Chapter 6

Surface Roughness

The proper functioning wear life of a part frequently depends upon the smoothness quality of its surfaces. Absolute smoothness is not possible. Any surface has minute peaks and valleys. Thus, surface roughness is an important factor when dealing with issues such as friction, lubrication, and wear. It also has a major impact on applications involving thermal or electrical resistance, fluid dynamics, noise and vibration control, dimensional tolerance, and abrasive processes, among others.

Definition

Surface Roughness is produced by the direct effect of the cutting process (chip formation), deformation from blasting, crystallization, corrosion and other chemical processed. The spacing to depth ratio between successive peaks is of the order 5:1 to 150:1.There is another term which is very similar to surface roughness named waviness. Waviness refers to periodic regularities in the surface of a part, but at a scale smaller than that which is controlled by geometric dimensions and tolerances. The spacing to depth ratio between successive peaks is of the order 100:1 to 1000:1. It is produced by eccentric fixture, form deviations in the cutting tool and vibration.One technique for distinguishing between roughness, waviness and form tolerance is by the spacing to depth ratio as shown in Fig.6-1. Roughness is measured at a much smaller scale than waviness and is an indication of very small local imperfection in surface.

(a) actual surface profile;(b) surface roughness; (c) waviness; (d)form toleranceFigure 6-1 Roughness and Waviness

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6.1 Basic Terms and Definitions

The concept of roughness is often described with terms such as ‘uneven’, ‘irregular’, ‘coarse in texture’, and other similar ones. Similar to some surface properties such as hardness, the value of surface roughness depends on the scale of measurement. In addition, the concept roughness has statistical implications as it considers factors such as sample size and sampling interval. The microscopic geometrical property formed by the small clearance and the rise and fall on the machined surface is called surface roughness. Its basic terms and definitions are introduced as follows:

Sampling Length l (shown in Fig.6-2): The nominal spacing within a surface characteristic is measured including roughness sampling length and waviness sampling length.

Evaluation Length ln (shown in Fig.6-2) : is the part of the traversing length from where the values of the surface parameters are determined. It normally comprises five consecutive sampling lengths.

.

Figure 6-2 Sampling Length l and Evaluation Length ln

Mean Line of the Profile m: is the quantitative calculation of the baseline roughness value. Two methods of determining the center line profile are described as follows:(a)Least square mean line of the profile (shown in Fig.6-3): is the l ine having the form of the geometrical profile and dividing the effective such that, within the sampling length l the sum of distance squares between the effective points and the mean line is minimum.

Figure 6-3 Least Square Mean Line of the Profile

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(b)Centre arithmetical mean line of the profile (shown in Fig.6-4): is the line parallel to the general direction of the profile for which the areas embraced by the profile above and below the line are equal. When the waveform is repetitive, the mean line and centre line are equivalent. Normally for practical purposes, the mean line and center line are considered equivalent.

Figure 6-4 Centre Arithmetical Mean Line of the Profi le

6.2 Main Evaluation Parameters of Surface Roughness

Parameters used to describe surface roughness are largely statistical indicators obtained from many samples of the surface height. There are six forms in which the roughness height may be expressed: arithmetical mean deviation of the profile (Ra), ten point height of irregularities (Rz), maximum height of the profile (Ry), mean spacing of the profile irregularities(Sm), mean spacing of local peaks of the profile (S), and profile bearing length ratio(tp). Ra is a parameter the most generally used in evaluation of surface roughness. Rz and S represent the amplitude and wavelength, respectively, of wavelike transverse profiles.

Arithmetical Mean Deviation of the Profile Ra (shown in Fig.6-5): is the absolute arithmetic mean of contour deviated distance (distance between each point of the contour surface and the base line ox) within a sample range of the part surface. It can be calculated as

(6-1)

where z is the contour offset distance and lr is the sampling length.

Figure 6-5 Arithmetical Mean Deviation of the Profile Ra

The common values of arithmetical mean deviation of the profile Ra is given in

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Table6-1.

Ten Point Height of Irregularities Rz (shown in Fig. 6-6): is the distance between the maximum peak height and the maximum valley depth from the mean line in each sampling length. It is defined as the sum of average of 5 contour peak heights and the average of 5 contour bottom depths. It can be calculated as

(6-2)

where ypi is the ith maximum peak height of profile and yvi is the ith largest valley deep of profile.

Figure 6-6 Ten Point Height of Irregularities Rz

The common values of ten point height of irregularities Rz is given in Table6-2 in which symbol BS represents basic series and symbol SS represents supplementary series.

Table6-2 Values of Ten Point Height of Irregularities Rz (GB/T1031-95) ( )

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Maximum Height of the Profile Ry (shown in Fig. 6-7): is defined as the distance within the sample length from the peak line to the bottom line and can be calculated as

(6-3)

where zp is the maximum peak height of profile and zv is the largest valley deep of profile.

Figure 6-7 Ten Point Height of Irregularities Rz

Mean Spacing of the Profile Irregularities Sm (shown in Fig. 6-8): is the mean spacing of the profile irregularities within sampling length and can be calculated as

(6-4)

where Smi is the ith profile irregularities, n is the spacing number of the profile irregularities within sampling length.

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Figure 6-8 Mean Spacing of the Profile Irregularities Sm

Mean Spacing of Local Peaks of the Profile S: is the mean spacing of local peaks of the profile within sampling length and can be calculated as

(6-5)

where Si is the ith local peak of the profile, n is the spacing number of local peaks of the profile within sampling length.

Profile Bearing Length Ratio tp (shown in Fig.6-9): is that the profile bearing length

divided by sampling length l when level intercept is c.

(6-6)

Figure 6- 9 Profile Bearing Length Ratio tp

6.3 Principles for Selecting Surface Roughness Parameters

The principles for selecting the surface roughness can be described as follows:

The first series is preferred. Parameters on working surfaces are smaller than that on non-working surfaces.

Parameters on the moving surface are smaller than on still surfaces.

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Select parameters according to production cost. Surface roughness should be as large as possible to reduce machining cost, provided design or usage requirements are met.

Some examples are given in Table6-3. Relationship between arithmetical mean roughness (Ra) and conventional symbols is given in Table6-4.

Table6-3 Examples for Selecting the Surface Roughness

Surface condition Ra value/µm Surface condition Ra value/µm

Relative movement 0.4, 0.8, 1.6, 3.2 Non-contact 12.5, 25

Static contact 3.2 , 6.3 Non-removing material

Special symbol

Table6-4 Relationship between Arithmetical Mean Roughness (Ra) and Conventional Symbols

6.4 Symbols and Designation Methods

The common used symbols of surface roughness are three types which are described as follows:

: Basic symbol, there is no significance to use this symbol alone.

: The surface roughness is obtained by machining of removing materials, e.g.

turning, milling, drilling, grinding

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: The surface roughness is obtained by processing of not removing materials, e.g.

casting, forging, punching, pressing

The specification drawing of surface roughness and the noting locations of other symbols of surface roughness are given in Fig.6-10.

Figure 6-10 Surface Roughness Symbols

wherea1 and a2----The permissible maximum and minimum value of Ra(in ), respectively. Generally, the minimum value of Ra may be omitted.b----Machining process, such as coating and other surface treatment.c----Sampling length (in mm).d----Lay symbol.e-----Machining allowance (in mm).f-----Spacing of the profile irregularities (sm) or mean spacing of local peaks of the profile (S) in mm, or profile bearing length ratio tp.Generally, in engineering practice only the symbol with roughness height values is applied to the drawing. Add a small circle to the basic symbol, this means that the surface roughness is obtained by machining operation through which no material on the surface is to be removed, e.g., casting, forging, punching, pressing, etc. Some examples are shown in Fig.6-11. The lay symbols are illustrated in Fig.6-12. The surface roughness values of different machining processes are given in Table 6-5.

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Figure 6-11 Symbol Examples

Figure 6-12 Lay Symbols

Table 6-5 Ra Values of Different Machining Processes

Ra/µm Microcosmic surface features Primary machining methods50 Obviously visible tool marks Casting, forging, rough turning, rough milling,

rough planning, drilling, rubber and coarse wheel

25 Visible tool marks

12.5 Occasional tool marks Rough turning, planning, milling, drilling6.3 Visible machining marks Fine turning, fine milling, fine planning,

reaming, boring, rough grinding3.2 Occasional machining marks 1.6 Invisible machining marks

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0.80 Recognizable machining veins Fine turning, rough reaming, fine broaching, fine boring, fine grinding0.40 Occasional machining veins

0.20 Invisible machining veins

6.5 Method for Designing the Surface Roughness Symbols on a Drawing

The national standard provides various classes of surface finish. Each class of surface roughness corresponds to a definite range of values, expressed as Ra or Rz. Method for designing the surface roughness symbols on a drawing is described as follows:

The symbol position is placed toward the surface machined. It may be placed on the visible contour or extension line.

Each machined surface can be designated only once. In some situation, the symbol must be revolved in a clockwise direction and the

numerals must be agreed with the direction of the dimension numerals. When all the surface of a part are in the same surface condition, the surface

roughness number can be shown in a unified way at the right upper corner of the drawing.

When most surface of a part are in the same surface condition, then the surface roughness symbols of such surfaces can be taken out of the figure and drawn at the right upper corner of the drawing with the word “remainder” preceding it.

If different surface condition is required in one continuous surface, a thin line with a dimension to show its length should separate the surface roughness symbols of the two different portions.

For gear and spline shafts, if their teeth are not drawn, the surface roughness symbols may be designated on the pitch lines.

For screw threads that are drawn without their profiles in the drawing, the surface roughness symbol should be designated together with their symbols for profile, if necessary. 

According to this method, some examples are given in Fig.6-13.

 

(a) (b)

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(c) (d)

(e)

Figure 6-13 Design Examples on a Drawing

6.6 Measurement Techniques

6.6.1 Stylus InstrumentsStylus instruments are based on the principle of running a probe across a surface in order to detect variations in height as a function of distance. One of the early stylus instruments employed a system of levers to magnify the vertical displacement of the stylus and recorded the profile on a smoked-glass plate. The next step in the development of the stylus instruments was to incorporate a transducer, which converted the vertical displacement into an electrical signal. This signal can then be

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processed by the instrument electronics to calculate a suitable roughness parameter. The type of transducer used largely affects instrument performance. A piezoelectric crystal is often used as the transducer in the less expensive instruments. One type of stylus instruments is shown in Fig. 6-14. Other transducer mechanisms include moving coil transducers, capacitance transducers, and linear variable differential transformers (LVDT). The resolution of a stylus instrument depends on its manufacturer and model. The Tensor P2 (SP-P2), for instance, has a horizontal resolution of 0.02 , while the Tensor alpha-step 200 (SP-α200) has a horizontal resolution of 0.04 .

Figure 6-14 Tomlinson Roughness Meter

6.6.2 Optical InstrumentsThe interaction of polarized light with a surface can also be employed to evaluate surface roughness. Such is the case of the long-path length optical profiler, which focuses a laser beam onto a surface by means of an arrangement of mirrors. Before reaching the specimen, the laser goes through a Wollaston prism that polarizes the beam into two orthogonal components. The beams are then focused onto the surface where they reflect back to the prism. Finally, the reflected beams are directed to a beam splitter, which sends each beam to a different detector. The phase difference of the polarized beams, which is related to the height difference at the surface, results in a voltage difference that can be measured. This instrument was reported to have a vertical range and resolution of 2 and 0.025nm, respectively. A schematic diagram of the instrument is shown in Fig.6-15.

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Figure 6-15 Long-path Length Optical Profiler

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