering wheel with twist of a torsion bar interposed between the upper and lower shafts. 
     A rotation detector  17  for detecting a rotational position of the motor  8  is attached to the rotation shaft of the motor  8 . 
     The control unit  7  is supplied with a rotation detection signal of the rotation detector  17  and an output signal of a vehicle speed detector  18  for detecting a vehicle speed as well as the above-mentioned output signal of the torque sensor  6 , and outputs a drive signal for driving the motor  8  and an electromagnetic clutch  16 . 
     A torque detection signal outputted by the torque sensor  6  is supplied to each of a phase compensating unit  71   a  for stabilizing a system by advancing the phase of the torque detection signal, an angular acceleration calculating unit  71   b  for calculating an angular acceleration ω′ of turn of the steering wheel, a middle point determining unit  71   c  for determining the middle point of the steering wheel of a vehicle traveling in a straight direction, and a lock detecting unit  71   f  for detecting whether the motor  8  is locked. 
     Moreover, a vehicle speed detection signal outputted by the vehicle speed detector  18  is supplied to each of the lock detecting unit  71   f , middle point determining unit  71   c , directing current function unit  73   a , correction current function unit  73   b  and change current function unit  73   c.    
     The directing current function unit  73   a  is supplied with an output signal of the phase compensating unit  71   a  and a later-described change current Ia, determines a directing current I for the motor  8  based on the steering torque, change current Ia and vehicle speed detection signal, and outputs the determined directing current I. 
     The correction current function unit  73   b  is supplied with the angular acceleration ω′ of the steering wheel outputted by the angular acceleration calculating unit  71   b , determines a correction current Ic for correcting the force of inertia of the motor  8  during acceleration and deceleration and the force of inertia of the traveling system of the vehicle based on the angular acceleration ω′ and vehicle speed detection signal, and outputs the determined correction current Ic. 
     The change current function unit  73   c  is supplied with a steering angle θ outputted from a later-described steering angle determining unit  71   d , determines a change current Ia for changing the characteristic of the directing current I based on the steering angle θ and vehicle speed detection signal, and outputs the determined change current Ia. 
     The rotation detection signal of the rotation detector  17  is supplied to the lock detecting unit  7  If, middle point determining unit  71   c , angular acceleration calculating unit  71   b  and steering angle determining unit  71   d.    
     The steering angle determining unit  71   d  determines a steering angle θ based on the rotation detection signal and the middle point determined by the middle point determining unit  71   c , and outputs the determined steering angle θ. 
     The lock detecting unit  71   f  detects whether the motor  8  is locked, based on the rotation detection signal, when the supplied torque detection signal and vehicle speed detection signal are larger than their predetermined values, respectively. When the lock detecting unit  71   f  detects that the motor  8  is locked, a driving circuit  72   b  disconnects the electromagnetic clutch  16 . 
     The output signal of the directing current function unit  73   a  and the output signal of the correction current function unit  73   b  are added together by an adder  74   a , and the result of addition is supplied to an error amplifier  74   b . The error amplifier  74   b  calculates the difference between the result of addition and a feedback signal from a current detecting circuit  71   e  for detecting a current flowing in the motor  8 , and a voltage corresponding to the calculation result is supplied to the motor  8  by a PWM (Pulse Width Modulation) driving circuit  72   a.    
     The following description will explain an operation of an electric power steering apparatus having such structures. 
     The directing current function unit  73   a  determines a directing current I for the motor  8  based on the torque detection signal whose phase has been compensated by the phase compensating unit  71   a , the change current Ia outputted by the change current function unit  73   c  and the vehicle speed detection signal outputted by the vehicle speed detector  18 , and outputs the determined directing current I. 
     Meanwhile, the change current function unit  73   c  determines a change current Ia for changing the characteristic of the directing current I, based on the steering angle θ given by the steering angle determining unit  71   d  and the vehicle speed detection signal outputted by the vehicle speed detector  18 , and outputs the determined change current Ia. 
     The angular acceleration calculating unit  71   b  reads a torque detection signal T supplied from the torque sensor  6  and a motor rotational speed ω m  of the motor  8  supplied from the rotation detector  17 , and calculates the angular acceleration ω′ of the steering wheel according to the following equation. 
     
       
         ω′= T″/K+ω   m   ′/n   (1)  
       
     
     Here, equation (1) can be given by the following equations. 
     
       
           T=K (θ i −θ o )  
       
     
     where 
     θ i : a steering angle of the upper shaft of the steering shaft, 
     θ o : a steering angle of the lower shaft of the steering shaft, 
     K: a spring constant of the torsion bar. 
     
       
         θ i −θ o   =T/K    
       
     
     
       
         θ i   ″−θ   o   ″T″/K    
       
     
     
       
         θ i   ″=T″K+θ   o ″  (2)  
       
     
     Meanwhile, 
     
       
         θ o ′=ω m   /n    
       
     
     
       
         θ o ″=ω m   ′/n    
       
     
     (n: the deceleration ratio of the motor rotation shaft to the lower shaft) 
     ∴ According to equation (2), 
     
       
         θ i   ″=ω′=T″/K+ω   m   ′/n   (1)  
       
     
     The correction current function unit  73   b  calculates a correction current Ic for correcting the effects of the force of inertia of the motor  8  and the force of inertia of the traveling system of the vehicle, based on the angular acceleration ω′ calculated by the angular acceleration calculating unit  71   b  and a vehicle speed detection signal V outputted by the vehicle speed detector  18 . 
     The adder  74   a  adds the correction current Ic calculated by the correction current function unit  73   b  to the directing current I calculated by the directing current function unit  73   a , and outputs the resultant current. Hence, it is possible to improve a feel of steering. 
     The error amplifier  74   b  calculates the difference between the result of addition outputted by the adder  74   a  and a current flowing in the motor  8  detected by the current detecting circuit  71   e , and supplies a voltage corresponding to the calculation result to the PWM driving circuit  72   a . The PWM driving circuit  72   a  controls driving of the motor  8  according to the supplied voltage. 
     In the above-described electric power steering apparatus, the effects of the force of inertia of the motor  8  and the force of inertia of the traveling system of the vehicle are compensated using the motor rotational speed ω m  of the motor  8  supplied from the rotation detector  17 , and thus there is a problem that the cost of the parts of the rotation detector  17  is required. 
     Moreover, although not shown in the drawings, friction compensation of the steering system is performed by controlling a motor current flowing in the motor  8  based on the motor rotational speed ω m  of the motor  8  detected by the rotation detector  17 , but the torsion bar of the torque sensor  6  twists and the motor  8  does not rotate from the start of steering made by the driver until the friction compensation overcomes the friction torque of the motor  8  and reduction gear. Therefore, friction compensation is not carried out at the start of steering and control of friction compensation is started slightly later, resulting in a problem that the effect of friction compensation is small. 
     BRIEF SUMMARY OF THE INVENTION 
     An object of the present invention is to provide an electric power steering apparatus capable of solving the above problems. 
     An electric power steering apparatus according to the first invention, being provided with a torque detector for detecting a steering torque applied to a steering wheel and a steering assist motor which is driven under control based on a drive current corresponding to the steering torque detected by the torque detector, is characterized by comprising: an angle detector for detecting a turn angle of the steering wheel; angular velocity calculating means for calculating an angular velocity of turn of the steering wheel from the turn angle detected by the angle detector; friction compensating means for calculating an angular acceleration of turn of the steering wheel for friction compensation from the angular velocity of turn calculated by the angular velocity calculating means; and adding means for adding a current related to the angular velocity of turn and a current related to the angular acceleration of turn calculated by the friction compensating means to the drive current. 
     In this electric power steering apparatus, the torque detector detects a steering torque applied to the steering wheel, and driving of the steering assist motor is controlled based on a drive current corresponding to the detected steering torque. The angle detector detects a turn angle of the steering wheel, and the angular velocity calculating means calculates an angular velocity of turn of the steering wheel from the detected turn angle. The friction compensating means calculates angular acceleration of turn of the steering wheel for friction compensation from the angular velocity of turn calculated by the angular velocity calculating means, and the adding means adds a current related to the angular velocity of turn and a current related to the angular acceleration of turn calculated by the friction compensating means to the drive current. 
     Accordingly, friction compensation is performed at the start of steering and more accurate friction compensation of a steering system is carried out, thereby achieving an electric power steering apparatus having a good feel of steering. 
     An electric power steering apparatus according to the second invention, being provided with a torque detector for detecting a steering torque applied to a steering wheel and a steering assist motor which is driven under control based on a drive current corresponding to the steering torque detected by the torque detector, is characterized by comprising: a current detecting circuit for detecting a current flowing in the motor; a voltage detecting circuit for detecting a voltage applied to the motor; motor rotational speed calculating means for calculating a rotational speed of the motor based on the current detected by the current detecting circuit and the voltage detected by the voltage detecting circuit; angular acceleration calculating means for calculating an angular acceleration of turn of the steering wheel by adding up a value corresponding to first-order differentiation of the rotational speed calculated by the motor rotational speed calculating means and a value corresponding to second-order differentiation of the steering torque; and adding means for adding a current determined in relation to the angular acceleration of turn calculated by the angular acceleration calculating means to the drive current. 
     In this electric power steering apparatus, the torque detector detects a steering torque applied to a steering wheel, and driving of the steering assist motor is controlled based on a drive current corresponding to the detected steering torque. The current detecting circuit detects a current flowing in the motor, and the voltage detecting circuit detects a voltage applied to the motor. The motor rotational speed calculating means calculates a rotational speed of the motor based on the current detected by the current detecting circuit and the voltage detected by the voltage detecting circuit, and the angular acceleration calculating means calculates angular acceleration of turn of the steering wheel by adding up a value corresponding to first-order differentiation of the rotational speed calculated by the motor rotational speed calculating means and a value corresponding to second-order differentiation of the steering torque. The adding means adds a current determined in relation to the angular acceleration of turn calculated by the angular acceleration calculating means to the drive current. 
     Accordingly, it is possible to achieve an electric power steering apparatus which requires no rotation detector and enables a reduction in the cost of parts. 
     An electric power steering apparatus according to the third invention, being provided with a torque detector for detecting a steering torque applied to a steering wheel and a steering assist motor which is driven under control based on a drive current corresponding to the steering torque detected by the torque detector, is characterized by comprising: a current detecting circuit for detecting a current flowing in the motor; a voltage detecting circuit for detecting a voltage applied to the motor; motor rotational speed calculating means for calculating a rotational speed of the motor based on the current detected by the current detecting circuit and the voltage detected by the voltage detecting circuit; angular velocity calculating means for calculating an angular velocity of turn of the steering wheel by adding up a value related to the rotational speed calculated by the motor rotational speed calculating means and a value related to first-order differentiation of the steering torque; angular acceleration calculating means for calculating an angular acceleration of turn of the steering wheel from the angular velocity of turn calculated by the angular velocity calculating means; and adding means for adding a current related to the angular velocity of turn and a current related to the angular acceleration of turn calculated by the angular acceleration calculating means to the drive current. 
     In this electric power steering apparatus, the torque detector detects a steering torque applied to the steering wheel, and driving of the steering assist motor is controlled based on a drive current corresponding to the detected steering torque. The current detecting circuit detects a current flowing in the motor, and the voltage detecting circuit detects a voltage applied to the motor. The motor rotational speed calculating means calculates a rotational speed of the motor based on the current detected by the current detecting circuit and the voltage detected by the voltage detecting circuit, and the angular velocity calculating means calculates an angular velocity of turn of the steering wheel by adding up a value related to the rotational speed calculated by the motor rotational speed calculating means and a value related to first-order differentiation of the steering torque. The angular acceleration calculating means calculates angular acceleration of turn of the steering wheel from the angular velocity of turn calculated by the angular velocity calculating means, and the adding means adds a current related to the angular velocity of turn and a current related to the angular acceleration of turn calculated by the angular acceleration calculating means to the drive current. 
     Accordingly, friction compensation is performed at the start of steering and more accurate friction compensation of a steering system is carried out, thereby achieving an electric power steering apparatus having a good feel of steering. Moreover, it is possible to achieve an electric power steering apparatus having a good feel of steering by only changing software, without changing conventional hardware. 
     The above and further objects and features of the invention will more fully be apparent from the following detailed description with accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
     FIG. 1 is a block diagram showing an example of the constitution of a conventional electric power steering apparatus; 
     FIG. 2 is a block diagram showing the constitution of an embodiment of an electric power steering apparatus according to the present invention; 
     FIG. 3 is a block diagram showing an example of the constitution of a friction compensating unit; 
     FIG. 4 is a block diagram showing the constitution of an embodiment of an electric power steering apparatus according to the present invention; 
     FIG. 5 is a graph showing the relationship among a motor current, motor voltage and motor rotational speed; and 
     FIG. 6 is a block diagram showing the constitution of an embodiment of an electric power steering apparatus according to the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following description will explain some embodiments of an electric power steering apparatus according to the present invention with reference to the drawings illustrating the embodiments. 
     First Embodiment 
     FIG. 2 is a block diagram showing the constitution of the First Embodiment of an electric power steering apparatus according to the present invention. In this electric power steering apparatus, an output signal of a torque sensor (torque detector)  6  is inputted to a control unit  7   a . The control unit  7   a  supplies a drive signal to a steering assist motor  8  based on this signal. The steering assist motor  8  transmits its torque to the lower shaft of a steering shaft. 
     The torque sensor  6  detects, as the steering torque applied to a steering wheel, a relative displacement in a circumferential direction which is generated between the upper and lower shafts of the steering shaft turning about the axis of the steering wheel according to turn of the steering wheel with twist of a torsion bar interposed between the upper and lower shafts. 
     A rotation detector  17  for detecting a rotational position of the motor  8  is attached to the rotation shaft of the motor  8 . 
     The control unit  7   a  is supplied with a rotation detection signal of the rotation detector  17 , an output signal of a vehicle speed detector  18  for detecting a vehicle speed and an output signal of an angle detector  20  for detecting a turn angle of the steering wheel as well as the above-mentioned output signal of the torque sensor  6 , and outputs a drive signal for driving the motor  8  and an electromagnetic clutch  16 . 
     A torque detection signal outputted by the torque sensor  6  is supplied to each of a phase compensating unit  71   a  for stabilizing a system by advancing the phase of the torque detection signal, an angular acceleration calculating unit  71   b  for calculating an angular acceleration ω′ of turn of the steering wheel, a middle point determining unit  71   c  for determining the middle point of the steering wheel of the vehicle traveling in a straight direction, and a lock detecting unit  7  If for detecting whether the motor  8  is locked. 
     Moreover, a vehicle speed detection signal outputted by the vehicle speed detector  18  is supplied to each of the lock detecting unit  71   f , middle point determining unit  71   c , directing current function unit  73   a , correction current function unit  73   b  and change current function unit  73   c.    
     The directing current function unit  73   a  is supplied with an output signal of the phase compensating unit  71   a  and a later-described change current Ia, determines a directing current I for the motor  8  based on the steering torque, change current Ia and vehicle speed detection signal, and outputs the determined directing current I. 
     The correction current function unit  73   b  is supplied with the angular acceleration ω′ of the steering wheel outputted by the angular acceleration calculating unit  71   b , determines a correction current Ic for correcting the force of inertia of the motor  8  during acceleration and deceleration and the force of inertia of the traveling system of the vehicle based on the angular acceleration ω′ and vehicle speed detection signal, and outputs the determined correction current Ic. 
     The change current function unit  73   c  is supplied with a steering angle θ outputted from a later-described steering angle determining unit  71   d , determines a change current Ia for changing the characteristic of the directing current I based on the steering angle θ and vehicle speed detection signal, and outputs the determined change current Ia. 
     The rotation detection signal of the rotation detector  17  is supplied to the lock detecting unit  71   f , middle point determining unit  71   c , angular acceleration calculating unit  71   b  and steering angle determining unit  71   d.    
     The steering angle determining unit  71   d  determines a steering angle θ based on the rotation detection signal and the middle point determined by the middle point determining unit  71   c , and outputs the determined steering angle θ. 
     The lock detecting unit  71   f  detects whether the motor  8  is locked, based on the rotation detection signal, when the supplied torque detection signal and vehicle speed detection signal are larger than their predetermined values, respectively. When the lock detecting unit  7  If detects that the motor  8  is locked, a driving circuit  72   b  disconnects the electromagnetic clutch  16 . 
     An angle signal of the steering wheel outputted by the angle detector  20  is supplied to an angular velocity calculating unit (angular velocity calculating means)  23 . The angular velocity calculating unit  23  calculates an angular velocity of the steering wheel by differentiating the supplied angle signal, and outputs an angular velocity signal. The angular velocity signal outputted by the angular velocity calculating unit  23  is supplied to a friction compensating unit  24 . The friction compensating unit  24  generates a current for friction compensation based on the supplied angular velocity signal, and outputs the current. 
     The output signal of the directing current function unit  73   a  and the output signal of the correction current function unit  73   b  are added together by an adder (adding means)  74   a , and an adder (adding means)  25  adds the current for friction compensation supplied from the friction compensating unit  24  to the result of addition given by the adder  74   a . The result of addition given by the adder  25  is supplied to an error amplifier  74   b.    
     The error amplifier  74   b  calculates the difference between the result of addition given by the adder  25  and a feedback signal from a current detecting circuit  71   e  for detecting a current flowing in the motor  8 , and a voltage corresponding to the calculation result is supplied to the motor  8  by a PWM (Pulse Width Modulation) driving circuit  72   a.    
     FIG. 3 is a block diagram showing an example of the constitution of the above-described friction compensating unit  24 . 
     In this friction compensating unit  24 , the angular velocity signal ω of the steering wheel from the angular velocity calculating unit  23  is supplied to a dynamic friction compensating unit  24   a  and a differentiation calculating unit (differentiation calculating means)  24   b.    
     The dynamic friction compensating unit  24   a  outputs a substantially constant current for dynamic friction compensation when the angular velocity signal ω is not close to zero. The differentiation calculating unit  24   b  differentiates the angular velocity signal ω and supplies the differential value to a static friction compensating unit (adding means)  24   c . The static friction compensating unit  24   c  outputs a current for static friction compensation proportional to the differential value of the angular velocity signal ω only when the differential value is close to zero, or outputs a substantially constant current when the differential value is not close to zero. 
     The currents outputted by the respective dynamic friction compensating unit  24   a  and static friction compensating unit  24   c  are added together by an adder (adding means)  24   d , and outputted to the adder  25  (FIG.  2 ). 
     The following description will explain an operation of the electric power steering apparatus having such structures. 
     The directing current function unit  73   a  determines a directing current I for the motor  8  based on the torque detection signal whose phase has been compensated by the phase compensating unit  71   a , the change current Ia outputted by the change current function unit  73   c  and the vehicle speed detection signal outputted by the vehicle speed detector  18 , and outputs the determined directing current I. 
     Meanwhile, the change current function unit  73   c  determines a change current Ia for changing the characteristic of the directing current I, based on the steering angle θ given by the steering angle determining unit  71   d  and the vehicle speed detection signal outputted by the vehicle speed detector  18 , and outputs the determined change current Ia. 
     The angular acceleration calculating unit  71   b  reads a torque detection signal T supplied from the torque sensor  6  and a motor rotational speed ω m  of the motor  8  supplied from the rotation detector  17 , and calculates the angular acceleration ω′ of the steering wheel according to the following equation. 
     
       
         ω′= T″/K+ω   m   ′/n   (1)  
       
     
     Here, equation (1) can be given by the following equations. 
     
       
           T=K (θ 1 −θ o )  
       
     
     where 
     θ i : a steering angle of the upper shaft of the steering shaft, 
     θ o : a steering angle of the lower shaft of the steering shaft, 
     K: a spring constant of the torsion bar. 
     
       
         θ i −θ o   =T/K    
       
     
     
       
         θ i ″−θ o   ″=T″/K    
       
     
     
       
         θ i   ″=T″/K+θ   o ″  (2)  
       
     
     Meanwhile, 
     θ o ′=ω m   /n    
     θ o ″=ω m   ′/n    
     (n: the deceleration ratio of the motor rotation shaft to the lower shaft) 
     ∴ According to equation (2), 
     
       
         θ i   ″=ω′=T″/K+ω   m   /n   (1)  
       
     
     The correction current function unit  73   b  calculates a predetermined correction current Ic for correcting the effects of the force of inertia of the motor  8  and the force of inertia of the traveling system of the vehicle, based on the angular acceleration ω′ calculated by the angular acceleration calculating unit  71   b  and vehicle speed detection signal V outputted by the vehicle speed detector  18 . 
     The angular velocity calculating unit  23  calculates an angular velocity of the steering wheel by differentiating the angle signal supplied from the angle detector  20 , and outputs an angular velocity signal to the friction compensating unit  24 . 
     In the friction compensating unit  24 , the dynamic friction compensating unit  24   a  outputs a substantially constant current for dynamic friction compensation when the angular velocity signal ω is not close to zero, and the differentiation calculating unit  24   b  differentiates the angular velocity signal ω and supplies the resultant differential value to the static friction compensating unit  24   c . The static friction compensating unit  24   c  outputs a current for static friction compensation proportional to the differential value of the angular velocity signal ω only when the differential value is close to zero, or outputs a substantially constant current when the differential value is not close to zero. 
     The friction compensating unit  24  adds up the currents outputted by the respective dynamic friction compensating unit  24   a  and static friction compensating unit  24   c  by the adder  24   d , and outputs the resultant current to the adder  25 . 
     The adder  74   a  adds the correction current Ic calculated by the correction current function unit  73   b  to the directing current I calculated by the directing current function unit  73   a , and outputs the resultant current. Consequently, the correction current Ic corresponding to the force of inertia of the motor  8  and the force of inertia of the traveling system of the vehicle is added to the directing current I. 
     The adder  25  adds the current outputted by the friction compensating unit  24  to the current outputted by the adder  74   a , and supplies the resultant signal to the error amplifier  74   b.    
     The error amplifier  74   b  calculates the difference between the current supplied from the adder  25  and a current flowing in the motor  8  detected by the current detecting circuit  71   e , and supplies a voltage corresponding to the calculation result to the PWM driving circuit  72   a . The PWM driving circuit  72   a  controls driving of the motor  8  according to the supplied voltage. 
     Second Embodiment 
     FIG. 4 is a block diagram showing the constitution of the Second Embodiment of an electric power steering apparatus according to the present invention. In this electric power steering apparatus, an output signal of the torque sensor  6  is inputted to a control unit  7   b . The control unit  7   b  supplies a drive signal to the steering assist motor  8  based on this output signal. The steering assist motor  8  transmits its torque to the lower shaft of the steering shaft. 
     The control unit  7   b  is supplied with an output signal of the vehicle speed detector  18  for detecting a vehicle speed as well as the above-mentioned output signal of the torque sensor  6 , and outputs a drive signal for driving the motor  8  and electromagnetic clutch  16 . 
     In the control unit  7   b , a torque detection signal outputted by the torque sensor  6  is supplied to each of the phase compensating unit  71   a , angular acceleration calculating unit (angular acceleration calculating means)  71   b , middle point determining unit  71   c , lock detecting unit  71   f  for detecting whether the motor  8  is locked, and angular velocity calculating unit  27  (angular velocity calculating means). 
     In this electric power steering apparatus, instead of the rotation detector  17  (FIG.  2 ), a motor rotational speed calculating unit (motor rotational speed calculating means)  22  within the control unit  7   b  calculates a motor rotational speed ω m (=2πN, N: motor rotations per second) based on a motor current from the current detecting circuit  71   e  for detecting a current flowing in the motor  8  and a motor voltage from a voltage detecting circuit  21  for detecting a voltage applied to the motor  8 . 
     The motor rotational speed ω m  can be calculated from the relationship among the motor current, motor voltage and motor rotational speed ω m  as shown in FIG.  5 . The relationship shown in FIG. 5 can be readily obtained from the characteristics of so-called T-N curve (torque-rotations curve) and T-I curve (torque-current curve) of a DC motor. 
     The motor rotational speed ω m  calculated by the motor rotational speed calculating unit  22  is supplied to the lock detecting unit  71   f , middle point determining unit  71   c , steering angle determining unit  71   d  and angle velocity calculating unit  27 . 
     The steering angle determining unit  71   d  determines a steering angle θ from the motor rotational speed ω m  and the middle point determined by the middle point determining unit  71   c , and outputs the determined steering angle θ. 
     The lock detecting unit  71   f  detects whether the motor  8  is locked, based on the motor rotational speed ω m , when the supplied torque detection signal and vehicle speed detection signal are larger than their predetermined values, respectively. When the lock detecting unit  71   f  detects that the motor  8  is locked, the driving circuit  72   b  disconnects the electromagnetic clutch  16 . 
     The angular velocity calculating unit  27  calculates an angular velocity of the steering wheel from the supplied motor rotational speed ω m  and torque detection signal, and outputs an angular velocity signal. The angular velocity signal of the steering wheel outputted by the angular velocity calculating unit  27  is supplied to the friction compensating unit  24 . The friction compensating unit  24  generates a current for friction compensation based on the supplied angular velocity signal, and outputs the current. Other structures are the same as those of the electric power steering apparatus explained in the First Embodiment, and therefore similar parts will be designated with the same reference symbols and explanation thereof will be omitted. 
     The following description will explain an operation of the electric power steering apparatus having such structures. 
     The directing current function unit  73   a  determines a directing current I for the motor  8  based on the torque detection signal whose phase has been compensated by the phase compensating unit  71   a , the change current Ia outputted by the change current function unit  73   c  and the vehicle speed detection signal outputted by the vehicle speed detector  18 , and outputs the determined directing current I. 
     Meanwhile, the change current function unit  73   c  determines a change current Ia for changing the characteristic of the directing current I, based on the steering angle θ given by the steering angle determining unit  71   d  and the vehicle speed detection signal outputted by the vehicle speed detector  18 , and outputs the determined change current Ia. 
     The motor rotational speed calculating unit  22  calculates a motor rotational speed ω m  from the relationship shown in FIG. 5, based on the motor current from the current detecting circuit  71   e  and the motor voltage from the voltage detecting circuit  21 . 
     The angular acceleration calculating unit  71   b  reads the torque detection signal T supplied from the torque sensor  6  and the motor rotational speed ω m  of the motor  8  supplied from the rotational speed calculating unit  22 , and calculates the angular acceleration ω′ of the steering wheel according to the following equation. 
     
       
         ω′= T″/K+ω   m   ′/n   (1)  
       
     
     The correction current function unit  73   b  calculates a predetermined correction current Ic for correcting the effects of the force of inertia of the motor  8  and the force of inertia of the traveling system of the vehicle, based on the angular acceleration ω′ calculated by the angular acceleration calculating unit  71   b  and the vehicle speed detection signal V outputted by the vehicle speed detector  18 . 
     The angular velocity calculating unit  27  calculates an angular velocity ω of the steering wheel according to the following equation based on the motor rotational speed ω m  given by the motor rotational speed calculating unit  22  and the torque detection signal T from the torque sensor  6 . 
     
       
         ω= T′/K+ω   m   /n   (3)  
       
     
     Here, equation (3) can be given by the following equations. 
     
       
           T=K (θ i −θ O )  
       
     
     where 
     θ i : a steering angle of the upper shaft of the steering shaft, 
     θ o : a steering angle of the lower shaft of the steering shaft, 
     K: a spring constant of the torsion bar. 
     
       
         θ i −θ o   =T/K    
       
     
     
       
         θ i ′−θ o   ′=T′/K    
       
     
     
       
         θ i   ′=T′/K+θ   o ′  (4)  
       
     
     Meanwhile, 
     θ o ′=ω m /n 
     (n: the deceleration ratio of the motor rotation shaft to the lower shaft) 
     ∴ According to equation (4), 
     
       
         θ i   ′=ω=T′/K+ω   m   /n   (3)  
       
     
     The angular velocity calculating unit  27  supplies the calculated angular velocity ω of the steering wheel to the friction compensating unit  24 . Other operations are the same as those of the electric power steering apparatus explained in the First Embodiment, and therefore explanation thereof will be omitted. 
     Third Embodiment 
     FIG. 6 is a block diagram showing the constitution of the Third Embodiment of an electric power steering apparatus according to the present invention. In this electric power steering apparatus, an output signal of the torque sensor  6  is inputted to a control unit  7   c . The control unit  7   c  supplies a drive signal to the steering assist motor  8  based on this output signal. The steering assist motor  8  transmits its torque to the lower shaft of the steering shaft. 
     The motor rotational speed ω m  calculated by the motor rotational speed calculating unit  22  and the torque detection signal T from the torque sensor  6  are supplied to the angular velocity calculating unit  27 . The angular velocity calculating unit  27  calculates an angular velocity of the steering wheel from the supplied motor rotational speed ω m  and torque detection signal T, according to equation (3) shown above, and outputs the angular velocity. The angular velocity signal of the steering wheel outputted by the angular velocity calculating unit  27  is supplied to the friction compensating unit  24  and angular acceleration calculating unit  26 . The friction compensating unit  24  generates a current for friction compensation, based on the supplied angular velocity signal, and outputs the current. The angular acceleration calculating unit  26  calculates an angular acceleration signal ω′ of the steering wheel by differentiating the supplied angular velocity signal ω, and outputs the angular acceleration signal ω′. 
     The correction current function unit  73   b  calculates a predetermined correction current Ic for correcting the effects of the force of inertia of the motor  8  and the force of inertia of the traveling system of the vehicle, based on the angular acceleration ω′ calculated by the angular acceleration calculating unit  26  and the vehicle speed detection signal V outputted by the vehicle speed detector  18 . Other structures and operations are the same as those of the electric power steering apparatus explained in the Second Embodiment, and therefore parts having similar structures will be designated with the same reference symbols and explanation thereof will be omitted. 
     As this invention may be embodied in several forms without departing from the spirit of essential characteristics thereof, the present embodiments are therefore illustrative and not restrictive, since the scope of the invention is defined by the appended claims rather than by the description preceding them, and all changes that fall within metes and bounds of the claims, or equivalence of such metes and bounds thereof are therefore intended to be embraced by the claims.