Mechanical test stand for the measurement of the vibration levels of chain saws during cutting operations

Journal of Sound and Vibration (1983) 88(l),

MECHANICAL

TEST

STAND

THE VIBRATION DURING

65-84

FOR THE MEASUREMENT

LEVELS

CUTTING

OF CHAIN

OF

SAWS

OPERATIONS

D. D. REYNOLDS Joiner-Pelton-Rose,

Inc., 10110 Monroe Drive, Dallas, Texas 75229,

U.S.A.

AND

F. L. WILSON Garrett, Air Research Industrial Division, Torrance, California, U.S.A. (Received 11 November 1981, and in revised form 22 July 1982)

A mechanical test stand and corresponding test procedures for measuring the vibration levels of chain saws during cutting operations was developed for the Chain Saw Manufacturers Association. The stand includes mechanical coupling devices that approximate the dynamic response characteristics of the hand to clamp the top and rear saw handles. The stand is designed so that saws of all types and shapes can be tested. Results of hand-held and machine-held vibration tests on chain saws are discussed. The overall correlation between the vibration levels obtained from the hand-held and machine-held vibration tests on specified chain saws was good.

1. INTRODUCTION Vibration of hand tools has long been a problem for the operators of those tools. Such problems may vary from simple discomfort to vibration related diseases. For this reason many countries have established maximum vibration levels which they deem tolerable. Any tools sold in these countries must undergo tests verifying that they conform to that country’s established maximum levels. The project reported in this paper was concerned with the vibration testing of chain saws. To date, most vibration tests of saws have been done by hand, simulating actual field conditions. Hand-held tests usually result in a lack of repeatability between tests with the same saw operator, and especially between tests conducted in different laboratories. This lack of repeatability is usually associated with the different grip forces and methods of manipulating a saw that are used by the many chain saw operators. As a result, the Chain Saw Manufacturers Association (CSMA) initiated a program to investigate and evaluate the concepts associated with the development of a mechanical test stand and corresponding test procedures for measuring the vibration levels of chain saws. The objectives of the program as outlined by the CSMA were as follows: (1) design and construction of a machine to hold a chain saw for vibration testing; (2) acceleration measurements made on a saw held in the machine must (a) be repeatable, and (b) correlate with measurements taken when the saw is hand-held; (3) the machine must (a) not introduce any preload on the saw other than that introduced by human hands and arms in normal use, (b) not develop any resonant interaction with the saw other than that occurring with human hands and arms, (c) provide for tests whether or not the saw is cutting wood, (d) be so designed that identical machines may 65

0022-460X/83/090065 +20 %03.00/O

0 1983 Academic

Press Inc. (London)

Limited

66

D. D.

REYNOLDS

AND

F. L. WILSON

be readily constructed by others, and (e) include a calibrating means so that machine performance may be frequently checked against a standard and against other machines; (4) the relationship between the machine and hand-held tests is to be developed with a mathematical model and verified experimentally, and variations in grip force and operational parameters such as mass, stiffness, and damping of the hand-arm system are to be explored; (5) establish the required instrumentation; (6) determine the useful operating range and the limitations of the machine; (7) identify proper operating procedures. 2. DESCRIPTION OF VIBRATION TEST MACHINE Figures l(a)-(c) show pictures of a chain saw mounted in the CSMA chain saw vibration test machine. The basic superstructure of the machine was constructed of solid steel 2 in diameter circular shafts and 2 in square bars. These were fastened together by using Thomson pillow blocks so that the machine is rigid in all directions. The machine is

Figure 1. Chain mountings.

saw mounted

in test stand.

(a) Front

view;

(b) side view;

(c) close-up

showing

handle

CHAIN

SAW

VIBRATION

LEVELS

TEST

STAND

67

massive (around 1000 lb) so that no resonant interactions occur between the test stand and the saw being supported. The basic support structure for the chain saws is adjustable to accommodate saws of all shapes and sizes. The two clamp support brackets attached to the top circular shaft of the test machine can be moved back and forth or rotated from side to side to line up with the top and back handle configurations of different chain saws. The handle clamps which grip the saws can also be positioned to match the handle configurations of various saws (see Figure 2). The top circular shaft, to which the clamp support brackets are attached, can be moved from side to side to align the saws properly with the wood during cutting tests (see Figure 3). The wood is raised on a steel carriage, which is lifted by two hydraulic cylinders. The carriage rides on eight self-adjusting linear bearings, which are adjusted to provide a

Figure

Figure

2. Chain saw clamping

3. Adjustable

support

mechanism:

structure:

CSMA chain saw test stand.

CSMA chain saw test stand.

68

D. D. REYNOLDS

AND

F. L. WILSON

zero tolerance between the bearings and shafts (see Figure l(a)). The bearings were kept clean by commercial plastic window shades, which were affixed to the stand so as to move in conjunction with the carriage (the window shades can be seen in Figure 9 of section 5). The hydraulic operation is controlled by an electric switching circuit. This enables the operator to control the upward motion of the carriage, or to lower it immediately in case of emergency. The circuit also causes the carriage to reverse direction automatically when it reaches the limiting height of its travel. A chain saw is mounted in the CSMA test stand by means of molded elastomers (see Figure 4) that are wrapped around the saw handles and then are placed inside rigid circular clamps that are rigidly attached to the support structure of the test stand (see Figures l(c) and 2). In this manner it is possible to mount a chain saw in the CSMA test stand without attaching additional mass to the saw handles.

Figure 4. Elastomer

3. DESCRIPTION

for CSMA chain saw test stand.

OF MOLDED

ELASTOMER

Figure 5 shows a sketch of the elastomer configuration that was used for the machineheld chain saw vibration tests (see also Figure 4). The elastomer was constructed in the following manner. First, a 0.16 cm (A in) thick by 6.35 cm (2.5 in) wide single layer of 30 durometer neoprene rubber, cut to a length equal to the circumference of the inner core of the elastomer mold, was wrapped around the inner core. The, two ends of the 30 durometer neoprene rubber were bonded together with Eastman 910 contact cement. Second, a single layer of closed cell sponge neoprene measuring 0.64 cm ($ in) thick by

2+1n

outsIde

3%~

dlometer

dlometer round

hole

1/161n 30 durometer rubber V41n closed cell sponge neoprene 1/81n closed Flexone 30

Figure

5. Final elastomer

cell

sponge

configuration.

neoprene

CHAIN

SAW

VIBRATION

LEVELS

TEST

STAND

69

6.35 cm (2.5 in) wide was cut to a length equal to the circumference around the 30 durometer rubber. Goodyear Contact Cement (trade name) was applied to the outside of the 30 durometer rubber and to one side and the two ends of the closed cell sponge neoprene. The cement was allowed to dry for 5-10 min. The closed cell sponge neoprene was then wrapped around the 30 durometer rubber. It is important to insure that the ends of the closed cell sponge neoprene are pressed securely together. Third, a single layer of closed cell sponge neoprene measuring 0.32 cm (Bin) thick by 6.35 cm (2.5 in) wide was cut to a length equal to the circumference around the 0.64 cm (f in) thick layer of closed cell sponge neoprene. Goodyear Contact Cement was used to attach the 0.32 cm (i in) thick layer of closed cell sponge neoprene to the 0.64 cm (din) layer as previously described. Fourth, the elastomer assembly was placed in a mold and a 064 cm (: in) layer of Flexane 30 (trade name) was poured around the assembly and allowed to cure for a minimum of 24 h. Finally, before being used for a machine-held chain saw test, two 2.54 cm (1 in) sections were cut from the finished elastomer assembly. The above basic elastomer configuration when attached between the saw handles and the test machine clamps supported the saw in the machine without applying any static compressive pressure on the saw handles. This worked well for lightweight chain saws. However, when this configuration was used for heavier saws, the larger static weight of the saws resulted in the breaking of the cement bond between the handles and elastomers or excessive static deformation of the elastomers during testing. These problems were solved by using Goodyear Contact Cement, as previously described, to attach a 0.08 cm (& in) thick layer of 50 durometer neoprene rubber to the outside surface of the Flexane 30. This resulted in a compressive static pressure being applied to the handles of heavier saws, eliminating the above difficulties. The results of the machine-held chain saw tests, when compared with the hand-held tests, indicated that the increased dynamic stiffness of the elastomer associated with the 0.08 cm (A in) thick layer of 50 durometer neoprene rubber had no apparent adverse effects upon the test results. It was decided at the beginning of the CSMA project to design a chain saw clamping mechanism that was relatively simple in nature and easy to construct and use. It was considered neither desirable nor practical to exactly duplicate the dynamic properties of the hand in such a mechanism. Past investigations have shown that the dynamic mass of the hand, when excited by a vibration input, is very small when compared with the mass of a saw handle [l, 21. Thus, any elastomer of clamping configuration should add little or no additional rigid mass to a saw handle. The elastomer configuration was designed such that it would roughly approximate the one-degree-of-freedom dynamic stiffness and damping coefficients K and R for vibration in each of three mutually orthogonal directions. With reference to Figure 6, vibration in the x and z directions is defined as the state where the rubber elastomer was loaded or excited in compression and vibration in the y direction is defined as the state where the elastomer was excited

Figure

6. Biodynamic

co-ordinate

system.

70

D. D. REYNOLDS

AND

F. L. WILSON

in shear. Acceptable values for K and R for the elastomers excited in compression are K = 5 x lo4 to 4 x 10’ N/m and R = 26-263 N s/m. Acceptable values for K and R for the elastomers excited in shear are around l/10 to l/2 the corresponding values for the elastomers excited in compression. These values for K and R resulted in a one-degree-offreedom displacement mobility that would roughly approximate the actual displacement mobility of the hand at frequencies above 60-70 Hz. At frequencies below these values, the displacement mobility associated with the elastomer would be lower than that associated with the hand by up to a factor of 10 or more. Table 1 shows the K and R values for elastomers with a 2 cm diameter, 2.5 cm diameter and 2.5 cm x 3.5 cm rectangular cross-section hole in the center measured in both compression and shear. The values are for the elastomers tested in the configuration indicated in Figures 4 and 5. A description of how these tests were conducted has been presented in reference [3]. If one notes that the one-degree-of-freedom natural frequency is given by w, = K/M, then the maximum variation from lowest to highest natural frequency for the elastomers without the 50 durometer rubber was less than 15%. The maximum variation for the elastomers with the 50 durometer rubber was less than 15%. There was only an average of a 20% variation in natural frequencies between the elastomers with and without the 50 durometer rubber. These variations were judged to be acceptable and the results of the chain saw vibration tests indicated this to be true. Several elastomer configurations with K and R values substantially different from those reported above were tested before the above elastomer configuration was selected. TABLE K

I

and R values for elastomers of various cross-section ~~ ~ Compression h

fK (N/m)

2.5 cm. round hole With 50 durometer added

K (N/m)

R (N s/m)

2.10 x lo5 3.85 x lo5

35.00 35.00

1*75x105 1.75 x lo5

26.25 26.25

rubber

1.40 x lo5 2.98 x 10’

40.25 40.25

2.10x lo5 1.93 x lo5

35.00 26.25

2.63 x 10’ 3.50 x lo5

52.50 52.50

1*58x10S 1.49 x lo5

43.75 40.25

2.5 x 3.5 cm square hole With 50 durometer rubber added

TABLE K

I

R (N s/m)

rubber

2 cm dia. round hole With 50 durometer added

Shear h

2

and R values for four elastomers with identical cross-section: round, 2.5 cm diameter inner hole with 50 durometer rubber outer layer Shear

Compression K (N/m) No. No. No. No.

1 2 3 4

2.98 3.16 2.63 2.98

x x x x

lo5 10’ lo5 lo5

R (N s/m) 40.25 52,50 36.75 40.25

K (N/m) 1.93 1.84 1.93 1.93

x x x x

lo5 10’ lo5 lo5

R (N s/m) 26.25 26.25 26.25 26.25

CHAIN

SAW

VIBRATION

LEVELS

TEST

STAND

71

Table 2 shows the K and R values of four identical elastomers constructed on four separate days. These elastomers had a 2.5 cm diameter hole in the center and a 0.08 cm layer of 50 durometer rubber added to the outside surface. These were the elastomers that were used on the top handle of chain saw D for the four machine-held vibration tests for which the results are shown; Figures 1 l(a)-(f) of section 6. The results in Table 2 indicate that the maximum variation from lowest to highest in the one-degree-offreedom natural frequency was less than 10%. These elastomers were tested in the configuration indicated in Figures 4 and 5. In general the values of K and R for the elastomers loaded in compression were within the ranges stated earlier. The stiffness coefficients K were always at or near the upper limit of acceptable values and the damping coefficients were at or near the lower limit of acceptable values. For the case where the elastomers were loaded in shear the R values were generally within acceptable limits, but the K values were always above the desired design values. The results of the machine-held chain saw vibration tests indicated this was not a problem, so no measures were taken to design an elastomer with lower K values in shear. Relative to the construction of the elastomer, all the materials that were used were readily available “off-the-shelf” items. These materials have been referred to by either their trade or generic names. It was not possible to obtain any more specific information relative to these materials than has already been presented. Static test procedures could be devised to determine such properties as density, static stiffness, etc. However, the static properties of individual components of the elastomer configuration may not be indicative of what their overall dynamic properties are when combined to form the elastomer configuration used for machine-held vibration tests of chain saws. As the results from Tables 1 and 2 indicate, for the laboratory test conducted during this project, constructing elastomers with similar dynamic properties did not prove to be a problem. How much of a problem this may or may not be relative to constructing elastomers at different laboratories is at present not known. The inner core of all the elastomers was shaped to conform to the shapes of the handles around which they were placed. It was initially thought that all elastomers could be made with circular center sections even though they would be placed around handles which had non-circular cross-sections. This did not work. Elastomer life and deterioration was a concern throughout this project. For any machine-held chain saw test, no chain saw was placed in the machine until just before the cutting tests were to begin. Allowing the dead weight of the saw to hang on the elastomers for a period of over 40 to 60 min before testing could result in the elastomer taking a permanent set. This, in many cases, could affect the test results. No set of front and back handle elastomers was ever used for more than one series of tests. The static loads applied to the elastomers during cutting operations usually resulted in some deterioration of the elastomers. The elastomers on the front handle always experienced greater deterioration than the elastomers on the back handle. Also, since it was necessary to glue the elastomers to saw handles and test machine clamps, they were usually seriously damaged when removing the saw from the stand after a series of tests was completed. Some concern was expressed relative to the deterioration of the elastomers as a result of their exposure to vibration. If they would have been exposed to vibration over a period of several hours or even days, this could have been a problem. However, the average series of tests for the front and back handles together usually took around 40-60 min. Thus, vibration deterioration was not considered a problem. The greatest deterioration to the elastomers was associated with the static forces applied to the elastomer when the saw was cutting or when it was just hanging, being supported by the elastomers.

12

D. D. REYNOLDS 4. HAND-HELD

CHAIN

SAW

AND F. L. WILSON VIBRATION

TEST

PROCEDURES

Two tri-axial accelerometer modules were mounted on the top and back handles of the saw to be tested. Each accelerometer weighs about 2 g, and the entire module (including the mounting block) weighs approximately 11 g. When compared with the weight of an average chain saw (approximately 10 kg), 11 g is negligible. This small mass will in no way preload the saw enough to alter the results. The accelerometer module on the top handle was mounted just to the right of where the hand clasps the handle. The module on the rear handle was mounted just to the rear of where the hand clasps the handle. Figure 7 shows the approximate accelerometer mounting locations on the

Figure 7. Accelerometer

locations

top and back handles of one of the chain saws that was tested. The accelerometers were located such that their principle axes corresponded roughly to the biodynamic co-ordinate system specified in the IS0 Draft International Standard No. 5349 “Guide for the Measurement and Evaluation of Human Exposure to Vibration Transmitted to the Hand” (see Figure 6). Figure 7 and Table 3 show the exact position of the accelerometer blocks on the four saws tested. During testing, the signals from the Endevco accelerometers were directed into charge amplifiers and then into a Hewlett-Packard 4 channel FM tape recorder. The running speed of the saw was monitored by using a tachometer. The output of the tachometer was directed into Channel 4 of the tape recorder, and also into a Hewlett-Packard TABLE 3

Saw specifications Saw

\ A

Weight (kg) Engine displacement (cm3) Chain bar length (cm) Chain pitch (cm) Chain type Type wood cut Width of cut (cm) Dimension A (cm) Dimension B (cm)

4.5 32 40.6 (16 in) 0.6125 (4 in) Oregon chipper Green oak 20 (8 in) 3.5 10.0

B

C

D

4.9 32

9.7 66

40.6 (16 in)

48.3 (19 in) 0.9525 (i in)

10.0 69 48.3 (19 in)

0.9525 (fin)

Oregon chipper Green oak 30.5 (12 in) 3.0 13.0

Oregon chipper Green oak 30.5 (12 in) 3.0 12.0

O-6125 (! in) Oregon chipper Green oak 20 (8 in) 4.0 12.5

CHAIN

SAW

VIBRATION

LEVELS

TEST STAND

73

Oscillograph so that the running speed of the saw could be continuously monitored during the tests. The data was analyzed by playing the recorded vibration signals through a General Radio 1921 l/3 Octave Band Real Time Analyzer and then directing it into a HewlettPackard 9820A Calculator via an HP A/D converter. These data were then plotted on a Hewlett-Packard 9862A Plotter. The wood used in all the tests was fresh cut green oak. A 30.5 cm X 30.5 cm square cross-section log was used for the larger saws. On the smaller saws, the guide bar was not long enough to extend through a 30 cm thick log. The log used for these saws had a 20 cm x 30.5 cm rectangular cross-section. All vibration tests were conducted with the saws operating at full throttle. The wood was cut with the operator applying sufficient pressure to the saw to keep its engine speed as constant as possible. The desired engine speed for each saw was determined by instructing the saw operator to cut the log in what he judged to be an optimum manner. Several cuts were made in this manner to establish desired engine speeds for each saw. TABLE Saw

Saw A: Saw B:

7500 RPM 7000 RPM

4

engine speeds Saw C: Saw D:

8000 RPM 9000 RPM

Table 4 lists the corresponding engine speeds for each saw that were maintained for each series of tests. During the sawing operations used to determine the described engine speeds, the operator was instructed to remember the “sensations” produced by the particular saws to achieve the desired engine speeds. During the chain saw vibration tests, the operator was not allowed to monitor the tachometer. He was instructed to operate each saw in a manner to produce the same “sensations” that were experienced during the tests used to determine the engine operating speeds. An instrument technician monitored the tachometer during the cutting tests. He conveyed by means of hand signals information to the saw operator to press harder to slow the engine speed down or to press lighter to allow the saw engine speed to increase. During the hand-held cutting tests, efforts were made to maintain the engine speed to within +400 RPM of the desired engine speed for each test. For each cutting test, the signals from three accelerometers (one tri-axial module) and the tachometer signal were recorded on the FM tape recorder. The procedure was run for the tri-axial accelerometer module on the top saw handle and was then repeated for the accelerometer module on the rear handle. Separate tests were run until there were at least 10 4 s stretches of data for each handle during which the engine RPM remained within the desired speed range. It was usually necessary to run a minimum of five separate cutting tests for each handle to obtain these data records. For the data analysis, 10 sections of recorded data where the desired chain saw engine speed remained within the desired speed range were found for each of the three accelerometers on each handle. Each section of data was played back through the General Radio 1921 l/3 Octave Band Real Time Analyzer. After all 10 data samples had been stored in the HP 9820A, the average acceleration levels and 90% confidence bands at each center frequency were calculated for the 10 tests.

74

D. D. REYNOLDS

AND

F. L. WILSON

5. MACHINE-HELD SAW VIBRATION TEST PROCEDURES For the machine-held tests the instruments were calibrated and manipulated in the same manner as for the hand-held chain saw tests. The accelerometers were attached to chain saws in exactly the same locations as used in the hand-held tests. Reasonable care was exercised when attaching the elastomers to the saw handles. First, a cleaning solvent was used to remove all dirt, oil, grease, etc., from the saw handles and brass clamps. For saw handles that had rubber coverings, the coverings were left on the handles. One inch wide 3-M masking tape was placed on the surface areas of the chain saw handles over which the elastomers were to be attached. The insides of the brass clamps that were to be in contact with the elastomers were also covered with 1 in wide 3-M masking tape. Care must be taken to insure that a high quality masking tape with excellent adhesive qualities is used. Two 1 in sections of elastomer placed approximately 1 in apart were used for each handle (see Figures 4 and 5). A single slit along one side of each elastomer was made so that the elastomers could be wrapped around the handles, Goodyear Contact Cement was applied to the taped handle surfaces to which the elastomers were to be attached, the inside surface of the elastomers to be in contact with the handles, and the two opposed surfaces associated with the slits in the elastomers. The cement was allowed to dry for 5-10 min. The elastomers were then attached to the handles. Caution was exercised to insure that the elastomers were securely cemented to the complete circumferences of each handle and that the sides of the slits were securely cemented together. Goodyear Contact Cement was applied to the outside surface of the elastomers and to the inside, tape-covered surfaces of the brass cylinders (for top and rear handles) that were cut in half lengthwise along the cylinders. The cement was allowed to dry and the cylinder half-sections were placed around the top and rear handles (Figure 8). The cylinders associated with each handle were placed in the circular clamps attached to the support structure of the test stand (see Figure l(c)).

Figure

8. Chain saw prepared

for vibration

testing

in CSMA chain saw test stand

The test machine was adjusted to accommodate the saw being tested. It was important to insure that the clamps were aligned properly with the handles of the saw. The saw was visually aligned so that the wood carriage could be fed into the saw without the cutting chain of the saw coming into contact with any metal parts and with the saw properly cutting the wood when the carriage was fed into the saw. The saw was also aligned so the static weight of the saw was evenly distributed along the elastomers of each handle. It was important that the clamps and elastomers not be twisted or skewed

CHAIN

SAW

VIBRATION

LEVELS

TEST

75

STAND

relative to the handles. This part of the saw alignment was also done visually. The saw was not placed in the test stand until after the instruments had been calibrated and the cutting tests were ready to begin. Allowing the saw to hang in the test stand even up to an hour before the tests were to start could result in the elastomers experiencing a permanent set in a deformed state. The limiting carriage height was adjusted to ensure a complete cut without the cutting chain coming into contact with the carriage base. Figures l(a)-(c) show the prepared chain saw. It was necessary to attach the nozzle of an air blower to the front of the test stand during tests. The air was directed such that it flowed over the section of the saws containing the exposed engine cooling fins. This prevented the saw from overheating, since the saw did not receive enough air due to its confined location. The air flow also carried the exhaust fumes into a small room, where they were evacuated via a fume hood. The blower can be seen in use in Figure 9.

Figure 9. Machine-held chain saw vibration test in progress.

It was discovered when analyzing some of the preliminary vibration data that on some of the larger saws possible structural vibration resonances in the chain saw handles were present at frequencies corresponding to the running speed and the first harmonic of the running speed. For this reason, air adjustable dampers were attached to the tri-axial accelerometer blocks when machine tests were conducted on the larger chain saws. These were mounted in two directions on the top handle and two directions on the back handle. The tests were conducted with the saws operating at full throttle. At the beginning of the cut, the wood was raised slowly, allowing the saw to begin its cut without binding. The feed rate of the wood was increased until the load on the saw was sufficient to decrease the engine speed to within the desired speed range. The speed range for each saw was usually within ~t200 RPM of the values shown in Table 4. The machine tests were conducted exactly as were the hand-held tests. Since the top handle elastomer sustained more damage during the testing, the top handles were tested first to insure optimum results. The raw data were analyzed in the same manner as the data from the hand-held tests. Figure 9 shows a machine-held chain saw test in progress. 6. HAND-HELD

AND

MACHINE-HELD

CHAIN

SAW

TEST

RESULTS

Table 3 shows the saw specifications for four chain saws that were tested during the CSMA project. Figure 10(a) shows a typical plot of the average acceleration levels and

76

D. D. REYNOLDS

04

31.5

63

125

250

50

AND F.

31.5

1000 Center

L. WILSON

frequency

63

125

250

500

1000

(Hz)

Figure 10. Typical plots of average acceleration levels and confidence handle, hand-held; (b) saw C, X direction, rear handle, machine-held.

limits. (a) Saw A. X direction,

top

90% confidence bands for a hand-held test and Figure 10(b) shows a typical plot of the average acceleration levels and 90% confidence bands for a machine-held test. Figures 11(a)-(f) show a comparison between the hand-held and machine-held tests of the vibration levels measured on a medium size chain saw. Two separate sets of hand-held tests by a single saw operator were conducted for chain saws A, B and C. Two separate sets of hand-held tests were conducted by each of three different operators for chain saw D. Of interest from these tests was the variation between the l/3 octave band vibration levels for the different vibration tests associated with each chain saw. Table 5 shows a summary of the results, the maximum levels for the respective l/3 octave frequency bands being compared with the minimum levels in the same bands for all four chain saws tested. The results for saws A, B and C indicate the typical data spread between two tests by the same operator. The data spread between the two tests associated with each individual operator for saw D was similar to that obtained for saws A, B and C. However as indicated by Table 5, the data spread associated with all of the tests for the three operators for saw D was larger than the data spread for saws A, B and C. Figures 11(a)-(f) show the maximum and minimum acceleration TABLE

S

Range of ratios for maximum band level divided by minimum band level for the l/3 octave band acceleration levels associated with the hand-held chain saw vibration tests of the indicated saws _ Range of ratios for

Saw A B

C D

Maximum

band level

Minimum

band level

Freq. bands below engine operating speed

Freq. band at engine operating speed

Freq. bands above engine operating speed

1.4-1.6 1.7-2.5 1.2-2.0 1.6-3.0

1.2-1.8 1.3-1.7 1.2-1.8 1.4-3.0

1.2-1.5 1.2-1.5 1.1-1.3 1.4-2.0

CHAIN SAW VIBRATION OOr

I

I

I

I 31.5

I 63

I 125

I

I

I

I 250

I 500

I 1000

77

L EVELS TEST STAND

IO-

I -

0.1 -

Ioc

(e)

IC

I

0.

Center

I 31.5 frequency

63

125

250

500

1000

(Hz)

Figure 11. Saw D: maximum and minimum of hand-held and machine-held tests top handle: (a) vertical (X) direction; (b) axial (Y) direction; (c) horizontal (2) direction; back handle: (d) axial (X) direction; (e) horizontal (Y) direction; (f) vertical (Z) direction. Running speed 9000 RPM; weight 10.0 kg; engine displacement 69 cm3, &S&XX, Maximum and minimum of hand-held test results; =, maximum and minimum of machine-held test results.

levels associated with all of the tests for saw D. Compared with the data spread that has been obtained for different operators of single chain saws in other laboratory testing programs, the results of the hand-held chain saw vibration tests obtained during this project are very good.

78

D. D. REYNOLDS

AND

F. L. WILSON

The confidence bands shown on Figure 10(a) are indicative of the confidence bands that were obtained for all of the hand-held chain saw tests. In general, the average amplitudes of the 90% confidence bands for the frequency bands below the frequency equal to the engine operating speed were around 0.23 times the amplitudes of the average band levels. The average amplitude of the 90% confidence band for the frequency band at the frequency equal to the engine operating speed was around 0.21 times the amplitude of the average band level. The average amplitudes of the 90% confidence bands for the frequency bands above the frequency equal to the engine operating speed were around 0.06 times the amplitudes of the average band levels. Some vibration tests yielded 90% confidence band amplitudes which were consistently greater than two to three times the above values. This was usually an indication that something was wrong relative to the series of tests: i.e., the cutting chain was not properly sharpened, the engine was not running properly, the section of the wood being cut had knots in it, etc. When

this happened,

the test results

were discarded

TABLE

and the tests repeated.

6

Range of ratios for maximum band level divided by minimum band level for the I/3 octave band acceleration levels associated with the machineheld chain saw vibration tests of the indicated chain saws Range of ratios for

Saw

A B C D

Maximum band level Minimum band level

Freq. bands below operating speed

Freq. bands at engine operating speed

Freq. bands above engine operating speed

1.2-1.4 1.2-3.0 l.O-1.8 1.2-1.7

1.0-1.2 1.1-1.7 1.2-2.0 1.2-2.0

1.0-1.3 1.1-1.3 1.0-1.5 1.3-1.6

Chain saws A, B and C were tested in the test machine twice. The saw D tests were repeated four times. Table 6 shows a summary of the results, the maximum levels for the respective l/3 octave frequency bands being compared with the minimum levels in the same bands for all four chain saws tested. With the exception of saw B at frequencies below the frequency equal to the saws engine operating speed, the repeatability of the tests associated with all of the saws was nearly the same. A quick comparison of the results in Table 6 with those of Table 5 indicates that the repeatability associated with the machine-held tests of saws A, B and C was not much different from the repeatability associated with the hand-held tests of these same saws where only one operator was involved. However, the repeatability associated with the four machine-held tests associated with saw D was improved relative to the repeatability associated with the six hand-held tests of saw D conducted by three different operators. The confidence bands shown in Figure 10(b) are indicative of the confidence bands that were obtained for all of the machine-held saw tests. The average amplitudes of the confidence bands for the machine-held tests were nearly the same as those obtained for the hand-held tests. The same comments associated with using the amplitudes of the confidence bands for determining the acceptability of the results of hand-held saw vibration tests also applied to machine-held tests.

CHAIN

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79

STAND

For machine-held tests, it was confirmed that the following previously mentioned precautions had to be taken in using the elastomers. It was necessary for the elastomers to be firmly bonded to both the chain saw handles and the test stand handle clamps. When the saw was cutting through wood, unbonded elastomers pulled away from the handles. This altered the stiffness associated with the elastomer and resulted in the saw being poorly constrained in and aligned relative to the test stand. If a saw was not properly constrained in the test stand, it tended to cut irregularly. For all tests, it was necessary to place the saw in the test stand after the instruments had been calibrated and just prior to the beginning of a test. Allowing a saw (particularly the medium and large size professional saws) to hang in the test stand for periods of time greater than 30 min before beginning a test often resulted in the elastomer taking a “permanent set” which affected the test results. A set of elastomers was used for only one set of tests because they were usually destroyed when the saw was removed from Lhe test stand after the test had been completed. It was necessary to align the test stand clamps properly with respect to the chain saw handles. Clamps in an improper orientation (i.e., twisted or skewed relative to the handle) put a pre-load upon the elastomer that altered the test results. When it is not possible to measure the vibration levels on the top and back handle of a chain saw simultaneously, it is usually desirable to measure the top handle first. 7. COMPARISON

OF MACHINE-HELD

AND HAND-HELD

RESULTS

One reason for which this test machine was designed was to alleviate the variability in vibration test results associated with hand-held tests. An advantage of the machine in this area is that the RPM of the saw can be held much steadier than with the hand-held method. A more constant running speed can potentially produce more consistent results. Figure 12 contains typical RPM plots (obtained from the oscillograph during cutting

(bl

(0) Figure 12. Engine speed 9000 RPM.

operating

speed

charts.

(a) Machine-held

test;

(b) hand-held

test. Desired

operating

tests) of a machine and a hand-held test with the same saw. It can be seen that with the machine the RPM was controlled to within &200 RPM of a desired engine RPM. In the hand-held test it was possible to control the engine RPM only to within +400-500 RPM of the desired engine speed. One of the major design objectives associated with the chain saw vibration test machine was to achieve machine-held vibration test results for chain saws that are nearly the same as or correlatable to hand-held vibration test results for respective chain saws. For this project, four chain saws were tested. Saw A was a small hobby saw which was not vibration isolated. Saw B was a small anti-vibration hobby saw, and saws C and D were medium weight anti-vibration professional chain saws. Table 7 shows a comparison of the results for the machine-held and hand-held chain saw vibration tests for the saws

D. D. REYNOLDS

80

AND

F. L.

WILSON

TABLE 7 Range of ratios of the amplitude of the I/3 octave band acceleration levels measured during machine-held tests divided by the corresponding levels measured during hand-held tests

Range of ratios for accel. levels

Saw Saw A---top H vert. (X) dir. axial (Y) dir. horiz. (2) dir. -back H axial (X) dir. horiz. (Y) dir. vert. (Z) dir. Saw B--top H vert. (X) dir. axial (Y) dir. horiz. (Z) dir. -back H axial (X) dir. horiz. (Y) dir. vert. (Z) dir. Saw C--top H vert. (X) dir. axial (Y) dir. horiz. (Z) dir. -back H axial (X) dir. horiz. (Y) dir. vert. (Z) dir. Saw D---top H vert. (X) dir. axial (Y) dir. horiz. (Z) dir. -back H axial (X) dir. horiz. (Y) dir. vert. (Z) dir.

Machine-held Hand-held

test results test results

Freq. bands below engine operating speed

Freq. band at engine operating speed

Freq. bands above engine operating speed

l.O-2.0 1.0-1.7 1.0-2.3

1.2 1.3 1.1

1.2-2.2 1.2-2.5 1.0-4.0

1.0-1.9 1.6-4.2 1.2-2.8

1.0-1.6 1.0-1.4 1.2

1.1-2.3 1.0-1.6 1.2-1.8

0.2-0.6 0.2-0.5 0.2-0.6

3.2 2.5 1.7

1.0-1.8 1.1-3.0 1.1-2.8

0.07-0.5 0.09-0.6 0.2-0.4

1.0-1.4 1.4-2~0 3.4

1.1-2.1 1.1-1.5 1.0-1.7

0.2-0.7 0.3-1.5 0.3-0.9

1.0-1.4 0.5-0.8 1.7

1.0-1.6 1 ~0~-1~4 1.0.-1.6

0.2-1.0 0.4-1.0 0.2-1.0

0.8-1.7 1.0-1.9 1.1

1.1-1.7 1.2-2.5 1.2.-2.7

0*3-1.0 o-2-1.0 0.3-1.0

1.1-1.4 1.0-1.6 1.0-1.1

1 .o-2.0 1 .O-2.5 1 .O-2.3

0.3-1.0 0.2-1.0 0.4-1.0

3.5 1.3-3.0 2.0-2.2

0.6-2.1 0.6-1.5 0.5-4.0

that were tested. The machine-held vibration tests for saw A corresponded reasonably well to the hand-held tests. The machine-held vibration results were typically from 1.0 to 2.8 times the corresponding hand-held vibration levels for frequencies below the engine operating speed. The machine-held results in this frequency range were up to 4.2 times the corresponding hand-he!d results for the horizontal (Y) direction on the back handle. At the frequency corresponding to the engine operating speed during cutting, the machine-held test results were from 1.1 to 1.6 times the comparable hand-held results. At frequencies above the engine operating speed, the machine-held vibration levels were typically from 1.0 to 2.5 times the comparable hand-held results. The machine-held results were higher by a factor of around 4-O for the horizontal (2)

CHAIN

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VIBRATION

LEVELS

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STAND

81

direction in this frequency range. For frequencies at or above the engine operating speed, it is not uncommon for rather broad-band structural resonances to be present in chain saw handles. The consistently higher vibration levels at these frequencies for the machineheld vibration tests could be associated with the fact that the damping associated with the elastomer used to hold the chain saw in the test stand was substantially lower than the damping that exists in the hand. Increasing the amount of damping associated with the machine clamping mechanism can reduce the above differences between the machineand hand-held test results for lightweight non-isolated chain saws. For saw B, a lightweight anti-vibration hobby saw, the machine- and hand-held vibration test results agree fairly well at frequencies equal to or above the engine operating speed. In this frequency range, the machine-held test results were from 1.0 to 2.8 times the corresponding hand-held results. In some instances, the difference was as high as a factor of 3.4. At frequencies below the engine operating speed, the machine-held vibration levels were consistently 0.06 to 0.2 times the comparable hand-held levels. The upper curve in Figure 13 is a curve that shows the type of general relationship that is thought to exist between the machine- and hand-held test results for saw B. More saws of the same size and type as saw B must be tested to determine the exact relationship that is indicated in Figure 13.

Figure 13. Suggested shapes of correction factor curves for correlating machine-held vibration test results to the corresponding hand-held test results. Upper curve, small anti-vibration hobby saws; lower curve, medium weight anti-vibration professional saws.

An understanding of the dynamic properties of the elastomer used in the test stand as compared to the dynamic properties of the hand is needed in understanding the nature of the differences between the machine- and hand-held test results at low frequencies for saw B. The dynamic compliance associated with the elastomer is substantially lower than that associated with the hand at frequencies below 70 Hz. The net implication of this is that the overall dynamic stiffness of the elastomer is greater (possibly by a factor of 10 or more) than that associated with the hand at frequencies less than 70 Hz. Coupled to this, the vibration isolation mechanism associated with saw B possibly has resonant frequencies in the frequency range 25-80 Hz. When this is the case, the manner in which the saw is clamped or held will have a very definite and noticeable influence upon the measured vibration levels associated with the saw. Since the stiffness associated with the elastomer is much greater than that associated with the hand at low frequencies, it is reasonable to expect that the machine-held vibration levels would be lower than the corresponding hand-held results at these frequencies.

82

D. D. REYNOLDS

AND

F. I.. WILSON

In general, the machine-held test results for saws C and D compared reasonably well with the corresponding hand-held tests. At frequencies below the engine operating speed, the machine-held results were typically 0.02 to 1-O times the comparable hand-held results. At the engine operating speed, the machine-held vibration levels were usually from 1.0 to 2.2 times the corresponding hand-held results. Two notable exceptions were for saw D in the axial (X) and horizontal (Y) directions on the rear handle where the differences were factors of 3.5 and 3.0, respectively. The difference of 3.0 in the horizontal direction was associated with the fact that one of the hand-held operators had vibration levels that were consistently low. If his results are deleted, the difference factor of 3.0 would be reduced to 2.0. At frequencies above the engine operating speed, the machineheld test results were typically from 1.0 to 2.7 times the corresponding hand-held test results. A combination of the explanations given for saws A and B account for these differences. The bottom curve in Figure 13 indicates a probable form of the relation that exists between the machine- and hand-held vibration test results at frequencies less than the engine operating speed for saws C and D. Adding damping to the clamping mechanism should reduce the differences between the machine- and hand-held test results at frequencies above 125 Hz. The damping that was present in the elastomer was near the lower acceptable limit for damping. It was initially anticipated that this damping would be sufficient. However, some machine-held test results indicated the presence of substantial structural resonances at frequencies above 100 Hz. Sufficient time was not left before completion of the project to adequately investigate this problem. In a stop-gap measure, air dampers were purchased and added to the clamping mechanism as is indicated in Figure l(c). Some improvement was achieved by doing this. More work is necessary to determine more precisely the amount of damping that is necessary and the type of dampers that can be most effectively used with the saw clamping mechanism.

8. CONCLUSIONS THF: ELASTOMER 8.1. CONCI~USIONS CONCERNING 1. The elastomer configuration is simple in nature and easy to construct. The components needed for assembly are readily available from local suppliers. 2. The inner core shape of the elastomer must conform to the shape of the handle around which it is wrapped. 3. Relative to elastomers with different sized and shaped cores (round cores of different sizes and rectangular cores), the variations in K and R values obtained during this project did not noticeably affect the chain saw vibration test results. In general, the maximum variation in the natural frequencies associated with the elastomers of different core shapes that was obtained during this project was less than 15%. 4. Relative to elastomers with the same shape and size core that were constructed on different days, the variation in K and R values obtained during this project did not noticeably affect the chain saw vibration test results. In general, the maximum variation in the natural frequencies associated with the elastomers that were constructed on different days was less than 10%. 5. It is necessary to allow the molded rubber in the elastomers to cure for a minimum of 24 h before it could be used for a machine-held vibration test. 6. It is necessary to bond the elastomer to both the chain saw handles and to the clamps. 7. The elastomers can be used for only one set of machine-held vibration tests; a new elastomer must be constructed for each series of tests. 8. Test should be done on the top handle first.

CHAIN

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LEVELS

TEST

83

STAND

8.2. CONCLUSIONS CONCERNING THE TEST MACHINE 1. The machine does not introduce any preload on the saw other than that introduced by human hands and arms in normal use. 2. The test machine is massive so that it does not develop any resonant interaction with the saw other than that occurring with human hands and arms. 3. The stand is designed such that tests may be conducted whether or not the saw is cutting wood. 4. The test stand may be reproduced exactly using either off-the-shelf or easily manufactured components 5. The test stand is reliable, in that no failure or malfunction occurred during approximately one year of testing. 6. Overall, the test stand behaves very well in all areas for which it was designed. 8.3.

CONCLUSIONS MACHINE-HELD

CONCERNING CHAIN

SAW

THE

CORRELATION

VIBRATION

BETWEEN

HAND-HELD

AND

TESTS

1. The running speed of the saw can be held to within *I200 RPM of a desired speed by using the test machine. In the hand-held tests, it was possible to hold the engine speed to within *400-500 RPM of a desired value. 2. Tables 5 and 6 indicate the repeatability associated with the vibration test results for both the hand-held and machine-held methods for saws A, B and C was nearly the same. For these tests only two hand-held tests by a single operator and two machine-held tests were conducted. 3. Tables 5 and 6 indicate the scatter in the data for the hand-held tests for saw D was around an average of 1.5 times the data scatter for the corresponding machine-held tests of saw D. Two hand-held tests by each of three different operators for a total of six tests and four separate machine-held tests were conducted with saw D. 4. For the hand-held tests conducted by single operators during this project, the normal spread in data for each operator was nearly the same. However, as is indicated in Table 5, the data spread for three separate operators operating saw D was increased by an average factor of around 1.6 relative to the data spread for a single operator. 5. There is insufficient damping in the elastomer. It was necessary to add additional damping in the form of an air damper to the damping mechanism of the test machine. 6. For the small vibration isolated saw, the vibration levels below 80 Hz as measured when using the test machine were consistently lower than those obtained when using the hand-held test method. Above 80 Hz, the machine-held test results correlated well with the hand-held results. 7. The small, non-vibration isolated saw produced vibration levels that correlated reasonably well between the machine- and hand-held tests throughout the entire frequency range of interest. 8. Generally, the vibration levels of the vibration isolated, medium-size professional saws correlated well between the hand-held and machine-held tests. 9. For all tests where the machine-held test results varied from the hand-held test results at frequencies btlow 125 Hz, the machine-held test results were consistently lower than the hand-held results. This was caused by the fact that the dynamic stiffness of the elastomers is greater than the corresponding dynamic stiffness of the hands at these frequencies. When these differences occur, correction factors similar to those indicated in Figure 13 must be used to transform the machine-held test results to correspond to the hand-held test results. 10. For all tests where the machine-held test results varied from the hand-held test results at frequencies above 125 Hz, the machine-held test results were consistently

84

D. D. REYNOLDS

AND

F. L. WILSON

higher than the hand-held test results. This was possibly caused by the fact that the damping present in the machine saw clamping mechanisms was lower than desired. This deviation can be improved or eliminated by properly increasing the damping in the clamping mechanisms. 11. Relative to the average l/3 octave band vibration levels and 90% confidence bands for both the hand- and machine-held vibration tests, the average amplitudes of the 90% confidence bands for frequency bands below the frequency equal to the engine operating speed were around 0.23 times the amplitudes of the average band levels. The average amplitude of the 90% confidence band for the frequency band at the frequency equal to the engine operating speed was around 0.21 times the amplitude of the average band level. The amplitudes of the 90% confidence bands above the frequency equal to the engine operating speed were around 0.06 times the amplitude of the average band levels. 12. To maximize the repeatability and reliability of the test procedure, the saw must always be in the best operational condition. This includes proper carburetor turning, clean spark plug, and a sharp chain.

ACKNOWLEDGMENTS

The research reported in this paper was carried out under a contract funded by the Chain Saw Manufacturers Association of the United States while the main author Dr Douglas D. Reynolds was an associate professor in the Department of Mechanical Engineering at the University of Pittsburgh.

REFERENCES 1. D.D. REYNOLDS~~~W.SOEDEL~~~~JCXU~U~O~SOU~~~~~ Vibration 21,339-353. Dynamic response of the hand-arm system to a sinusoidal imput. 2. D. D. REYNOLDS and R. H. KEITH 1977 Journal of Sound and Vibration 51, 237-253. Hand-arm vibration, part I: Analytical model of the vibration response characteristics of the hand. 3. D. D. REYNOLDS and F. L.WILSON 1979 Final Report, Chain Saw Manufacturing Association. The design and development of a standardized test machine for measuring the vibration of chain saws.