Patent GB-1525697-A (GB)
Title: Surface measurement apparatus
IPC: G01B7/34
Filed: 1975-04-23
Abstract: 1525697 Surface measurements RANK ORGANISATION Ltd 7 April 1976 [23 April 1975 7 Jan 1976] 16813/75 and 00475/76 Heading GIN Surface measurement apparatus in which a sensor is traversed along a path in contact with or adjacent the surface 15 of a component under test utilizes a sensor comprising three transducers 12, 13, 14, each sensitive to variations of surface height and mounted in a row spaced from one another on a common support such that in use each traverses substantially the same path upon relative movement of the support and the test surface, the spacing of the support from the surface under test providing a reference datum for the transducers in generating the output signals thereof the transducer sensitivities being a, 1 and b respectively or the output signals from the transducers being amplified by respective amplifiers having gains of a, 1 and b respectively the output signals P 1 , P 2 , P 3 , from the transducers being combined to produce a composite signal S having the form S = aP 2  + bP 3  - 2P 1  which includes no component due to imperfections in the reference datum. Thus the provision of a separate reference datum is not required. In a preferred embodiment the transducers 12, 13, 14 are spaced apart by predetermined distances l 1 , l 2  where a+ b = 2 and al 1  - b1 2  = 0, To derive information concerning the test surface texture e.g. its roughness the composite signal s is analyzed to derive the amplitude and phase of the various terms of its Fourier transform. It is stated that it can be shown that the relation between the Fourier transform Fs of the composite signal and the Faurier transform F# of the true roughness signal is given by:- From this expressions for the amplitude and phase of a harmonic of wavelength # on the surface are computed. So, to derive the Fourier components of the surface roughness signal, the composite signal from the sensor is analyzed to produce the transform Fs of which the various harmonics are weighted by factors opposite in sign to the amplitude and  phase of the harmonics computed from the equations: In cases where the traversing speed of the transducers is not constant the transducer support carriage (21), Fig. 6 (not shown) has a device driven by a wheel of the carriage to provide pulses representing the movement of the carriage. The embodiment of Fig. 9 uses four transducers 27, 28, 29, 30 producing output signals p 1 , p 2 , p 3 , p 4  respectively and spaced from a nominal mid position by distances l 1 , l 2 , l 3  and l 4  respectively. The transducer output signals are amplified by amplifiers (not shown) with amplification factors 1, a, b, c respectively where from which the amplification factors may be computed for a given spacing. The composite signal s is produced by combining the signals according to the expression s = p 1  + ap 2  + bp 3  + cp 4 . The analysis of the composite signal and subsequent synthesis of the appropriate components of the Fourier transform to effect the desired weighting is performed as described above. In an embodiment for determining roundness of a component 46, Fig. 11 three transducers are supported in such a way that their lines of action meet at a common point. Fig. 10 is a schematic diagram of three transducers 31, 32, 33 disposed in this way, their lines of action meeting at a point 0 spaced by distance e from the component centre 0'. The transducer signals are p 1 , p 2 , p 3  and amplifier gains are a, 1, b as before. The angles between transducers 31, 32 and 32, 33 are α, # respectively. It is stated that for the composite signal s to include no component due to the eccentricity of the sensor path relative to the component centre then s = e {(-cos# + a cos(# + α) + b cos(# - #)} where # is the angle between the line of action of the middle transducer and the line joining points 0, 0'. From this it may be shown that: A further embodiment, Fig. 13, (not shown) uses transducers, disposed as in Fig. 1, with the circuit blocks shown for determining radius of curvature of a curved surface of a test component. The block 11a represents the sensor head bearing three transducers from which the signals p 1 , p 2 , p 3  are amplified by a, 1, b respectively and combined to form a composite signal s according to s = p 2  + p 3 -p 1  where p 1 , p 2  and p 3  are the amplified output signals from the first, second and third transducers. A computer 16 computes the co-efficients of the components of the Fourier transformer of the composite signal. The computer output feeds a high pass filter 17 and from there to a synthesizer 18 which weights the coefficients of the harmonics of the transform so as to provide an output which represents the harmonics of the transform without errors due to the variations in the reference datum. The zeroth order component of the transform is fed to a divider 71 pre-set to divide its input signal by the factor (1-a-b) to provide an output to display device 72 calibrated to display radius.