Paper dust particulates wreak havoc with just about every aspect of paper converting machinery, especially the bearings. Linear guides, planar bearings and shafts, even with wipers, lubricators, scrapers or bellows, tend to draw particulates into the bearings. Without adequate protection, paper dust mixes with bearing lubricant and damages bearing raceways and balls. We found BishopWisecarver's DualVee® guide-wheel carriages protected the bearings and track from particulates, resulting in higher machine performance ratings without sacrificing accuracy.
A moving carriage may be unable to distribute loads equally. A guide-wheel carriage system handles these unequal load distributions — as much as two to three ft — by utilizing four high-capacity wheels/ bearings with a relatively small separation distance. Planar bearing shafts can bend under such conditions.
Even when the mounting surface of the track is uneven, we can hold tight tolerances and the guide-wheel carriage functions properly, providing a smooth rolling motion. Additionally, parallel tracks are easier and faster to assemble because guide-wheel track alignment is very forgiving.
Paper dust is less of a problem than it might be in this Bretting convertor, thanks in part to guide-wheel carriages that protect bearings from particulates.
Wheel Carriage Configurations
Using the correct combination of eccentric and concentric guide wheels in the guide-wheel carriage configuration ensures a robust design. Linear systems always have two concentric wheels and the remaining guide wheels are eccentric. The eccentric wheels remove the play (preload) between the wheels and track, equally loading all the
wheels so they roll instead of sliding or skipping on the track during acceleration or deceleration. When the wheel carriage is loaded in the radial direction, the concentric wheel carries the primary load (see figure below).
It is important to note the location of the eccentric wheel is dependent on whether the track guide way is on the outside or inside of the wheel carriage. Below are several wheel carriage configurations.
Loads
We start by determining the type of loads — radial and/or axial. A radial load (LR) is applied perpendicular to the bearing shaft, while an axial load (LA) is applied parallel to the bearing shaft. We have found the formulas provided by BishopWisecarver for determining lifespan and sizing to be easy to apply.
Axial loading on a guide wheel is a moment load, because it is on one side. Since the ball bearing elements are not equally loaded, one side of the wheel is free while the other side interacts with the track. This creates a moment load on the wheel and, in turn, the bearing. To offset the moment load, we increase the radial preload, allowing higher axial loads. However, by increasing the radial preload the wear rate increases.
Load/Life Equation — Size and Selection
To estimate load/life requires an understanding of the principles of statics, such as the ability to analyze free-body diagrams and the capability to transfer externally-applied forces on the carriage into radial and axial reaction forces at each guide wheel. To calculate system life, we use the wheel with the heaviest load.
The process for sizing and selecting a wheel carriage assembly includes three steps:
Determine radial and axial loads
Calculate load factor for wheel with heaviest load
Apply safety factors to compensate for speed, vibration, shock and environment
Typical Guide-Wheel Load Ratings
Part number
Radial dynamic load (N)
Radial dynamic load (lbf)
Radial static load (N)
Radial static load (lbf)
Axial dynamic load (N)
Axial dynamic load (lbf)
Axial static load (N)
Axial static load (lbf)
W0
1050
236
500
112
135
30
123
28
W1
2180
490
1110
250
277
62
252
57
W2
4700
1057
2780
625
688
155
625
141
W3
9150
2057
5050
1135
1871
421
1701
382
W4
12800
2878
7900
1776
4401
989
4001
900
Step OneCalculate the radial (LR) and axial (LA) loads on each bearing element in the guide-wheel system design. This is computed by applying statics to the application. Step TwoAll standard statics calculations must be considered, including inertial forces, gravitational forces and such external forces as tool pressure, bearing element spacing and payload magnitude and travel direction. Additionally, external forces generating a reaction through the wheel-track interface must be considered: LF = LA / LAmax + LR / LRmax Where: LF= Load Factor LA= Axial load on guide wheel LAmax= Maximum axial working load capacity of wheel LR=Radial load on wheel LRmax=Maximum radial working load capacity of wheel Bearings should be sized such that LF = 1. A safety factor must be applied to the maximum axial (LAmax) and radial (LRmax) working load capacities. This is because load, speed, shock, vibration, contamination and duty cycle requirements may vary.
Safety Factors*
Application Requirement
1.0 - 0.7
Clean, low speed, low shock, low duty
0.7 - 0.4
Moderate contaminants, medium duty, medium shock, low to medium vibration, moderate speed
0.4 - 0.1
heavy contamination, high acceleration, high speed, medium to high shock, high vibration, high duty cycle
Safety factors applied to the maximum axial (LAmax) and radial (LRmax) working load capacities
*The ratings and calculations are theoretical values based on ideal conditions. Most of our applications involve less than optimum conditions. Hence, we use the next largest size, ensuring the machines never reach the critical limits of a guide-wheel.
Step ThreeThe load factor is applied to the equation below for determining system life expectancy:
Life constant (LC)
DualVee size
Inches of travel
Kilometers of travel
1
2.19 × 106
55
2
3.47 × 106
87
3
5.19 × 106
130
Life=LC / (LF) 3 Where: Lf= Load Factor LRmax= Life Constant Calculation Example: LA= 50 lbf LR= 200 lbf Wheel Size: 2 Environment: Moderate shock loading and contamination with intermittent motion What is the expected wheel life? Following the outlined procedure, we know the information from Step 1, radial (LR) and axial (LA) loads on each wheel, therefore we are ready to calculate: LA= 50 lbf LAmax= 140 lbf LR=200 lbf LRmax=625 lbf LF= 50/140 + 200/625 = .68 Life = 3.47 × 106 /(.68)3× 0.6 = 6.21 × 106 inches of travel *Note an adjustment factor of 0.6 was used because of environmental issues. Conclusion Speed, productivity, reliability and durability are crucial factors for buyers of such capital equipment as paper converting machinery. However, higher speeds also lead to durability and reliability issues. We found the BishopWiseCarver DualVee guide-wheel carriage to be very efficient. It exhibits less friction, allowing higher speeds with practically no impact on accuracy. The wheel bearings resist paper dust, while reducing maintenance, dramatically improving machine design robustness and durability. To achieve even higher productivity, our new paper converting machines are migrating from reciprocating motion to circular or elliptical motion that moves in one direction. The Bishop Wisecarver guide-wheel ring and track system allows the next generation machines to achieve even higher productivity, while improving reliability and durability.
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